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The present invention relates to a semiconductor process, and more particularly, to technologies for fabricating an erasable and programmable read-only memory (EPROM), a flash EPROM and a Flash electrically erasable programmable ROM (Flash EEPROM).
FIG. 3 is a schematic top view of a conventional memory cell array. In FIG. 3, there are at least word lines 302 and 304 and bit lines 312 and 314. Theoretically, if the word line 302 and the bit line 312 are turned off, and if the word line 304 and the bit line 314 are turned on, only the cell 320 has an xe2x80x9conxe2x80x9d state (other cells have xe2x80x9coffxe2x80x9d states). However, in fact, some cells theoretically having off states may be judged to have on states, since some current (actually leakage current) has been read through them.
In addition to the reading process, leakage current also brings trouble in the programming process. For example, to make a cell 320 have an on state in a programming process, the cell 320 will be biased until a predetermined voltage is achieved. However, in some cases, the cell 320 already has an on state even though the predetermined voltage has not been achieved, because the cell 320 has leakage current through it. Such leakage current causes the the device to fail. There is therefore a need of a solution for suppressing the leakage current.
A purpose of the present invention is to improve the characteristic of a memory cell. Another purpose of the present invention is to prevent a memory cell from having bit line to bit line leakage.
To achieve the above or other purposes, the present invention provides a method for suppressing bit line to bit line leakage in a memory cell. In the method, a plurality of word lines are formed on a silicon substrate. A Tetra-ethyl-ortho-silicate (TEOS) oxide layer is then formed on the word lines. Thereafter, the TEOS oxide layer is etched back, to form spacers on the sidewalls of the word lines, whereby the silicon substrate between the word lines is damaged in this etching back step. After the bit lines are annealed, an ion implantation step is performed to implant boron ions into the silicon substrate between word lines by using the word lines and the spacers as masks, for preventing the damage from inducting leakage current.
Implementing the present invention centralizes the implanted ions, and the centralized ions are not thermally diffused to the channel region to decrease the driving force of the devices. Moreover, the narrow width effect is also reduced.
In another aspect, the present invention provides a process for fabricating a memory cell array. A silicon substrate having a plurality of bit lines is provided. A plurality of word lines are formed on the substrate. On the word lines, an oxide layer is deposited. The oxide layer is etched back to form word lines on their sidewalls. An annealing step is performed. After the annealing step is performed, an ion implantation step is performed to implant ions into the silicon substrate between the word lines by using the word lines and the spacers as masks for suppressing the leakage current between the bit lines (bit line to bit line leakage).
In still another aspect, the present invention provides a method for suppressing the bit line to bit line leakage in a silicon substrate. In this method, after the oxide spacers are formed on the sidewalls of word lines of a memory cell array, an ion implantation step is performed to implant ions into the silicon substrate between the word lines by using the word lines and the oxide spacers as masks, for suppressing the bit line to bit line leakage. | 2024-02-04T01:27:04.277712 | https://example.com/article/4345 |
6 thoughts on “Sesquipedalian Fool”
Emotions…It’s good you realized you should control it since you’re so young. I don’t realize how harmful it is until I’m so much older than you. I made mistakes and had regrets when I was much older than you :-)
I have perfect good friends who lost control and turned to fires and monsters from charming prince and lovely lady. I also launched a war myself.
You see, until we make huge mistakes and have huge regrets we don’t change.
Now I appear calm because I train myself so. It’s not easy. In this way I keep my brain function.
Hey, thought this a poem we’ve got to look at. I think the poem has that weight rarely carried by a short piece. And I am in love with the title. About the feelings, well, next time don’t be stupid And Min Min, love is the best position you can ever be in. what matters is , which kind of love?? | 2023-10-12T01:27:04.277712 | https://example.com/article/7285 |
Description
Psychotic Gold Pre-Workout: Crazy Pumps, Performance, And Gains
If you’re like most, by the time you get to the gym, you’re barely running on half a tank. The workday drains you. Your daily obligations take even more energy. You need to get the next workout in but where are you going to find a boost? Introducing Psychotic Gold. Does the name look familiar? It should. We’ve taken the foundation of our insanely popular Psychotic and taken it to the next level.
What Is Psychotic Gold?
Psychotic Gold is a half stimulant, half nootropic pre-workout supplement that is perfectly dosed to spike your energy and performance levels. Taken 20 to 30 minutes before your workout, Psychotic Gold uniquely addresses energy on several levels: mental focus, muscle performance, and overall endurance. Jacked up with a number of proven ingredients that are ideal for pre-workout, Psychotic Gold is one hell of a performance accelerator.
Who Is Psychotic Gold Ideal For?
Sound like a pre-workout you can use during your toughest workouts? Here are just a few ways that Psychotic Gold can help you finish any workout from Leg Day to kickboxing.
PUMP-FOCUSED:
Psychotic Gold takes pumps to the next level as it features a few hard-hitting nitric oxide boosters. Getting in that pump is important, especially if your goal is muscle building. Nitric oxide can help you complete a few more reps than you’re accustomed. That means more time under tension, and the potential for serious growth.
MIDDAY CRASH:
Whether you’re a student or you’re running in the rat race of 9-to-5, everyone needs a boost right around lunch time. Psychotic Gold, aside from powering your workouts, can help you have a more productive day. It’s packed with nootropic, or brain boosting ingredients, that have been shown to promote alertness while supporting cognitive performance.
STRENGTH AND POWER:
Maybe muscle comes second fiddle to being able to toss around big plates. If you want an extra boost to add another 45 to each side of the barbell, Psychotic Gold has your back. It’s packed with performance and strength-supporting ingredients to help you achieve new personal bests on the bench or the rack. | 2024-01-22T01:27:04.277712 | https://example.com/article/2737 |
Time-profiling fluorescent reporters in the Arabidopsis root.
Confocal laser scanning microscopy is a useful nondestructive approach for the visualization of fluorescent reporters in planta. Samples are usually placed between a slide and a cover slip which, although suited to single time-point imaging, does not allow long-term observation. Here, we describe a technique to monitor changes in fluorescence in the Arabidopsis root over a long period of time. Treatment can easily be performed, and this approach is suitable for use in low-throughput chemical screens. We also present a rapid method to analyze fluorescence intensity profiles generated using this protocol. | 2024-05-27T01:27:04.277712 | https://example.com/article/9074 |
Saturday, 1 October 2016
THIRUMAZHAPADI – PONNIYIN SELVAN MEET AT THANJAVUR PERIYA KOIL 2016
...a
Continuation post.
26th
September 2016.
On
the second day of our Ponniyin Selvan meet at Tanjore, Periya Koil, Mr Anusha Vekatesh, the historian and writer
also joined with us for the Thirumalapadi
and Mela Palur ( Constructed by Pazhuvetaraiyar during 7th century ). For the second
day Program we vacated the Lodge at Kumbakonam and hired the same Taxi up to Thanjavur via Thirumalapadi and Mela Palur.
THIRUMALAPADI
During
one of the Nandhiyamperuman’s Marriage urchavam, I had the opportunity to see
the function sitting on the banks of river Kollidam. It is a popular belief in this area that
impediments in getting married will be overcome if they see the marriage
festival of Nandi Devar. Sundarar has sung
the Devara hymns start with ‘Ponnar meniyane’ on this temple God Sri
Vaidyanatha Swamy. During morning dharshan we had the opportunity of hearing
this hymn through the othuvar. During this time we
looked the temple with History and Heritage point of view. ( for Details of my first visit : Click Here )
HISTORY
The antiquity of
this place goes back to the Sangam Period. It was an army camp of the valiant
Malavar Clan of the Sangam Age and hence called Malavar-padi and later as
Thirumalapadi. There is another saying that Lord Shiva danced in this temple
with a Mazhu in his hand for Markandeya maharishi, hence called as Thiru
mazhapadli. This temple has thedevara
hymns of Appar, Sambandar also. It was
also visited by Ayyadigal Kadavarkon who praised it in his hymns of
Shetravenba. This saint has been identified with the Pallava king Simhavarman
(540-558), the grandfather of Mahendra Varman Pallava (598-630).
HERITAGE
& ARCHITECTURE
The
outer walls of the temples has about 140 inscriptions of Chozha, Rajaraja -1,
Marathas and Vijayanagara kings. Which
speaks about the Queens of Aditya–I, Rajaraja–I, and Rajendra–I
made gifts to the temple in the form of lands and ornaments. The first and
second gopurams of this temple were built during the periods of the Pandyas and
Cholas respectively.
Chembian Mahadevi, grandmother of
Rajaraja the Great, hailed from Chembiakudi, 4 kms from Thirumazhaipadi. Other
historical places like Pazhuvur, Alambakkam, Kandaradithyam (birthplace of
Kandraditha Chola) are all situated within a radius of 15 kms. There are quite
a few references to the Thirumazhaipadi Temple in the famous Tamil litterateur
Kalki’s work, ‘Ponniyin Selvan’.
The Siva temple was built of stone during
the period of Aditya–I (871-907). Rajaraja–I ordered for its rebuilding and was
completed by his son Rajendra–I. Again it was repaired by the Hoysala king
Viranarasimha in A.D. 1235-36. They are superb examples of the meticulous care
taken by the Pallavas who rebuilt built it in the 7th century CE. The 108-ft
tall, seven-tiered Rajagopuram of Thirumazhaipadi Temple faces east and towers
over the landscape of the banks of the Kollidam. It looks magnificent when
viewed from the river bed. The second gopuram with five tiers is about 80 ft.
tall. Both the rajagopurams are decorated with a rich array of stucco sculptures
that tell the many stories from the Thiruvilayadal, the history of Lord Shiva. The
Somaskandhar of this temple made of single stone. The Vaidyanathaswami Temple
at Thirumazhaipadi and the temple of Sundarambika lie within a sprawling 10-hectare
campus full of coconut and palm trees. The Amman
temple has the contribution of
Nattukottai Nagarathars also. | 2024-01-30T01:27:04.277712 | https://example.com/article/9539 |
Souidmy
Brand Overview
Souidmy has altogether 2 products
in Comparaboo's top 10 lists
Souidmy receives a quality score of 7.6 out of
10 based 38331 customer reviews from across the web.
The overall sentiment of Souidmy customers is
20 better than the average satisfaction on sentiment of Juicers consumers. | 2024-06-01T01:27:04.277712 | https://example.com/article/7052 |
Pleasance Pendred
Pleasance Pendred (1864 – 29 September 1948) was a British campaigner for women's rights, an activist and suffragette who during her imprisonment in Holloway Prison went on hunger strike as a consequence of which she was force-fed.
She was born in 1864 as Kate Pleasance Jackson in Lutterworth in Leicestershire, the daughter of Thomas Jackson, a grocer, and Elizabeth née Pendred; her late maternal aunt was called Pleasance Pendred (1843-1858). In 1881 aged 16 Kate Jackson was a Pupil Teacher at Osney House School in Oxford. By 1891 she and her now widowed father were boarders at 46 Langdon Park Road in Hornsey; by this time she was a School Board Teacher. Ten years later Kate Pleasance Jackson was still living at Langdon Park Road, and here she was to stay until at least 1927. For 25 years she worked as a teacher in London but was an active member of the Hornsey branch of the Women's Social and Political Union which is probably why she adopted the name 'Pleasance Pendred' as her employers were not likely to look favourably on her activities on behalf of women's suffrage. From 1909 until 1910 as 'Miss Jackson' she was the Literature Secretary for the Hornsey branch of the WSPU (renamed 'North Islington' in summer 1910) but she resigned from this office as stated in the 30 September 1910 issue of The Suffragette. However, she continued to work as a collector of money and object donations for the Hornsey branch of the WSPU until October 1912.
She resigned her teaching post just before she began her militant action for the WSPU on 28 January 1913 when she and three other women smashed the windows of various shops including an antiquities shop at 167 Victoria Street and of government offices in Westminster. During her trial in February 1913 she gave the name Pleasance Pendred and under that name she was sentenced to four months hard labour in Holloway Prison. As she was sentenced Pendred used the dock to complain publicly concerning the treatment received by herself and the other suffragettes arrested with her at Rochester Row Police Station. She stated that the Home Secretary Reginald McKenna had lied when he said that the four arrested women slept on camp beds in their cells and that they were supervised by women warders. She claimed that in fact her cell had a plank bed, the sanitary arrangements were disgusting and that five times during the night a male warder had come into her cell. The jury requested that the Chairman of the Sessions investigate these claims.
In Holloway Pendred went on hunger strike for about two months<ref>Lucy Delap, Maria Di Cenzo, Leila Ryan (editors), [https://books.google.co.uk/books?id=o03IyAJFHRcC&pg=PP255&lpg=PP255&dq 'Feminism and the Periodical Press, 1900-1918, Volume ], Routledge (2006) - Google Books</ref> during which period she was forcibly-fed, suffering illness as a result. The 4 April 1913 issue of The Suffragette recorded: "On her partial recovery, Miss Pendred who is still confined to her bed, continued the hunger strike, and is now being fed by cup." On her release from prison Pendred received a hunger strike medal from the WSPU for her outstanding bravery. On her early release from prison she received a welcome picnic from the Hornsey branch of the WSPU, as recorded in The Suffragette on 11 July 1913. After her release from prison in 1913 she held a few talks for the North Islington (formerly Hornsey) WSPU branch and is last recorded as a speaker in August 1913. Her article 'Why Women Teachers Break Windows' was published in Woman's Press, with a copy of it being republished in the Daily Herald'' on 25 February 1913.
She died in Lewes in Sussex in 1948 having never married. Her Holloway brooch and Hunger Strike Medal issued by the WSPU and named to her as Pleasance Pendred was auctioned in 2001, selling for £3,600.
References
Category:1865 births
Category:1948 deaths
Category:People from Lutterworth
Category:Schoolteachers from Leicestershire
Category:English suffragettes
Category:Women's Social and Political Union
Category:British feminists
Category:British women's rights activists
Category:Women's suffrage in the United Kingdom
Category:People from Hornsey
Category:Prisoners and detainees of England and Wales | 2023-11-13T01:27:04.277712 | https://example.com/article/7490 |
National Day of Prayer
Dozens of people gathered on the square in downtown Anderson for a ceremony marking the National Day of Prayer on Thursday.
Pastor Sam Duncan of the Gethsemane Baptist Temple says an opening prayer for the National Day of Prayer service in downtown Anderson on Thursday.
Anderson Independent Mail
Pastor Bill Rigsby says a prayer for public servants at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
Duane Garrett prays during Thursday's service for the National Day of Prayer in Anderson.
Anderson Independent Mail
Julie Dixon of the Anderson Care Pregnancy Clinic says a prayer for the family at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
People bow their heads at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
Elva Martin prays during Thursday's service for the National Day of Prayer.
Anderson Independent Mail
People bow their heads at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
Pastor Bill Rigsby says a prayer for public servants at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
People gather on the downtown square for Thursday's service for the National Day of Prayer.
Anderson Independent Mail
Linda Hanvey, left, holds Barbara Jones Fields hand during a prayer for the military performed by Pastor Brent Lollis of the Taylor Memorial Pentecostal Holiness Church during the National Day of Prayer service in downtown Anderson on Thursday. Fields said she has four children serving in the military.
Anderson Independent Mail
People attending the National Day of Prayer service in downtown Anderson applaud after Kim Phillips performed a song titled American Christian.
Anderson Independent Mail
People bow their heads at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
People bow their heads at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
People gather on the downtown square for Thursday's service for the National Day of Prayer.
Anderson Independent Mail
Pastor Sam Duncan of the Gethsemane Baptist Temple says an opening prayer for the National Day of Prayer service in downtown Anderson on Thursday.
Anderson Independent Mail
The T.L. Hanna Band performs the national anthem at the National Day of Prayer service.
Anderson Independent Mail
U.S. Rep. Jeff Duncan says a prayer for national leadership at Thursday's service marking the National Day of Prayer in downtown Anderson on Thursday.
Anderson Independent Mail
People attending Thursday's National Day of Prayer Service in downtown Anderson stand for the playing of the national anthem.
Anderson Independent Mail
Elaine Wales raises her hand in prayer during the prayer of repentance and spiritual warfare by Elva Martin at the National Day of Prayer service in downtown Anderson on Thursday.
Anderson Independent Mail
Pastor Donald Owens says a prayer for churches and pastors at Thursday's service for the National Day of Prayer.
Anderson Independent Mail
U.S. Rep. Jeff Duncan says a prayer for national leadership at Thursday's service marking the National Day of Prayer in downtown Anderson on Thursday.
Anderson Independent Mail
U.S. Rep. Jeff Duncan says a prayer for national leadership at Thursday's service marking the National Day of Prayer in downtown Anderson on Thursday.
Anderson Independent Mail
Linda Hanvey, left, holds Barbara Jones Fields hand during a prayer for the military by Pastor Brent Lollis of the Taylor Memorial Pentecostal Holiness Church during the National Day of Prayer service in downtown Anderson on Thursday. Fields said she has four children serving in the military.
Anderson Independent Mail
People bow their heads at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
U.S. Rep. Jeff Duncan says a prayer for national leadership at a service marking the National Day of Prayer in downtown Anderson.
Anderson Independent Mail
Pastor Bill Rigsby says a prayer for public servants at the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
Pastor Donald Owens says a prayer for churches and pastors at Thursday's service for the National Day of Prayer.
Anderson Independent Mail
Pastor Brent Lollis says a prayer for the military during the National Day of Prayer service in downtown Anderson.
Anderson Independent Mail
People gather on the downtown square for Thursday's service for the National Day of Prayer.
Anderson Independent Mail
People gather on the downtown square for Thursday's service for the National Day of Prayer.
Anderson Independent Mail
Jeff Hales leads the Pledge of Allegiance at the National Day of Prayer service. | 2024-01-19T01:27:04.277712 | https://example.com/article/5672 |
Q:
What is the definition of function in ZF/ZFC?
In ZF there is axiom schema of replacement, which can be stated as
the image of a set under any definable function will also fall inside a
set
Is there a definition of the concept of function in ZF/ZFC? What is it? I mean set-theoretically speaking. That is, in naïve set theory function can be understood as a set of pairs (triples, etc.), but what about ZF/ZFC?
A:
There are two different notions which are both called "function". A function internally to ZFC is a set of pairs, where the first element of the pair is understood to be mapped to the second by the function. For example, the successor function $S :\mathbb N \to \mathbb N$ is a function internally in ZFC, and it is given by
$$
S = \{(n,m) \in \mathbb N \times \mathbb N \mid m = n + 1\}.
$$
However, the function from the axiom schema of replacement refers to a function on the universe given by a formula. Slightly simplified, if $\phi(x,y)$ is a formula with two free variables such that ZFC proves that $\forall x \exists y \phi(x,y)$ and $\forall x \forall y \forall y'(\phi(x,y) \land \phi(x,y') \to y = y')$, then there is an instance of the schema axiom of replacement which states
$$
\forall X \exists Y(\forall x\forall y(\phi(x,y) \land x \in X \to y \in Y)).
$$
| 2023-08-28T01:27:04.277712 | https://example.com/article/4946 |
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Effects of corn processing method and dietary inclusion of corn wet distillers grains with solubles on odor and gas production in cattle manure.
The growing ethanol industry in the Southern Great Plains has recently increased the use of wet distillers grains with solubles (WDGS) in beef cattle finishing diets. Two experiments were conducted to evaluate odorous compound production in urine and feces of feedlot steers fed diets with different concentrations of WDGS and different grain processing methods. In both experiments, a Latin square design was used. In Exp. 1, a 2× 2 factorial arrangement of treatments was used and the factors consisted of corn processing method [steam-flaked corn (SFC) or dry-rolled corn (DRC)] and inclusion of corn-based WDGS (0 or 30% on a DM basis). Thus, the 4 treatment combinations consisted of: 1) SFC-based diet with 0% WDGS (SFC-0); 2) SFC-based diet with 30% WDGS (SFC-30); 3) DRC-based diet with 0% WDGS (DRC-0); and 4) DRC-based diet with 30% WDGS (DRC-30). In Exp. 2, all diets were based on SFC and the 4 treatments consisted of: 1) 0% WDGS (SFC-0); 2) 15% WDGS (SFC-15); 3) 30% WDGS (SFC-30); and 4) 45% WDGS (SFC-45). In both experiments, diets were balanced for degradable intake protein and ether extract by the addition of cottonseed meal and fat. Fecal slurries were prepared from a 5-d composite of urine and feces collected from each treatment. The slurries were analyzed using a gas chromatograph for VFA, phenol, p-cresol, indole, skatole, hydrogen, methane (CH(4),) and total gas production. In Exp. 1, the DRC fecal slurries had greater initial total VFA concentration compared with the SFC-based slurries and accumulated a greater concentration of total gas throughout the incubation; however, the SFC-based manure resulted in more CH(4) production. In Exp. 2, total VFA concentrations did not differ across all fecal slurries initially and on d 28; however, throughout the incubation, slurries with 0 and 15% WDGS had the greatest total VFA concentration. Overall, the presence of starch in the feces was likely the determining factor for the accumulation of odorous compounds in the fecal slurries initially, which was especially evident in diets including DRC, and once methanogenic microorganisms were established they likely converted VFA to CH(4). | 2024-02-11T01:27:04.277712 | https://example.com/article/5091 |
Q:
What is "Zest" - In particular: lime/lemon zest?
I saw a recipe that asked for Lime Zest and was wondering what it was?
A:
The very thin outside layer of the Lime, Lemon, Orange, and other citrus. It contains aromatic and flavorful oils that will enhance your meals.
When you zest your citrus fruit (usually with a fine grater) you need make sure that you only pull off the zest and not the white pith that lies underneath. The pith is bitter and generally not something you want in your dish.
A:
It's the colorful outer layer of the peel. The white part is the pith, and you don't want that as it imparts bitterness.
You can remove the zest by using the part of a cheese grater that you would use for parmesian cheese. If you're really careful, you can also use a vegetable peeler, but it's difficult to avoid the pith.
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Sliced Agate on Burnished Gold Stand
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Measures 4"L x 4"W x 7"H. Note that agate slice will vary between pieces, as this is a natural material. Currently the pieces we have in stock are mostly white. | 2024-07-27T01:27:04.277712 | https://example.com/article/1434 |
Outdoor Gas Fireplace in Clarkson, NY
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Our pros realize that this might not be the most enjoyable time in your life, but, that doesn’t imply our pros need to act like you’re just another customer and cause additional stress. Instead, our company's Clarkson, New York Outdoor Gas Fireplace specialists are sure to give you their complete attention while guiding you through the process in an effort to make things as simple as possible.
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We understand that when you contact our Clarkson, NY Outdoor Gas Fireplace organization, you’re likely looking for advice rather than simply buying a product. As opposed to merely taking your order and delivering the product(s) you ordered, our specialists actually educate you on the variety of options you have to pick from.
You Close the Sale, Not Our Specialists
When you get in touch with a great deal of Outdoor Gas Fireplace companies, they’ll be requesting your credit card before their staff know what you’re planning to order. At Value Out Door Fireplaces, however, our experts take a very different approach of actually listening to what it is you’re looking to execute and making suggestions to ensure you’ll receive exactly what you need. This makes the procedure a lot more relaxed for you as the consumer and it’ll probably save a little money too. | 2023-10-07T01:27:04.277712 | https://example.com/article/7878 |
After her adult charity event with Able Gamers got shut down I reached out to Mercedes Carrera to give her side of the story. A former STEM engineer, current adult film actress and outspoken GamerGate advocate, TechRaptor speaks to Carrera about her experiences as a women in these industries.
You have worked in both STEM and erotica, two industries which are associated with misogyny or patriarchy. What were your experiences in regards to that and your work? Why did you decide to change from one to the other?
My experiences in STEM and "porn" all relate directly to the common denominator in all my experiences: me. Therefore, I do not experience the world as a victim but rather as an opportunity to learn and better myself. I have experienced my challenges and struggles as a part of life and particularly in STEM I never experienced “misogyny” or “patriarchy”. Many corporations are, nowadays especially, very female friendly due to the valiant efforts of first and second wave feminism. Additionally, particularly in engineering and technology, I worked in merit based environments. Now, that’s not to say I always succeeded in such environments, but my lack of success was directly related to my capacity and work ethic, not a result of my gender. In reality I was doing well in corporate America but the restrictions were not preferable so I went into doing freelance production. From there I kind of fell into doing adult film work as a one off event (I had continued modeling on and off during that time as well).
Why did you choose the STEM industry originally? And what advice would you give to women who are looking into going into STEM?
My father was a technician and mechanic and I grew up in garages fixing things. Because we were not a higher income family and my father in particular had grown up in poverty, we generally fixed cars or objects repeatedly rather than buying new ones. I learned to use most tooling at a young age and it was common that I was assigned labor tasks around the house. As a result I developed a decent aptitude and capacity for that kind of manual labor and my interest in how things worked was deeply embedded in my psyche. Initially I actually wanted to study physics or astronomy, but the nature of the job market pushed me into manufacturing engineering. From there I secured an internship in aerospace engineering, stayed there for about 4 years, and later worked in telecommunications.
My advice would be: pursue a profession you love regardless of what you are told about the “job market” or “industry”. Passion for one’s work is one of the most important cornerstones of happiness. A very successful mentor of mine had had over five careers in his lifetime because he always pursued his passions, and I believe that is a life well lived.
You have been very outspoken about GamerGate. What made you take up the cause, and why is it so personal for you?
My perception of the consumer revolt that has aligned under GamerGate: I believe GamerGate now not only represents ethics in gaming journalism, but also the ongoing fight for free speech and liberty. When people are being silenced by cabals, be they totalitarians or “PC” social commentators, that is censorship. And as a supporter of free speech and liberty, I see that not only are gamers fighting for fair and equitable treatment by gaming journalists, they are also fighting for their voices to not be silenced. We see now social critics who are not gamers such as Anita Sarkeesian using gaming as a platform to push their social agenda of censorship, and I believe that more of us on the side of liberty must speak out lest we be silenced forever.
I have heard you say that feminist critics do not speak for you as a woman. Do you feel that many feminist critics attempt to speak for all women and why is this a problem?
I have found that many of the feminist critics are the most outspoken on things that they know nothing about. Take for example their stories that all women in STEM are subject to misogyny, or the idea that only men enjoy sexually empowered female characters: those are perceptions borne of the minds of sex-negative women who largely do not work in the STEM fields. They also critique pornography as though all porn actresses are sex slaves devoid of agency or self determination. As a conscious and willing participant in the field, I find this to not only be insulting but much more condescending than any supposed misogyny I should have experienced in any of my careers. There is often also a passive aggressive tone to the 3rd wave radfem critique of women who disagree- as though our voices must be dismissed as we obviously are either tools of the patriarchy or have “internalized misogyny”. Again, all highly insulting, condescending and most of all, inaccurate. It’s a great shame that they claim to support empowered women, but when a woman points out the glaring inaccuracies of their ideology she is quickly dismissed.
Which environment do you feel is the most "female friendly": STEM, the adult industry or Gaming?
That’s a tough call- I believe STEM environments are most friendly to inquisitive and hard workers, regardless of gender. In actuality the corporations are so careful now to avoid sexual harassment cases that in some ways it is prohibitive to be a female in such environments. For example, as an intern during my engineering rotation, it was understood that I was not to be left “alone” with men lest they harass me. Now, I worked with some of the nicest engineers so it wasn’t that they were a risk but that there had been a lawsuit prior regarding such things. As a result, there were times when it was difficult for me to learn if there was only one other male technician or engineer scheduled in the lab as I got less time with mentorship. "Porn" is very female friendly from a compensation standpoint. Also there are many successful and empowered women within the adult industry. However many of the female performers are quite young and leave the industry rather than grow it into a full career. So it depends largely on the person and their goals. However a dedicated and responsible woman in the adult industry can be quite successful and well compensated for her contribution. Additionally there are multiple ways to leverage such a career into other goals, plus having free time and a high wage affords the performers tremendous freedom.
As for gaming, never having worked as a developer I cannot speak to that side of the industry (although what I’ve heard of it sounds quite similar to my engineering experiences). However, as a player and participant I’ve found the gaming industry to be quite female positive and accepting. I’ve never experienced misogyny from gamers as a group at all. In fact, many of the male gamers are currently choosing to play empowered female characters such as Bayonetta in their free time, which speaks to the acceptance gamers have to gaming protagonists of both genders.
Congratulations on your charity event for The Fine Young Capitalists. Do you think you'll be working together again?
Those of us at The Porn Charity were quite pleased at the outcome of the event in coordination with The Fine Young Capitalists. They are managing and administering the scholarship fund we created with and for them, so our relationship will be ongoing. At this moment we do not have any plans for a future event together, but I greatly enjoyed our collaboration and hope we are able to collaborate again with them in the future!
We are currently in the development and planning stages for our next event. Details will be forthcoming, but we plan to address issues in the adult industry, female wellness and safety and an ongoing support of students in the STEM fields.
Techraptor would like to thank Mercedes for taking the time to talk to us. You can find her on twitter.
What are you experiences as a woman in these fields? Leave your comments below. | 2024-04-27T01:27:04.277712 | https://example.com/article/4622 |
DateSmart-1 uses a realistic approach to teach students how to support the choice for abstinence. Each program uses NotSmart/LifeSmart examples to focus on issues every student must address: how to set sexual boundaries; how not to be emotionally manipulated; how to avoid people with "one-track" mi…
DateSmart-1 uses a realistic approach to teach students how to support the choice for abstinence. Each program uses NotSmart/LifeSmart examples to focus on issues every student must address: how to set sexual boundaries; how not to be emotionally manipulated; how to avoid people with "one-track" minds; what social situations to avoid; how to protect their personal space and how to use "I'll PASS," a new way to say "No" that fosters partner support; how to learn that sex and love are not the same -- and much more.
DateSmart-2 teaches students how to control their emotions and avoid impulsive reactions to intimate situations. Through humorous NotSmart examples, students learn what actions can lead to trouble. The program teaches men not to date minors and how to refrain from manipulative actions that exploit women. Women learn how to recognize trouble and how to avoid behavior that can send unintentional, provocative signals. Common misconceptions about the opposite sex are addressed.
Notes
Although originally designed for students with mild to moderate learning, emotional and cognitive disabilities, LifeSmart Curriculum series is appropropriate for any population in need of a comprehensive review of basic life skills. | 2024-05-17T01:27:04.277712 | https://example.com/article/3952 |
Q:
How does Moles differ from other isolation frameworks, such as Moq, RhinoMocks etc
Pretty much as it says above. I'm wondering how it's different. Being a product from Microsoft, does it do similar things to more common frameworks, but with new names, or slightly differently; just apparently to make like difficult... e.g. MsTest.
How fully-fledged is it? Production-ready? It is meant to do more than Moq etc. (like MsTest is not simply a unit-testing framework). Does it cover the same mocking-ground. Does it do some things worse? Better?
I'm thinking of taking a look at it, but with so many frameworks around these days, I'm wondering what the benefit is.
A:
Mocking frameworks and isolation frameworks are really two similar but different things. Mocking and stubbing frameworks typically are referenced libraries that allow you to create a stub implementation of an interface (to fake out behavior) or mocking (to verify that behavior was called). Isolation frameworks generally work at the CLR and allow you to instrument into just about any area of code (your own others) you want.
Moles (which is part of Pex) is an isolation framework still in the research division of Microsoft (http://research.microsoft.com/en-us/projects/pex/). With Moles, you can pretty much isolate any section of your code (or any code in the CLR) and control how it behaves. For example with Moles, you could intercept the DateTime.Now() and return a set date and time to use for testing date-dependent calculation. It is also useful when you have a black-box third-party library that you cannot control.
The downside to Moles is that it is a little bit more complicated than using a mocking framework like Moq or RhinoMocks. This added functionality makes Moles' learning curve a little steeper. Also, while you can stub an interface with Moles fairly easily and use it in a CI build, when you actually instrument into Moles you "mole" and generate a new assembly with the proper hooks into new .dll. On larger projects, this might increase the build-time slightly. Finally, I've had some issues getting Moles to work in TFS build and test deployments (but that could just be me).
I wouldn't really make this an "either-or" situation. I would primarily use Moq for most of my needs and try to write my code to be testable using a conventional framework. If, however, you get stuck in a situation where you cannot easily isolate your code for various unit tests, I'd use Moles for those situations.
Finally, go read Martin Fowler's article "Mocks Aren't Stubs" (http://martinfowler.com/articles/mocksArentStubs.html). In my opinion it is the best description of what you really want to try to do with mocking and stubbing.
| 2024-05-29T01:27:04.277712 | https://example.com/article/3547 |
Madhur Canteen
Madhur Canteen () is a familiar name in the history of the Dhaka University as well as in the national politics of Bangladesh because of its association with various political movements which originated from the Dhaka University. The canteen's current location holds important architectural and heritage value.
Madhusudan Dey (Modhu), the canteen's founder, is an equally important figure in the socio-political history of the region. He was killed on 25 March 1971 at the beginning of the Bangladesh Liberation War. As part of Operation Searchlight, the Pakistan Army attacked the Dhaka University. Madhusudan Dey was taken to Jagannath Hall by the Pakistani armed forces where he was executed along with many University students. After the Liberation War, Arun Kumar Dey assumed the responsibility of running the canteen. Years after Modhu's death, the canteen remains a significant landmark and also a place for gathering in the community.
History of the canteen
Origin
Madhur Canteen was started in 1921, when Madhusudan Dey (Modhu) came to Dhaka with his father, Aditya Chandra, at the age of 15. Aditya Chandra, with the permission of the university authorities, began selling food in the Dhaka University Campus which was, at the time, located in the present Dhaka Medical College building . The canteen was shifted later when the Arts Faculty of the University was shifted to a new building at Nilkhet.
Madhur canteen played a pivotal role in the Bangladesh Liberation Movement . It was the focal point for the start of various political movements in the country .The canteen played a significant part in the Language Movements of 1948 and 1952, the movement of fourth-class Dhaka University employees in 1949, the student's revolt against the black laws (kala kanoon) of the university, and the 1969 mass uprising in East Pakistan . During these critical political moments, Madhur Canteen was a social epicentre frequented by student leaders and activists. The Pakistani army targeted Madhur Canteen on 25 March 1971, with the beginning of operation Searchlight.
Massacre
Madhusudan Dey was killed on 26 March 1971. The Pakistani military stormed his house and started firing in the early morning hours. Dey's wife, son and daughter-in-law were amongst those killed. Madhusudan Dey was injured in the firing, arrested and taken to the Jagannath Hall playground where he was killed alongside many students.
Present location
Madhur Canteen was reconstructed after suffering severe damage during the liberation war. The canteen was relocated from its original location in the present-day Dhaka Medical college building to an old structure. The canteen's present location served as the Durbar Hall of the Dhaka Nawabs. Apart from being used as a venue for formal and informal meetings, it also served as a skating rink and ballroom for the enjoyment of the Nawabs. Construction of the building began in 1873 which continued over several years. In 1906, a conference was held in the building, sponsored by Nawab Khwaja Salimullah, the Nawab of Dhaka that led to the formation of the All-India Muslim League.
Toufiq Hosen Khan, a student of fine arts, engraved a statue of Madhusudan Dey in 1995, which remains in front of the Madhur Canteen to the present day.
See also
Haji Biriyani
Star Kabab
References
Further reading
Muntassir Mamoon 2003 Dhaka Shomogro,
Mahbubur Rahman 2011, City of an architect,
Gopal Das 2007, Manidipto Campus
Category:University of Dhaka
Category:Politics of Bangladesh
Category:Dhaka
Category:Restaurants in Dhaka
Category:Bangladeshi cuisine
Bangladeshi
Category:Bangladeshi culture | 2023-09-25T01:27:04.277712 | https://example.com/article/8047 |
Q:
Fechar o DataInputStream sempre fecha o InputStream?
Eu preciso usar temporariamente um DataInputStream com um inputStream de um socket.
Eu preciso usar close no DataInputStream?
E se eu usar eu estaria fechando o inputStream do socket também ?
A:
Se você fechar o DataInputStream, ele vai fechar a stream que você passou no seu construtor (no seu caso, a inputStream do socket).
Da documentação de DataInputStream, na seção métodos herdados da classe FilterInputStream tem o link pro método close. Clicando nele a descrição fala que ele chama o close na inner stream ("This method simply performs in.close().").
| 2024-06-09T01:27:04.277712 | https://example.com/article/5522 |
Background {#Sec1}
==========
Crises and health system performance: where do we stand in the debate? {#Sec2}
----------------------------------------------------------------------
How health services are planned, purchased, and delivered has a direct impact on the key dimensions of health system performance, i.e., efficiency, quality, and access \[[@CR1]\]. In the aftermath of the economic and financial crisis that hit most member countries of the European Union, the question is raised of whether the impact of cuts in public funding and other austerity measures had neutral effects or have undermined the performance of health services \[[@CR2]\].
As the crisis grew in intensity, the WHO Regional Office for Europe \[[@CR3]\] recommended that member states monitor the effects of their policy responses on health indicators. Few countries did so, and existing assessments have focused mainly on measuring changes in access and efficiency, thus the need for further evidence on the dimension of quality of care delivery \[[@CR4]\].
The analysis of health services delivery needs to take into account that the operation of provider organizations is more complex than assumed by political decision-makers \[[@CR5]\]. This premise is based on the neo-institutional literature that argues that macro-level policies are affected by workplace-level contingencies that produce "perverse or non-expected" effects \[[@CR6], [@CR7]\].
This has received little attention in the debates on the effects on the quality of health services of political responses to the crisis. This paper is a contribution to the debate through a deeper look at how different levels of care, e.g., hospital and primary care, and the internal stratification of the medical profession, e.g., by specialty and years of service, constitute such contingencies \[[@CR8]--[@CR10]\]. That may explain why various categories of physicians, working in different environments, have reacted differently to the pressures generated by policy responses to the crisis.
Additionally, although public services have been the main target of austerity measures, complementarity with the private sector and growing pressure for marketization in many countries \[[@CR11]\] raises the issue of understanding better how private providers have adapted to the economic crisis. There has not yet been systematic research into this matter even though some authors suggest that public regulation can be less effective in monitoring and penalizing for-profit investors for patient selection \[[@CR12]\].
The situation in Portugal {#Sec3}
-------------------------
In 2011, a Memorandum of Understanding (MoU) between the Portuguese Government and the International Monetary Fund, The European Central Bank, and the European Commission designed a €78 billion, 3-year financial adjustment program with specific timelines and policy targets to reduce the budget deficit from 9.8 to 3% of GDP in 2013. Cost containment in the health sector was considered feasible without undermining the quality of services \[[@CR13]\]. Direct cuts in the health sector were initially estimated at €550 million. However, they doubled after 1 year and reached €1.3 billion in 2013 \[[@CR14]\].
Specific health-related policies were aimed at different targets: more cost-sharing, better drug-market regulation, tighter control over physicians' prescribing and of the management of public provider organizations, more transparent public-private partnership, expansion of primary health care services, and savings on workforce costs. Table [1](#Tab1){ref-type="table"} shows the extent to which these objectives were achieved.Table 1Implementation of the MoU in Portugal 2011--2014Policy outcomeAccomplishedPartially accomplishedNot accomplishedWithdrawn/omittedCost sharingReview and increase patient feesxReduction of exemption categoriesxIncrease inflation-indexed feesxCut tax allowances for healthcare, including private insurancexReduce the cost of health benefits schemes for public servantsxReduce costs for patient transportationxRegulation of the drug marketControl retail pricexMove the responsibility of pricing to the Ministry of HealthxRevise the international reference-pricing systemxMonitor expenditure monthly and limit public spendingxRemove barriers to generic medicinesxChange the calculation of pharmacies' profit marginxGradually increase the share of generic medicinesxImplement existing legislation on the regulation of pharmaciesxSpeed up the reimbursement of genericsxIntroduce a contribution paid by pharmaciesxControl of doctors' prescriptionMake electronic prescription of medicines and diagnostic tests covered by public reimbursement fully compulsory for physicians (public and private sectors)xEncourage physicians to prescribe generic medicines and less costly branded products (public and private sectors)xIntroduce international prescription guidelines for drugs, exams and treatmentxImprove monitoring of prescription of medicines and diagnostic services and impose systematic assessments by each doctor of quantity and cost. Introduce sanctions and penaltiesxControl of operating costs and performance in the NHSLegislative and administrative framework for a centralized procurement system for the purchase of medical goodsxChange in the existing accounting framework in hospitals SOEs to that of private companies and other SOEsxConcentration and rationalization of non-hospital care provisionxConcentration and rationalization of the hospital networkxContinued publication of clinical guidelines and introduction of an auditing systemxBenchmarking of hospital performancexInteroperability of IT systems in hospitalsxFinalization and regular updates of uniform coding system for medical suppliesxImplement the centralized purchasing of medical goods using the uniform coding systemxClearing of existing arrears in the hospital sector and prevention of accumulation of new arrearsxCompletion of patient electronic medical recordsxPublic-private relationshipIncrease in competition between private providers and reduction in NHS payment of exams and treatmentsxCentralized monitoring of public-private partnership contractsxRegular revision of fees paid by the NHS for exams and treatment by private providersxAssessment of compliance with European competition rules for the provision of services in the private healthcare sectorxAccess to healthcareReinforce primary health careIncrease the number of patients per primary care unit/family doctorxIncrease the number of primary care units using salary and performance-related paymentsxSeparate HR from hospitals and reconsider the role of nurses and other professionalsxReview geographical distribution of GPsxMove hospital outpatient services to primary care unitsxWorkforceUpdate working time, increase mobility, adopt flexible time arrangements and review payment mechanismsxConduct an annual inventory of doctorsxMake human resource allocation plansxIncrease mobility of healthcare staff within and between regionsxEnsure transparent selection of the chairs and members of hospital boardsxLegend: Own elaboration from \[[@CR26], [@CR27]\]
Overall, the massive reduction in public expenditure came more from cost-sharing, tighter drug-market regulation, control over prescribing, and of the management of provider organizations. Improvements in public-private partnership, better access to primary healthcare, and workforce changes contributed to a lesser extent. Available studies of the effects of those reductions have focused mainly on efficiency and access \[[@CR15]\] and planning and purchasing of services \[[@CR16], [@CR17]\].
Objectives of the study {#Sec4}
-----------------------
The aim of this research is to provide more evidence about the effects of an adjustment program on the quality of healthcare. Its contribution to the debate is threefold. First, quality needs to be considered as important as efficiency and access. Second, it highlights to what extent an analysis of delivery of healthcare requires looking at different sources of information than those on planning and purchasing of services. Health workers' daily experiences are a rich source of information in this regard \[[@CR18]\]. Third, it presents comparisons between and within the public and private sectors, a neglected aspect in research on policy responses to economic crises in Europe.
Methods {#Sec5}
=======
Study design and participants {#Sec6}
-----------------------------
A two-step model (Fig. [1](#Fig1){ref-type="fig"}) was designed to describe the experiences of physicians working in public and private services (main-effect model) and analyze variations between the two groups based on years of experience and specialty (model with moderated effects). All types of public providers were included in the public sector, as were for-profit and professional-based insurers in the private sector.Fig. 1Analytical model
Data was collected in a national survey asking physicians about their experiences after 2011, when the financial adjustment program began. A structured, self-administered questionnaire was sent by post from May 2013 to January 2014 to all physicians registered with the Portuguese Medical Council (*N* = 43,874). The key aim was to reach as many physicians as possible with no previous criteria underpinning the selection of cases. A total of 3442 questionnaires from physicians practicing in Portugal at that time were returned and validated through consistency and readability analysis. Even though it is one of the largest national-level databases of physicians in Europe, it was not possible to define a probabilistic sample of practicing physicians in Portugal because (i) there are no standardized data on the number of doctors who have retired or emigrated or on their distribution by sector or type of medical services and (ii) confidentiality criteria imposed by the Medical Council's ethics committee prevented us from collecting the respondents' age or geographical location.
Measures {#Sec7}
--------
### Dependent variables {#Sec8}
Quality of care is analyzed in different ways depending on disciplinary backgrounds \[[@CR19]\]. The analysis adopted here lay in a structure-process link, as it was intended to ascertain whether reforms changed how care was actually delivered \[[@CR20]\]. Given that the questionnaire was sent to all registered physicians, we had to find suitable ways of comparing people in different positions and workplace settings. Therefore, the structure-process analysis was empirically driven according to the implementation of the MoU in Portugal from 2011 to 2014. Quality of care was addressed in terms of changes physicians said they had experienced in three key aspects of their daily practice: control of prescriptions, operating costs, and performance, as detailed in Table [1](#Tab1){ref-type="table"}. Six dependent variables (DVs) were defined as follows:-Administrative interference in decision making, i.e., less autonomy in physicians' decision-making in favor of organizational control: more rejections of innovative treatments (DV1), pressure to choose cheaper treatments exerted by the administration (DV4), and pressure not to prescribe certain drugs exerted by the administration (DV5)-Insufficient resources, i.e., possible limitation of material resources for the provision of care: regular shortages of supplies (gloves, masks, needles, etc.) (DV2) and regular shortages of drugs (DV3)-Deterioration in medical residency, i.e., organizational changes that directly affected physicians' advanced training: less favorable conditions for medical residencies (DV6) (e.g., overworked residents and less time for tutors' work)
The list of questions was preceded by: "Based on your personal experience and in comparison to 2011", and dichotomous dummy variables were defined with the answer "no" as a reference category (0). The proportion of "yes" answers was also used to make group comparisons.
### Independent variables {#Sec9}
The sector was analyzed at two levels: physicians working exclusively for the National Health Service (NHS) or exclusively in the private sector. The NHS included hospitals and primary health care and the private sector included small offices, clinics, and private hospitals.
### Moderator variables {#Sec10}
Years of practice meant the length of time physicians had been registered with the Medical Council (a compulsory requirement after post-graduate medical training). They were measured in months as a quantitative variable.
The 21 selected medical specialties (of a total of 41) were those of physicians working exclusively in the NHS or exclusively in the private sector. These were combined as follows: anesthesiology, cardiology, dermatology, gastroenterology, general practice/family medicine, general surgery, internal medicine, neurology, obstetrics and gynecology, oncology (medical and radiation oncology), ophthalmology, orthopedics, other surgical specialties (angiology and vascular, cardiothoracic, maxillofacial, pediatric surgery and plastic and reconstructive surgery, neurosurgery, and urology), ENT, pediatrics, physical medicine and rehabilitation, psychiatry, public health, pulmonology, radiology (nuclear medicine, neuroradiology, and radiology), and stomatology.
Data analysis {#Sec11}
-------------
Descriptive statistical analysis was used to examine the distribution of the variables, including non-answers. The independent *t* test and analysis of variance (ANOVA) were used to examine group differences on the basis of the proportion of "yes" answers for each dependent variable. A multivariate logistic regression was conducted to evaluate the moderator effect of years of practice and medical specialty in the relationship between sector of activity and quality of care using the Process Macro \[[@CR21]\]. A General Linear Model (GLM) Univariate Analysis was conducted to assess the moderator effect of medical specialty testing interaction effects. Since some of the combinations of the factorial design showed a small number of cases, a non-parametric method (bootstrap) was also used to validate the results obtained by the parametric procedure. Some of the initial medical specialties had to be excluded in order to avoid empty combinations in the factorial design. Post hoc probing was conducted to interpret significant interactions utilizing estimates obtained from the fitted models \[[@CR22]\] and also to achieve plotting interactions. All analyses were conducted using SPSS (version 23).
Results {#Sec12}
=======
Descriptive statistics {#Sec13}
----------------------
The final sample comprised 2063 physicians who had valid data according to the main inclusion criteria, working exclusively in the public or private sector (Table [2](#Tab2){ref-type="table"}). Most respondents were general practitioners and working exclusively in the public sector. The percentage of younger doctors was slightly higher. As regards dependent variables, results were as follows: 17.3% reported more refusals of innovative treatments, 64.9% regular shortages of supplies, 30.6% regular shortages of drugs, 23.8% greater pressure to choose less costly treatments, 15.6% greater pressure to limit the prescription of certain drugs, and 48.9% less favorable conditions for medical residencies (Table [2](#Tab2){ref-type="table"}).Table 2Descriptive statisticsAnalyses variables and categories*N*%Independent variableSector of activityExclusive in public120958.6Exclusive in private85441.4Total2063100.0Exclusive in publicPrimary healthcare50942.1Public hospitals63452.4Non answer665.5Total1209100.0Exclusive in privateSmall-size offices27432.1Clinics23026.9Hospital799.3Non answer27131.7Total854100.0Moderator variablesYears of practiceUp to 12 years64431.213--25 years47322.926--39 years52025.2Over 40 years42620.0Total2063100.0Medical specialtyAnesthesiology592.9Cardiology281.4Dermatology17.8Gastroenterology231.1General practice/family medicine49824.1General surgery1105.3Internal medicine1326.4Neurology16.8Obstetrics and gynecology783.8Oncology381.8Ophthalmology412.0Orthopedics492.4Other surgical specialties542.6Otorhinolaryngology291.4Pediatrics1095.3Physical medicine and rehabilitation261.3Psychiatry643.1Public Health281.4Pulmonology311.5Radiology361.7Stomatology301.5Non answer56727.5Total2063100.0Dependent variables---quality of careDV1No146582.7Yes30717.3Total1772100.0DV2No63935.1Yes118464.9Total1823100.0DV3No114969.4Yes50630.6Total1655100.0DV4No138476.2Yes43223.8Total1816100.0DV5No181984.4Yes33615.6Total2155100.0DV6No74751.1Yes71648.9Total1463100.0Notes: (1) Sums of subject numbers for the dependent variables are not always equal because of missing data; percentages are based on number of subjects for whom data were available; (2) DV1---refusal of innovative treatments; DV2---regular shortage of work supplies; DV3---shortage of drugs; DV4---pressure to choose less-expensive treatments; DV5---pressure not to prescribe specific drugs; DV6---inferior medical training
Group comparisons {#Sec14}
-----------------
A comparison of means between sectors showed that they significantly affected physicians' evaluation of quality of care in several indicators: usual shortage of supplies (*t* (1054) = 14.379, *p* \< .001) (DV2), shortage of drugs (*t* (938) = 4.809, *p* \< .001) (DV3), pressure to choose cheaper treatments (*t* (1049) = 3.001, *p* = .003) (DV4), pressure to limit the prescription of certain drugs (*t* (1276) = 6.044, *p* \< .001) (DV5), and less favorable conditions for medical residencies (*t* (684) = − 2.439, *p* = .015) (DV6). Except for the latter, there were more "yes" answers among physicians working exclusively in the public sector (see 1st step, Table [3](#Tab3){ref-type="table"}).Table 3Comparisons of quality of care between groups (t-test and one-way ANOVA)Sector of activityDV1DV2DV3DV4DV5DV6Mean^a^MeanMeanMeanMeanMean1st step Public0.1530.7310.3000.2620.2000.435 Private0.1340.2280.1100.1580.0580.571 Model test*t* (1026) = 0.683*t* (1054) = 14.379\*\*\**t* (938) = 4.809\*\*\**t* (1049) = 3.001\*\**t* (1276) = 6.044\*\*\**t* (684) = − 2.436\*2nd step PublicPrimary healthcare0.0650.8470.0910.3510.2670.385Public hospitals0.2340.6370.4370.2010.1430.471 Model test*t* (786) = − 6.663\*\*\**t* (815) = 6.893\*\*\**t* (751) = − 10.914\*\*\**t* (820) = 4.869\*\*\**t* (910) = 4.741\*\*\**t* (554) = − 1.996\* PrivateSmall-size offices0.2860.1250.1000.1610.0560.636Clinics0.0740.3330.1290.2390.0610.308Hospital0.1670.1880.1330.1940.1000.750 Model test*F* (2, 116) = 3.682\**F* (2, 115) = 2.768*F* (2, 78) = 0.0660*F* (2, 105) = 1.609*F* (2, 201) = 0.514*F* (2, 48) = 3.299\*^a^Mean = proportion of answer "yes"\**p* \< .05; \*\**p* \< .01; \*\*\**p* \< .001
Significant differences were found among physicians working exclusively at public hospitals and in primary care in all dependent variables (*p* \< .05). Physicians working exclusively in public hospitals mentioned refusal of innovative treatments (*t* (786) = − 6.663, *p* \< .001) (DV1), drug shortages (*t* (751) = − 10.914, *p* \< .001) (DV3) and, with a smaller difference, less favorable conditions for medical residencies (*t* (554) = − 1.996, *p* = .023) (DV6). Physicians working in primary care services mentioned shortages of equipment (*t* (815) = 6.893, *p* \< .001) (DV2), pressure to choose cheaper treatments (*t* (820) = 4.869, *p* \< .001) (DV4), and pressure not to prescribe certain drugs (*t* (910) = 4.741, *p* \< .001) (DV5).
Significant differences were found among physicians working in the private sector only regarding refusal of innovative treatments (*F* (2, 116) = 3.682, *p* = .028) (DV1) and, to a lesser extent, less favorable conditions for medical residencies (*F* (2, 48) = 3.299, *p* = .045) (DV6). There were fewer "yes" answers in both indicators among physicians working in clinics (see 1nd step, Table [3](#Tab3){ref-type="table"}).
Moderator analysis {#Sec15}
------------------
A moderator effect of years of practice was tested to provide a more detailed understanding of the differences between working in the public or private sector (Fig. [1](#Fig1){ref-type="fig"}). The interaction effect between sector and years of practice had a significant effect on refusal of innovative treatments (*B =* − 0.005, *Z =* − 2.396, *p* = .017, 95% CI = − 0.008, − 0.001) (DV1), pressure not to prescribe certain drugs (*B =* 0.005, *Z =* 2.884, *p* = .004, 95% CI = 0.002, 0.009) (DV5) and less favorable conditions for medical residencies (*B =* − 0.004, *Z =* − 2.075, *p* = .038, 95% CI = − 0.007, − 0.001) (DV6) (Table [4](#Tab4){ref-type="table"}).Table 4Multivariate logistic regression model with the moderator effect of years of practice on quality of careDV1DV2DV3DV4DV5DV6Exclusive in public^a^1.5561.160^\*^− 0.104− 0.115− 0.8140.571(0.857)(0.580)(0.714)(0.640)(0.710)(0.692)Years of practice (exclusive in private)0.002− 0.003^\*\*^− 0.005^\*\*^− 0.002− 0.006^\*\*^0.001(0.002)(0.001)(0.002)(0.002)(0.002)(0.002)Exclusive in public \* Years of practice^b^− 0.005^\*^0.0020.0020.0020.005^\*\*^− 0.004^\*^(0.002)0.001(0.002)(0.002)(0.002)(0.002)Constant− 2.742^\*\*^0.212− 0.229− 0.775− 0.5220.172(0.843)(0.563)(0.703)(0.626)(0.694)(0.645)Model LL =18.316^\*\*\*^186.426^\*\*\*^57.636^\*\*\*^13.628^\*\*^52.207^\*\*\*^24.265^\*\*\*^Post hoc testsYears of practice (exclusive in public)− 0.003^\*\*\*^− 0.002^\*\*^− 0.003^\*\*\*^− 0.002^\*\*^− 0.0020.000(0.001)(0.001)(0.002)(0.001)(0.001)(0.002)Non-standardized coefficients and standard errors (in brackets) are reported^a^Exclusive private (baseline)^b^Interaction effect\**p* \< .05; \*\**p* \< .01; \*\*\**p* \< .001
Figure [2](#Fig2){ref-type="fig"} shows that refusal of innovative treatments tended to be reported more by older physicians in the private sector and younger physicians in the public sector. Post hoc tests revealed a significant effect of years of practice only in the public sector (*B =* − 0.003, *Z =* − 3.941, *p* = .000, 95% CI = − 0.004, − 0.001).Fig. 2Interaction between sector and years of practice in refusal of innovative treatments
As presented in Fig. [3](#Fig3){ref-type="fig"}, the pressure not to prescribe certain drugs was not affected by years of practice in the public sector (*p* \> .05). A significant negative effect was found in the private sector and was less likely to occur among older physicians (*B =* − 0.006, *Z =* − 3.121, *p* = .002, 95% CI = − 0.009, − 0.002) (Fig. [3](#Fig3){ref-type="fig"}).Fig. 3Interaction between sector and years of practice in pressure not to prescribe certain drugs
In contrast, less favorable conditions for medical residencies were not affected by years of practice in the private sector (*p* \> .05), while a significant negative effect was observed in the public sector (*B =* − 0.003, *Z =* − 4.219, *p* \< .001, 95% CI = − 0.005, − 0.002) (Fig. [4](#Fig4){ref-type="fig"}).Fig. 4Interaction between sector and years of practice in deterioration in medical training
Regarding regular shortages of supplies and drugs, only the main effect was significant, as years of practice did not have a moderating effect (*p* \< .05) (Table [4](#Tab4){ref-type="table"}). Older physicians made less mention of regular shortages of supplies in both the private and public sectors (*B =* − 0.003, *Z =* − 2.594, *p* = .01, 95% CI = − 0.006, − 0.001 and *B =* − 0.002, *Z =* − 3.238, *p* = .001, 95% CI = − 0.003, − 0.001, respectively). Drug shortages also produced fewer "yes" answers from older physicians and this significant effect occurred in both sectors (*B =* − 0.005, *Z =* − 2.622, *p* = .009, 95% CI = − 0.008, − 0.001 and *B =* − 0.003, *Z =* − 4.821, *p* \< .001, 95% CI = − 0.004, − 0.002, private and public respectively).
Moderation by medical specialty was also tested (Fig. [1](#Fig1){ref-type="fig"}). The interaction between sector and medical specialty had a significant effect on refusal of innovative treatments (*F* (11, 595) = 1.988, *p* = .035) (DV1) and shortages of drugs (*F* (11, 520) = 4.206, *p* \< .001) (DV3) (Table [5](#Tab5){ref-type="table"}).Table 5GLM Univariate Analysis with the moderator effect on the relationship between medical specialty and quality of careDV1DV2DV3DV4DV5DV6Sector*F* (1, 595) = 0.842*F* (1, 609) = 68.809\*\*\**F* (1, 520) = 23.010\*\*\**F* (1, 606) = 0.006*F* (1, 764) = 0.571*F* (1, 382) = 2.038Medical specialty*F* (11, 595) = 2.701\*\**F* (11, 609) = 3.447\*\*\**F* (11, 520) = 0.898*F* (11, 606) = 1.130*F* (11, 764) = 1.143*F* (11, 382) = 0.927Interaction between sector and medical specialty*F* (11, 595) = 1.988\**F* (11, 609) = 1.370*F* (11, 520) = 4.206\*\*\**F* (11, 606) = 0.993*F* (11, 764) = 0.822*F* (11, 382) = 1.353*GLM* General Linear Model\**p* \< .05; \*\**p* \< .01; \*\*\**p* \< .001
There was a significant difference between the two sectors for refusal of innovative treatments in stomatology (*p* = .024) and radiology (*p* = .004). On the other hand, the answer "yes" was more frequent for oral medicine in the private sector and radiology in the public sector (Fig. [5](#Fig5){ref-type="fig"}). Shortages of drugs were significantly different between the sectors in various specialties: physical medicine and rehabilitation (*p* = .001), internal medicine (*p* = .020), general practice/family medicine (*p* = .020), general surgery (*p* = .006), ophthalmology (*p* = .038), and psychiatry (*p* \< .001). With the exception of general practice/family medicine, the answer "yes" was more frequent in the public sector for all the other medical specialties (Fig. [6](#Fig6){ref-type="fig"}).Fig. 5Interaction between sector and medical specialty in refusal of innovative treatments Fig. 6Interaction between sector activity and medical specialty on shortage of drugs
Discussion {#Sec16}
==========
The understanding of the effects of adjustment programs like those of Greece, Portugal, Ireland, and Cyprus fills an important gap in the literature on policy responses in Europe to the recent economic crisis. Conclusions result in non-convergent evidence and therefore further analysis is required. The framework for this study was built on two overlooked assumptions. First, the understanding of the effects of the crisis on health systems performance is still limited given that few analyses have been conducted on quality of care as compared to efficiency and access. Second, looking at healthcare delivery is likely to reveal differences in relation to the analysis of planning or purchasing due to workplace-level contingencies. This led us to assess, based on the experience of those who provide care, whether structural reforms impacted the care delivery process and the quality of services.
Accordingly, we suggest that the reforms made under the Portuguese adjustment program had negative effects on the quality of care, namely in terms of shortages of work resources, less favorable conditions for medical residencies, and to a lesser extent, more administrative interference in clinical decisions. Reports of negative effects were consistently higher among physicians working exclusively for the NHS, which illustrates that the public sector was the main target of health-related austerity measures, even though these were expected to apply to all types of providers without exception.
Our findings show also that the austerity measures were felt differently in the public and private sectors. Results in the NHS suggest insufficient resources and greater constraints on physicians' individual decision-making (e.g., equipment shortages and administrative interference in clinical decisions). In the private sector, the main outcome of reforms was the negative impact on medical residencies due to overworked residents and to less time for tutors to provide training. Constraints in both sectors require further studies for a better understanding of its effects on clinical autonomy and training and ultimately on health outcomes.
Looking at public and private services, physicians in public hospitals reported more denials of innovative treatments, more drug shortages, and less favorable conditions for medical residencies. Primary care physicians reported more equipment shortages and administrative interference in medical decisions. In the private sector, physicians in small offices reported more refusals of innovative treatments than those in clinics and private hospitals, while the latter complained more deterioration in medical residency.
The argument that physicians' experiences depend on the sector of activity is reinforced when we analyzed the moderating effects of two key factors in medical hierarchy (years of practice and specialty). The reporting of denial of innovative treatments decreases with seniority in the public sector, while it increases in the private sector. Administrative interference was perceived as higher by less-experienced physicians in the private sector, while in the public sector years of service made no difference as to the pressure to limit the prescription of certain drugs. More less-experienced physicians in the public sector mentioned less favorable conditions for medical residencies, while this trend was not found in the private sector. As to differences between medical specialties, refusal of innovative treatments was more reported by stomatologists in the private sector than those in the public sector and by radiologists in the public sector than those in the private sector. Shortage of drugs was more reported by public-sector physiologists, internists, surgeons, ophthalmologists, and psychiatrists than by these specialists in the private sector, while general practitioners in the private sector reported it more than their colleagues in the NHS.
Our study shows that physicians in public and private sectors and within each sector have different perceptions, depending on their specific characteristics, of the impact of the same policy responses.
A number of potential long-term effects that this empirical study cannot address are associated with these results. One in particular is here uncovered to highlight possible directions for research. Lower quality healthcare services presumably affect health professionals' and patients' individual choices. Given that the influence of trust in individuals' decisions is well understood \[[@CR23], [@CR24]\], the understudied link is the effects of lower quality on the undermining of trust relationships in health. The issue is to know how lower quality affect professionals' and patients' individual choices and whether these choices can affect health systems structurally.
As to the NHS, the quality-trust link builds on the moral contract between authorities, citizens, and professionals. Professionals feeling that they are not being given the conditions they need for their work and patients questioning the need for higher taxation to fund access to services that are less trustworthy can translate into the growth of the private market in parallel to the public sector. As to the private sector, the quality-trust link is a key element in market competition. Greater pressure is put on the supply side in investment in communication strategies and patient-centered care approaches. Consequently, it is relevant to discuss possible increases in households' spending and growing exposure to deregulation of the health labor market.
Limitations {#Sec17}
-----------
We were unable to establish the representativeness of the respondents, even though the total number of over 3000 is high. Also, the instrument does not permit a clear assessment of the moderating effect of physicians' years of practice and specialties, selected as proxy of internal stratification of the medical profession. More empirical in-depth research into this issue is needed. Lastly, the measurements of quality of care delivery reflect physicians' personal experiences and views and are therefore not comparable to those of health workers.
Conclusion {#Sec18}
==========
The aim of this article was to add to the understanding of the effects of policy responses to the 2008 crisis on health system performance in Europe. In Portugal, there is an institutional discourse that the health system adapted well to cost containment \[[@CR25]\]. By focusing on the perceptions of professionals of the effects of the crisis on their work and on the quality of care, we offer a complementary contribution. Also, our findings show that the outcomes of policy responses may not have been the same in all national health care systems, therefore requiring context-sensitive analyses.
The added value of an analysis built on a macro (political)-micro (organizational) link is likely to reveal a different reality from that showed by general statistics, which do not reflect concrete experiences. It also shows the non-linearity between policy setting and expected outcomes, which is particularly relevant in assessing the effects of austerity measures. The fact that only physicians were surveyed and the lack of standardized data on physicians in Portugal are limitations that further research can help mitigate.
DV
: Dependent variable
MoU
: Memorandum of Understanding
NHS
: National Health Service
This article is a partial outcome of broad scientific collaboration between a research team at the University Institute of Lisbon, coordinated by Dr. Tiago Correia, and the Portuguese Medical Council, with the aim of studying the effects of the adjustment program on physicians. We are very grateful to all the physicians who agreed to participate in the study and to Joana Vieira for helping collect some institutional information.
Funding {#FPar1}
=======
TC holds a research grant funded by FCT \[SFRH/BPD/84175/2012\]. No additional funding was received for this study.
Availability of data and materials {#FPar2}
==================================
The datasets generated and/or analyzed during the current study are not publicly available due to the ethics approval by the Portuguese Medical Council's ethics committee.
TC had the idea for the paper, developed the conceptual approach, wrote the first draft, and revised the manuscript. GC participated in the development of the conceptual approach and revised the first draft of the manuscript. HC developed the data analysis and co-wrote parts of the manuscript. JMS created the tool of data collection and coordinated the process of data gathering. GD participated in the development of the conceptual approach and revised the second draft of the manuscript. All authors read and approved the final manuscript.
Ethics approval and consent to participate {#FPar3}
==========================================
The authors hereby declare that (1) the content of the questionnaire, (2) the storage in paper format and digital records, and (3) data analysis received the approval by the Portuguese Medical Council's ethics committee.
Consent for publication {#FPar4}
=======================
Not applicable.
Competing interests {#FPar5}
===================
TC, GC, HC, and GD declare that they have no competing interests. JMS was at the time of the study President of the Portuguese Medical Council.
Publisher's Note {#FPar6}
================
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
| 2024-01-07T01:27:04.277712 | https://example.com/article/8418 |
You think of Luol Deng as talented but not living up to his potential.
For the English national team, he is a savior.
And Deng has been cleared to play for England this summer, according to Britball. That drive starts Tuesday in a game against Hungary. He is hoping to help them qualify for the European Championships next summer, a run up to the 2012 Olympics in London (where England gets a spot as host nation).
“I’m glad Luol’s back,” said (team captain Drew) Sullivan. “Last summer he was around the team as much as he could and you could see how upset he was that he couldn’t play at the Eurobasket finals, which is something we’d spent two years working towards. He was devastated that he’d helped us qualify and then, unfortunately, got hurt with the Bulls and didn’t recover in time. From our perspective, we need him. We’re a much better team with him.”
He was a little late joining the team, due to Amare-like insurance issues. But he is there now.
Who else is on that England roster? Pops Mensah-Bonsu for one. Former Vanderbilt player Andrew Sullivan, and Dan Clark who plays in Europe. And from there it gets more obscure.
Deng makes that team far, far more formidable. But maybe still not good enough for the European Championships. | 2024-07-24T01:27:04.277712 | https://example.com/article/9682 |
Cape Town revs up for World Rallycross action
World Rallycross will visit Africa for the first time this year. Picture: David Ritchie
Cape Town - The circuit is ready, the new grandstands are well underway - are you ready for the 12th and final round of the 2017 World Rallycross championship, to be run at the Killarney International Raceway in November?
Deputy mayor Ian Neilson said at the launch of the event on Thursday: “Normally, we sign three-year deals, but we’re delighted to have signed a five-year deal as hosts.
“Globally, there is massive interest in World Rallycross, with 180 million television viewers worldwide; now they’ll know about Cape Town and South Africa. They’ll know that Cape Town is the events capital of Africa.”
The last round of the series has been run in Argentina each year since the championship’s inception in 2014, but a new deal signed in conjunction with the City of Cape Town and Killarney International Raceway will see the showpiece come to the Cape for the next five editions. About 30 000 people are expected to attend the weekend event.
Killarney executive manager Des Easom was delighted to be hosting the championship, which will include a full weekend of racing around a new multi-surface track, purpose-built at Killarney for the November 10-12 race weekend.
“Killarney is one of the only multipurpose events venues in the country," Easom said. "It’s one of the best speedways in SA. We’ve enjoyed the support of many international visitors who have all praised the track and its environment and facilities."
“We felt the time was right and the city was ready for a world championship.”
World Rallycross managing director Paul Bellamy said they were “hugely impressed by the passion at Killarney” which was why it was an easy decision to move the event to Cape Town.
Taking part in the RX2 championship, one tier down from the supercar division, is South African John Williams who was excited to be driving the vehicles for the first time.
"It’s great for Cape Town, and its great for South Africa,” he said.
Rocketship launch
A World Rallycross supercar is quicker off the line than a Formula One car, taking less than two seconds to reach 100km/h.
Multiple motorsport title-holder and three-times World Rallycross champion Petter Solberg said these cars were the best he had driven. | 2024-05-05T01:27:04.277712 | https://example.com/article/9941 |
Sell mobile phone in order to switch to iPad 2
Consumers across the UK – and indeed the world – could be preparing to sell their mobile phones in order to create a gap for the new Apple iPad 2.
Stuart Dredge, writing for CNET UK, explains the US manufacturer is to launch the new tablet at an event in San Francisco next week.
However, there is speculation about exactly what customers can expect for their money should they invest in the model and whether Apple has a third incarnation of the device up its sleeve for later this year.
Summing up other blogs and sources, Mr Dredge states: "[There's] a strong hint that the long-expected cloud/streaming iTunes is on the way, not to mention the recently rumoured revamp of MobileMe as an ambitious social-media locker service."
The original version of the iPad is the most popular tablet available to the public, with Frost and Sullivan this week revealing it enjoyed a 90 per cent market share in 2010. | 2023-11-15T01:27:04.277712 | https://example.com/article/1744 |
Storage systems generally utilize large fast memories for caching data, so as to accelerate performance of I/O operations, e.g., shorten data access time and reduce latency of I/O operations. A cache memory stores data that is likely to be accessed, such as: most frequently accessed data, most recently accessed data, and data assumed to be accessed according to access patterns detected by prefetch algorithms.
SSD (solid-state drive) is a flash based device that is often used for caching data, due to its characteristics allowing fast access and large storage capacity.
Being a device that is separate from the controlling processor, the controlling processor may lose connection with the SSD, or the SSD itself may be subject to failures.
Though the loss of cached data, upon SSD failure, may not be considered as a critical failure, since the data is not really lost and can be read from the permanent devices—losing the option of fast access to the most frequency accessed data can dramatically degrade the I/O performance.
There is a need to maintain the system performance in the event of a cache memory failure or upon losing connection to the cache memory. | 2023-11-02T01:27:04.277712 | https://example.com/article/3291 |
Steven Rose loves Jesus and pepperoni pizza.
But when the Searcy, Arkansas restaurateur decided to mix church and cheese it gave a group of out-of-town atheists a bad case of indigestion.
The Freedom From Religion Foundation (FFRF) is threatening to sue Steven after he offered a discount to customers who bring in a church bulletin. They said Bailey’s Pizza is violating the Civil Rights Act of 1964.
[pullquote]
“The law requires places of public accommodation to offer their services to customers without regard to race, color, religion or national origin,” FFRF spokesperson Elizabeth Cavell told television station KTHV.
Steven, who opened the pizza parlor in July, told me there’s nothing nefarious about the church bulletin discount.
“It was a straight-up marketing tool to give a discount to people I love and care about – and have them come in and have lunch with me,” he said. “I thought it was a sweet idea. I didn’t say you had to go to church to get it. Go get a bulletin from your neighbor and come in and have a pizza.”
CLICK HERE TO JOIN TODD ON FACEBOOK FOR CONSERVATIVE CONVERSATION!
The trouble started a few weeks ago when someone posted a Facebook photo of the sign promoting the discount.
“It was from a guy whose Facebook name is Bong Hits for Jesus,” Steven told me. “It said, ‘good luck with the discrimination lawsuit.’”
Steven said he didn’t consider the post to be a credible threat -- seeing how the Facebook user’s name is “Bong Hits for Jesus.”
Two weeks later, he received the letter from the Wisconsin-based atheist group. They said that if he did not stop offering a church discount, they would “take appropriate steps.”
“I’m just selling pizzas,” Steven told me. “I love my Lord and you see it expressed all over my building – but I’m just selling pizzas.”
And he’s not kidding. The local television station reports that customers are allowed to write Bible verses on the walls. And in the center is a message from the owners “God is the center of our lives, so our scripture wall is the center of Bailey’s Pizza.”
“To me, if making a pepperoni pizza furthers the Kingdom – well I’m excited about that,” he said.
But just because Steven is a Christian business owner doesn’t mean he has a problem with non-believers.
“They’re coming at us and saying we’re discriminating,” he said. “I don’t hate anybody.”
The FFRF has a history of targeting and bullying Christian business owners. Earlier this month, a North Carolina diner dropped a discount for customers who prayed before their meal.
“We are no longer issuing the 15% praying in public discount,” read a sign posted at the Mary’s Gourmet Diner. “It is illegal and we are being threatened by lawsuit. We apologize to our community for any offense this discount has incurred.”
Why must atheist groups like FFRF be so ill-tempered?
So is it really unconstitutional for restaurants to provide religious-themed discounts? Not at all, says Hiram Sasser, director of litigation for Liberty Institute.
“In fact, if what FFRF is saying were true, restaurants and other businesses would be precluded from giving veterans and military members discounts because that would technically be discriminating based on veteran status,” Sasser tells me. “Is that what FFRF wants? Give me a break!”
The folks at Bailey’s Pizza are still not sure why the Wisconsin atheists are targeting their restaurant.
“They may have something against my pizza,” he said.
Or maybe they’re upset because Bailey’s Pizza won’t deliver to Wisconsin. Who knows?
Whatever the reason, Steven is still contemplating what to do next. He fears a legal battle would be costly – and he’s quick to point out -- he’s no Papa John’s.
“It’s just me and my wife running this place,” he said. “I’ve got window units at my house. We’re not rich. We’re just trying to be our own bosses and be an American success story.”
Steven tells me it’s really sad that the FFRF is spending their money attack his restaurant.
“The 75 cents that somebody saves when they bring in a church bulletin – is that really what they need to be spending their money on?” he asked. “How about spending that money helping the homeless?”
For now – the church discount will remain at Bailey’s Pizza.
“As for me and my house, we’ll serve the Lord,” he told me.
And he will also keep serving their 32 varieties of pies – from Frito chili to baked potato pizza. "We pride ourselves in crazy pies,” he said. “But I’m old school. I eat the pepperoni – that’s all I need.”
You really can’t go wrong with a large pepperoni. Just be sure to hold the anchovies – and the atheists. | 2024-05-03T01:27:04.277712 | https://example.com/article/7442 |
(0, eval)(`console.log("L1");
console.log("L2");
console.log("L3");
`);
| 2024-07-06T01:27:04.277712 | https://example.com/article/6706 |
Q:
Methods for applying is.infinite() to a data frame in R
I'm wondering why I can't apply is.infinite() to a data frame in the same way I can apply is.na to a dataframe in R:
data[is.infinite(data)]<-0
Error in is.infinite(data) :
default method not implemented for type 'list'
data[is.na(data)] <-0
Produces no error, however, the documentation on is.infinite implies the same behavior as is.na?.
Does anyone know how I can replace inf values?
A:
Here is one method, using lapply and ifelse:
# create data.frame
df <- data.frame(a=1:10, b=letters[1:10], c=rnorm(10))
df$a[c(2,6)] <- Inf
df$c[c(3,9)] <- Inf
# take care of those infs:
df[] <- lapply(df, function(i) if(is.numeric(i)) ifelse(is.infinite(i), 0, i) else i)
The problem I think is the x is.infinite(x) and is.na(x). The help file for ?is.infinite says
x R object to be tested: the default methods handle atomic vectors
while for ?is.na, it says
x an R object to be tested: the default method for is.na handles atomic vectors, lists and pairlists: that for anyNA also handles NULL.
So the default method of is.infinite does not handle lists (data.frames) where are is.na does.
| 2024-04-02T01:27:04.277712 | https://example.com/article/2347 |
Sounds good so far.
---------------------- Forwarded by Kay Mann/Corp/Enron on 08/23/2000 01:24
PM ---------------------------
Enron North America Corp.
From: Mitch Robinson 08/23/2000 01:21 PM
To: Kay Mann/Corp/Enron@Enron
cc:
Subject: Re: Edgecombe Energy and Capacity Contract
Kay -
That should work, since our 3:00 is being obviated by our 12:30.
Mitch
---------------------- Forwarded by Mitch Robinson/Corp/Enron on 08/23/2000
01:22 PM ---------------------------
From: Suzanne Adams@ECT on 08/23/2000 01:17 PM
To: Kay Mann/Corp/Enron@ENRON
cc: Christi L Nicolay/HOU/ECT@ECT, Heather Kroll/HOU/ECT@ECT, Herman
Manis/Corp/Enron@ENRON, John Moore/Corp/Enron@Enron, Larry
Soderquist/HOU/ECT@ECT, Matthew F Gockerman/HOU/ECT@ECT, Mitch
Robinson/Corp/Enron@Enron, Ozzie Pagan/HOU/ECT@ECT, Sheila Tweed/HOU/ECT@ECT
Subject: Re: Edgecombe Energy and Capacity Contract
It doesn't look like Friday morning will work. How do you guys look for
Thursday afternoon at 3:00 p.m. We can have the meeting in EB38C1. Please
advise via telephone (x37340) or email asap! Thanks!
Kay Mann@ENRON
08/22/2000 05:06 PM
To: John Moore/Corp/Enron@Enron, Christi L Nicolay/HOU/ECT@ECT, Mitch
Robinson/Corp/Enron@Enron, Larry Soderquist/HOU/ECT@ECT, Herman
Manis/Corp/Enron@ENRON, Matthew F Gockerman/HOU/ECT@ECT
cc: Heather Kroll/HOU/ECT@ECT, Ozzie Pagan/HOU/ECT@ECT, (bcc: Suzanne
Adams/HOU/ECT)
Subject: Edgecombe Energy and Capacity Contract
In an effort to pull the pieces together, a meeting has been scheduled to
discuss the draft energy and capacity contract (formerly the PPA). It is
scheduled for Thursday, August 24th, at 900am. We are still in the process
of locating a conference room, so the location is TBD.
Thanks,
Kay
Here are the most recent comments from VEPCO:
Some of you may have received this already. I have not compared it against
what we last sent them. | 2023-08-03T01:27:04.277712 | https://example.com/article/9409 |
Q:
Scrapy/Python Issue: [count] does not collect entire table
This is a spin off of a previous XPath thread (dude told me it's not XPath related).
So I am trying to scrape this web page: http://www.baseball-reference.com/teams/BOS/2013.shtml for Rank, Position, Name, Age, etc.
Whenever I use:
item['rank'] = stat.select('//table[@id="team_batting"]/tbody/tr/td[1]//text()')[count].extract()
item ['position'] = stat.select('//table[@id="team_batting"]/tbody/tr/td[2]//text()')[count].extract()
It only gives me 5 results:
[{"position": "C", "rank": "1"},
{"position": "1B", "rank": "2"},
{"position": "2B", "rank": "3"},
{"position": "SS", "rank": "4"},
{"position": "3B", "rank": "5"}]
If I remove [count], it gives me all of the ranks and positions, but not in the correct format, and it gives me 4 duplicate lines of it (I condensed this to fit in here,there are 44):
{"position": ["C", "1B", "2B", "SS", "3B", "LF"], "rank": ["1", "2", "3", "4", "5", "6", "7"]}
Here is my parser code is this will help:
def parse(self, response):
hxs = HtmlXPathSelector(response)
stats = hxs.select('//div[@class="table_container"]')
count = 0
items = []
for stat in stats:
item = MlbrefItem()
items .append(item)
count +=1
return items
I am so confused. When I did this tutorial: http://davidwalsh.name/python-scrape [count] pulled all of the results. I also had no issue trying this on a different website. But this is the website I need.
Any help is greatly appreciated. Thanks
EDIT: Here is the actual code (ignore the comments): https://www.dropbox.com/s/rk29kotd09kioeg/mlbref_spyder.py
A:
The code you have posted does not have the definition for the MlbrefItem class. Also, it appears from the posted code that you have incorrect indentation at the following line:
items.append(item)
You are appending an item object outside the for loop. This means you end up appending only the final instance of the type MlbrefItem. Please try the below code snippet for the for-loop and let us know if it works:
for stat in stats:
item = MlbrefItem()
items .append(item)
count +=1
A big edit based on discussion with AngryWhopper
There are multiple aspects to consider here:
There are 5 divs on the page with style table_container The statement stats = hxs.select('//div[@class="table_container"]') selects all these 5 elements
The source code at the reference link provided is shown below. I have added comments to code beginning with my user name where you increment count (count += 1). Since this is within the for loop this happens only 5 times. Hence each of the 5 times, you end up selecting only a single element from the list of rows returned by the XPATH selectors for position and rank. This explains why you get only 5 pairs when you use the count variable within your code.
stats = hxs.select('//div[@class="table_container"]')
count = 0
items = []
for stat in stats:
item = MlbrefItem()
item['rank'] = stat.select('//table[@id="team_batting"]/tbody/tr/td[1]//text()').extract()
item ['position'] = stat.select('//table[@id="team_batting"]/tbody/tr/td[2]//text()').extract()
items .append(item)
count +=1 #PrahaladDeshpande - This count variable is incremented only 5 times since it is within the for loop
return items
Without the count variable, you get all rows - however they are not in the correct format. Well, here you will have to to do some work. I tried the some experiments on the scrapy terminal and the below code snippet should hopefully work for you
stats = hxs.select('//div[@class="table_container"]')
for stat in stats:
rank_list = stat.select('//table[@id="team_batting"]/tbody/tr/td[1]//text()').extract()
position_list = stat.select('//table[@id="team_batting"]/tbody/tr/td[2]//text()').extract()
//TODO : verify that the length of the rank_list and position_list are the same. Else throw an error
for i in range(0, len(rank_list)):
item = MlbrefItem()
item['rank'] = rank_list[i]
item['position'] = position_list[i]
items.append(item)
You can then return the items variable from your method.
Hope this points you towards a solution
| 2023-08-17T01:27:04.277712 | https://example.com/article/2821 |
/**
* OWASP Benchmark Project v1.2
*
* This file is part of the Open Web Application Security Project (OWASP)
* Benchmark Project. For details, please see
* <a href="https://owasp.org/www-project-benchmark/">https://owasp.org/www-project-benchmark/</a>.
*
* The OWASP Benchmark is free software: you can redistribute it and/or modify it under the terms
* of the GNU General Public License as published by the Free Software Foundation, version 2.
*
* The OWASP Benchmark is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without
* even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* @author Nick Sanidas
* @created 2015
*/
package org.owasp.benchmark.testcode;
import java.io.IOException;
import javax.servlet.ServletException;
import javax.servlet.annotation.WebServlet;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
@WebServlet(value="/weakrand-06/BenchmarkTest02703")
public class BenchmarkTest02703 extends HttpServlet {
private static final long serialVersionUID = 1L;
@Override
public void doGet(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
doPost(request, response);
}
@Override
public void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
response.setContentType("text/html;charset=UTF-8");
org.owasp.benchmark.helpers.SeparateClassRequest scr = new org.owasp.benchmark.helpers.SeparateClassRequest( request );
String param = scr.getTheValue("BenchmarkTest02703");
String bar = doSomething(request, param);
float rand = new java.util.Random().nextFloat();
String rememberMeKey = Float.toString(rand).substring(2); // Trim off the 0. at the front.
String user = "Floyd";
String fullClassName = this.getClass().getName();
String testCaseNumber = fullClassName.substring(fullClassName.lastIndexOf('.')+1+"BenchmarkTest".length());
user+= testCaseNumber;
String cookieName = "rememberMe" + testCaseNumber;
boolean foundUser = false;
javax.servlet.http.Cookie[] cookies = request.getCookies();
if (cookies != null) {
for (int i = 0; !foundUser && i < cookies.length; i++) {
javax.servlet.http.Cookie cookie = cookies[i];
if (cookieName.equals(cookie.getName())) {
if (cookie.getValue().equals(request.getSession().getAttribute(cookieName))) {
foundUser = true;
}
}
}
}
if (foundUser) {
response.getWriter().println(
"Welcome back: " + user + "<br/>"
);
} else {
javax.servlet.http.Cookie rememberMe = new javax.servlet.http.Cookie(cookieName, rememberMeKey);
rememberMe.setSecure(true);
rememberMe.setHttpOnly(true);
rememberMe.setDomain(new java.net.URL(request.getRequestURL().toString()).getHost());
rememberMe.setPath(request.getRequestURI()); // i.e., set path to JUST this servlet
// e.g., /benchmark/sql-01/BenchmarkTest01001
request.getSession().setAttribute(cookieName, rememberMeKey);
response.addCookie(rememberMe);
response.getWriter().println(
user + " has been remembered with cookie: " + rememberMe.getName()
+ " whose value is: " + rememberMe.getValue() + "<br/>"
);
}
response.getWriter().println(
"Weak Randomness Test java.util.Random.nextFloat() executed"
);
} // end doPost
private static String doSomething(HttpServletRequest request, String param) throws ServletException, IOException {
StringBuilder sbxyz50196 = new StringBuilder(param);
String bar = sbxyz50196.append("_SafeStuff").toString();
return bar;
}
}
| 2024-01-28T01:27:04.277712 | https://example.com/article/6062 |
Dragon Quest XI S: Echoes Of An Elusive Age Definitive Edition Out On September 27th
Square Enix has announced when Dragon Quest XI S: Echoes of an Elusive Age Definitive Edition will release on Nintendo Switch.
This grand role-playing game is filled with memorable characters, an enchanting story, and classic RPG gameplay that you can now play on the go.
You play as a young man who, about to participate in his village’s coming of age ceremony, learns that he is the reincarnation of a legendary hero from a forgotten age.
He sets out to unravel the mystery of his past, but, after revealing his identity to the King, he is branded as “The Darkspawn” and hunted by a relentless army.
In this enhanced version, you can expect the same sprawling content as in the original release, but the developer has added new character-specific stories, the option to increase the battle speed, fully orchestrated field and battle music, and the chance to switch between HD and retro-inspired 16-bit visuals.
Dragon Quest XI S: Echoes of an Elusive Age Definitive Edition launches for Nintendo Switch worldwide on September 27th.
After starting out with a Yellow Game Boy and a copy of Donkey Kong Land, Alex once hid in his room to play The Legend of Zelda: Ocarina of Time one Christmas. Now he shares his thoughts on Nintendo Insider, keeping track of everything to do with Nintendo. | 2024-07-10T01:27:04.277712 | https://example.com/article/4501 |
The latest issue of Famitsu magazine (via DualShockers) has revealed in its ‘The Truth on 2014’s Rumors’ feature that The Last Guardian will get a release date announcement fairly soon.
According to the publication, Sony reiterated that it is waiting for the best opportunity to re-reveal Team ICO’s long-delayed adventure.
Interestingly, however, it added that if development of the game continues as planned, then Sony will be able to divulge more information, including a release date, fairly soon.
It’s been nearly five years since The Last Guardian was unveiled for the first time at Sony’s 2009 E3 press conference. Originally scheduled to ship in holiday 2011, the game was delayed and has been in limbo ever since, with Sony issued sporadic updates on its progress over the past few years.
At this point, it remans unknown if the project has been quietly moved to PS4. Stay tuned to PSU.com for more details. | 2024-07-01T01:27:04.277712 | https://example.com/article/5356 |
Influence of chemical compositions and molecular weights of humic acids on Cr(VI) photo-reduction.
Humic acids (HA) strongly affect the fate of trace metals in soils and aquatic environments. One of the remarkable properties of HA is its ability to reduce Cr(VI), an extremely toxic anion. However, it is unclear which HA components are involved in Cr(VI) reduction and possess the photo-induced properties. In this study, an ultrafiltration technique was used to fractionate HAs into four fractions of different nominal molecular weights (M(w)): >100, 50-100, 10-50 and <10 kDa. Each HA fraction was characterized by spectroscopic analyses followed by examining Cr(VI) removal on each fraction of HA at pH 1-5. Spectroscopic results indicated that low-M(w) HA was enriched with polar and aromatic domains. These polar, including polar C in aliphatic region, and aromatic groups were the major sites for Cr(VI) reduction because they disappeared rapidly upon interaction with Cr(VI). As a result, low M(w) of HA exhibited greater efficiency of Cr(VI) reduction. Light induced the rapid transfer of electrons between chromate-phenol/carboxyl ester, or the formation of peroxide radicals or H(2)O(2) through the ready decay of peroxy radicals associated with polar substituents, explained the rapid scavenging of Cr(VI) on polar and aromatic groups of HAs under illumination. | 2024-04-01T01:27:04.277712 | https://example.com/article/5752 |
Modifying OS Image
Using the cross compile wiki (Omega1 FWIW) I built a new OS image and have successfully installed that image. However, I tried to modify the image by adding things through menuconfig (i.e. gdb support, etc.) but the compiled image size never changes.
Is there something else I need to do to modify the openwrt-generic-onion-...-factory.bin file?
@Mitch-Christensen Forgive me if I'm pointing out the obvious to you.
A module in menuconfig can be in one of 3 states indicated as follows:
< > - indicates the module is NOT selected
<M> - indicates that the module will be built as a separate package (a .ipk file that can be copied over and installed with opkg)
<*> - indicates that the module will be included in the built image
Repeatedly selecting a module in menuconfig will cycle it through the above states - you need it to be in the <*> state to be included in the image. This is covered in brief in the heading of the menuconfig screen.
Also, of course, you need to re-run make after making and saving any changes in menuconfig
Yeah, I was aware of the tri-state (< >, <M>, <asterisk>) marking in menuconfig. I was careful to select the <*> version. Also, running make following my selections succeeded, and resulted in the set of expected .bin files (in bin/ar71xx/).
I have two clones of the source code. One stock/unmodified and one modified to include gdb (and a few other modules). Comparing the sizes for the onion images from each show the exact same size, leading to my suspicion that I'm not actually changing anything by modifying the build via menuconfig. | 2023-09-10T01:27:04.277712 | https://example.com/article/1561 |
Paul Bernard (director)
Paul Bernard was born in London, England on 20 June 1929, and died there on 25 September 1997.
He is remembered as a television director, though he was also a designer on television, most notably on productions of The Avengers.
His TV direction credits include Coronation Street, The Tomorrow People, Z-Cars and the Doctor Who stories Day of the Daleks (1972), The Time Monster (1972) and Frontier in Space (1973).
He also directed four episodes of Virgin of the Secret Service in which he also worked as a supervising producer with Robert D. Cardona.
References
External links
Category:1929 births
Category:1997 deaths
Category:British television directors
Category:Television people from London | 2024-07-01T01:27:04.277712 | https://example.com/article/8958 |
Sinopsis :
CyberFuck V1. 0 is a new 3dcg SFM hentai work by a popular author from Russia “26RegionSFM”. You can support the author on his official page patron (patreon.com/26regionsfm).
The main character of hentai Samus Aran from the game Metroid goes to his next sexual journey. This time she has depraved sex with a terrible cybernetic monster robot… | 2024-07-17T01:27:04.277712 | https://example.com/article/9651 |
Ovoid Pipes
Ovoid concrete pipes are produced and tested in accordance with the relevant provisions of BS EN1916:2002/BS5911-1:2002 Class 150 including dimensional tolerances, crushing, hydrostatic, water absorption and joint tests.
The ovoid pipe has better velocity characteristics at low flows than equivalent circular pipes, which provides:
Lower operating costs, where some sewers may be laid without the need for pumping.
Better self cleansing and therefore less risk of siltation and blockage.
Are there any precautions to take for concrete pipes laid to steep gradients?
It is recommended that anchor blocks be cast into the ground every 3 or 4 pipe joints behind the socket (also consider installing packers on the face of sockets to prevent concrete to concrete contact).
How frequent should I be testing the pipeline during installation?
It is highly recommended to test the pipeline every 3 or 4 pipes laid as an absolute minimum (do not wait until whole line is installed before carrying out such test).
What are the appropriate ‘roughness values’ for concrete pipes?
Roughness values are:
Foul sewers: 1.5mm.
Surface water sewers: 0.6mm.
What are the recommended minimum depths of cover for concrete pipes?
Minimum depth of cover to top of pipes is 0.6m with bedding class S (360o granular bedding). For cover depths less than 0.6m, then the pipeline should be protected with either a full concrete surround, or a reinforced concrete slab should be placed over it (spanning sufficient distance onto trench walls).
What concrete pipes are generally reinforced?
Marshalls CPM concrete pipes are generally reinforced in sizes DN675 and above (it is possible to reinforce some of the smaller sizes and also to provide un-reinforced pipes in some of the larger sizes – usually made to order).
What is the maximum permissible velocity in concrete pipes?
Limits are not normally placed on maximum velocities but certain criteria such as the potential for erosion should be considered for steep gradients.
What is the maximum working pressure that concrete pipes can withstand?
Concrete pipes are designed to operate at low heads of water. The BS performance requirement is set at a minimum of 0.5 bar.
What is the most likely cause of air test failure for a concrete pipeline on site?
Common causes of air tests failures include:
Displaced seals (usually due to use of wrong pipe lubrication during installation). | 2024-04-23T01:27:04.277712 | https://example.com/article/3485 |
Robert Wiles was employed by the family owned business, Toledo-based National Flight Services, an aircraft maintenance company. Wiles was a business development manager at the company's branch in Lakeland, Florida. Wiles was a pilot, diver, fisherman, and an athlete.
Details:
Robert Arthur Wiles disappeared from Lakeland-Linder Regional Airport in Florida, where he worked. He was last seen at work at approximately 6:30 p.m. on April 1, 2008. A few days later, his parents received a ransom note, but no further demands were made.
On January 31, 2012, Toby Holt was found guilty of manslaughter, extortion, and writing a threatening letter in connection with Wiles' disappearance. However, Wiles has not been found. Therefore, the FBI in Tampa, Florida is seeking information that will lead to the recovery of Wiles. | 2024-05-30T01:27:04.277712 | https://example.com/article/4261 |
/*
* Copyright (C) the libgit2 contributors. All rights reserved.
*
* This file is part of libgit2, distributed under the GNU GPL v2 with
* a Linking Exception. For full terms see the included COPYING file.
*/
#ifndef INCLUDE_hash_hash_collisiondetect_h__
#define INCLUDE_hash_hash_collisiondetect_h__
#include "hash.h"
#include "sha1dc/sha1.h"
struct git_hash_ctx {
SHA1_CTX c;
};
#define git_hash_ctx_init(ctx) git_hash_init(ctx)
#define git_hash_ctx_cleanup(ctx)
GIT_INLINE(int) git_hash_global_init(void)
{
return 0;
}
GIT_INLINE(int) git_hash_init(git_hash_ctx *ctx)
{
assert(ctx);
SHA1DCInit(&ctx->c);
return 0;
}
GIT_INLINE(int) git_hash_update(git_hash_ctx *ctx, const void *data, size_t len)
{
assert(ctx);
SHA1DCUpdate(&ctx->c, data, len);
return 0;
}
GIT_INLINE(int) git_hash_final(git_oid *out, git_hash_ctx *ctx)
{
assert(ctx);
if (SHA1DCFinal(out->id, &ctx->c)) {
git_error_set(GIT_ERROR_SHA1, "SHA1 collision attack detected");
return -1;
}
return 0;
}
#endif
| 2024-01-01T01:27:04.277712 | https://example.com/article/7026 |
Not slots? Electronic Lucky 7 machines may be N.H.’s next gambling game
Not slots? Electronic Lucky 7 machines may be N.H.’s next gambling game
New machines may be featured at Minnesota-based company’s four planned charitable gaming facilities
By Bob Sanders
Published: March 24, 2014
Shutterstock
A player in the gambling industry plans to enter the Granite State market with hopes of installing electronic Lucky 7 devices that look something like slot machines, but proponents say are definitely not, under current New Hampshire law.
The World Poker Store Inc., a small publicly traded company based in Minnesota, announced Monday its intention to set up four charitable gaming facilities in New Hampshire. It has hired Rick Newman, a longtime industry lobbyist and consultant, to help smooth the way with regulators.
World Poker (which changed its corporate name to New Entertainment Technology in 2010) trades for 8 cents a share on the Pink Sheets. The company, with a capitalization of about $3.3 million, operates bar poker leagues in Europe, Canada, Mexico, China and the U.S. and sells various gambling related items online and through various retail locations.
Newman didn’t have too many details to offer on the company’s plans for New Hampshire, saying that he was just contacted about being involved on Friday. But at the very least he envisions four large storefronts, each with about 20 poker and table stations and bingo. There are currently about 10 similar charitable gaming operations in the state.
All told, some $150 million is spent on charitable gaming in New Hampshire each year, about half at casinos and the other half through bingo ($17 million) and Lucky 7 ticket sales (about $58 million).
The new electronic Lucky 7 pull-tab machines offered by World Poker would essentially bring Lucky 7 to the casinos.
Traditionally, Lucky 7 tickets are sold primarily at bingo halls and resemble a lottery scratch ticket. If a buyer, for instance, scratches off three pictures in a row, he or she can cash the ticket for a cash prize usually worth hundreds of dollars.
While often sold in person, some are dispensed by vending machines that are mechanical in nature, often at a VFW or similar hall. But in 2011, state lawmakers halted installation of new machines until the New Hampshire Racing and Charitable Gaming Commission drew up regulations that would cover electronic models that were then being introduced.
The commission did so only after a state Supreme Court ruling ordered it do so at the behest of a manufacturer of one of those machines.
At the earliest, those regulations won’t even be formally introduced until June, and even then wouldn’t be approved until fall, but already the World Poker Store said it plans to introduce the new electronic pull-tab machines at its four proposed casinos.
The electronic pull-tab machine dispenses a Lucky 7 card, but almost renders them as souvenirs. The machine tells you that you’ve won and adds up your winnings, which can then be printed out on a paper voucher, which you can either cash in, or use as credit to gamble more.
All the customer has to do is keep on feeding quarters and push buttons.
But Michael Williams, the procedures administrator at the Racing and Charitable Gaming Commission, and Newman were both quick to differentiate the pull-tab machines from slot machines.
Slot machines are totally random, theoretically allowing unlimited winnings. With the Lucky 7 machines, there is a set amount of winning tickets out of each set of tickets sold. At least 45 percent must be paid in prizes, but in reality the payout is much higher.
According to Newman, for every 3,800 tickets sold at 50 cents apiece, about $120 goes to the manufacturer, close to $400 goes to the charity and the remaining $1,200 is distributed as winnings. Essentially, the electronic dispensing machines are the same as the old manual model – “they just go a little faster,” Newman said.
Still, Williams said, he has to make sure that the machines are not in nature like slot machines.
“The Legislature is worried about crossing the line,” he said.
Indeed, Williams said he wouldn’t be surprised if lawmakers intervened. After all, the House in particular has been cool to allowing large-scale gambling with slot machines, regularly voting down different bills establishing a high-end casino.
Newman is betting that it will continue to do so.
“The idea of a monopoly casino isn’t going to fly with this Legislature,” he said.
If there is any expansion of gaming, he said, it will be in the existing charitable gaming industry.
And even before the commission formally examines regulating pull-tab machines, Newman has put another idea on the table: electronic poker tables.
Such machines allow people to play poker without the cards. The electronic “dealer” gives give out electronic cards to the players, who can then bet as if they were at a real poker game.
The technology can enable the state and charities to better track money at cash games, making sure each gets its share, Newman said.
He plans to bring an example of the poker machines to the next Racing and Charitable Gaming Commission meeting.
This article appears in the April 4 2014 issue of New Hampshire Business Review | 2024-01-12T01:27:04.277712 | https://example.com/article/3500 |
Fulton County Animal Services (FCAS) is overrun with cats. The shelter, which can house 90 cats at a time, is currently housing 175. To save as many of the kitties as possible and encourage people to adopt, FCAS is waiving the adoption fee for all cats and kittens from July 27 to Aug. 10. Potential adopters will still be screened to ensure the animals are being placed in good homes.
According to FCAS Director Lara Hudson, the shelter wants to get as many cats adopted out as possible. “It would break our hearts to have to euthanize all of these beautiful animals, but we have completely run out of space,” says Hudson. “We are asking the community to help us save lives by coming in and adopting cats free of charge.”
For absolutely no cost, adopters will receive a cat that has been spayed or neutered, has had all vaccines and is microchipped. To view cats available for adoption, please visit the shelter at 860 Marietta Blvd. NW or go to their website at fultonanimalservices.com/adopt.
UPDATE: 60 cats were adopted last week after this story appeared online. Now the shelter is turning its attention to adopting out dogs. Read the story at this link. | 2024-02-27T01:27:04.277712 | https://example.com/article/2981 |
Commercial Fishing in Crisis
Outlaws are marauding on the Chesapeake
By Dennis Doyle
The term waterman, unique to Chesapeake Bay, refers to a commercial fisherman harvesting oysters, blue crabs and finfish or otherwise making a living from Bay waters. Maryland has a 300-year tradition of this noble endeavor.
Fish Are Biting ...
The yellow perch run is on in the mid-Bay. Anglers are catching good numbers of these beautiful and tasty devils as the males are running up into the tributaries in advance of the spawn. Although the smaller fish run earliest, you will find some larger neds in the mix. Minnows, grass shrimp and worms fished on shad darts under a bobber remain the traditional method. The minimum size is nine inches and the limit is 10 fish.
Pickerel are also hot, with some good-sized fish being caught. Spinner baits, small crank baits and minnows will entice these toothy rascals into striking. Minimum size is 14 inches, a citation is 24 inches and the limit is five fish.
In freshwater, crappie are becoming active and taking small minnows. There is no minimum size for these fish, but the limit is 15.
In Season
Lore typifies the waterman as among the most romantic, hardy and adventurous figures that have graced the Chesapeake. Wresting a living in the manner of generations of their forefathers, watermen still ply the Bay in their long, white, graceful workboats in all types of weather, gathering crabs, oysters, clams and rockfish, and providing Maryland seafood markets and restaurants with table fare second to none.
But there is another perception of this figure that has been simmering beneath the surface for many years and is now emerging onto the headlines of newspapers and Internet websites, not only in Maryland but across the nation. It a picture of commercial greed, rapacity and contempt for law, regulation and the very natural resources on which this profession’s livelihood depends.
What was once described as the waterman’s fierce and rugged independence has for some individuals apparently corrupted into a vicious outlaw attitude that seems bent on the destruction of an entire profession.
Natural Resources Police, heeding persistent rumors of illegal gill netting for rockfish, have been uncovering the extent of its existence the past few weeks. It appears the practice has been substantial. Defiantly, some of the nets discovered were set in the midst of an intense police presence and after the commercial fishery had already been closed by emergency decree.
Tons upon tons of striped bass, many laden with roe and ripe for spawning, were found in these nets. This scandal comes on the heels of an illegal commercial operation that was federally prosecuted in 2008. That one involved some 300 tons of rockfish over a four-year period of illegal activity.
The commercial associations representing watermen have been working hard to portray these incidents as the acts of a few bad apples, holding that the overwhelming majority of their numbers (approximately 600 active, full- and part-time) are composed of honest, hard-working individuals. But that may not be a completely accurate picture.
A recent DNR analysis of four years of commercial fishing arrest records found that almost half of all Maryland watermen had been cited for illegal operations during that period, with some being arrested multiple times.
Consider also in these alarming statistics the chances of actually getting caught doing something illegal on the Tidewater. The number of Natural Resource Police (160 field officers) is miniscule compared to the area that has to be policed: 500,000 acres of parks and recreational areas; 17,000 miles of shoreline; 6,400 square miles of water.
Arguably, the traditions of Maryland watermen deserve to be preserved and nurtured. Despite the recent scandals, most Marylanders, myself included, continue to hold to that belief. Three hundred years of hard work, perseverance and history should not be discarded because of the acts of outlaws, whatever their number.
The reward fund for the arrest and conviction of those responsible for illegal gill net fishing now exceeds $30,000. Information and tips are slowly coming in to DNR hotlines, but arrests have yet to be made. Gill net prosecutions are extremely difficult unless the individuals are caught in the act.
Natural Resources Police have emphasized that their ongoing investigations are expected to be long-term and intense. New legislation is being proposed significantly increasing the penalties for this kind of illegal activity.
Perversely, while the outrages of the net fishery are capturing headlines, in the background there remains pervasive commercial oyster poaching. Bills are being presented in the Maryland legislature increasing the penalties for those activities as well and providing for the stripping of commercial licenses for watermen caught poaching or violating oyster sanctuaries.
Whatever happens in the near future, one thing is becoming clear. Marylanders may love their watermen — but the current crop working the Chesapeake has a lot of housecleaning to do if they expect to retain the privilege of maintaining this tradition. | 2024-05-07T01:27:04.277712 | https://example.com/article/2687 |
Editor's note, July 1, 2019: For the first time in more than 30 years, Japan has resumed commercial whale hunting. On July 1, a fleet of five ships set sail in the morning and returned in the afternoon with two minke whales. This year’s quota has been set at 227 Bryde’s, minke, and sei whales.
Japan has decided to withdraw from the International Whaling Commission (IWC) and resume whaling in its coastal waters, a government spokesman confirmed. The commission, with 89 member governments, was established in 1946 to conserve whales and manage whaling around the world. It banned commercial whaling in 1986.
Although Japan is the main market for whale meat, consumption there is limited—about an ounce per person per year, or about 4,000 to 5,000 tons, according to a report by the Animal Welfare Institute, a nonprofit that seeks to alleviate animal suffering, and the Environmental Investigation Agency, which tracks international wildlife crime.
According to Astrid Fuchs, whaling program manager for the U.K.-based nonprofit Whale and Dolphin Conservation, who spoke to National Geographic before the news was confirmed, Japan’s withdrawal would primarily be a political move, sending the message that the country can use the oceans as they please. (Learn more about how the international community recently moved to stop Japan from hunting sei whales.)
“For decades Japan has aggressively pursued a well-funded whaling campaign to upend the global ban on commercial whaling," says Kitty Block, president of Humane Society International. "It has consistently failed but instead of accepting that most nations no longer want to hunt whales, it has now simply walked out.”
Because Japan is a leading voice among pro-whaling countries, Fuchs says, its withdrawal may inspire other countries, such as South Korea and Russia, to follow suit. (Read how whales are deliberately hunted 'by accident' in some countries.)
Under the ban, whaling for scientific purposes—biologists studying reproductive status, stomach contents, and effects of environmental change, for example—is exempt. Japan has long been accused of using that exemption as a cover, with whalers supplying some body parts to researchers and selling the rest of the meat for human consumption.
“They’ve been thumbing their nose at the moratorium and the will of international citizens for a long time,” Block says.
In a vote this summer during the commission’s annual meeting, Japan’s proposal to allow commercial whaling was rejected.
“They put a lot of money into it,” Fuchs says. “Part of the government really expected that they might be able to swing the mood with some countries at the meeting.”
After the meeting, officials, including Masaaki Taniai, vice minister for fisheries, and Joji Morishita, Japan’s IWC commissioner, said they’d consider withdrawing from the commission—a threat Japan has made in the past.
Fuchs predicted that this time was different. “It very much [sounded] like they’re actually doing it,” she said earlier.
Block agreed. “When they don’t get their way at these international meetings, they say they’re going to leave, and they’ve been making that idle threat for many, many years now. This time [seemed] to be a little more vociferous.”
By withdrawing from the commission, Japan can no longer take advantage of the IWC’s exemption for scientific whaling in international waters and would therefore have to halt whaling on the high seas. That’s because the United Nations Convention on the Law of the Seas requires its signatories, which include Japan, to work through “the appropriate international organizations” for marine mammal conservation. That’s widely interpreted by legal scholars to mean the IWC—even if a country is not party to the IWC. The one benefit Japan gets by withdrawing is it could likely resume whaling in its own backyard without oversight.
This would be beneficial for whales in Antarctica—where Japan killed upwards of 300 in 2016, including more than 200 pregnant females—but bad for species in Japanese waters.
There’s particular concern about the status of minke whales called the J-stock, found off the coast of Japan and frequently hunted. Minke whales are targeted because they’re relatively abundant, not having been decimated during commercial whaling’s peak years during the 1970s.
If Japan were to be more open about its intent to continue commercial whaling, it might simplify things in some ways, says Natalie Barefoot, a University of Miami law professor and expert in whale law.
“We’re having this dialogue essentially pretending that they’re performing scientific research,” she says. “If they change their position and say, ‘Hey, we are, this is what we’re doing. We are commercial whaling’—in some ways, it’s a bit of a relief, because we can have an actual honest conversation on their activities in ocean waters.”
By Japan withdrawing from the commission, it will face no formal consequences, but other countries could take matters into their own hands and impose sanctions—for example, by denying Japan access to fishing in their waters. It also means that Japan would no longer be a part of the international dialogue on whaling.
“As we become an increasingly global community, it’s better to have everyone at the table, even if you disagree, and just to continue to work,” Barefoot says. “These are global issues we’re addressing, and we need to address them together.”
According to commission spokesperson Kate Wilson, in order for Japan to bow out by the end of June 2019, it would need to send formal notification of withdrawal to the U.S. State Department, which would inform the commission secretariat, by January 1.
A representative from the U.S. embassy in Japan was not immediately available for comment.
The timing of this latest intimation by Japan of its withdrawal from the commission may not be coincidental, Fuchs says. With the holidays season, they may expect less opposition.
This story was originally published on Dec. 21, 2018, under the headline, "Japan may resume commercial whaling. Get the facts." The story was updated Dec. 26 when the Japanese government confirmed the country is leaving the IWC and again on July 1, 2019, after whaling officially began.
| 2024-05-13T01:27:04.277712 | https://example.com/article/5372 |
As easy and enjoyable as the season, this delightful dress is styled just for her with ruffles at the front and back neckline, crochet trim at the cap raglan sleeves and hem, and a twirl-tastic tulip hem that moves as she grooves. Crafted in airy linen and cotton. * Relaxed fit * Ruffles at front and back neckline * Cap raglan sleeves * Tulip hem * Knee length * Linen/cotton * Imported | 2024-05-10T01:27:04.277712 | https://example.com/article/5061 |
Arun Jaitley lashes out at media for not acting in a responsible manner
Information and Broadcasting Minister Arun Jaitley held a meeting for the media where he asked them to act responsibly on matters involving national security and sensitive issues.
While holding the first Justice J. S. Verma Memorial lecture Jaitley commented on the ‘Freedom and Responsibility of Media’ in New Delhi. He said that the media’s occupation was to ensure quality and credibility of the matter presented to the audience.
He advised the media to circumvent conducting trials in parallel to reporting matters that were under judicial consideration and therefore prohibited from public discussion elsewhere.
Jaitley said there was an urgent need to discuss roles played by media in relation to freedom and responsibility.
Indicating that government was not predisposed to create obstruction either in the content or the matters of media body. And that the government was not inclined to put a cap on advertising for TV or print media.
“It will be music to the years of media persons that my ministry, a couple of years ago came out with a statutory law that no channel will telecast advertisements beyond a certain set of minutes.” He mused on how such a cap fit with Article 19 1 A of the constitution that guaranteed the freedom of the media.
The legislations are particularly questioned and the matter, currently, holds a pending position in the court. Jaitley has also battled for incrementing FDI in media from the present restriction of 26% commenting that while global newspapers are already available online in India, there was no justification opposing the move.
During elections, it is not a tongue held secret that a high percentage of all the candidates’ election budget is consumed on managing news, he said. The Election Commission attempts to constrict it down but because of the critical behavior of the transaction, it is a difficult task to detect.
This was probably the first time that instead of leading to huge protests for an incident, the government apologized, which sent a message that it was acting responsibly. | 2024-03-07T01:27:04.277712 | https://example.com/article/7747 |
BEIRUT (Reuters) - Incidents of political violence including an assault on one candidate and an attack on the office of another are casting a shadow over Lebanon’s first general election in nine years.
Posters of Lebanese parliament candidates Rania Shmaitilly and Nabil Bader are seen on a building in Beirut, Lebanon April 23, 2018. REUTERS/ Mohamed Azakir
The May 6 vote will take place using a complicated new electoral law. It is not expected to cause major changes to the government or its policies. Analysts expect Prime Minister Saad al-Hariri will head the next cabinet.
But the law has made the outcome less predictable in some places. This has sharpened local rivalries and is encouraging parties to campaign extra hard.
“The threats to candidates, men and women, are escalating. We expect more of them as we approach the election, and we expect an increase in violence,” said Omar Kabboul, the executive director of the Lebanese Association for Democratic Elections (LADE), a group of independent electoral observers.
“The outcome of the elections is uncertain. The more uncertain the outcome, the more fear there is within the parties and the bigger the agitation in speeches.”
Some 28 years after Lebanon’s civil war, nobody expects any major strife, but the country has been plagued by repeated bouts of political instability that have weighed on its economy.
The Lebanese system divides up power according to strict sectarian quotas, with parliament’s 128 seats split evenly between Christian and Muslim groups. The flare-ups reported so far have pitted rivals from the same sect against each other.
The army intervened on Sunday night to break up a confrontation between supporters of rival Druze parties south of Beirut in which guns were fired in the air, a security source said. The standoff spiraled from a row over electoral posters.
Also on Sunday, an independent Shi’ite candidate said Hezbollah supporters beat him up in their southern Lebanon stronghold, where he is standing against the two dominant Shi’ite parties Hezbollah and Amal.
Slideshow ( 3 images )
Ali al-Amin said a group of more than 30 Hezbollah supporters accosted him while he was hanging an election poster in his home village of Shaqra in Bint Jbeil district.
“I accuse... a political side, which is Hezbollah, of arranging this incident and I hold it mainly responsible,” he said, adding that the group “could not tolerate the presence of one photo or poster of a candidate who is against them”.
Ali Saleh, the pro-Hezbollah head of the local council, said it was an “individual incident” that was now in the hands of the judiciary and security forces. “Ali al-Amine is a candidate ... and every candidate has the right to practice his media campaign and his electoral campaign,” he said.
CONFRONTATION
The heavily armed, Iran-backed Hezbollah, which gained legitimacy among many Shi’ites by fighting Israeli forces that occupied the south until 2000, has taken part in Lebanese elections since the early 1990s, enjoying an effective duopoly of the Shi’ite vote with Amal.
The parliamentary election has been postponed three times, chiefly because Lebanon’s fractious politicians could not agree on the new election law that was demanded by Christian parties.
It has redrawn constituency boundaries and introduced a new proportional representation system that experts say has been engineered to suit the dominant political players but has still left a good deal of uncertainty at the local level.
Last week, supporters of Hariri’s Future Movement attacked the offices of an electoral rival in the capital, breaking his windows, the rival candidate said.
First, his election posters were torn down, then his supporters were attacked after a rally, and then his campaign office was assaulted, prompting some volunteers to quit, said Nabil Badr.
Interior Minister Nohad Machnouk, a Future Movement member, acknowledged on television that some of the party’s supporters had carried out the attack. He said they had been provoked by Badr’s bodyguards, who had themselves assaulted a local figure.
“All the parties are tense because they don’t know the outcome of this electoral law,” said Badr. “The electoral battle will be strong in Beirut.” | 2024-01-03T01:27:04.277712 | https://example.com/article/9396 |
The primary goal of this work is to contribute to the investigation and solution of basic biological and medical problems. This is to be done by the development of chemical methods and reagents for the study of the structures of biomolecules, by the study, development, and application of organic and photo chemical reactions, and by the synthesis of selected chemical compounds. Areas of special interest are photocyclizations, photorearrangements, selenium chemistry, medicinal chemistry, and cancer chemotherapy. | 2024-06-13T01:27:04.277712 | https://example.com/article/1061 |
Longtime Facebook contributor Glenn Mumberson has been beavering deep in his Mancave creating some fairly spectacular works. He has been good enough to allow us to have some galleries of his works to share with you.So, without further ado, lets meet The Gruffet
It started innocently enough. Gruffy told Ross over Facebook "We should try and do something with puppets"The response: "Yeah we should"It became an idea that Ross would have to explain something he enjoys to a Puppet version of Gruffy, and see how long he could keep a straight face, as a video.Then, The Lenton Experiment (created by Robert Coy) began, as it does each year to raise money for charity.Then Matt Clarke happened with a picture he created for the Lenton Experiment.
And then, out of nowhere.....came Glenn
But the story does not stop here. Oh no.....
to be continued
Glenn has a PHD at shouting at Street Fighter characters and lives a life surrounded by trees and animals. His interests involves Warner Bros cartoons and making weapons of slight destruction | 2024-03-28T01:27:04.277712 | https://example.com/article/2412 |
Villains beware, Batgirl and Black Panther have joined forces – to headline Heritage’s current Sunday Internet Comics Auction. Batgirl’s origin and first appearance as well as Black Panther production cels and his comic debut will be sold this weekend on Sunday, March 18, 2018.
With a potential Batgirl movie in the works, now is a great time for savvy collectors to purchase a copy of Detective Comics #359 CGC 5.5 with the first comic appearance and origin of Batgirl. This issue depicts cover and art by Carmine Infantino and Murphy Anderson, and also features the first appearance of Killer Moth.
Batgirl was created by Infantino, William Dozier, and Julius Schwartz per a request from producers of the Batman TV show that the Caped Crusader get a heroine. Batgirl, a/k/a Barbara Gordon, had a popular run during the Silver Age, thanks in part to the TV show.
Black Panther has been extremely successful in the theaters and fans, old and new alike, are clamoring for the chance to collect comics and artwork for the character. Heritage is selling some rare Black Panther production cels and the character’s first comic book appearance in Fantastic Four #52 VG+.
The five Black Panther cels come with painted backgrounds and animation drawings, from the Fantastic Four animated show season two episode “Prey of the Black Panther.” The comic depicts art and cover by Jack Kirby, who worked with Stan Lee to create this popular character. In this issue, Black Panther and the Fantastic Four compete in tests created to decide if the Fantastic Four can help T’Challa on a mission.
These Batgirl and Black Panther items will be sold in the 902-lot comics, original art, and memorabilia auction at Heritage. Bidding opens at 6 PM CT on March 18. | 2024-03-12T01:27:04.277712 | https://example.com/article/9176 |
Huffman Prize winner approaches bioengineering with an artist's eye
The web site of Payam Yousefi, this year's winner of the Baskin School of Engineering's Huffman Prize, has links to two different resumés, one technical and the other design-oriented. A closer look reveals a technical resumé that is unusually eye-catching and well designed, while the design one is unusually detailed technically. This dual resumé shows Yousefi's extraordinary talents in multiple fields: science, technology, and art.
"I do both technical and creative work together—I consider them both the same thing," Yousefi said. "An engineer also has to be a designer because engineering requires creativity. Whether you're designing something or engineering something, you're coming up with something new."
The Huffman Prize is awarded annually to a Baskin School of Engineering graduating senior whose academic career at UCSC exhibits extraordinary creativity, depth of inquiry, and overall excellence. The prize honors the memory and the legacy of its namesake, David A. Huffman, professor emeritus of computer science.
In addition to winning the Huffman Prize, Yousefi, who graduates in June with a B.S. in bioengineering and a minor in bioinformatics, will also receive the Baskin School of Engineering Dean's Award, and he was one of 15 students chosen to receive a Chancellor's Award.
Laboratory research
Yousefi was recommended for the Huffman Prize by assistant professor of biomolecular engineering Rebecca DuBois, in whose lab Yousefi has been working for the past year. DuBois is a structural biologist studying viral proteins. Her work is used to design novel vaccines and to develop nanoscale drug delivery vehicles and antiviral therapeutics.
"Payam impressed me from the moment he first contacted me," said DuBois. When she gave a lecture as part of the hiring process for her faculty position, Yousefi was there, showing an interest and asking intelligent questions. Later, when DuBois was hired, Yousefi sent her an e-mail praising her research and asking if she might have space for him in her lab.
"I think that taking that initiative is an important part of being a leader—I was happy to see that Payam would show that initiative as an undergraduate," said DuBois. "Payam is also an excellent critical thinker who understands the big picture and also understands the small steps that it takes to get there. He has had a challenging project, and he's been persistent and has used his own ideas to push it forward. He is a very independent worker."
DuBois said that from what she has read, David Huffman, the professor whom the award is named after, was a creative researcher, and that Yousefi displays a similarly creative approach. "For example, when we hit a major roadblock in our research, Yousefi went home and researched the problem online, did some bioinformatics analyses, and came up with a solution that I wouldn't have thought of myself," said DuBois.
In DuBois' lab, Yousefi researches the human astrovirus, a small virus that causes gastroenteritis. While it generally does not affect healthy adults, it can sometimes have a devastating effect on young children, the elderly, and immunocompromised people.
"My project is to understand the virus better on a molecular level," said Yousefi. Specifically, Yousefi has been studying the outer coat of the virus called the capsid protein, which has two major parts: the core that surrounds the viral genome and the star-shaped spikes that give the astrovirus its name. The ultimate goal is to understand the molecular process of how 180 capsid proteins assemble to form one virus particle. Yousefi uses x-ray crystallography, in which an x-ray beam is focused on the protein's crystals and the resulting diffraction data allow scientists to create a three-dimensional map of the protein's molecular structure.
Ironically, although the virus is potentially destructive, DuBois' lab is studying it for its therapeutic potential. Astrovirus has the unusual ability to survive the entire intestinal tract, and DuBois wants to understand how it does that.
"The protein I'm studying could have new properties that we don't know about. It could also be a nanoparticle that we can use for targeted therapy," said Yousefi.
Working independently
As the year progressed, Yousefi began to work in the lab more independently, relying on his experience and the notes he made in his lab books. His lab work will form the basis for his senior thesis, "Crystal Structure of the Human Astrovirus Capsid Core," which he is finishing up now.
"I couldn't have asked for a better lab experience," Yousefi said, adding that he often spends about 20 hours a week in DuBois' lab, which has become a second home to him on campus and where he goes between classes. "I wanted to do hands-on research and participate in making discoveries, and Dr. DuBois allowed me to do that. It's been incredible."
He particularly appreciates his lab co-workers, whom he describes as being very helpful, positive, and fun to work with.
In addition to his coursework, his work in DuBois' lab, and his senior thesis, Yousefi worked two on-campus jobs, doing web work and design for Undergraduate Admissions and for the Dean of Students, and he spent a quarter in Japan on the UC Education Abroad Program, studying Japanese language and culture at International Christian University.
Yousefi's design work can be seen in a series of full-page advertisements that the Dean of Students placed in City on a Hill Press, and in Admissions' eSlug electronic newsletter for guidance counselors. He has also been generous with his time in communicating with prospective UCSC students through Admissions social media and through the Admissions Student Profile web page.
"I like looking back and knowing that I've contributed something, whether it is designing an advertisement or conducting lab research," said Yousefi of his busy schedule. "I like the feeling of giving back, creating something. I have all these responsibilities, but I'm happy to have them."
"Payam just seems to be one of those people who are good at everything," said DuBois. "He's savvy with computer software, programming, and design, he's an excellent communicator, and he also has what we call 'good lab hands' and excels at lab research."
After graduation, Yousefi plans to work in a biotechnology company. Eventually, he would like to apply to graduate school and pursue a Ph.D., continuing similar research to what he has done at UCSC, in addition to researching other topics. Yousefi said he is grateful for the education he has received at UC Santa Cruz and the people he has met here, including fellow students in Porter College.
"UCSC has allowed me to not be afraid to express the different sides of myself, and a lot of that has to do with my choice of college," Yousefi said. "Being in Porter was exciting because I met so many different people. Psychology, art, history of art and visual culture—I've learned so much from my friends. I never go around saying I'm just a bioengineer. I want to be more than that." | 2024-07-15T01:27:04.277712 | https://example.com/article/6294 |
Four Restaurants That Opened In NYC This Week
When one restaurant's doors close, another's open in fast-paced New York City, and every Friday, we'll fill you in on what opened up around town. This week: an Italian restaurant with a burrata bar, a nautical-themed bar in Greenwich Village, and another steakhouse in Midtown.
Restaurateur Shelly Fireman brings us Florian, an Italian restaurant serving pastas, pizzas, soups, and selections from a 12-seat burrata bar. The cocktail menu has been crafted by Florence-born bar manager Francesco Desideri and includes classics such as limoncello and negronis.
Hollywood hangout Mastro's Steakhouse has opened a location in New York City. The restaurant offers a menu of steaks, seafood, and sushi, sides like lobster mashed potatoes, and desserts like warm butter cake.
Located on Edgecombe Avenue in Harlem, The Edge is a café serving coffee, pastries and small bites. The brick-lines space has a cozy, quintessential coffee shop vibe.
The Folly, 92 West Houston Street
Owned by the team behind The Brooklyneer, The Folly is a cocktail bar with nautical touches. The restaurant's dinner menu is seafood-heavy, with dishes such as lobster mac and cheese, kombucha oyster shooters, and salt cod tater tots. | 2023-11-26T01:27:04.277712 | https://example.com/article/4946 |
Hill could see a path to victory if the numerous Baltimore-centric candidates in the race divide the city’s share of the votes, Coale said, but she would need to run the table in Howard. That will be difficult, given that other candidates have campaigned heavily there, he said. Democrat Kweisi Mfume represented the 7th District when he served in Congress from 1987 to 1996, and Maya Rockeymoore Cummings, Cummings’ widow, spent time in Howard when she was state party chairwoman, Coale said. | 2023-11-13T01:27:04.277712 | https://example.com/article/5831 |
[Analysis of infant mortality from congenital malformations in Argentina during the 2002-2006 period].
To analyze the trend and spatial distribution of infant mortality from congenital malformations in Argentina between 2002 and 2006. Data were provided by the Ministry of Public Health. Congenital malformations were classified according to the International Classification of Diseases, 10th revision. Early neonatal, late neonatal and postneonatal infant mortality components, congenital malformations subgroups and specific malformations were estimated by departments, provinces, and regions to determine: a) Congenital malformations- related death rate; b) infant mortality rate due to congenital malformations. Both indicators were correlated with the respective departmental latitude/longitude. Infant mortality rate due to congenital malformations was 3.33 per thousand and congenital malformations- related death rate 22.7%. Both indicators showed great spatial variability and did not correlate to latitude/longitude. The lowest infant mortality rate due to congenital malformations and congenital malformations-related death rates were found in Patagonia and the Argentine northeast, respectively. The early neonatal period showed the highest infant mortality rate due to congenital malformations and congenital malformations-related death rates was over 20% in the 3 periods. The Argentine northwest and Argentine northeast showed the lower congenital malformations rates-related death rates in the three components than Centro, Cuyo and Patagonia. The pattern of infant mortality from congenital malformations in Argentina is similar to that of developed countries, characterized by a decrease of infant mortality rate due to congenital malformations and increase of congenital malformations-related death rates, with a prevailing contribution of heart and nervous system malformations. | 2023-09-29T01:27:04.277712 | https://example.com/article/3109 |
REA Reaction
The interactive museum Spyscape highlighted the power and danger of 21st century persistent surveillance and celebrated the history of clandestine operatives.
Through interactive challenges, Spyscape engaged the skills (or abstractions of those skills) necessary to function within an espionage organization. It then evaluated what type of spy each visitor would be.
The exhibits within Spyscape were generally well written and thoughtful without being worshipful of the double-edged sword that is the conglomerated international surveillance apparatus. That being said, the Hacking exhibit was a bit thin and the Deception exhibit presented glaring factual misrepresentations. A few missteps notwithstanding, Spyscape was impressively executed.
Spyscape was an artfully created, playfully intense interactive museum. It would be great for families, anyone interested in clandestine operations, and those who enjoy interactive puzzle challenges.
Why play?
Story
Spyscape was an interactive museum where visitors explored the various aspects of surveillance and espionage in the 21st century through education and mini-games.
The museum monitored us over the course of the experience and evaluated our skills and personalities.
Setting
Sypscape spread out over six primary exhibits:
Encryption
Deception
Surveillance
Hacking
Special Ops
Intelligence
Each of these exhibits included historical items or movie props and beautifully written, concise explanations of the history of the subject matter.
Each exhibit (except for Hacking) concluded with an activity that tested our competency with the material in the exhibit. This wasn’t a pop quiz; it was an engaging activity such as encrypting/ decrypting a message or lying/ detecting lies.
We rounded out a personality profile by solving three collections of puzzles on touch screens and answering an assortment of personality questions that asked us to make value judgments about ourselves.
The museum tracked our progress throughout the experience via an RFID wristband. At the conclusion the experience, we could view our scores on screens and find out our ideal job within a spy organization. I got “spymaster” and my friend received “special ops officer.” (In her case this seemed wildly off-base.)
Gameplay
The gameplay within Spyscape varied heavily from challenge to challenge.
First we solved traditional puzzles on touch screens. Next we exercised the basics of substitution ciphers. Following this, we had to lie to a computer. Next we looked for suspicious behavior on a massive surveillance system. Finally we completed tasks while navigating the obligatory laser maze. The museum followed this order, but visitors could complete these challenges in any order.
The gameplay varied heavily; it included something for everyone. While none of the challenges were obligatory, if you skip them, your evaluation will be incomplete.
Analysis
➕ Spyscape was well equipped and fantastically laid out. It provided lockers, was designed for accessibility, and allowed us to explore the space in our own way and at our own pace.
➕ The opening sequence of Spyscape brilliantly established the thesis of the entire museum and painted a stark, realistic, and slightly frightening picture of the breadth of modern surveillance.
➕ Spyscape had an Enigma Machine!
➖ One odd exhibit lacked clear value or meaning. The rather thin Hacking exhibit that devoted a strange amount of its limited space to random stuff like prison art from convicted hacker Jake Davis. ¯\_(ツ)_/¯
➕ The RFID bracelet tracking our progress through the museum worked well as an interaction… and was also an elegant metaphor for how our phones track us throughout our real lives.
➕While I found some challenges to be easier than others, I generally had fun solving them. I enjoyed the Surveillance challenge most.
➖ The Encryption challenge will bore anyone with even a basic grasp of substitution ciphers.
❓ While some of Spyscape’s challenges were legitimately difficult (a handful of the puzzles they threw at us stumped me), it wasn’t as engaging as the continual gameplay of an escape room. We divided our time between the challenges and more traditional exhibits. Spyscape was still a museum, not an immersive adventure.
➖ It was strangely unclear how many rounds of puzzle challenges and personality questions we’d encounter. We only realized this when we went to get our scores at the end of the experience and realized that we hadn’t finished everything… so we went back to finish.
➖ When we wanted to complete the touchscreen challenges rapidly, we encountered a strangely long cool-down period before the touchscreens would allow us to start the next challenge. This was by far the biggest annoyance that we encountered in Spyscape.
➕ I loved the look and layout of the museum. Everything about the space – the logo, exhibits, and challenges – was deliberately designed. You can tell that they know how great their logo is by how creatively they use it throughout the experience and in their merchandise (which was actually pretty nice).
➕ The worlds of espionage, surveillance, code making, and code breaking exist entirely within shades of gray. I had worried going into Spyscape that the entire museum would be groveling at the feet of the alphabet soup of spy organizations. I found their exhibits to be a fair bit more honest than I had been expecting. Spyscape largely embraced the moral murkiness of the subject matter.
➖ Oh boy, did Spyscape overstate the power of the lie detector. The overstatements of this pseudoscience would have been funny if we weren’t using these devices entirely too much throughout our government and justice system where their inaccurate nonsense actually ruins lives.
➖ I really respected Spyscape’s Surveillance exhibit, but was saddened to see them framing up the false “privacy vs security” debate. Like so many politicians from across the political spectrum, they neglected to mention that data isn’t private without security. If we whittle away our privacy in the name of security we’re sacrificing both. If it isn’t private, it isn’t secure.
Tips For Visiting
Spyscape has thoroughly explained parking, transportation, and accessibility on their website.
All activities are isolated player moments. You don’t complete these challenges as a team.
Post navigation
2 thoughts on “Spyscape NYC [Review]”
Sounds like an interesting afternoon. Gotta agree with the Lie Detector comments having personally been affected by the inaccuracy of the test and the misuse of the “results” by decision makers. Also, “data isn’t private without security” is sooooo true. One only has to read headlines to know that data isn’t private without security, and there is no security. | 2023-10-28T01:27:04.277712 | https://example.com/article/6099 |
Wednesday, April 27, 2011
A new proposal has been reached between Senate Democratic and Republican leadership for the Senate redistricting plan.As of this posting, the details have not been released, and the proposal still needs approval from both caucuses before it is likely to pass out of the General Assembly and be signed into law.At least one left leaning blog is lamenting that Senate majority leader Dick Saslaw caved in the negotiations.
“What I'm hearing from multiple sources is that the legal advisers to Dick Saslaw apparently changed their mind, suddenly deciding that the courts were more of a problem than they had thought. So, they advised Saslaw to avoid that route at (almost) all costs.”
IF this is accurate, the legal advice is sound.As I indicated here, what happens if no plan is reached is up in the air, but the Howell plan for redistricting is a highly unlikely outcome because it raises serious Constitutional questions on its own.
Instead, if no agreement is reached the likely outcome is a very safe plan with an emphasis on compact districts, with little consideration for the protection of incumbents.Compact districts will generally favor Republicans, as Democrats will generally have districts of overwhelming influence in urban areas, thereby diluting Democratic strength in non-urban areas.For this reason a compromise on redistricting is the smart outcome for Senate Democrats.
Who made the mistake?
Dick Saslaw made the strategic mistake when he said there was no way he would change the plan, and that he would send the same plan back to McDonnell even if it is vetoed again.In the grand scheme of things that is a much smaller political mistake than failing to compromise on redistricting.
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On this weeks episode of the GeekCast Syndicate, Curtis and Jon discuss Marvel Studios President Kevin Feige's comments about the Marvel universe being all connected. Some major movie news from Kingsman 3 to Avatar 2 casting their lead. Curtis and Jon break down the possibility of Sony or Universal buying or merging with Funimation. Curtis announces the news of the Hellboy reboot, while the hosts comment on which franchises they would reboot. Jon runs down the worst selling consoles after the sales numbers come out on the Nintendo Switch. | 2023-09-07T01:27:04.277712 | https://example.com/article/7531 |
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bibliography:
- 'KdVonRplus.bib'
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**THE GENERALIZED KORTEWEG-DE VRIES\
EQUATION ON THE HALF LINE**
J. E. Colliander [^1] and C. E. Kenig [^2]
. The initial-boundary value problem for the generalized Korteweg-de Vries equation on a half-line is studied by adapting the initial value techniques developed by Kenig, Ponce and Vega and Bourgain to the initial-boundary setting. The approach consists of replacing the initial-boundary problem by a forced initial value problem. The forcing is selected to satisfy the boundary condition by inverting a Riemann-Liouville fractional integral.
Introduction
============
\[1\]
This paper introduces a method to solve initial-boundary value problems for nonlinear dispersive partial differential equations by recasting these problems as initial value problems with an appropriate forcing term. This reformulation transports the robust theory of initial value problems to the initial-boundary value setting. The procedure is applied here to solve the initial-boundary value problem for the generalized Korteweg-de Vries equation on the half-line. We expect that generalizations of the ideas described below will be useful in solving problems in higher dimensions, such as the nonlinear Schrödinger equation posed on a spatial domain under Dirichlet boundary conditions. The methods introduced here may be viewed as a dispersive generalization of the classical Calderón Projector method [@Calderon] used in elliptic and parabolic problems.
Consider the [*initial-boundary value problem for the generalized Korteweg-de Vries equation on the right half-line,*]{} $$\label{1.1}
\begin{cases}
\partial_tu + \partial_x^3u + \frac{1}{k + 1}\partial_xu^{k + 1} = 0, & x > 0, t \in [0, T]\text{ and }k \in {\mathbb N} \\
u(x, 0) = \phi(x), & x \geq 0 \\
u(0, t) = f(t), & t \in [0, T]
\end{cases}$$ with $\phi$ and $f$ satisfying certain regularity hypotheses, and $T > 0$. This problem will be solved using a [*forced initial value problem for the generalized Korteweg-de Vries equation on the line,*]{} $$\label{1.2}
\begin{cases}
\partial_t\tilde{u} + \partial_x^3\tilde{u} + \frac{1}{k + 1}\partial_x\tilde{u}^{k + 1} = \delta_0(x)g(t), & x \in {\mathbb R}\text{ and }t \in [0, T] \\
\tilde{u}(x, 0) = \tilde{\phi}(x), & x \in {\mathbb R},
\end{cases}$$ where $\delta_0$ denotes the Dirac mass at $x = 0$ and $\tilde{\phi}$ is a nice extension of $\phi$. The [*boundary forcing function*]{} $g$ is selected to ensure that $$\label{1.3}
\tilde{u}(0, t) = \tilde{f}(t), \quad t \in [0, T],$$ where $\tilde{f}$ is a nice extension of $f$. We will sometimes refer to [(\[1.3\])]{} as a boundary condition, even though $\{x = 0\}$ is not a boundary for the $\tilde{u}$ problem [(\[1.2\])]{}. Upon constructing the solution $\tilde{u}$ of [(\[1.2\])]{}, we obtain the solution $u$ of [(\[1.1\])]{} by restriction, as $$\label{1.4}
u = \tilde{u}\big|_{\{x \geq 0\} \times \{t : t \in [0, T]\}}.$$ The solution of [(\[1.2\])]{} satisfying [(\[1.3\])]{} is constructed using the initial value machinery in [@5], [@10] and [@11] and the inversion of a Riemann-Liouville fractional integration operator. First, an explicit solution of the linearization of [(\[1.1\])]{}, using the linearization of [(\[1.2\])]{} satisfying [(\[1.3\])]{}, is constructed. This reveals the natural regularity relationships among $\phi$, $f$ and $g$. We verify that the space-time norms (used in [@5] and [@10]) of the linear solution $\tilde{u}$ are bounded by related norms of $\tilde{\phi}$ and $\tilde{f}$. Next, we consider [(\[1.2\])]{} with the nonlinear term replaced by a given function $h$ of space-time. The solution of the resulting inhomogeneous analogue of [(\[1.2\])]{} satisfying [(\[1.3\])]{} is explicitly constructed in terms of $\tilde{\phi}$, $\tilde{f}$ and $h$, and the natural inhomogeneous estimates from [@5] and [@10] are established. Finally, the nonlinear term is treated as an inhomogeneity and a multilinear estimate exploiting time localization and/or scaling proves the required contraction estimate.
The linearization of [(\[1.2\])]{}, obtained by removing the nonlinear term $\frac{1}{k + 1}\partial_xu^{k + 1}$, is solved using Duhamel’s formula, $$\label{1.5}
u(x, t) = S(t)\tilde{\phi}(x) + \int_0^t S(t - t')\delta_0(x)g(t')dt',$$ where $S$ is the linear solution operator given by $$\label{1.6}
S(t)\phi(x) = \int e^{i(x\xi + t\xi^3)}\Hat{\Tilde{\phi}}(\xi)d\xi = \int t^{-1/3}A\biggl(\frac{x - x'}{t^{1/3}}\biggr)\tilde{\phi}(x')dx',$$ where $A$ is the Airy function. We describe how to select the boundary forcing $g$ in this context and reveal the natural regularity relationships among $\tilde{\phi}$, $\tilde{f}$ and $g$. The condition [(\[1.3\])]{} determines the boundary forcing function if we can solve $$\label{1.7}
\int_0^t S(t - t')\delta_0(x)g(t')dt'\Bigr|_{\{x = 0\}} = \tilde{f}(t) - S(t)\tilde{\phi}(x)\Bigr|_{\{x = 0\}}$$ for $g$. The right-hand side of [(\[1.7\])]{} suggests that the regularity properties of $\tilde{f}$ should be the same as those expressed by $S(t)\tilde{\phi}\bigl|_{\{x = 0\}}$. For $\tilde{\phi} \in \dot{H}^s({\mathbb R}_x) = \bigl\{f : |\xi|^s\hat{f}(\xi) \in L^2({\mathbb R}_\xi)\bigr\}$, the change of variables argument used to prove the local smoothing property shows that $S(t)\tilde{\phi}\bigl|_{\{x = 0\}} \in \dot{H}^{(s + 1)/3}({\mathbb R}_t)$. The convolution representation of $S(t)$ allows the left-hand side of [(\[1.7\])]{} to be reexpressed as $$\int_0^t \frac{1}{(t - t')^{1/3}}A\biggl(\frac{x}{(t - t')^{1/3}}\biggr)g(t')dt'.$$ Since the Airy function $A$ is continuous and $A(0) \neq 0$, we can evaluate at $x = 0$ and rewrite [(\[1.7\])]{} as $$A(0){\!}\int_0^t \frac{1}{(t - t')^{1/3}}g(t')dt' = \tilde{f}_1(t),$$ where we have introduced the notation $\tilde{f}_1(t) = \tilde{f}(t) - S(t)\tilde{\phi}\bigl|_{\{x = 0\}} \in \dot{H}^{(s + 1)/3}_0({\mathbb R}_t)$. Recalling the theory in [@14] (see also \[3\] below) of the Riemann-Liouville fractional integral $$\label{1.8}
{{\mathbb I}}_\alpha(h)(t) = \frac{1}{\Gamma(\alpha)}{\!}\int_0^t (t - s)^{\alpha - 1}h(s)ds,$$ we reexpress [(\[1.7\])]{} as $$\label{1.9}
{{\mathbb I}}_{2/3}(g) = \frac{1}{A(0)\Gamma(2/3)}\tilde{f}_1.$$ This equation is solved for $g$ by applying ${{\mathbb I}}_{-2/3}$. Moreover, the operator ${{\mathbb I}}_{\alpha}$ is smoothing of order $-\alpha$, so the boundary forcing function $g$ is seen to have $2/3$ fewer derivatives in $L^2$ than $\tilde{f}_1$. These remarks reveal that, for $\tilde{\phi} \in H^s({\mathbb R}_x)$, it is natural to assume that $\tilde{f} \in H^{(s + 1)/3}({\mathbb R}_t)$ and to look for $g \in H^{(s - 1)/3}({\mathbb R}_t)$. Certain technical distinctions among the spaces $H^\sigma({\mathbb R}_t)$ and $\dot{H}^\sigma({\mathbb R}_t)$ will be clarified below using time localization.
We apply this basic idea – [*apply boundary forcing to ensure that the $\{x = 0\}$ condition $u(0, t) = f(t)$ holds with the forcing $g$ selected by inverting a certain fractional integral*]{} – in the nonlinear setting using a contraction mapping argument to obtain the following results for the initial-boundary value problem [(\[1.1\])]{}. Let ${\mathbb R}_y^+$ denote the open right half-line $\{y : y > 0\}$.
\[Th1.1\] Consider [(\[1.1\])]{} in the cases $k \in {\mathbb N}$ and set $s_1 = 0$, $s_2 = 1/4$, $s_3 = 1/12$ and $s_{k}$k$ as above?
= \frac{1}{2} - \frac{2}{{k}}$ (for ${k}\geq 4$). For any $\phi \in H^{s_{k}}({\mathbb R}_x^+)$ and $f \in H^{(s_{k}+ 1)/3}({\mathbb R}_t^+)$, there exists a $T = T(\phi, f) > 0$ and a solution $u \in C\bigl([0, T]; H^{s_{k}}({\mathbb R}_x^+)\bigr)$ of the initial-boundary value problem [(\[1.1\])]{}. When ${k}< 4$, $T = T(||\phi||_{H^{s_{k}}}, ||f||_{H^{(s_{k}+ 1)/3}})$. The map $(\phi, f) \mapsto u$ taking the initial and boundary data to the solution is Lipschitz-continuous from $H^{s_{k}}({\mathbb R}_x^+) \times H^{(s_{k}+ 1)/3}({\mathbb R}_t^+)$ to $C\bigl([0, T]; H^{s_{k}}({\mathbb R}_x^+)\bigr)$.
The cases where ${k}\geq 2$ are proved using the selected boundary forcing procedure outlined above in the function space framework introduced by Kenig, Ponce and Vega in [@10] to treat the corresponding initial value problems. The proof in the case ${k}= 1$ uses the forcing procedure and a contraction mapping argument in a [modification of a]{} function space introduced by Bougain in [@5]. The need for the modified spaces is explained in Remark \[Rk5.1’\]. An optimization of the approach in [@5], carried out in [@11], established local well-posedness of the initial value problem for the standard (i.e., ${k}= 1$) KdV equation in $H^s({\mathbb R})$ for $s > -3/4$. An improvement in the $k = 1$ case of Theorem \[Th1.1\] to $s_1 > -3/4$ is likely to be true, but we have chosen not to carry it out in the present paper[[^3]]{}. In particular, the selected forcing procedure extends the theory of the initial value problem for the generalized KdV equations to the initial-boundary value setting.
Our local (in time) results can be combined with integration by parts to yield global (in time) results. For instance, we have:
\[Th1.2\] [ ]{}
1. \[Th1.2(i)\] When ${k}= 1$, $\phi \in L^2({\mathbb R}^+)$ and $f \in H^{7/12}({\mathbb R}^+)$, the results of Theorem \[Th1.1\] extend to any interval $[0, T]$.
2. \[Th1.2(ii)\] When ${k}= 2$, $\phi \in H^1({\mathbb R}^+)$, $f \in H^{11/12}({\mathbb R}^+)$ and $\phi(0) = f(0)$, we have well-posedness of [(\[1.1\])]{} in $H^1 \times H^{2/3}$ (in the sense of Theorem \[Th1.1\]) on any interval $[0, T]$, provided that $||f||_{L^2({\mathbb R}^+)}$ is sufficiently small.
3. \[Th1.2(iii)\] When ${k}= 3$, the result in [(\[Th1.2(ii)\])]{} holds for $f \in H^{5/4}({\mathbb R}^+)$, provided that $||f||_{L^2({\mathbb R}^+)}$ is sufficiently small.
4. \[Th1.2(iv)\] For ${k}\geq 4$, the result in [(\[Th1.2(ii)\])]{} holds for $f \in H^{11/12}({\mathbb R}^+)$, provided that $||f||_{L^2({\mathbb R}^+)}$ and $||\phi||_{L^2({\mathbb R}^+)}$ are sufficiently small.
[(See \[7\].) Note that $7/12 > 1/3$; $11/12 > 2/3$; and $5/4 > 2/3$. This is because “conservation laws” are not “exact” in the quarter-plane setting. (Again, see \[7\] and [@3].) ]{}
The boundary forcing method is flexible. In particular, Theorem \[Th1.1\] applies to the initial-boundary value problem obtained by replacing $\partial_x^3$ by $\partial_x^3 + c\partial_x$ for some $c \in {\mathbb R}$ in [(\[1.1\])]{}. [See Remarks \[Rk6.4\] and \[Rk7.5\]. (Transport terms arise naturally in physical models.)]{} The method also constructs solutions to the analogous initial value problem on the left half-line $\{x < 0\}$. (Uniqueness in the linear problem in the left half-line is not established here, and indeed does not hold. See [@F], [@FS]. Also, the global (in time) results of Theorem \[Th1.2\] do not apply to the left half-line.) We plan to apply this approach to the generalized KdV problem on a finite interval with Dirichlet boundary conditions in a future publication. Recent work of Colin and Ghidaglia on the problem on a finite interval has just appeared [@CG2001]. Initial-boundary value problems for other dispersive equations in one spatial dimension may also be studied using the method and the estimates obtained in [@12]. We plan to extend these ideas to treat higher-dimensional initial-boundary value problems, such as NLS on a domain $\Omega \subseteq {\mathbb R}^2$ with Dirichlet boundary conditions (see [@6] and the references therein). We believe that this paper is the first application of a general method for treating initial-boundary value problems for nonlinear dispersive PDEs.
The initial-boundary value problem [(\[1.1\])]{} (with a first-order transport term) physically models the evolution of small-amplitude shallow water long waves propagating in a channel with forcing applied at the left end (see [@9]). Bona and Winther (in [@2] and [@4]), employing energy methods, treated the right half-line problem [(\[1.1\])]{} with a transport term in the case ${k}$k$?
= 1$ with more regular initial and boundary data ($(\phi, f) \in H^s({\mathbb R}_x) \times H^{1 + [s/3]}({\mathbb R}_t^+)$). Polynomial generalizations of the standard KdV equation were studied by Bona and Luo in [@3] under higher regularity assumptions on the data. A recent preprint of Bona, Sun and Zhang ([@1]) uses a Laplace transform technique in the framework of function spaces developed in [@10] to treat the ${k}= 1$ version of the right half-line problem [(\[1.1\])]{} with transport term for initial data $\phi \in H^s({\mathbb R}^+)$ and boundary data $f \in H^{(s + 1)/3}({\mathbb R}^+)$ provided $s > 3/4$. The half-line problem for KdV (and generalizations) has also been considered by Faminski[ĭ]{} [@F88], [@F96], [@F].
We outline the rest of the paper. The next two sections present background material required for the proof of Theorem \[Th1.1\]. \[2\] develops the theory of $L^2$-based Sobolev spaces on half-lines and intervals. \[3\] recalls the Riemann-Liouville fractional integral and establishes its mapping properties between $L^2$-based Sobolev spaces. \[4\] provides estimates in space-time mixed-norm spaces for the linear solution operator and the inhomogeneous and boundary forcing Duhamel terms. \[5\] establishes similar space-time estimates in Bourgain spaces. In \[6\], we construct and estimate solutions of homogeneous and inhomogeneous linear analogues of [(\[1.2\])]{}; \[6\] also contains a uniqueness result. The nonlinear problems are addressed in \[7\].
Sobolev Spaces on Half-Lines and Intervals
==========================================
\[2\]
This section develops the $L^2$-based Sobolev spaces on half-lines and intervals required for our treatment of certain initial-boundary value problems in later sections.
\[Df2.1\] For $s \geq 0$, we write $$H^s({\mathbb R}^+) = \bigl\{f = F\bigl|_{{\mathbb R}^+} : F \in H^s({\mathbb R})\bigr\}$$ and ${||f||_{H^{s}({\mathbb R}^+)}} = \inf {||F||_{H^{s}(\mathbb R)}}$. Similarly, for $s \geq 0$, $$\dot{H}^s({\mathbb R}^+) = \bigl\{f = F\bigl|_{{\mathbb R}^+} : F \in \dot{H}^s({\mathbb R})\bigr\}$$ and ${||f||_{\dot{H}^{s}({\mathbb R}^+)}} = \inf {||F||_{\dot{H}^{s}(\mathbb R)}}$. For $-\infty < s < +\infty$, $$H^s_0({\mathbb R}^+) = \bigl\{f \in H^s({\mathbb R}) : \operatorname{supp}f \subseteq [0, \infty)\bigr\}$$ and $$\dot{H}^s_0({\mathbb R}^+) = \bigl\{f \in \dot{H}^s({\mathbb R}) : \operatorname{supp}f \subseteq [0, \infty)\bigr\}.$$
Recall that $H^s({\mathbb R})$ is the set of distributions satisfying $(1 + |\xi|)^s\hat{f}(\xi) \in L_\xi^2$, where $\hat{f}$ denotes the Fourier transform in $x$. The space $\dot{H}^s({\mathbb R})$ is the homogeneous analogue consisting of distributions satisfying $|\xi|^s\hat{f}(\xi) \in L_\xi^2$.
\[Rk2.1\] For $k = 0, 1, 2, \ldots$, define $$W\^[2, k]{}([R]{}\^+) = {f : D\_x\^f L\^2([R]{}\^+) = H\^0([R]{}\^+)|| k}.$$ There is a bounded extension operator $E_k : W^{2, k}({\mathbb R}^+) \rightarrow W^{2, k}({\mathbb R})$. Hence $H^k({\mathbb R}^+) = W^{2, k}({\mathbb R}^+)$. (In fact, the operator $E_k$ can be defined independently of $k$, so that we have a single operator $E : W^{2, k}({\mathbb R}^+) \rightarrow W^{2, k}({\mathbb R})$ for each $k$.) Note that this implies that ${||f||_{H^{k}({\mathbb R}^+)}} \sim ||f||_{W^{2, k}({\mathbb R}^+)}$ for $k = 0, 1, 2, \ldots$. Consequently, the spaces $H^s({\mathbb R}^+)$ interpolate by the complex method $\bigl[L^2({\mathbb R}^+), W^{2, k}({\mathbb R}^+)\bigr]_\theta = H^{\theta k}({\mathbb R}^+)$ for $0 \leq \theta \leq 1$. By reiteration, similar results hold for $H^s({\mathbb R}^+)$, and we see that $H^s({\mathbb R}^+)$ is a complex interpolation scale for $s \geq 0$. (See, for instance, [@8].)
\[Rk2.2\] The space $C_0^\infty({\mathbb R}^+)$ is dense in $H^s_0({\mathbb R}^+)$ for $-\infty < s < +\infty$.
\[Df2.2\] For $0 < \alpha < +\infty$, $H^{-\alpha}({\mathbb R}^+)$ is the space of linear functionals on $C_0^\infty({\mathbb R}^+)$, with the norm $$||g||_{H^{-\alpha}({\mathbb R}^+)} = \sup \{|g(f)| : f \in C_0^\infty({\mathbb R}^+)\text{ and }||f||_{H^\alpha({\mathbb R})} \leq 1\}.$$ Let ${\cal S}({\mathbb R}^+) = \{f = F\bigl|_{{\mathbb R}^+} : F \in {\cal S}({\mathbb R})\}$ and define, for $s > 0$, $$\dot{H}^{-s}({\mathbb R}^+) = \bigl\{g \in {\cal S}'({\mathbb R}) : \sup |g(f)| < +\infty\bigr\},$$ where the $\sup$ in the definition above is taken over $f \in C_0^\infty({\mathbb R}^+)$ satisfying ${||f||_{\dot{H}^{s}({\mathbb R}^+)}} \leq 1$.
\[Pn2.1\] For $\alpha \geq 0$, $H^{-\alpha}({\mathbb R}^+)$ is the dual space of $H^\alpha_0({\mathbb R}^+)$, and $H^{-\alpha}_0({\mathbb R}^+)$ is the dual space of $H^\alpha({\mathbb R}^+)$. Also, ${\cal S}({\mathbb R}^+)$ is dense in $H^\alpha({\mathbb R}^+)$ for $-\infty < \alpha < +\infty$.
The first assertion follows from Remark \[Rk2.2\]. Now suppose that $f \in H^{-\alpha}_0({\mathbb R}^+)$ and define a linear functional on $H^\alpha({\mathbb R}^+)$ by $u \mapsto f(u_1)$, where $u_1 \in H^\alpha({\mathbb R})$ satisfies $u_1\bigl|_{{\mathbb R}^+} = u$. Such a functional is well-defined because, if $u_2$ is another extension of $u$, then $u_1 - u_2 \in H^\alpha_0({\mathbb R}^-)$, so $u_1 - u_2$ is the limit in the $H^\alpha$ norm of functions in $C_0^\infty({\mathbb R}^-)$ by Remark \[Rk2.2\], and $f$ kills such functions. Thus, we have a natural mapping $H^{-\alpha}_0({\mathbb R}^+) \rightarrow \bigl(H^\alpha({\mathbb R}^+)\bigr)^*$. This map has an inverse given by restriction, as follows: If $f \in \bigl(H^\alpha({\mathbb R}^+)\bigr)^*$, then we define $\tilde{f} \in H^{-\alpha}_0({\mathbb R}^+)$ by $\tilde{f}(F) = f\bigl(F\bigl|_{{\mathbb R}^+}\bigr)$. Clearly, $\tilde{f} \in H^{-\alpha}_0({\mathbb R}^+)$; and $f \mapsto \tilde{f}$ is the inverse of the previous map.
The fact that ${\cal S}({\mathbb R}^+)$ is dense in $H^\alpha({\mathbb R}^+)$ for $\alpha \geq 0$ follows from the density of ${\cal S}({\mathbb R})$ in $H^\alpha({\mathbb R})$. It is easy to see that $H^\alpha_0({\mathbb R}^+)$ is reflexive, since it is a closed subspace of $H^\alpha({\mathbb R})$ for $-\infty < \alpha < +\infty$. Hence $H^{-\alpha}({\mathbb R}^+)$ is reflexive for $\alpha > 0$. If ${\cal S}({\mathbb R}^+)$ were not dense, by the Hahn-Banach theorem there would exist $f \neq 0$ in $\bigl(H^{-\alpha}({\mathbb R}^+)\bigr)^* = H^\alpha_0({\mathbb R}^+)$ such that $\int f\phi dx = 0$ for all $\phi \in {\cal S}({\mathbb R}^+)$, which is a contradiction.
\[Co2.1\] For $\alpha \geq 0$, $H^{-\alpha}_0({\mathbb R}^+)$ is a complex interpolation scale.
Remark \[Rk2.1\] showed that $H^\alpha({\mathbb R}^+)$ is a complex interpolation scale, and Proposition \[Pn2.1\] established that $H^{-\alpha}_0({\mathbb R}^+)$ is the dual space of $H^\alpha({\mathbb R}^+)$. The dual space of a complex interpolation scale is a complex interpolation scale.
\[Pn2.2\] For $\alpha \geq 0$, $H^\alpha_0({\mathbb R}^+)$ is a complex interpolation scale.
See Proposition 2.11 in [@8].
Note that, if $F \in H^\alpha({\mathbb R})$ for some $\alpha > 1/2$, then $F$ is uniformly continuous, and hence $F(0)$ is well-defined. If $f \in H^\alpha({\mathbb R}^+)$ and $F\bigl|_{{\mathbb R}^+} = f$, then we set $\operatorname{Tr}(f) = F(0)$. For $f \in {\cal S}({\mathbb R}^+)$, we have $\operatorname{Tr}(f) = f(0)$.
\[Pn2.3\] If $\alpha > 1/2$, then $\operatorname{Tr}$ is a well-defined bounded linear operator from $H^\alpha({\mathbb R}^+)$ to $\mathbb R$.
\[Pn2.4\] If $1/2 < \alpha < 3/2$, then $$H^\alpha_0({\mathbb R}^+) = \{f \in H^\alpha({\mathbb R}^+) : \operatorname{Tr}(f) = 0\}.$$
Since $C_0^\infty({\mathbb R}^+)$ is dense in $H^\alpha_0({\mathbb R}^+)$, it is clear that, if $f \in H^\alpha_0({\mathbb R}^+)$, then $\operatorname{Tr}(f) = 0$. For the converse direction, we use two lemmas from [@8]:
\[Lm2.1\] [**(3.7 from [@8].)**]{} If $1/2 < \alpha < 3/2$, then $$\int_0^\infty |f(x) - f(0)|^2\frac{dx}{x^{2\alpha}} \leq C{||f||_{H^{\alpha}(\mathbb R)}}^2.$$
\[Lm2.2\] [**(3.8 from [@8].)**]{} If $1/2 < \alpha < 3/2$, then $${||\chi_{(0, +\infty)}f||_{H^{\alpha}(\mathbb R)}} \leq C\Biggl[{||f||_{H^{\alpha}(\mathbb R)}} + \biggl(\int_0^\infty |f(x)|^2\frac{dx}{x^{2\alpha}}\biggr)^{1/2}\Biggr].$$
We now complete the proof of the proposition by showing that, if $f \in H^\alpha({\mathbb R}^+)$ satisfies $\operatorname{Tr}(f) = 0$, then ${||\chi_{(0, +\infty)}f||_{H^{\alpha}(\mathbb R)}} \leq C{||f||_{H^{\alpha}({\mathbb R}^+)}}$. This is a direct consequence of the lemmas above.
\[Lm2.3\] [**(3.5 from [@8].)**]{} For $0 \leq \alpha < 1/2$, $${||\chi_{(0, +\infty)}f||_{H^{\alpha}(\mathbb R)}} \leq C{||f||_{H^{\alpha}(\mathbb R)}}.$$
\[Pn2.5\] Let $\mu \in C^\infty({\mathbb R})$ be such that $\partial_x^j\mu$ is bounded. Then, for $f \in H^\alpha_0({\mathbb R}^+)$, with $-\infty < \alpha < +\infty$, $${||\mu f||_{H^{\alpha}_{0}({\mathbb R}^+)}} \leq C{||f||_{H^{\alpha}_{0}({\mathbb R}^+)}}.$$
We need only prove this for $f \in C_0^\infty({\mathbb R}^+)$. First, consider the case where $0 \leq \alpha < +\infty$. By complex interpolation, it suffices to treat the case where $\alpha = k$, where $k$ is an integer, which follows by the Leibniz rule since, for $f \in C_0^\infty({\mathbb R}^+)$, ${||f||_{H^{k}_{0}({\mathbb R}^+)}} = ||f||_{W^{2, k}({\mathbb R}^+)}$. Note that, by taking $f \in {\cal S}({\mathbb R}^+)$, we see that the same result applies to $H^\alpha({\mathbb R}^+)$ for $\alpha \geq 0$ since ${||f||_{H^{k}({\mathbb R}^+)}} \sim ||f||_{W^{2, k}({\mathbb R}^+)}$. Therefore, to treat the case $\alpha < 0$, we use duality and Proposition \[Pn2.1\].
\[Pn2.6\] For $0 \leq \alpha < 3/2$ and $\alpha \neq 1/2$, we have that $${||f||_{H^{\alpha}_{0}({\mathbb R}^+)}} \sim {||f||_{H^{\alpha}({\mathbb R}^+)}}$$ for $f \in H^\alpha_0({\mathbb R}^+)$.
By density of $C_0^\infty({\mathbb R}^+)$ in $H^\alpha_0({\mathbb R}^+)$, it is enough to do this for $f \in C_0^\infty({\mathbb R}^+)$. Then we clearly have ${||f||_{H^{\alpha}({\mathbb R}^+)}} \leq {||f||_{H^{\alpha}_{0}({\mathbb R}^+)}}$. For the other inequality, assume first that $0 \leq \alpha < 1/2$. Let $F \in H^\alpha({\mathbb R})$ satisfy $F\bigl|_{{\mathbb R}^+} = f$ and ${||F||_{H^{\alpha}(\mathbb R)}} \leq 2{||f||_{H^{\alpha}({\mathbb R}^+)}}$. Then, by Lemma \[Lm2.3\], $${||f||_{H^{\alpha}(\mathbb R)}} = {||\chi_{(0, +\infty)}F||_{H^{\alpha}(\mathbb R)}} \leq C{||F||_{H^{\alpha}(\mathbb R)}} \leq 2C{||f||_{H^{\alpha}({\mathbb R}^+)}}.$$ For $1/2 < \alpha \leq 3/2$, a similar proof works by noting that the inequality $${||\chi_{(0, +\infty)}F||_{H^{\alpha}(\mathbb R)}} \leq C{||F||_{H^{\alpha}(\mathbb R)}}$$ holds for all $F \in H^\alpha({\mathbb R})$ satisfying $F(0) = 0$.
\[Pn2.7\] For $0 < \alpha < 1/2$ and $f \in H^{-\alpha}_0({\mathbb R}^+)$, we have $${||f||_{H^{-\alpha}_{0}({\mathbb R}^+)}} \sim {||f||_{H^{-\alpha}({\mathbb R}^+)}}.$$
Let $h \in C_0^\infty({\mathbb R}^+)$ satisfy ${||h||_{H^{\alpha}(\mathbb R)}} \leq 1$. Consider now that $$|f(h)| \leq {||f||_{H^{-\alpha}(\mathbb R)}}{||h||_{H^{\alpha}(\mathbb R)}} \leq {||f||_{H^{-\alpha}(\mathbb R)}} = {||f||_{H^{-\alpha}_{0}({\mathbb R}^+)}}.$$ Thus, ${||f||_{H^{-\alpha}(\mathbb R)}} \leq {||f||_{H^{-\alpha}_{0}({\mathbb R}^+)}}$. We need to show that ${||f||_{H^{-\alpha}_{0}({\mathbb R}^+)}} \leq C{||f||_{H^{-\alpha}({\mathbb R}^+)}}$. Again, it suffices to assume that $f \in C_0^\infty({\mathbb R}^+)$. Let now $g \in C_0^\infty({\mathbb R})$ satisfy ${||g||_{H^{\alpha}(\mathbb R)}} \leq 1$. Then $${||f||_{H^{-\alpha}_{0}({\mathbb R}^+)}} = {||f||_{H^{-\alpha}(\mathbb R)}} = \sup_g |f(g)| = \sup_g |f(\chi_{(0, +\infty)}g)|.$$ Now, ${||\chi_{(0, +\infty)}g||_{H^{\alpha}(\mathbb R)}} \leq C{||g||_{H^{\alpha}(\mathbb R)}} \leq 1$, and so $\chi_{(0, +\infty)}g \in H^\alpha_0({\mathbb R}^+)$ satisfies ${||g||_{H^{\alpha}_{0}(\mathbb R)}}\linebreak \leq C$. By Proposition \[Pn2.1\], $$\sup_g |f(g)| \leq {||f||_{H^{-\alpha}({\mathbb R}^+)}}{||\chi_{(0, +\infty)}g||_{H^{\alpha}(\mathbb R)}},$$ and the proposition follows.
\[Pn2.8\] Suppose that $f \in H^\alpha_0({\mathbb R}^+)$ for some $-1/2 < \alpha < 1/2$ and that $\operatorname{supp}f \subseteq [0, 1]$. Then $${||f||_{\dot{H}^{\alpha}_{0}({\mathbb R}^+)}} \sim {||f||_{H^{\alpha}_{0}({\mathbb R}^+)}}.$$
It is enough to show the result for $f \in C_0^\infty\bigl((0, 1)\bigr)$. Note that, for $\alpha \geq 0$, ${||f||_{\dot{H}^{\alpha}(\mathbb R)}} \leq {||f||_{H^{\alpha}(\mathbb R)}}$, and, for $\alpha < 0$, ${||f||_{H^{\alpha}(\mathbb R)}} \leq {||f||_{\dot{H}^{\alpha}(\mathbb R)}}$. Suppose that $0 \leq \alpha < 1/2$. We need to show that ${||f||_{H^{\alpha}(\mathbb R)}} \leq C{||f||_{\dot{H}^{\alpha}(\mathbb R)}}$. Since $${||f||_{H^{\alpha}(\mathbb R)}} \sim ||f||_{L^2({\mathbb R})} + ||D^\alpha f||_{L^2({\mathbb R})} = ||f||_{L^2({\mathbb R})} + {||f||_{\dot{H}^{\alpha}(\mathbb R)}},$$ we only need to show that $||f||_{L^2({\mathbb R})} \leq C||D^\alpha f||_{L^2({\mathbb R})}$. We know, however, that $f = {\cal I}{}_\alpha D^\alpha f$, where ${\cal I}_\alpha$ is the standard fractional integral operator; so, by the fractional integration theorem, $$||f||_{L^q({\mathbb R})} \leq C||D^\alpha f||_{L^2({\mathbb R})}, \quad \frac{1}{q} = \frac{1}{2} - \alpha.$$ Since $f$ has compact support, Hölder’s inequality gives the desired bound. Next, we wish to show that $${||f||_{\dot{H}^{-\alpha}(\mathbb R)}} \leq C{||f||_{H^{-\alpha}(\mathbb R)}}, \quad 0 < \alpha < \frac{1}{2}.$$ Choose $\mu \in C_0^\infty({\mathbb R})$ satisfying $\operatorname{supp}\mu \subseteq (-2, 2)$ and $\mu \equiv 1$ on $[0, 1]$, so that $g = \mu f = f$. We will show that $|\hat{f}(\tau)| \leq C{||f||_{H^{-\alpha}(\mathbb R)}}$ for $|\tau| \leq 1$. In fact, $$\begin{gathered}
|\hat{f}(\tau)| = |\hat{\mu} * \hat{f}(\tau)| = \Bigl|\int \hat{\mu}(\tau - \eta)\hat{f}(\eta)d\eta\Bigr| \\
= \biggl|\int \hat{\mu}(\tau - \eta)(1 + |\eta|)^\alpha\frac{\hat{f}(\eta)}{(1 + |\eta|)^\alpha}d\eta\biggr| \leq C{||f||_{H^{-\alpha}}}\end{gathered}$$ for $|\tau| \leq 1$, since $\hat{\mu} \in {\cal S}({\mathbb R})$.
\[Rk2.3\] The conclusion of Proposition \[Pn2.8\] also holds for $0 \leq \alpha \leq 1$. We need to show that, for $f \in H^\alpha_0\bigl((0, 1)\bigr)$, $||f||_{L^2} \leq C||D^\alpha f||_{L^2}$ for $1/2 \leq \alpha \leq 1$. The result clearly holds for $\alpha = 1$. For $1/2 < \alpha < 1$, note that $|f(x) - f(y)| \leq C|x - y|^{\alpha - 1/2}$, where $C \leq C||D^\alpha f||_{L^2}$. In fact, if $$u(x, t) = \int e^{ix\xi}e^{-t|\xi|}\hat{f}(\xi)d\xi$$ is the harmonic extension of $f$, then $\bigl|{\frac{\partial u}{\partial t}}(x, t)\bigr| \leq \frac{C}{t^{1/2}t^{1 - \alpha}}$ by a simple use of Cauchy-Schwarz, and hence the result follows from the proof of Proposition 7, Chapter V in [@15]. (For $\alpha = 1/2$, we can instead obtain a BMO estimate for $f$.) Taking $y = 0$, we see that $|f(x)| \leq C||D^\alpha f||_{L^2}$, as desired.
\[Rk2.4\] With $f$ as in Proposition \[Pn2.8\] and $-1/2 < \alpha \leq 1$ with $\alpha \neq 1/2$, we have ${||f||_{\dot{H}^{\alpha}_{0}({\mathbb R}^+)}} \simeq {||f||_{H^{\alpha}({\mathbb R}^+)}}$. This is because of Propositions \[Pn2.6\], \[Pn2.7\] and \[Pn2.8\] and Remark \[Rk2.3\].
The Riemann-Liouville Fractional Integral
=========================================
\[3\]
Our method for constructing solutions of certain initial-boundary value problems below exploits properties of a fractional integration operator whose properties are described in this section.
\[Df3.1\] For $h \in C_0^\infty({\mathbb R}^+)$ and $\Re \alpha > 0$, let $${{\mathbb I}}_\alpha(h)(t) = \frac{1}{\Gamma(\alpha)}{\!}\int_0^t (t - s)^{\alpha - 1}h(s)ds.$$
The operator ${{\mathbb I}}_\alpha$ is the [*Riemann-Liouville fractional integration operator*]{} (of order $\alpha$). It is shown in [@14] that ${{\mathbb I}}_\alpha(h)(t)$ extends to an analytic function of $\alpha \in {\mathbb C}$ with the following properties: $$\begin{gathered}
{{\mathbb I}}_{-k}(h)(t) = \frac{d^kh}{dt^k}(t), \quad k \in {\mathbb N}, \\
{{\mathbb I}}_1(h)(t) = \int_0^t h(s)ds, \\
{{\mathbb I}}_0(h) = h \\
\intertext{ and }
{{\mathbb I}}_\alpha {{\mathbb I}}_\beta(h) = {{\mathbb I}}_{\alpha + \beta}(h).\end{gathered}$$
The rest of this section establishes mapping properties of the family $\{{{\mathbb I}}_\alpha\}$ on the $H^s_0({\mathbb R}^+)$ spaces.
\[Pn3.1\] The estimate $$||{{\mathbb I}}_{i\gamma}(h)||_{L^2({\mathbb R}^+)} \leq C||h||_{L^2({\mathbb R}^+)}$$ holds for all $h \in C_0^\infty({\mathbb R}^+)$ and $\gamma \in {\mathbb R}$.
We postpone the proof of Proposition \[Pn3.1\] until later in this section.
\[Co3.1\] For $0 \leq \Re \alpha \leq 1$, we have that $$||{{\mathbb I}}_{-\alpha}(h)||_{L^2({\mathbb R}^+)} \leq C{||h||_{H^{\alpha}_{0}({\mathbb R}^+)}}.$$
Take $h \in C_0^\infty({\mathbb R}^+)$. Since ${{\mathbb I}}_{-1}(h) = \frac{dh}{dt}$, $${{\mathbb I}}_{-1 + i\gamma}(h) = {{\mathbb I}}_{i\gamma}{{\mathbb I}}_{-1}(h) = {{\mathbb I}}_{i\gamma}\biggl(\frac{dh}{dt}\biggr)$$ and, since ${{\mathbb I}}_0(h) = h$, the result follows from complex interpolation using Propositions \[Pn2.2\] and \[Pn3.1\].
\[Pn3.2\] For $0 < r \leq \alpha$ and $0 \leq \alpha \leq 1$, we have $${||{{\mathbb I}}_{-\alpha}(h)||_{H^{r - \alpha}_{0}({\mathbb R}^+)}} \leq C{||h||_{H^{r}_{0}({\mathbb R}^+)}}.$$
We will prove the inequality by complex interpolation. Note that $r - \alpha \leq 0 < r$, so both sides are complex interpolation scales. Thus, it suffices to prove this when $\Re \alpha = r$ and when $\Re \alpha = 1$. When $\Re \alpha = r$, this is Corollary \[Co3.1\]. When $\Re \alpha = 1$, write $\alpha = 1 - i\gamma$ with $\gamma \in {\mathbb R}$, so that ${{\mathbb I}}_{-\alpha}(h) = {{\mathbb I}}_{i\gamma}\bigl(\frac{dh}{dt}\bigr)$. We need to prove the following facts:
\[Fc3.1\] For $0 \leq r \leq 1$, $\frac{d}{dt} : H^r_0({\mathbb R}^+) \rightarrow H^{r - 1}_0({\mathbb R}^+)$.
\[Fc3.2\] For $|\alpha| \leq 1$ and $\gamma \in {\mathbb R}$, ${{\mathbb I}}_{i\gamma} : H^\alpha_0({\mathbb R}^+) \rightarrow H^\alpha_0({\mathbb R}^+)$.
If Facts \[Fc3.1\] and \[Fc3.2\] hold, then the proof is finished. First we prove Fact \[Fc3.1\]. If $r = 1$, then the fact is clear. Next, we need to check the case $r = 0$. Note that $r - 1 \leq 0 \leq r$, so both sides are complex interpolation scales. We need to show that, if $h \in L^2({\mathbb R}^+)$, then $\frac{dh}{dt} \in H^{-1}_0({\mathbb R}^+)$. By density, it suffices to consider the case $h \in C_0^\infty({\mathbb R}^+)$. Then, however, $\operatorname{supp}\frac{dh}{dt} \subseteq (0, +\infty)$, so we only need to verify that $\bigl|\bigl|\frac{dh}{dt}\bigr|\bigr|_{H^{-1}({\mathbb R})} \leq C||h||_{L^2({\mathbb R})}$, which is obvious.
We turn our attention to proving Fact \[Fc3.2\]. For $\Re \alpha = 0$, this is Proposition \[Pn3.1\]. For $\Re \alpha = 1$, we must verify that ${{\mathbb I}}_{i\gamma} : H^1_0({\mathbb R}^+) \rightarrow H^1_0({\mathbb R}^+)$. It suffices to consider the case $h \in C_0^\infty({\mathbb R}^+)$. We have that $$\begin{gathered}
{||{{\mathbb I}}_{i\gamma}(h)||_{H^{1}({\mathbb R}^+)}} \sim ||{{\mathbb I}}_{i\gamma}(h)||_{L^2({\mathbb R}^+)} + \biggl|\biggl|\frac{d}{dt}{{\mathbb I}}_{i\gamma}(h)\biggr|\biggr|_{L^2({\mathbb R}^+)} \\
= ||{{\mathbb I}}_{i\gamma}(h)||_{L^2({\mathbb R}^+)} + \biggl|\biggl|{{\mathbb I}}_{i\gamma}\frac{dh}{dt}\biggr|\biggr|_{L^2({\mathbb R}^+)} \leq ||h||_{L^2({\mathbb R}^+)} + \biggl|\biggl|\frac{dh}{dt}\biggr|\biggr|_{L^2({\mathbb R}^+)}.\end{gathered}$$ Therefore, ${{\mathbb I}}_{i\gamma}(h) \in H^1({\mathbb R}^+)$. To show that ${{\mathbb I}}_{i\gamma}(h) \in H^1_0({\mathbb R}^+)$, in light of Proposition \[Pn2.4\], all we need to show is that ${{\mathbb I}}_{i\gamma}(h)(0) = 0$.
Let $M^\alpha(h)(t) = t^{-\alpha}{{\mathbb I}}_\alpha(h)(t)$. Then $$M^\alpha(h)(t) = t^{-\alpha}\frac{1}{\Gamma(\alpha)}{\!}\int_0^t (t - s)^{\alpha - 1}h(s)ds = \frac{1}{\Gamma(\alpha)}{\!}\int_0^1 (1 - s)^{\alpha - 1}h(st)ds.$$ We break the last expression into two pieces by writing $$M^\alpha(h)(t) = \frac{1}{\Gamma(\alpha)}{\!}\int_0^{1/2} (1 - s)^{\alpha - 1}h(st)ds + \frac{1}{\Gamma(\alpha)}{\!}\int_{1/2}^1 (1 - s)^{\alpha - 1}h(st)ds =: I + II.$$ The first piece is bounded and the second piece may be rewritten as $$II = \frac{1}{\Gamma(\alpha + 1)}{\!}\int_{1/2}^1 (1 - s)^\alpha\frac{d}{ds}h(st)ds + \frac{1}{\Gamma(\alpha + 1)}\biggl(\frac{1}{2}\biggr)^\alpha h\biggl(\frac{1}{2}t\biggr).$$ In this form, it is clear that $$\lim_{\Re \alpha \rightarrow 0^+} \lim_{t \rightarrow 0^+} t^\alpha M^\alpha(h)(t) = 0$$ and so ${{\mathbb I}}_{i\gamma}(h)(0) = 0$. Thus ${{\mathbb I}}_{i\gamma} : H^1_0({\mathbb R}^+) \rightarrow H^1_0({\mathbb R}^+)$ and Fact \[Fc3.2\] holds for $0 \leq \Re \alpha \leq 1$.
We next need to check that ${{\mathbb I}}_{i\gamma} : H^{-1}_0({\mathbb R}^+) \rightarrow H^{-1}_0({\mathbb R}^+)$. Since $H^{-1}_0({\mathbb R}^+)$ is dual to $H^1({\mathbb R}^+)$, we need only verify that, for $f \in H^1({\mathbb R}^+)$ and $h \in H^{-1}_0({\mathbb R}^+)$, $$\frac{1}{\Gamma(i\gamma)}{\!}\int_0^\infty \Bigl(\int_0^t (t - s)^{i\gamma - 1}h(s)ds\Bigr)f(t)dt = \frac{1}{\Gamma(i\gamma)}{\!}\int_0^\infty h(s)\Bigl(\int_s^\infty f(t)(t - s)^{i\gamma - 1}dt\Bigr)ds$$ is bounded – i.e., we need to show that, for $f \in H^1({\mathbb R}^+)$, $\Gamma(i\gamma)^{-1}\int_s^\infty f(t)(t - s)^{i\gamma - 1}dt \in H^1({\mathbb R}^+)$.
The $H^1({\mathbb R}^+)$ norm is comparable to the sum of the $L^2({\mathbb R}^+)$ norm and the $\dot{H}^1({\mathbb R}^+)$ norm. Proposition \[Pn3.1\] will imply that the $L^2$ contribution is appropriately bounded. The following integration by parts argument essentially reduces our consideration of the remaining contribution to Proposition \[Pn3.1\] as well. Replace $i\gamma$ by an $\alpha \in {\mathbb C}$ with $\Re \alpha > 0$. The object under examination satisfies $$\frac{1}{\Gamma(\alpha)}{\!}\int_s^\infty f(t)(t - s)^{\alpha - 1}dt = \int_s^\infty f(t)\frac{1}{\alpha\Gamma(\alpha)}\frac{d}{dt}(t - s)^\alpha dt.$$ Integrating by parts, we find that this equals $-\bigl(\alpha\Gamma(\alpha)\bigr)^{-1}\int_s^\infty f'(t)(t - s)^\alpha dt$. The boundary term vanishes since $\Re \alpha > 0$. Therefore, we observe that $$\frac{d}{dt}\biggl(\frac{1}{\Gamma(\alpha)}{\!}\int_s^\infty f(t)(t - s)^{\alpha - 1}dt\biggr) = \frac{1}{\Gamma(\alpha)}{\!}\int_s^\infty f'(t)(t - s)^{\alpha - 1}dt,$$ where we have again used the fact that $\Re \alpha > 0$. Taking the $L_s^2$ norm of both sides, we obtain what we want, provided that $$\label{3.1}
\Bigl|\Bigl|\lim_{\Re \alpha \rightarrow 0^+} \int_s^\infty g(t)(t - s)^{\alpha - 1}dt\Bigr|\Bigr|_{L_s^2} \leq C||g||_{L_s^2}.$$ Note that, by a Fourier transform computation (see 6.12 of Chapter II in [@15]), $\Gamma(i\gamma)^{-1}\int_0^\infty f(t)(t - s)^{i\gamma - 1}dt$ is $L^2$-bounded, so [(\[3.1\])]{} follows from Proposition \[Pn3.1\].
\[Pn3.3\] For $0 \leq \theta \leq \alpha$, $0 \leq \alpha \leq 1$ and $\mu \in C_0^\infty({\mathbb R})$, $${||\mu {{\mathbb I}}_\alpha(h)||_{H^{\alpha - \theta}_{0}({\mathbb R}^+)}} \leq C{||h||_{H^{-\theta}_{0}({\mathbb R}^+)}}.$$
Note that $-\theta \leq 0 \leq \alpha - \theta$, so we have complex interpolation scales on both sides of the inequality. We prove the result in the cases $\Re \alpha = \theta$ and $\Re \alpha = 1$; the result then follows by complex interpolation.
First we consider the case where $\Re \alpha = \theta$. We wish then to show that $$||\mu {{\mathbb I}}_{\theta + i\gamma}(h)||_{L^2({\mathbb R}^+)} \leq C{||h||_{H^{-\theta}_{0}({\mathbb R}^+)}}.$$ When $\theta = 0$, this is Proposition \[Pn3.1\]. When $\theta = 1$ and $\gamma = 0$, we see by duality that we need to show that $\int_s^\infty \mu(t)f(t)dt \in H^1({\mathbb R}^+)$ for $f \in L^2$. Since $\mu$ has compact support, the integral is zero for $s$ large, and hence the integral is in $L^2({\mathbb R}^+)$. Its derivative clearly is in $L^2$, and the proof of this case follows. When $\gamma \neq 0$ but $\theta = 1$, we have that ${{\mathbb I}}_{1 + i\gamma}(h) = {{\mathbb I}}_1{{\mathbb I}}_{i\gamma}(h)$; by Fact \[Fc3.2\] above, ${||{{\mathbb I}}_{i\gamma}(h)||_{H^{-1}_{0}({\mathbb R}^+)}} \sim {||h||_{H^{-1}_{0}({\mathbb R}^+)}}$, so we are done with this case.
Next we consider the case where $\Re \alpha = 1$. Here we want to verify that $${||\mu {{\mathbb I}}_{1 + i\gamma}(h)||_{H^{1 - \theta}_{0}({\mathbb R}^+)}} \leq C{||h||_{H^{-\theta}_{0}({\mathbb R}^+)}}.$$ We checked the case $\theta = 1$ above, so we need only to check the case $\theta = 0$. By writing ${{\mathbb I}}_{1 + i\gamma}(h) = {{\mathbb I}}_1{{\mathbb I}}_{i\gamma}(h)$, we see that Proposition \[Pn3.1\] shows that we only need to check $\gamma = 0$. Thus, we need to check that, if $h \in L^2({\mathbb R}^+)$, then $\mu(t)\int_0^t h(s)ds \in H^1_0({\mathbb R}^+)$. The quantity $\mu(t)\int_0^t h(s)ds$ is zero at $t = 0$, so, by Proposition \[Pn2.4\], it is enough to check that it belongs to $H^1({\mathbb R}^+)$. The $L^2$ contribution is bounded since $\mu$ has compact support. The derivative is in $L^2$ since $\mu$ has compact support, $\mu$ and $\mu'$ are bounded and $h \in L^2$. This completes the proof of Proposition \[Pn3.3\], modulo the proof of Proposition \[Pn3.1\].
Our task is to estimate ${{\mathbb I}}_{i\gamma}(h)(t) = \linebreak\Gamma(i\gamma)^{-1}\int_0^t (t - s)^{i\gamma - 1}h(s)ds$ in $L^2({\mathbb R}^+)$. We interpret this singular expression as the limit as $\alpha \rightarrow 0^+$ of ${{\mathbb I}}_{\alpha + i\gamma}(h)(t)$. We change variables by writing $s = tu$ (so $ds = t\,du$) to see that $${{\mathbb I}}_{i\gamma}(h)(t) = \frac{t^{i\gamma}}{\Gamma(i\gamma)}\int_0^1 (1 - u)^{i\gamma - 1}h(tu)du.$$ We change variables again by writing $t = e^{-y}$ and $u = e^x$ for $-\infty < x < 0$ (so that $du = e^xdx$) to see that $$\begin{aligned}
{{\mathbb I}}_{i\gamma}(h)(e^{-y}) & = \frac{e^{-iy\gamma}}{\Gamma(i\gamma)}\int_{-\infty}^0 (1 - e^x)^{i\gamma - 1}h(e^{x - y})e^xdx \\
& = \frac{e^{-iy\gamma}}{\Gamma(i\gamma)}e^{y/2}{\!}\int_{-\infty}^0 (1 - e^x)^{i\gamma - 1}e^{x/2}h(e^{x - y})e^{(x - y)/2}dx.\end{aligned}$$ Suppose that $A$ and $B$ are two functions satisfying $A(x) = B(e^{\pm x})e^{\pm x/2}$. Then a simple calculation shows that $B \in L^2({\mathbb R}^+)$ if and only if $A \in L^2({\mathbb R})$. Therefore, ${{\mathbb I}}_{i\gamma}(h)(t) \in L^2({\mathbb R}_t^+)$ if and only if ${{\mathbb I}}_{i\gamma}(h)(e^{-y})e^{-y/2} \in L^2({\mathbb R}_y)$, which in turn is true if and only if $$\frac{1}{\Gamma(i\gamma)}\int_{-\infty}^0 (1 - e^x)^{i\gamma - 1}e^{x/2}h(e^{x - y})e^{(x - y)/2}dx \in L^2({\mathbb R}_y).$$ The same simple calculation suggests writing $h(e^x)e^x = f(x)$, so that what we wish to show becomes $$\biggl|\biggl|\frac{1}{\Gamma(i\gamma)}\int_{-\infty}^0 (1 - e^x)^{i\gamma - 1}e^{x/2}f(x - y)dx\biggr|\biggr|_{L^2({\mathbb R}_y)} \leq C||f||_{L^2({\mathbb R})}.$$ Let $$k(x) = \begin{cases}
\Gamma(i\gamma)^{-1}(1 - e^x)^{i\gamma - 1}e^{x/2} & x < 0 \\
0 & x \geq 0.
\end{cases}$$ It suffices to show that $|\hat{k}(\xi)| \leq C$ – but $$\begin{gathered}
\hat{k}(\xi) = \int_{-\infty}^0 \frac{(1 - e^x)^{i\gamma - 1}}{\Gamma(i\gamma)}e^{x/2}e^{ix\xi}dx \\
= \int_{-\infty}^{-1/2} \frac{(1 - e^x)^{i\gamma - 1}}{\Gamma(i\gamma)}e^{x/2}e^{ix\xi}dx + \int_{-1/2}^0 \frac{(1 - e^x)^{i\gamma - 1}}{\Gamma(i\gamma)}e^{x/2}e^{ix\xi}dx \\
=: I(\xi) + II(\xi).\end{gathered}$$ The integrand in $I(\xi)$ is integrable, so this contribution is bounded. The remaining piece is rewritten as $$II(\xi) = \int_{-1/2}^0 e^{ix\xi}\biggl\{\frac{(1 - e^x)^{i\gamma - 1}}{\Gamma(i\gamma)}\biggr\}(e^{x/2} - 1)dx + \int_{-1/2}^0 e^{ix\xi}\frac{(1 - e^x)^{i\gamma - 1}}{\Gamma(i\gamma)}dx.$$ Since $|e^{x/2} - 1| \leq C|x|$ and $|(1 - e^x)^{i\gamma - 1}| \sim |x|^{-1}$, the first piece above has a bounded integrand. For the second piece of $II(\xi)$, write $$1 - e^x = -x + (1 + x - e^x).$$ Then we can take the Taylor expansion of the function $g(y) = y^{i\gamma - 1}$ and write $$(1 - e^x)^{i\gamma - 1} = (-x)^{i\gamma - 1} + O\biggl(\frac{1}{|x|^2}\biggr)(1 + x - e^x).$$ Since $1 + x - e^x$ vanishes to the second order at $x = 0$, we can ignore the error term. Finally, $$\biggl|\frac{1}{\Gamma(i\gamma)}\int_{-1/2}^0 e^{ix\xi}(-x)^{i\gamma - 1}dx\biggr| \leq C$$ by a classical calculation (see 6.12 of Chapter II in [@15]). This completes the proof of Proposition \[Pn3.1\] and our discussion of the properties of the Riemann-Liouville fractional integral.
Some estimates for the group and its associated Duhamel terms, in mixed norm spaces
===================================================================================
\[4\]
[This section begins by recalling the Airy function and its relationship to the linearized KdV equation. Next, we prove estimates on the three terms arising in the Duhamel representation of solutions of the linearization of [(\[1.2\])]{}. In particular, we establish bounds for the linear solution [*group*]{}, the [*Duhamel forcing term*]{} containing the function $g$ and the [*inhomogeneous Duhamel term*]{}.]{}
The Airy function and KdV
-------------------------
\[Df4.1\] Define the Airy function $A$ by the property $$\hat{A}(\xi) = e^{i\xi^3}.$$ Similary, define $A_\alpha$ by $$\hat{A}_\alpha(\xi) = |\xi|^\alpha e^{i\xi^3}.$$
\[Pn4.1\] The Airy function $A$ is bounded and continuous on $\mathbb R$. The value $A(0) = C_A \neq 0$.
Lemma 2.7 in [@12] shows that $A_\alpha$ is bounded for $0 \leq \alpha \leq \frac{1}{2}$. This proves that $A$ is bounded, and Sobolev inequalities imply that $A$ is continuous. Since $$A(x) = \int e^{ix\xi}e^{i\xi^3}d\xi,$$ we know that $$C_A = A(0) = \lim_{\varepsilon \rightarrow 0} \int{\nolimits}_{|\xi| < 1/\varepsilon} e^{i\xi^3}d\xi = \lim_{\varepsilon \rightarrow 0} \int{\nolimits}_{|\eta| < \varepsilon^{-1/3}} e^{i\eta}\frac{1}{3}\eta^{-2/3}d\eta = c{\cal F}^{-1}(\eta^{-2/3})(1) \neq 0.$$
\[Rk4.1\] The solution of the initial value problem $$\begin{cases}
\partial_tw + \partial_x^3w = 0 & \\
w(x, 0) = \phi(x), & x \in {\mathbb R},
\end{cases}$$ is given as a convolution of the initial data and a time-rescaled Airy function. Indeed, the solution is $$\label{4.(0.5)}
w(x, t) = S(t)\phi(x) = \int e^{i(x\xi + t\xi^3)}\hat{\phi}(\xi)d\xi = \int t^{-1/3}A\left(\frac{x - x'}{t^{1/3}}\right)\phi(x')dx'.$$
Group estimates
---------------
\[Lm4.1\] The function $w$ defined above satisfies the following estimates: $$\begin{gathered}
\label{4.1}\sup_t {||w(-, t)||_{H^{s}(\mathbb R)}} \leq C{||\phi||_{H^{s}(\mathbb R)}}, \quad -\infty < s < +\infty, \\
\label{4.2}\sup_{\gamma \in {\mathbb R}} ||D_x^{i\gamma}D_x^{s + 1}w||_{L_x^\infty L_t^2} \leq C{||\phi||_{\dot{H}^{s}(\mathbb R)}}, \quad -\infty < s < +\infty, \\
\label{4.(2.5)}||D_x^s\partial_xw||_{L_x^\infty L_t^2} \leq C{||\phi||_{\dot{H}^{s}(\mathbb R)}}, \quad -\infty < s < +\infty, \\
\label{4.3}||w||_{L_x^\infty L_T^2} \leq C_T{||\phi||_{H^{-1}(\mathbb R)}} \\
\intertext{and}
\label{4.4}||w||_{L_x^\infty\dot{H}^{(s + 1)/3}({\mathbb R}_t)} \leq C{||\phi||_{\dot{H}^{s}(\mathbb R)}}, \quad -\infty < s < +\infty.\end{gathered}$$ If $\Psi \in C_0^\infty({\mathbb R})$, then $$\label{4.(4.5)}
||\Psi(t)w(x, t)||_{C((-\infty, +\infty); H^{(s + 1)/3}({\mathbb R}_t))} \leq C{||\phi||_{H^{s}(\mathbb R)}}, \quad -1 \leq s \leq 1$$ (here $C$ depends on $\Psi$ and its support). If $1 \geq s > 1/2$, then $w(0, -)$ is continuous, and $w(0, 0) = \phi(0)$.
Also $$\label{4.5}
\sup_{\gamma \in {\mathbb R}}\, e^{-C|\gamma|}||D_x^{i\gamma}D_x^{s - 1/4}w||_{L_x^4L_t^\infty} \leq C{||\phi||_{\dot{H}^{s}(\mathbb R)}}, \quad -\infty < s < +\infty,$$ $$\label{4.(5.25)}
||D_x^sw||_{L_x^5L_t^{10}} \leq C||D_x^s\phi||_{L^2({\mathbb R})},$$ [$$\label{4.(5.5)}
||w||_{L_x^2L_T^\infty} \leq C{||\phi||_{H^{s}(\mathbb R)}}, \quad s > 3/4,\ \ T < 1$$ and $$\label{4.(5.75)}
||\partial_xw||_{L_t^4L_x^\infty} \leq C{||\phi||_{H^{3/4}(\mathbb R)}}.$$]{}
[(\[4.1\])]{} follows from the group property of $S$. [(\[4.2\])]{} follows from Theorem 3.5(i) in [@10], and its proof. To establish [(\[4.3\])]{}, write $\phi = \phi_1 + \phi_2$, where $\operatorname{supp}\hat{\phi}_1 \subseteq \{\xi : |\xi| \leq 1\}$. Note that ${||\phi_2||_{\dot{H}^{-1}(\mathbb R)}} \leq {||\phi||_{H^{-1}(\mathbb R)}}$, and hence the estimate for $\phi_2$ follows from [(\[4.2\])]{}. For the other term, we have $$\begin{gathered}
||S(t)\phi_1||_{L_x^\infty L_T^2} \leq C\bigl\{||S(t)\phi_1||_{L_x^2L_T^2} + ||\partial_xS(t)\phi_1||_{L_x^2L_T^2}\bigr\} \\
\leq CT^{1/2}||\phi_1||_{L^2} + CT^{1/2}||\partial_x\phi_1||_{L^2} \leq CT^{1/2}{||\phi||_{H^{-1}}}.\end{gathered}$$ To establish [(\[4.4\])]{}, note that $$w(x, t) = \int e^{ix\xi}e^{it\xi^3}\hat{\phi}(\xi)d\xi = \frac{1}{3}{\!}\int e^{ix\eta^{1/3}}e^{it\eta}\hat{\phi}(\eta^{1/3})\frac{d\eta}{\eta^{2/3}},$$ so that, for a fixed $x$, $${||w(x, -)||_{\dot{H}^{(s + 1)/3}({\mathbb R}_t)}}^2 = \frac{1}{9}{\!}\int |\eta|^{2(s + 1)/3}|\hat{\phi}(\eta^{1/3})|^2\frac{d\eta}{\eta^{4/3}} = \frac{1}{3}{||\phi||_{H^{s}}}^2.$$ Next, note that the decomposition $\phi = \phi_1 + \phi_2$, as above, corresponding to $w = w_1 + w_2$, together with the previous estimate, yields $||D_t^{(s + 1)/3}w_2(x, -)||_{L^2} \leq C{||\phi||_{H^{s}}}$. Moreover, ${||\phi_1||_{H^{-1}}} \leq {||\phi||_{H^{s}}}$, and hence $||w_1(x, -)||_{L_T^2} \leq C{||\phi||_{H^{s}}}$. Also, $\partial_tw_1(x, t) = -S(t)\partial_x^3\phi_1$ and ${||\partial_x^3\phi_1||_{H^{-1}}} \leq C{||\phi||_{H^{s}}}$, so that ${||\Psi w_1(x, -)||_{H^{1}_{t}}} \leq C{||\phi||_{H^{s}}}$ and hence ${||\Psi w_1(x, -)||_{H^{(s + 1)/3}_{t}}} \leq C{||\phi||_{H^{s}}}$. Next, if we use the Leibniz rule (Theorem A.12 in [@10]) and the bound $|D^\alpha\Psi| \leq \int |\xi|^\alpha|\hat{\Psi}(\xi)|d\xi$, we see that, for a fixed $x$, we have $$\begin{gathered}
\bigl|\bigl|D_t^{(s + 1)/3}\bigl(\Psi(t)w_2(x, t)\bigr) - \Psi(t)D_t^{(s + 1)/3}w_2(x, t) - D_t^{(s + 1)/3}\Psi(t)w_2(x, t)\bigr|\bigr|_{L_t^2} \\
\leq C||\Psi||_\infty||D_t^{(s + 1)/3}w_2(x, t)||_{L^2}.\end{gathered}$$ Using the bound above for $D_t^{(s + 1)/3}w_2$ and these bounds, we see that $$\bigl|\bigl|D_t^{(s + 1)/3}\bigl(\Psi(t)w_2(x, t)\bigr)\bigr|\bigr|_{L^2} \leq C{||\phi||_{H^{s}}}$$ and $||\Psi(t)w_2(x, t)||_{L^2} \leq C{||\phi||_{H^{s}}}$. To obtain the continuity into $H^{(s + 1)/3}$, note that, for $\phi \in H^\infty$, all $t$ and $x$ derivatives of $w$ are continuous; this, together with the previous bound, gives the desired continuity. The fact that, for $s > 1/2$, $w(0, -)$ is continuous follows from Sobolev embedding and the fact that $(s + 1)/3> 1/2$. That $w(0, 0) = \phi(0)$ for $s > 1/2$ is an elementary computation. [(\[4.5\])]{} is (3.9) (and its proof) and (3.11)[; [(\[4.(5.5)\])]{} is (3.38); and [(\[4.(5.75)\])]{} follows from the proof of (3.36), where the latter references are to]{} [@10].
\[Rk4.(1.5)\] The proof of [(\[4.(4.5)\])]{} given above uses properties of the cut-off function $\Psi$. We quantify the dependence of the constant $C$ on $\Psi$. The proof given above relies on the boundedness of $||\Psi||_{L^\infty}$ and $||D_t^{(s + 1)/3}\Psi||_{L^3}$. The $L^3$ norm emerges from the last term in the Leibniz rule using the fact that $w_2 \in L^6$ from fractional integration. By interpolation, $$||D_t^{(s + 1)/3}\Psi||_{L^3} \leq \sup_\gamma ||D^{i\gamma}D^{(s + 1)/3 + 1/6}\Psi||_{L^2}\cdot\sup_\gamma ||D^{i\gamma}\Psi||_{L^\infty}.$$ Since $\frac{s + 1}{3} + \frac{1}{6} < 1$, Sobolev’s inequality shows that $$C \leq c\{||\Psi||_{L^2} + ||\Psi'||_{L^2}\}.$$
Duhamel forcing term estimates
------------------------------
We now turn our attention to corresponding Duhamel terms of the form $$\label{4.6}
\int_0^t S(t - t')\delta_0(x)g(t')dt' = w(x, t),$$ for suitable $g$.
\[Lm4.2\] For $h \in C_0^\infty({\mathbb R})$, define $$w(x, t) = \int_0^t S(t - t')\delta_0(x)h(t')dt' = \int_0^t A\biggl(\frac{x}{(t - t')^{1/3}}\biggr)\frac{1}{(t - t')^{1/3}}h(t')dt'.$$ Then $w(x, -)$ and $w(-, t)$ are continuous for each fixed $x$ and $t$. Moreover, $w$ solves $$\label{4.7(1)}
\partial_tw + \partial_x^3w = \delta_0(x)h(t)$$ in ${\cal S}'({\mathbb R}^2)$, $w(x, 0) = 0$ and $$w(0, t) = \frac{1}{C_A\Gamma(2/3)}{{\mathbb I}}_{2/3}(h)(t),$$ where $C_A$ is as defined in Proposition \[Pn4.1\] and ${{\mathbb I}}_{2/3}$ is as defined in Definition \[Df3.1\].
By Proposition \[Pn4.1\], $$|w(x, t)| \leq C{\!}\int_0^t \frac{1}{(t - t')^{1/3}}|h(t')|dt',$$ which shows that $w$ is well-defined and that $|w(x, 0)| = 0$. To check the continuity statements, recall from the proof of Proposition \[Pn4.1\] that $A_\alpha$ is bounded for $0 \leq \alpha \leq 1/2$, and hence that $A$ is Hölder continuous of order $1/2$. (See, for instance Proposition 7 of Chapter 5 in [@15].) From this and the formula defining $w$, the continuity statements follow easily. From them and the fact that $C_A \neq 0$, the formula for $w(0, t)$ follows. Finally, [(\[4.7(1)\])]{} follows from the fact that $$\partial_t\Biggl(\frac{1}{t^{1/3}}A\biggl(\frac{x}{t^{1/3}}\biggr)\Biggr) + \partial_x^3\Biggl(\frac{1}{t^{1/3}}A\biggl(\frac{x}{t^{1/3}}\biggr)\Biggr) = \delta_{(0, 0)}(x, t)$$ in ${\cal S}'({\mathbb R}^2)$.
\[Lm4.3\] Let $w$ be as in Lemma \[Lm4.2\], with $h \in C_0^\infty({\mathbb R}^+$R$ before -- should it have a $\^+$ now?
)$. Then the following estimates hold:
[([[.]{}.]{})]{}
\[4.7\]We have [$$\begin{aligned}
\sup_x {||w(x, -)||_{\dot{H}^{(s + 1)/3}({\mathbb R}_t)}} \leq C{||h||_{\dot{H}^{(s - 1)/3}(\mathbb R)}}, && -1 \leq s \leq 1, \\
\operatorname*{ess\,sup}_x\, \sup_{\gamma \in {\mathbb R}}\, e^{-C|\gamma|}||D_x^{i\gamma}D_x^{s + 1}w(x, -)||_{L^2({\mathbb R}_t)} \leq C{||h||_{\dot{H}^{(s - 1)/3}(\mathbb R)}}, && -1 \leq s \leq 1, \\
\intertext{and}
\operatorname*{ess\,sup}_x ||D_x^s\partial_xw(x, -)||_{L^2({\mathbb R}_t)} \leq C{||h||_{\dot{H}^{(s - 1)/3}(\mathbb R)}}, && -1 \leq s < 1.\end{aligned}$$]{}
\[4.8\]Suppose that $\operatorname{supp}h \subseteq (0, 1)$ and $\Psi \in C_0^\infty\bigl((-2, 2)\bigr)$ is a cut-off function in $t$. Then $$\begin{aligned}
\Psi w(x, -) \in C\bigl((-\infty, +\infty); H^{(s + 1)/3}_0({\mathbb R}_t^+)\bigr), && -1 \leq s \leq 1, \\
\Psi w(x, -) \in C\bigl((-\infty, +\infty); H^{(s + 1)/3}({\mathbb R}_t)\bigr), && -1 \leq s \leq 1, \\
\sup_x {||\Psi w(x, -)||_{H^{(s + 1)/3}_{0}({\mathbb R}_t^+)}} \leq C{||h||_{H^{(s - 1)/3}_{0}({\mathbb R}^+)}} && \\
\intertext{and}
\sup_x {||\Psi w(x, -)||_{H^{(s + 1)/3}(\mathbb R)}} \leq C{||h||_{H^{(s - 1)/3}({\mathbb R}^+)}}. &&\end{aligned}$$
\[4.9\]Suppose that $h$, $\Psi$ are as in [(\[4.8\])]{}, and that $-1/2 < s \leq 1$. Then $$\sup_t {||\Psi(t)w(-, t)||_{\dot{H}^{s}({\mathbb R}_x)}} \leq C{||h||_{\dot{H}^{(s - 1)/3}}}$$ and $\Psi(t)w(-, t) \in C\bigl((-\infty, +\infty); H^s({\mathbb R}_x)\bigr)$, with $$\sup_t {||\Psi(t)w(-, t)||_{H^{s}({\mathbb R}_x)}} \leq C{||h||_{H^{(s - 1)/3}_{0}({\mathbb R}^+)}}.$$
\[4.10\] The operation $h \mapsto \Psi(t)w(x, t)$ has a natural extension (defined by density) to $H^{(s - 1)/3}_0({\mathbb R}^+) \cap \{h : \operatorname{supp}h \subseteq [0, 1]\}$. If $s > 1/2$, then $w(x, 0) = 0$ and $$\Psi(t)w(0, t) = \frac{\Psi(t)}{C_A\Gamma(2/3)}{{\mathbb I}}_{2/3}(h)(t)$$ pointwise. For other values of $s$ this is valid in the sense of [(\[4.8\])]{} and [(\[4.9\])]{}.
\[4.11\] We have $$\begin{gathered}
\sup_\gamma e^{-C|\gamma|}||D_x^{i\gamma}D_x^{3/4}w||_{L_x^4L_t^\infty} \leq C||h||_{L_t^2} \\
\sup_\gamma\, e^{-C|\gamma|}||D_x^{i\gamma}w||_{L_x^4L_t^\infty} \leq C{||h||_{\dot{H}^{-1/4}_{t}}} \\
||D_t^{1/4}w||_{L_x^4L_t^\infty} \leq C||h||_{L_t^2}.\end{gathered}$$ For $1/4 \leq s \leq 1$, $$\sup_\gamma\, e^{-C|\gamma|}||D_x^{s - 1/4}D_x^{i\gamma}w||_{L_x^4L_t^\infty} \leq C{||h||_{\dot{H}^{(s - 1)/3}_{t}}}.$$
\[4.12\] For $0 \leq s \leq 1$, $$||D_x^sw||_{L_x^5L_t^{10}} \leq C{||h||_{\dot{H}^{(s - 1)/3}}}.$$
We start out with [(\[4.7\])]{}. We prove the first statement by interpolation between the cases $s = 1$ and $s = -1$. Let $I$ be an interval. We claim that $$\label{4.14}
\biggl|\biggl|\int_0^t S(t - t')\biggl(\frac{\chi_I}{|I|}\biggr)h(t')dt'\biggr|\biggr|_{L_x^\infty\dot{H}^{2/3}_t} \leq C||h||_{L^2}$$ with $C$ independent of $I$. In fact, [(\[4.4\])]{} shows that $||D_t^{1/3}S(t)\phi||_{L_x^\infty L_t^2} \leq C||\phi||_{L^2}$. From this estimate, duality gives $$\Bigl|\Bigl|\int_{-\infty}^{+\infty} S(-t)D_t^{1/3}g(-, t)dt\Bigr|\Bigr|_{L_x^2} \leq C||g||_{L_x^1L_t^2}.$$ In turn, arguing as on page 554 of [@10], this implies that $$\Bigl|\Bigl|D_t^{1/3}\int_{-\infty}^{+\infty} S(t - t')D_{t'}^{1/3}g(-, t')dt'\Bigr|\Bigr|_{L_x^\infty L_t^2} \leq C||g||_{L_x^1L_t^2},$$ which is the same as $$\label{4.15}
\Bigl|\Bigl|D_t^{2/3}\int_{-\infty}^{+\infty} S(t - t')g(-, t')dt'\Bigr|\Bigr|_{L_x^\infty L_t^2} \leq C||g||_{L_x^1L_t^2}.$$ Finally, using Lemma 3.4 in [@10], we have $$\begin{gathered}
\label{4.16}
\lim_{\varepsilon \rightarrow 0} \int{\!\!\!}\int{\nolimits}_{\varepsilon < |\xi^3 - \tau| < 1/\varepsilon} e^{i(x\xi + t\tau)}\frac{1}{\xi^3 - \tau}\hat{g}(\xi, \tau)d\xi\,d\tau = 2{\!}\int_0^t S(t - t')g(-, t')dt' \\
- \int_{-\infty}^{+\infty} S(t - t')g(-, t')dt' + 2{\!}\int_{-\infty}^0 S(t - t')g(-, t')dt'.\end{gathered}$$ Let $$\label{4.17}
A(g) = \lim_{\varepsilon \rightarrow 0} \int{\!\!\!}\int_{\varepsilon < |\xi^3 - \tau| < 1/\varepsilon} e^{i(x\xi + t\tau)}\frac{1}{\xi^3 - \tau}\hat{g}(\xi, \tau)d\xi\,d\tau.$$ Then (3.26) in [@10] gives $$||D_t^{2/3}A(g)||_{L_x^\infty L_t^2} \leq C||g||_{L_x^1L_t^2},$$ whcih, combined with [(\[4.15\])]{} and [(\[4.16\])]{}, yields [(\[4.14\])]{}. Note that [(\[4.15\])]{} and [(\[4.14\])]{} also give $$\label{4.18}
\Bigl|\Bigl|D_t^{2/3}\int_t^\infty S(t - t')g(-, t')dt'\Bigr|\Bigr|_{L_x^\infty L_t^2} \leq C||g||_{L_x^1L_t^2}.$$ Now, to establish the first estimate in [(\[4.7\])]{} for $s = 1$, fix $x_0 \in {\mathbb R}$ and let $\phi \in C_0^\infty({\mathbb R}) \cap \dot{H}^{-2/3}({\mathbb R}_t)$. We use duality to obtain $$\begin{gathered}
\label{4.19}
\int_{-\infty}^{+\infty} \biggl(\int_0^t A\biggl(\frac{x_0}{(t - t')^{1/3}}\biggr)\frac{h(t')}{(t - t')^{1/3}}dt'\biggr)\phi(t)dt \\
= \int_{-\infty}^{+\infty} h(t')\biggl(\int_{t'}^{+\infty} \phi(t)A\biggl(\frac{x_0}{(t - t')^{1/3}}\biggr)\frac{1}{(t - t')^{1/3}}dt\biggr)dt'.\end{gathered}$$ The boundedness and continuity of $A$, together with the dominated convergence theorem, show that this equals $$\begin{gathered}
\label{4.20}
\int_{-\infty}^{+\infty} h(t')\lim_{|I| \rightarrow 0} \int_{t'}^{+\infty} \phi(t)S(t - t')\biggl(\frac{1}{|I|}\chi_{I - x_0}\biggr)(x_0)dt\,dt' \\
= \lim_{|I| \rightarrow 0} \int_{-\infty}^{+\infty} h(t')\!\!\int_{t'}^{+\infty} \phi(t)S(t - t')\biggl(\frac{1}{|I|}\chi_{I - x_0}\biggr)(x_0)dt\,dt'.\end{gathered}$$ Changing the order of integration and applying [(\[4.14\])]{} establishes the first estimate in [(\[4.7\])]{} for $s = 1$.
For the case $s = -1$, similar arguments reduce matters to proving that $$\label{4.21}
\biggl|\biggl|\int_0^t S(t - t')\biggl(\frac{1}{|I|}\chi_I\biggr)(x)h(t')dt'\biggr|\biggr|_{L_x^\infty L_t^2} \leq C{||h||_{\dot{H}^{-2/3}({\mathbb R}_t)}}.$$ To do this, we again proceed by duality to see that we need to show that $$\label{4.22}
\biggl|\biggl|D_{t'}^{2/3}{\!\!}\int_{t'}^\infty S(t - t')\biggl(\frac{1}{|I|}\chi_I\biggr)(x)f(t)dt\biggr|\biggr|_{L_x^\infty L_{t'}^2} \leq C||f||_{L_t^2}$$ for $f \in C_0^\infty({\mathbb R})$. This follows from [(\[4.18\])]{}. Thus, interpolation now establishes the first estimate in [(\[4.7\])]{}.
For the second estimate, note that, even though $D_x^{s + 1}A$ need not be continuous when $s > -1/2$, since we are interested in the $\operatorname*{ess\,sup}$ over $x$, a duality and limit argument similar to the one given above reduces matters to the estimate $$\label{4.23}
\sup_{\gamma \in {\mathbb R}} e^{-C|\gamma|}\biggl|\biggl|D_x^{i\gamma}D_x^{s + 1}{\!\!}\int_0^t S(t - t')\biggl(\frac{\chi_I}{|I|}\biggr)(x)h(t')dt'\biggr|\biggr|_{L_x^\infty L_t^2} \leq C{||h||_{\dot{H}^{(s - 1)/3}({\mathbb R}_t)}}.$$ In order to show [(\[4.23\])]{}, we proceed as in the proof of [(\[4.14\])]{}. We first note that $$||D_x^{i\gamma/2}D_x^{(s + 1)/2}D_t^{(1 - s)/6}S(t)\phi||_{L_x^\infty L_t^2} \leq C||\phi||_{L^2}.$$ In fact, $$\begin{aligned}
D_x^{i\gamma/2}D_x^{(s + 1)/2}D_t^{(1 - s)/6}S(t)\phi & = D_t^{(1 - s)/6}{\!\!}\int e^{ix\xi}e^{it\xi^3}|\xi|^{i\gamma/2}|\xi|^{(s + 1)/2}\hat{\phi}(\xi)d\xi \\
& = \frac{1}{3}D_t^{(1 - s)/6}{\!\!}\int e^{ix\eta^{1/3}}e^{it\eta}|\eta|^{i\gamma/6}|\eta|^{(s + 1)/6}\hat{\phi}(\eta^{1/3})\frac{d\eta}{\eta^{2/3}} \\
& = \frac{1}{3}{\!}\int e^{ix\eta^{1/3}}e^{it\eta}|\eta|^{i\gamma/6}|\eta|^{(s + 1)/6}|\eta|^{(1 - s)/6}\hat{\phi}(\eta^{1/3})\frac{d\eta}{\eta^{2/3}} \\
& = \frac{1}{3}{\!}\int e^{ix\eta^{1/3}}e^{it\eta}|\eta|^{i\gamma/6}|\eta|^{1/3}\hat{\phi}(\eta^{1/3})\frac{d\eta}{\eta^{2/3}},\end{aligned}$$ so that, by Plancherel, the $L^2$ norm in $t$, squared, equals $$\frac{1}{9}{\!}\int |\hat{\phi}(\eta^{1/3})|^2|\eta|^{2/3}\frac{d\eta}{\eta^{4/3}} = \frac{1}{3}{\!}\int |\phi|^2.$$ Once more, duality and the argument on page 554 of [@10] give $$\label{4.24}
\Bigl|\Bigl|D_x^{i\gamma}D_x^{s + 1}D_t^{(1 - s)/3}{\!\!}\int_{-\infty}^{+\infty} S(t - t')g(-, t')dt'\Bigr|\Bigr|_{L_x^\infty L_t^2} \leq C||g||_{L_x^1L_t^2}.$$ From [(\[4.24\])]{} and the fact that $\operatorname{supp}h \subseteq (0, \infty)$, we see that, in view of [(\[4.16\])]{}, [(\[4.23\])]{} will follow from $$\label{4.25}
||D_x^{i\gamma}D_x^{s + 1}D_t^{(1 - s)/3}A(g)||_{L_x^\infty L_t^2} \leq Ce^{C|\gamma|}||g||_{L_x^1L_t^2}.$$ If one follows then the proofs of Theorem 3.5, (3.8) and (3.26) in [@10], we see that this reduces to showing that $$\label{4.26}
\biggl|\int e^{ix\xi}\frac{|\xi|^{i\gamma}|\xi|^{s + 1}}{\lambda - \xi^3}d\xi\biggr|\!\cdot\!|\lambda|^{(1 - s)/3} \leq Ce^{C|\gamma|},$$ where $C$ is independent of $x$, $\lambda$. Scaling reduces matters to showing that $$\label{4.27}
\biggl|\int e^{ix\xi}\frac{|\xi|^{i\gamma}|\xi|^{s + 1}}{\xi^3 - 1}d\xi\biggr| \leq Ce^{C|\gamma|}.$$ To establish [(\[4.27\])]{}, we write $1 = \phi_1(\xi) + \phi_2(\xi) + \phi_3(\xi)$, where each $\phi_i$ is even and smooth and $\operatorname{supp}\phi_1 \subseteq \{\xi : |\xi| < \frac{1}{2}\}$, $\operatorname{supp}\phi_2 \subseteq \{\xi : \frac{1}{4} < |\xi| < \frac{5}{4}\}$ and $\operatorname{supp}\phi_3 \subseteq \{\xi : |\xi| \geq 1 + \frac{1}{8}\}$. The piece corresponding to $\phi_1$ is the Fourier transform of a bounded function with compact support, and hence is bounded. For the second piece, we write $\xi^3 - 1 = (\xi - 1)(\xi^2 + \xi + 1)$ and note that $\xi^2 + \xi + 1$ has no real zeroes. Thus, the piece corresponding to $\phi_2$ corresponds to $$\int e^{ix\xi}\frac{1}{\xi - 1}\theta(\xi)d\xi,$$ where $\theta \in C_0^\infty\bigl(\{\xi : \frac{1}{4} < |\xi| < \frac{5}{4}\}\bigr)$. The Fourier transform of $\frac{1}{\xi - 1}$ is $e^{ix}\operatorname{sgn}x$, so this last integral equals $$\int e^{iy}(\operatorname{sgn}y)\hat{\theta}(x - y)dy,$$ which is bounded. Finally, for the third piece we have $$\begin{gathered}
\int e^{ix\xi}\frac{|\xi|^{i\gamma}|\xi|^{s + 1}}{\xi^3 - 1}\phi_3(\xi)d\xi \\
= \int e^{ix\xi}|\xi|^{i\gamma}|\xi|^{s + 1}\biggl\{\frac{1}{\xi^3 - 1} - \frac{1}{\xi^3}\biggr\}\phi_3(\xi)d\xi + \int e^{ix\xi}\frac{|\xi|^{i\gamma}|\xi|^{s + 1}}{\xi^3}\phi_3(\xi)d\xi\end{gathered}$$ Since $\bigl|\frac{1}{\xi^3 - 1} - \frac{1}{\xi^3}\bigr| = \bigl|\frac{1}{\xi^3(\xi^3 - 1)}\bigr| \leq \frac{C}{|\xi|^6}$ on the support of $\phi_3$, the first integral is clearly bounded. So is the second one, as long as $s < 1$. When $s = 1$, we are left with $\int e^{ix\xi}\frac{|\xi|^{i\gamma}}{\xi}\phi_3(\xi)d\xi$, which is bounded by $C$C$ as is to come?
e^{C|\gamma|}$.
Finally, note that the third inequality in [(\[4.7\])]{} is proved in a similar manner. The restriction to $s < 1$ comes from the fact that, when $\gamma = 0$, the integral $\int e^{ix\xi}\phi_3(\xi)\frac{d\xi}{|\xi|}$ is not bounded.
To establish [(\[4.8\])]{}, note that, since $\operatorname{supp}h \subseteq (0, \infty)$, [(\[4.16\])]{} implies that $w = w_1 + w_2$, where $$w_1(x, t) = \frac{1}{2}A(\delta_0 \otimes h)(x, t)$$ and $$w_2(x, t) = \frac{1}{2}\int_{-\infty}^{+\infty} S(t - t')(\delta_0)(x)h(t')dt'.$$ Note also that, in obtaining the bounds in [(\[4.8\])]{}, since $(s - 1)/3\leq 0 \leq (s + 1)/3$, for each fixed $x$, the norms on both sides of the inequalities are complex interpolation scales (by Corollary \[Co2.1\] and Proposition \[Pn2.2\]). Thus, it is enough to establish the bounds for $s \neq 1/2$. Next, note that, since, by Lemma \[Lm4.2\], $w(x, 0) = 0$, Proposition \[Pn2.6\] shows that, for $s \neq 1/2$, we have $${||\Psi w(x, -)||_{H^{(s + 1)/3}_{0}({\mathbb R}_t^+)}} \approx {||\Psi w(x, -)||_{H^{(s + 1)/3}({\mathbb R}_t^+)}} \leq {||\Psi w(x, -)||_{H^{(s + 1)/3}(\mathbb R)}}.$$ Thus, to establish the estimates in [(\[4.8\])]{}, it suffices to show that $$\label{4.28}
{||\Psi w_i(x, -)||_{H^{(s + 1)/3}(\mathbb R)}} \leq C{||h||_{H^{(s - 1)/3}(\mathbb R)}}, \quad i = 1, 2.$$ In order to establish [(\[4.28\])]{}, write $h = h_1 + h_2$, where $h_i \in {\cal S}({\mathbb R})$ and $\operatorname{supp}\hat{h}_1 \subseteq \{\tau : |\tau| < 2\}$ and $\operatorname{supp}\hat{h}_2 \subseteq \{\tau : |\tau| > 1\}$. We first estimate $$\begin{gathered}
\Psi(t)A(h_1)(x, t) = \Psi(t){\!}\int{\!\!\!}\int e^{ix\xi}e^{it\tau}\frac{\hat{h}_1(\tau)}{\tau - \xi^3}d\tau\,d\xi \\
= \Psi(t){\!}\int e^{it\tau}\hat{h}_1(\tau)\biggl(\int e^{ix\xi}\frac{d\xi}{\tau - \xi^3}\biggr)d\tau = \Psi(t){\!}\int e^{it\tau}\frac{\hat{h}_1(\tau)}{\tau^{2/3}}K(x, \tau)d\tau,\end{gathered}$$ where $|K(x, \tau)| \leq C$. (See the proof of (3.26) in [@10].) Next, we claim that $|\hat{h}(\tau)| \leq C{||h||_{H^{(s - 1)/3}}}$ for $|\tau| \leq 2$. In fact, since $\operatorname{supp}h \subseteq (0, 1)$, we may choose $\mu \in C_0^\infty$ s.t. $\mu \equiv 1$ on $(0, 1)$ and $h = \mu h$. From this we compute that $$\hat{h}(\tau) = \int \hat{\mu}(\tau - \lambda)\hat{h}(\lambda)d\lambda = \int \hat{\mu}(\tau - \lambda)(1 + |\lambda|)^{(1 - s)/3}\frac{\hat{h}(\lambda)}{(1 + |\lambda|)^{(1 - s)/3}}d\lambda,$$ so that $$|\hat{h}(\tau)| \leq \Bigl(\int |\hat{\mu}(\tau - \lambda)|^2(1 + |\lambda|)^{2(1 - s)/3}d\lambda\Bigr)^{1/2}{||h||_{H^{(s - 1)/3}}}.$$ Since $\hat{\mu} \in {\cal S}$ and $|\tau| \leq 2$, the claim follows; but then $|\Psi(t)A(h_1)(x, t)| \leq C\Psi(t){||h||_{H^{(1 - s)/3}}}$, and hence $\Psi A(h_1)(x, -) \in L^2({\mathbb R}_t)$, uniformly in $x$. A similar argument gives us that ${\frac{\partial }{\partial t}}\bigl(\Psi A(h_1)(x, -)\bigr) \in L^2({\mathbb R}_t)$ uniformly in $x$, and hence we have the estimate $${||\Psi A(h_1)(x, -)||_{H^{(1 + s)/3}}} \leq C{||h||_{H^{(1 - s)/3}}}.$$ For the corresponding term in $w_2$, we have $$\begin{gathered}
\Psi(t){\!}\int{\!\!\!}\int e^{ix\xi}e^{i(t - t')\xi^3}h_1(t')dt'\,d\xi = \Psi(t){\!}\int{\!\!\!}\int e^{ix\xi}e^{it\tau}\hat{h}_1(\tau)\delta_0(\tau + \xi^3)d\tau\,d\xi \\
= \Psi(t){\!}\int e^{it\tau}\hat{h}_1(\tau)\Bigl(\int e^{ix\xi}\delta_0(\tau + \xi^3)d\xi\Bigr)d\tau \\
= \Psi(t){\!}\int e^{it\tau}\hat{h}_1(\tau)\biggl(\int e^{ix\eta^{1/3}}\delta_0(\tau + \eta)\frac{d\eta}{\eta^{2/3}}\biggr)d\tau = \Psi(t){\!}\int e^{it\tau}\frac{\hat{h}_1(\tau)}{\tau^{2/3}}e^{-ix\tau^{1/3}}d\tau,\end{gathered}$$ which is handled in the same way.
Finally, we turn to the terms corresponding to $h_2$. Note that ${||h_2||_{\dot{H}^{(s - 1)/3}}} \leq {||h||_{H^{(s - 1)/3}}}$, and that ${||h_2||_{\dot{H}^{-1}}} \leq {||h||_{H^{(s - 1)/3}}}$. We then use the proof of the first estimate in [(\[4.7\])]{} to obtain the bounds $$\begin{gathered}
||D_t^{(s + 1)/3}A(h_2)(x, -)||_{L_t^2} \leq C{||h||_{H^{(s - 1)/3}}}, \\
\Bigl|\Bigl|D_t^{(s + 1)/3}{\!\!}\int_{-\infty}^{+\infty} S(t - t')(x)h_2(t')dt'\Bigr|\Bigr|_{L_t^2} \leq C{||h||_{H^{(s - 1)/3}}}, \\
||A(h_2)(x, -)||_{L_t^2} \leq C{||h||_{H^{(s - 1)/3}}}\\
\intertext{and}
\Bigl|\Bigl|\int_{-\infty}^{+\infty} S(t - t')(x)h_2(t')dt'\Bigr|\Bigr|_{L_t^2} \leq C{||h||_{H^{(s - 1)/3}}}.\end{gathered}$$ These bounds, combined with the Leibniz rule and the bound $|D^\alpha\Psi| \leq C$, give us [(\[4.28\])]{}. Finally, the continuity statement follows from Lemma \[Lm4.2\] and the estimates already proved.
We now turn to [(\[4.9\])]{}. In view of [(\[4.16\])]{}, we are again reduced to studying two terms. For the term corresponding to $$A(\delta_0 \otimes h)(x, t) = \int{\!\!\!}\int e^{ix\xi}e^{it\lambda}\frac{\hat{h}(\lambda)}{\lambda - \xi^3}d\xi\,d\lambda,$$ we have $$D_x^sA(\delta_0 \otimes h)(x, t) = \int e^{ix\xi}\biggl(|\xi|^s{\!}\int e^{it\lambda}\frac{\hat{h}(\lambda)}{\lambda - \xi^3}d\lambda\biggr)d\xi.$$ By Plancherel, we are reduced to bounding (with $\cal H$ the Hilbert transform) $$\begin{gathered}
\biggl|\biggl||\xi|^s\int e^{it\lambda}\frac{\hat{h}(\lambda)}{\lambda - \xi^3}d\lambda\biggr|\biggr|_{L_\xi^2} = \biggl|\biggl||\xi|^s{\cal H}(e^{it-}\hat{h})(\xi^3)\biggr|\biggr|_{L_\xi^2} \\
= \biggl(\int |\eta|^{2s/3}|{\cal H}(e^{it-}\hat{h})|^2(\eta)\frac{d\eta}{\eta^{2/3}}\biggr)^{\!1/2}.\end{gathered}$$ Now, since $-1 < 2s/3 - 2/3$ (because $s > -1/2$) and $2s/3 - 2/3 \leq 0$ (because $s \leq 1$), the weight $|\eta|^{2s/3 - 2/3}$ is an $A_2$ weight (see, for instance, Chapter V of [@16]), and hence the Hilbert transform is bounded in $L^2$ with this weight. Thus we get that the last expression is bounded by $$C\biggl(\int |\eta|^{2s/3}|e^{it\eta}\hat{h}(\eta)|^2\frac{d\eta}{\eta^{2/3}}\biggr)^{1/2} = {||h||_{\dot{H}^{(s - 1)/3}}}.$$ To estimate the term $D_x^s\int_{-\infty}^{+\infty} S(t - t')(\delta_0)(x)h(t')dt'$, we are reduced by the group property to estimating $$\label{4.29}
\Bigl|\Bigl|D_x^s{\!}\int_{-\infty}^{+\infty} S(-t')(\delta_0)(x)h(t')dt'\Bigr|\Bigr|_{L^2} \leq C{||h||_{\dot{H}^{(s - 1)/3}}}.$$ We will establish [(\[4.29\])]{} by duality. Let $f \in C_0^\infty({\mathbb R}) \cap L^2({\mathbb R})$, and consider $$\int D_x^s{\!}\int_{-\infty}^{+\infty} S(-t')(\delta_0)(x)h(t')dt'\,\overline{f(x)}dx = \int_{-\infty}^{+\infty} \int \delta_0(x)h(t')\overline{D_x^sS(t')f(x)}dx\,dt'.$$ Note that $D_x^sS(t')f$ is a continuous function of $x$, since $D_x^sf \in H^\ell$ for all $\ell \geq 0$ (here we use $-1/2 < s$). Hence, this expression equals $\int_{-\infty}^{+\infty} h(t')\overline{D_x^sS(t')f(x)}\bigr|_{x = 0}dt'$. We thus need to show that $$\label{4.30}
||D_x^sS(t)f||_{L_x^\infty\dot{H}^{(1 - s)/3}({\mathbb R}_t)} \leq C||f||_{L^2},$$ but this is contained in the inequality after [(\[4.23\])]{}.
To establish the second inequality in [(\[4.9\])]{}, note first that, since $s > -1/2$, $-1/2 < (s - 1)/3 \leq 0$, and hence, since $\operatorname{supp}h \subseteq (0, 1)$, Remark \[Rk2.4\] and Proposition \[Pn2.7\] show that ${||h||_{\dot{H}^{\alpha}_{0}({\mathbb R}^+)}} \simeq {||h||_{H^{\alpha}({\mathbb R}^+)}} \simeq {||h||_{H^{\alpha}_{0}({\mathbb R}^+)}}$, where $\alpha = (s - 1)/3$. Next, we distinguish two cases: $-1/2 < s \leq 0$, and $0 \leq s \leq 1$. In the second case, by the first inequality, $$||D_x^sw(-, t)||_{L^2} \leq C{||h||_{\dot{H}^{(s - 1)/3}}} \simeq C{||h||_{H^{(s - 1)/3}_{0}({\mathbb R}^+)}}.$$ Also $$||w(-, t)||_{L^2} \leq C{||h||_{\dot{H}^{-1/3}}} \simeq C{||h||_{H^{-1/3}({\mathbb R}^+)}} \leq C{||h||_{H^{(s - 1)/3}({\mathbb R}^+)}} \leq C{||h||_{H^{(s - 1)/3}_{0}({\mathbb R}^+)}},$$ which gives the estimate. In the first case, we simply note that $${||w(-, t)||_{H^{s}}} \leq {||w(-, t)||_{\dot{H}^{s}}} \leq C{||h||_{\dot{H}^{(s - 1)/3}}} \simeq C{||h||_{H^{(s - 1)/3}_{0}}}.$$ Finally, the continutity statement follows from the estimate, together with Lemma \[Lm4.2\].
Next, note that [(\[4.10\])]{} is a direct consequence of [(\[4.8\])]{}, [(\[4.9\])]{} and Lemma \[Lm4.2\].
We turn to [(\[4.11\])]{}. The first estimate there is constained in Proposition 3.5(3) of [@7] and also in Proposition 2.3 of [@13]. We will present an alternate proof, using the method in [@5']. The first part of the proof consists in establishing the inequality $$\label{4.31}
\Bigl|\Bigl|D_x^{i\gamma}D_x^{3/4}{\!\!}\int_{-\infty}^{+\infty} S(t - t')(\delta_0)(x)h(t')dt'\Bigr|\Bigr|_{L_x^4L_t^\infty} \leq C||h||_{L^2}.$$ To prove [(\[4.31\])]{}, we use the ‘$T^*T$ method’. Thus, testing against an $f$ in $L_x^{4/3}L_t^1$, we see that [(\[4.31\])]{} follows from $$\label{4.32}
\Bigl|\Bigl|D_x^{i\gamma}D_x^{3/4}{\!\!}\int_{-\infty}^{+\infty} S(t - t')f(x, t)dt\Bigr|\Bigr|_{L_x^\infty L_{t'}^2} \leq C||f||_{L_x^{4/3}L_t^1}.$$ Fix $x_0$, and compute the $L_{t'}^2$ norm squared; we obtain $$\label{4.33}
\int{\!\!\!}\int f(x, t)\Bigl(\int{\!\!\!}\int K_{x_0}(x, y, t, s)\overline{f(y, s)}dy\,ds\Bigr)dx\,dt,$$ where $$K_{x_0}(x, y, t, s) = \int D_x^{i\gamma}D_x^{3/4}A(x_0 - x, t - t')D_y^{-i\gamma}D_y^{3/4}A(y - x_0, t' - s)dt'$$ and $A(x, t) = \frac{1}{t^{1/3}}A(x/t^{1/3})$, where $A$ is as defined in Definition \[Df4.1\]. We now proceed to compute $K_{x_0}$, using the fact that $A(x, t) = \int e^{ix\xi}e^{it\xi^3}d\xi$. We obtain $$\begin{gathered}
K_{x_0}(x, y, t, s) \\
= \int{\!\!\!}\int e^{i(x_0 - x)\xi}e^{i(t - t')\xi^3}|\xi|^{i\gamma}|\xi|^{3/4}d\xi\!\cdot\!\!\int e^{i(y - x_0)\eta}e^{i(t' - s)\eta^3}|\eta|^{-i\gamma}|\eta|^{3/4}d\eta\,dt' \\
= \int{\!\!\!}\int e^{i(x_0 - x)\xi}e^{it\xi^3}e^{-is\eta^3}|\xi|^{i\gamma}|\xi|^{3/4}e^{i(y - x_0)\eta}|\eta|^{-i\gamma}|\eta|^{3/4}\!\cdot\!\!\int e^{it'(\eta^3 - \xi^3)}dt'\,d\xi\,d\eta \\
= \int{\!\!\!}\int e^{i(x_0 - x)\xi}e^{it\xi^3}e^{-is\eta^3}|\xi|^{i\gamma}|\xi|^{3/4}e^{i(y - x_0)\eta}|\eta|^{-i\gamma}|\eta|^{3/4}\delta_0(\eta^3 - \xi^3)d\eta\,d\xi.\end{gathered}$$ Making the change of variables $\eta^3 = \alpha$ and computing the integral over $\eta$, we obtain $$K_{x_0}(x, y, t, s) = \frac{1}{3}{\!}\int e^{-i(x - y)\xi}e^{i(t - s)\xi^3}\frac{|\xi|^{3/2}}{|\xi|^2}d\xi = \frac{1}{3}{\!}\int e^{-i(x - y)\xi}e^{i(t - s)\xi^3}\frac{d\xi}{|\xi|^{1/2}}.$$ A well-known bound (see, for instance, Lemma 3.6 in [@10]) now gives $$\label{4.33(2)}|K_{x_0}(x, y, t, s)| \leq \frac{C}{|x - y|^{1/2}},$$ with $C$ independent of $x_0$, $t$ and $s$, which, combined with [(\[4.33\])]{} and the theorem on fractional integration, yields [(\[4.32\])]{}. We will now use the proof in [@5'] to deduce our estimate from [(\[4.31\])]{}. This is a general procedure. First, it is easy to see that it suffices to prove $$||\sup_n w(x, t_n)||_{L_x^4} \leq C||h||_{L^2}$$ for any sequence $0 < t_1 < t_2 < \cdots < t_n < t_{n + 1} < \cdots$, with a bound which does not depend on the particular sequence. Next, note that it suffices to show that, for any measurable function $N : {\mathbb R} \rightarrow {\mathbb N}$ with finite range, the linear operator $T^{(N)}$ defined by $$T^{(N)}(h)(x) = w(x, t_{N(x)})$$ satisfies the estimate $$\label{4.35}
||T^{(N)}(h)||_{L_x^4} \leq C||h||_{L^2},$$ with $C$ independent of $N$ and $\{t_n\}$. Assume that $||h||_{L^2} = 1$, and define a probability measure $\lambda$ on $(0, \infty)$ by $\lambda(S) = \int_S |h|^2dt$. The main tool is Lemma 2.1 in [@5']: Define $Y_n = [0, t_n]$, so that $Y_n \subseteq Y_{n + 1}$. Then there exists a collection $\{B_j^m\}$ of measurable subsets of $(0, \infty)$, indexed by $m \in \{0, 1, 2, \cdots\}$ and $1 \leq j \leq 2^m$, satisfying:
1. For each $m$, $\{B_j^m : 1 \leq j \leq 2^m$m$?
\}$ is a partition of $(0, \infty)$ into disjoint measurable subsets.
2. Each $B_j^m$ is a union of precisely two sets $B_{j_1}^{m + 1}$, $B_{j_2}^{m + 1}$.
3. $\lambda(B_j^m) = 2^{-m}$ for all $m, j$.
4. Each set $Y_n$ may be decomposed, modulo $\lambda$-null sets, as an empty, finite or countably infinite union $$Y_n = \bigcup_{i \geq 1} B_{j_i}^{m_i},$$ with $m_1 < m_2 < \cdots$. This decomposition may not be unique, but we fix one such decomposition for each $n$.
Next, define $$T^*(h)(x) = \sup_t \Bigl|\int_0^\infty D_x^{i\gamma}D_x^{3/4}S(t - t')(\delta_0)(x)h(t')dt'\Bigr|,$$ and note that, for $h$ satisfying $\operatorname{supp}h \subseteq (0, \infty)$, [(\[4.31\])]{} implies that $||T^*(h)||_{L_x^4} \leq C||h||_{L^2}$. Also note that we can write $$T^{(N)}(h)(x) = \int_0^{t_{N(x)}} D_x^{i\gamma}D_x^{3/4}S(t_{N(x)} - t')(\delta_0)(x)h(t')dt'.$$ Define now $A_n = \{x : N(x) = n\}$. Let $$R = \{(m, j, n) : B_j^m\text{ is one of the sets in the decomposition of }Y_n\}$$ and $D_j^m = \bigcup\limits_{(m, j, n) \in R} A_n$. Note that, for a fixed $m$, the sets $D_j^m$ are disjoint. In fact, if $D_j^m \cap D_i^m \neq \varnothing$, then, since the $A_n$s are disjoint, there exists an $n$ such that $A_n$ intersects, and hence is contained in, both $D_j^m$ and $D_i^m$. Hence, since $(m, j, n), (m, i, n) \in R$, $B_j^m$ and $B_i^m$ both occur in the decomposition of $Y_n$ – but then, by construction, $i = j$. Define now $h_j^m = h\chi_{B_j^m}$, so that $h\chi_{Y_n} = \sum\limits_{(m, j, n) \in R} h_j^m$. We then have $$\begin{gathered}
\int_0^{t_{N(x)}} D_x^{i\gamma}D_x^{3/4}S(t_{N(x)} - t')(\delta_0)(x)h(t')dt' \\
= \sum_n \chi_{A_n}(x){\!}\int_0^{t_n} D_x^{i\gamma}D_x^{3/4}S(t_n - t')(\delta_0)(x)h(t')dt' \\
= \sum_n \chi_{A_n}(x){\!}\int_0^\infty D_x^{i\gamma}D_x^{3/4}S(t_n - t')(\delta_0)(x)\chi_{(0, t_n)}(t')h(t')dt' \\
= \sum_n \sum_{(m, j, n) \in R} \chi_{A_n}(x){\!}\int_0^\infty D_x^{i\gamma}D_x^{3/4}S(t_n - t')(\delta_0)(x)h_j^m(t')dt'\end{gathered}$$ – but then $$|T^{(N)}(h)(x)| \leq \sum_n \sum_{(m, j, n) \in R} \chi_{A_n}(x)T^*(h_j^m)(x) = \sum_m \sum_j \chi_{D_j^m}(x)T^*(h_j^m)(x).$$ Now fix $m$, and compute (recalling that the $D_j^m$ are disjoint) that $$\begin{gathered}
\Bigl|\Bigl|\sum_j \chi_{D_j^m}(x)T^*(h_j^m)\Bigr|\Bigr|_{L_x^4}^4 = \sum_j \int_{D_j^m} |T^*(h_j^m)|^4 \\
\leq C\sum_j \Bigl(\int |h_j^m|^2\Bigr)^2 = C\sum_j 2^{-m}{\!}\int_{B_j^m} |h|^2 \leq C2^{-m},\end{gathered}$$ since the $B_j^m$ are disjoint. Thus $$||T^{(N)}(h)||_{L^4} \leq \sum_m 2^{-m/4} \leq C,$$ as desired. Unfortunately, this elegant general method does not seem to apply to the proof of the other two inequalities in [(\[4.11\])]{}, due to the presence of $t$ (fractional) derivatives. We will therefore give a different type of proof. We use formula [(\[4.16\])]{} to reduce matters to the corresponding two estimates. The first one, for the second inequality in [(\[4.11\])]{}, is $$\label{4.36}
\Bigl|\Bigl|D_x^{i\gamma}{\!\!}\int_{-\infty}^{+\infty} S(t - t')(\delta_0)(x)h(t')dt'\Bigr|\Bigr|_{L_x^4L_t^\infty} \leq C{||h||_{\dot{H}^{-1/4}}}.$$ Since this is a convolution in the $t$ variable and $D_x^{i\gamma}S(t - t')(\delta_0)(x)\linebreak = D_t^{i\gamma/3}S(t - t')(\delta_0)(x)$, the $D_x^{i\gamma}$ can be moved to $h$, and, since the $\dot{H}^{-1/4}$ norm is not changed by the action of $D_t^{i\gamma/3}$, we can take $\gamma = 0$. Writing $h = D_t^{1/4}g$ for $g \in L^2$, we see that [(\[4.36\])]{} becomes $$\label{4.37}
\Bigl|\Bigl|D_t^{1/4}{\!\!}\int_{-\infty}^{+\infty} S(t - t')(\delta_0)(x)g(t')dt'\Bigr|\Bigr|_{L_x^4L_t^\infty} \leq C||g||_{L^2}.$$ Following the argument used in the proof of [(\[4.31\])]{}, matters are reduced to estimating the kernel $$H_{x_0}(x, y, t, s) = \int D_t^{1/4}A(x_0 - x, t - t')D_s^{1/4}A(y - x_0, t' - s)dt'.$$ Recall that $$A(x, t) = \int e^{ix\xi}e^{it\xi^3}d\xi = \frac{1}{3}\int e^{ix\eta^{1/3}}e^{it\eta}\frac{d\eta}{\eta^{2/3}},$$ so that $$D_t^{1/4}A(x, t) = \frac{1}{3}\int e^{ix\eta^{1/3}}e^{it\eta}|\eta|^{1/4}\frac{d\eta}{|\eta|^{2/3}} = \frac{1}{3}\int e^{ix\xi}e^{it\xi^3}|\xi|^{3/4}d\xi,$$ and $H_{x_0}$ is just the kernel $K_{x_0}$ studied before. We next need an estimate for $A(\delta_0 \otimes h)$. We will first treat the case $\gamma = 0$. Writing $h = D_t^{1/4}g$ for $g \in L^2$, we see that this boils down to the estimate $$\label{4.38}
||D_t^{1/4}A(\delta_0 \otimes g)||_{L_x^4L_t^\infty} \leq C||g||_{L^2}.$$ Now, $$D_t^{1/4}A(\delta_0 \otimes g)(x, t) = \int{\!\!\!}\int e^{ix\xi}e^{it\tau}\frac{|\tau|^{1/4}}{\tau - \xi^3}\hat{g}(\tau)d\xi\,d\tau.$$ We first compute $\int e^{ix\xi}\frac{d\xi}{\tau - \xi^3}$. This has been carried out on page 562 of [@10], where it is shown that $$\int e^{ix\xi}\frac{d\xi}{\xi^3 - 1} = \alpha_1e^{-ix}\operatorname{sgn}x + \alpha_2e^{ix/2}e^{-a_1|x|} + \alpha_3e^{ix/2}(\operatorname{sgn}x)e^{-a_1|x|}$$ with $\alpha_i \in {\mathbb C}$ and $a_1 > 0$. Moreover, since $$\int e^{ix\xi}\frac{d\xi}{\tau - \xi^3} = \int e^{i(x\tau^{1/3})\eta}\frac{d\eta}{1 - \eta^3}{\!\cdot\!}\frac{1}{\tau^{2/3}},$$ we see that we have a sum of three terms, which we will label $T_1$, $T_2$ and $T_3$. We start out with $$\begin{gathered}
T_1(g)(x, t) = C_1{\!}\int e^{it\tau}|\tau|^{1/4}e^{-ix\tau^{1/3}}\operatorname{sgn}(x\tau^{1/3})\hat{g}(\tau)\frac{d\tau}{\tau^{2/3}} \\
= C_1(\operatorname{sgn}x){\!}\int e^{it\tau}e^{-ix\tau^{1/3}}(\operatorname{sgn}\tau^{1/3})\hat{g}(\tau)\frac{d\tau}{|\tau|^{5/12}}.\end{gathered}$$ Since $g \in L^2$, we are left with estimating $$\tilde{T}_1(h)(x, t) = \int e^{it\tau}e^{-ix\tau^{1/3}}\hat{h}(\tau)\frac{d\tau}{|\tau|^{5/12}}$$ in the $L_x^4L_t^\infty$ norm, in terms of the $L^2$ norm of $h$. This follows from Theorem 2.5 in [@12].
The remaining two terms are similar. We turn to $T_2$: $$T_2(g)(x, t) = C_2{\!}\int e^{it\tau}e^{ix\tau^{1/3}/2}e^{-a_1|x|\,|\tau^{1/3}|}\hat{g}(\tau)\frac{d\tau}{|\tau|^{5/12}}.$$ Following the proof of Theorem 2.5 in [@12], we see that, to obtain the desired estimate for $T_2$, we need merely to use the estimate mentioned on page 564 of [@10] (see also Corollary 2.9 of [@12]). Let $f \in L_x^{4/3}L_t^1$. Then $$\int{\!\!\!}\int \overline{f(x, t)}T_2(g)(x, t)dx\,dt = C_2{\!}\int \hat{g}(\tau)\,\overline{\int{\!\!\!}\int \frac{e^{-it\tau}e^{-ix\tau^{1/3}/2}e^{-a_1|x|\,|\tau|^{1/3}}}{|\tau|^{5/12}}f(x, t)dxdt}\,d\tau.$$ Thus, we need to estimate $$\biggl|\biggl|\int{\!\!\!}\int e^{-it\tau}e^{-x\tau^{1/3}/2}e^{-a_1|x|\,|\tau|^{1/3}}\frac{f(x, t)}{|\tau|^{5/12}}dx\,dt\biggr|\biggr|_{L_\tau^2} \leq C||f||_{L_x^{4/3}L_t^1}.$$ If we write out the $L^2$ norm, we obtain $$\begin{gathered}
\int\int{\!\!\!}\int e^{-it\tau}e^{-ix\tau^{1/3}/2}e^{-a_1|x|\,|\tau|^{1/3}}\frac{f(x, t)dx\,dt}{|\tau|^{5/12}} \\
\times \int{\!\!\!}\int e^{-is\tau}e^{iy\tau^{1/3}/2}e^{-a_1|y|\,|\tau|^{1/3}}\frac{\overline{f(y, s)}dy\,ds}{|\tau|^{5/12}}\,d\tau \\
= \int{\!\!\!}\int f(x, t){\!}\int{\!\!\!}\int K(x, y, s, t)\overline{f(y, s)}dyds\,dxdt\end{gathered}$$ where $$K(x, y, s, t) = \int e^{i\tau(s - t)}e^{i(y - x)\tau^{1/3}/2}e^{-a_1|x|\,|\tau|^{1/3}}e^{-a_1|y|\,|\tau|^{1/3}}\frac{d\tau}{|\tau|^{5/6}}.$$ The estimates mentioned above give the bound $$|K(x, y, s, t)| \leq \frac{C}{|x - y|^{1/2}},$$ from which our estimate follows easily.
Finally, note that, given [(\[4.16\])]{}, the third estimate in [(\[4.11\])]{} follows from [(\[4.37\])]{} and [(\[4.38\])]{}. To conclude the proof of [(\[4.11\])]{}, we are left with showing that $$\label{4.39}
||D_x^{i\gamma}D_t^{1/4}A(\delta_0 \otimes g)||_{L_x^4L_t^\infty} \leq Ce^{C|\gamma|}||g||_{L^2}, \quad \gamma \neq 0$$ The proof of this is a variant of the proof already given. We start out by introducing an operator $S_\eta$, given by $$\label{4.40}
S_\eta g(x, t) = \int_{-\infty}^{+\infty} e^{it\tau}e^{ix\tau^{1/3}\eta}\frac{|\tau|^{1/4}}{\tau^{2/3}}\hat{g}(\tau)d\tau.$$ We claim that $$\label{4.41}
||S_\eta g||_{L_x^4L_t^\infty} \leq \frac{C}{|\eta|^{1/4}}||g||_{L^2}.$$ This follows from scaling, and the bound for $\tilde{T}_1$ sketched above. Now, in order to obtain [(\[4.39\])]{}, write $$D_x^{i\gamma}D_t^{1/4}A(\delta_0 \otimes g) = \int e^{it\tau}\hat{g}(\tau)|\tau|^{i\gamma/3}\frac{|\tau|^{1/4}}{\tau^{2/3}}\biggl(\int e^{ix\tau^{1/3}\eta}|\eta|^{i\gamma}\frac{d\eta}{1 - \eta^3}\biggr)d\tau.$$ Writing $1 - \eta^3 = (1 - \eta)(1 + \eta + \eta^2)$, we see that $$K(x\tau^{1/3}, \eta) = e^{ix\tau^{1/3}\eta}|\eta|^{i\gamma}\frac{1}{1 - \eta^3}= e^{ix\tau^{1/3}\eta}\frac{|\eta|^{i\gamma}}{(1 - \eta)(1 + \eta + \eta^2)}.$$ Let now $\varphi_j \in C^\infty$\_$?
({\mathbb R})$ satisfy $1 = \varphi_1(\eta) + \varphi_2(\eta) + \varphi_3(\eta)$ and $\operatorname{supp}\varphi_1 \subseteq \{\eta : |\eta| < \frac{3}{4}\}$, $\operatorname{supp}\varphi_2 \subseteq \{\eta : \frac{1}{2} < \eta < \frac{3}{2}\}$ and $\operatorname{supp}\varphi_3 \subseteq \{\eta : \eta < -\frac{1}{2}\} \cup \{\eta : \eta > \frac{5}{4}\}$, and consider the corresponding kernels $K_j$, so that our operator is $L_1(g) + L_2(g) + L_3(g)$, where $$\label{4.42}
L_j(g)(x, t) = \int e^{it\tau}\hat{g}(\tau)\frac{|\tau|^{i\gamma/3}}{|\tau|^{5/12}}K_j(x\tau^{1/3}, \eta)d\tau\,d\eta.$$ Let us consider $$L_1(g) = \int |\eta|^{i\gamma}\frac{\varphi_1(\eta)}{(1 - \eta)(1 + \eta + \eta^2)}S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta.$$ Using the bound [(\[4.41\])]{}, the fact that $$||D_t^{i\gamma/3}g||_{L^2} = ||g||_{L^2}$$ and the fact that, on $\operatorname{supp}\varphi_1$, we have that $\bigl|\frac{1}{(1 - \eta)(1 + \eta + \eta^2)}\bigr| \leq C$, we see that $$||L_1(g)||_{L_x^4L_t^\infty} \leq C{\!}\int{\nolimits}_{|\eta| < 3/4} \frac{1}{|\eta|^{1/4}}||g||_{L^2}d\eta \leq C||g||_{L^2},$$ as desired. For $L_3$, we have $$L_3(g) = \int |\eta|^{i\gamma}\frac{\varphi_3(\eta)}{(1 - \eta)(1 + \eta + \eta^2)}S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta,$$ and, on $\operatorname{supp}\varphi_3$, $\bigl|\frac{1}{(1 - \eta)(1 + \eta + \eta^2)}\bigr| \leq \frac{C}{(1 + |\eta|)^3}$, thus yielding a similar bound. We next turn to $L_2$. We have $$\begin{gathered}
L_2(g) = \int |\eta|^{i\gamma}\frac{\varphi_2(\eta)}{(1 - \eta)(1 + \eta + \eta^2)}S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta \\
= \int (|\eta|^{i\gamma} - 1)\frac{\varphi_2(\eta)}{(1 - \eta)(1 + \eta + \eta^2)}S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta \\
+ \int \frac{\varphi_2(\eta)}{(1 - \eta)(1 + \eta + \eta^2)}S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta \\
= \int \frac{|\eta|^{i\gamma} - 1}{(1 - \eta)(1 + \eta + \eta^2)}\varphi_2(\eta)S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta \\
+ \int \frac{\varphi_2(\eta) - 1}{(1 - \eta)(1 + \eta + \eta^2)}S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta \\
+ \int \frac{1}{1 - \eta^3}S_\eta(D_t^{i\gamma/3}g)(x, t)d\eta\end{gathered}$$ For the first term, note that, on $\operatorname{supp}\varphi_2$, we have that $\bigl|\frac{|\eta|^{i\gamma} - 1}{(1 - \eta)(1 + \eta + \eta^2)}\bigr| \leq C|\gamma|$, and hence the argument used for $L_1$ applies. For the second one, note that, on $\operatorname{supp}(\varphi_2 - 1)$, $\bigl|\frac{1}{(1 - \eta)(1 + \eta + \eta^2)}\bigr| \leq \frac{C}{(1 + |\eta|)^3}$, and hence the argument we used for $L_3$ applies. Finally, the third term is identical to the one handled for the case $\gamma = 0$, and thus [(\[4.39\])]{} follows. Finally, to obtain the last estimate in [(\[4.11\])]{}, we estimate it by a well-known variant of the three lines theorem (see Lemma 4.2 in Chapter V of [@17], for instance), using the first two bounds. To establish [(\[4.12\])]{}, we use a similar argument, this time using the last estimate in [(\[4.11\])]{} and the second estimate in [(\[4.7\])]{}. Thus, we consider the analytic family $$\{D_x^{z(s - 1/4) + (1 - z)(s + 1)}w(x, t)\}.$$ When $\Re z = 0$, we use the estimate in [(\[4.7\])]{}, while, when $\Re z = 1$, we use the one in [(\[4.11\])]{}. Since $s = \frac{4}{5}\bigl(s - \frac{1}{4}\bigr) + \frac{1}{5}(s + 1)$, and $\frac{1}{5} = \frac{4}{5}{\!\cdot\!}\frac{1}{4} + \frac{1}{5}{\!\cdot\!}0$, $\frac{1}{10} = \frac{4}{5}{\!\cdot\!}0 + \frac{1}{5}{\!\cdot\!}\frac{1}{2}$, the estimate follows.
Inhomogeneous Duhamel term estimates
------------------------------------
\[Lm4.4\] Let $$w(x, t) = \int_0^t S(t - t')h(x, t')dt'.$$ Then the following estimates hold: $$\begin{gathered}
\label{4.43}||\partial_xw||_{L_t^\infty L_x^2} \leq C||h||_{L_x^1L_t^2}, \\
\label{4.44}\sup_\gamma ||D_x^{i\gamma}\partial_x^2w||_{L_x^\infty L_t^2} \leq Ce^{C|\gamma|}||h||_{L_x^1L_t^2}, \\
\label{4.45}||w||_{L_x^\infty\dot{H}^{2/3}_t} \leq C||h||_{L_x^1L_t^2}, \\
\label{4.46}||D_x^{-1/2}D_x^{i\gamma}w||_{L_x^4L_t^\infty} \leq C||h||_{L_x^{4/3}L_t^1} \\
\intertext{and}
\label{4.47}||w||_{L_x^5L_t^{10}} \leq C||h||_{L_x^{5/4}L_t^{10/9}}.\end{gathered}$$
[(\[4.43\])]{} is (3.7) in [@10]. [(\[4.44\])]{} is (3.8) in [@10] when $\gamma = 0$. The general case is contained in the proof of the second inequality in [(\[4.7\])]{} (for $s = 1$). [(\[4.45\])]{} follows from the proof of the case $s = 1$ of the first inequality in [(\[4.7\])]{}. [(\[4.46\])]{} is (3.10) in [@10], while [(\[4.47\])]{} is (3.12) in [@10].
\[Lm4.5\] Let $w$ be as in Lemma \[Lm4.4\]. Then the following estimates hold (for $h \in C_0^\infty\bigl({\mathbb R} \times [-T, T]\bigr)$:
For $0 \leq s \leq 1$ and $\Psi$ satisfying $\operatorname{supp}\Psi \subseteq [-T, T]$ and $|\Psi'(t)| \leq C/T$, we have (for $T < 1$, with $\beta(s) = \frac{1}{3} - \frac{s}{6}$) $$\begin{gathered}
\label{4.48}\begin{split}
{||\Psi w(0, -)||_{H^{(s + 1)/3}_{0}({\mathbb R}^+)}} \leq CT^{\beta(s)}||h||_{L_T^2H_x^s} \\
{||\Psi w(0, -)||_{H^{(s + 1)/3}(\mathbb R)}} \leq CT^{\beta(s)}||h||_{L_T^2H_x^s}, \\
\end{split} \\
\label{4.49}{||w(0, -)||_{\dot{H}^{2/3}({\mathbb R}_t)}} \leq C||h||_{L_x^1L_t^2}, \\
\label{4.50}{||w(0, -)||_{\dot{H}^{1/4}({\mathbb R}_t)}} \leq C||h||_{L_x^{4/3}L_t^1} \\
\intertext{and}
\label{4.51}{||w(0, -)||_{\dot{H}^{1/3}({\mathbb R}_t)}} \leq C||h||_{L_x^{5/4}L_t^{10/9}}.\end{gathered}$$
For the estimates in [(\[4.48\])]{}, first note that, for $h \in C_0^\infty\bigl({\mathbb R} \times [-T, T]\bigr)$, it is easy to see that $w$ satisfies $$\sup_{t \in [-T, T]} {||w(-, t)||_{H^{s}({\mathbb R}_x)}} < +\infty$$ for all $s$, and hence $w \in C^\infty\bigl({\mathbb R} \times (-T, T)\bigr)$ and $w(-, 0) \equiv 0$. Next, note that, because of this, if the second estimate in [(\[4.48\])]{} is established for $s \neq 1/2$, then the first will follow by Propositions \[Pn2.4\] and \[Pn2.6\], and hence, by Corollary \[Co2.1\], this will be the case for all $0 \leq s \leq 1$. Note also that, by Remark \[Rk2.3\] (applied to the interval $[-T, T]$), it suffices to estimate ${||\Psi w(0, -)||_{\dot{H}^{(s + 1)/3}(\mathbb R)}}$. Thus we will show that $$\label{4.52}
\biggl|\biggl|\Psi(t){\!}\int_0^t S(t - t')h(x, t')dt'\Bigr|_{x = 0}\biggr|\biggr|_{\dot{H}^{(s + 1)/3}_t({\mathbb R})} \leq CT^{\beta(s)}||h||_{L_T^2H_x^s}.$$ We first consider the left-hand side of [(\[4.52\])]{} for $s = -1$. By Minkowski’s integral inequality, we can bound it by $$\label{4.53}
\int_{-T}^T ||S(t)S(-t')h(x, t')||_{L_x^\infty L_T^2}dt' \leq CT^{1/2}||h||_{L_T^2H^{-1}({\mathbb R})},$$ where the second inequality follows from [(\[4.3\])]{}.
Next, consider the left-hand side in [(\[4.52\])]{} when $s = 2$. From the Leibniz rule, we have that $$\begin{gathered}
\partial_t\Bigl(\Psi(t){\!}\int_0^t S(t - t')h(x, t')dt'\Bigr) = \partial_t\Psi(t){\!}\int_0^t S(t - t')h(x, t')dt' + \Psi(t)h(x, t) \\
- \Psi(t){\!}\int_0^t \partial_x^3S(t - t')h(x, t')dt',\end{gathered}$$ and each of these terms is to be controlled in $L_x^\infty L_T^2$. For the first term, we have the estimate $$\begin{gathered}
\frac{C}{T}\Bigl|\Bigl|\int_0^t S(t - t')h(x, t')dt'\Bigr|\Bigr|_{L_x^\infty L_T^2} \\
\leq \frac{C}{T}\Bigl|\Bigl|\int_0^t S(t - t')h(x, t')dt'\Bigr|\Bigr|_{L_x^2L_T^2} + \frac{C}{T}\Bigl|\Bigl|\partial_x{\!}\int_0^t S(t - t')h(x, t')dt'\Bigr|\Bigr|_{L_x^2L_T^2} \\
\leq \frac{C}{T}{\!\cdot\!}CT||h||_{L_T^2L_x^2} + \frac{C}{T}{\!\cdot\!}CT||\partial_x h||_{L_T^2L_x^2} \leq C||h||_{L_T^2H_x^2}.\end{gathered}$$ For the second term we use the bound $$||h||_{L_x^\infty L_T^2} \leq C||h||_{L_T^2H_x^2}$$ to obtain a similar bound.
Finally, for the third term, using Minkowski’s integral inequality and [(\[4.2\])]{}, we obtain $$\int_{-T}^T ||S(-t')\partial_x^2h(x, t')||_{L_x^2}dt' \leq CT^{1/2}||h||_{L_T^2H_x^2},$$ so that $$\label{4.54}
\biggl|\biggl|\Psi(t){\!}\int_0^t S(t - t')h(x, t')dt'\Bigr|_{x = 0}\biggr|\biggr|_{\dot{H}^1_t({\mathbb R})} \leq C||h||_{L_T^2H_x^2}.$$ Hence, [(\[4.52\])]{} follows by interpolation of [(\[4.53\])]{} and [(\[4.54\])]{}.
In the proofs of [(\[4.49\])]{}–[(\[4.51\])]{}, we use [(\[4.16\])]{} and the observation that $\chi_{(-\infty, 0)}h$ is in the same space as $h$ to reduce matters to the corresponding estimates for $A(h)$ and $\int_{-\infty}^{+\infty} S(t - t')h(x, t')dt'$. In the case of [(\[4.49\])]{}, this is contained in the proof of the first inequality in [(\[4.7\])]{}. In the case of [(\[4.51\])]{}, duality reduces matters to the estimates proved in establishing the third inequality in [(\[4.11\])]{}. Finally, [(\[4.50\])]{} can be obtained either by interpolation of [(\[4.49\])]{} and [(\[4.51\])]{} or by duality from the proof of [(\[4.12\])]{}.
\[Rk4.2\] The restriction to $x = 0$ in the right-hand sides of [(\[4.48\])]{}–[(\[4.51\])]{} is not significant. In fact, if $X$ is the space of functions in $t$ in which the estimate has been made, the left-hand side can be replaced by $C({\mathbb R}; X)$. This is because of translation invariance and the first remark in the proof of Lemma \[Lm4.5\].
Some estimates for the group and its associated Duhamel terms in Bourgain’s spaces
==================================================================================
\[5\]
This section introduces a modification of the spaces introduced by Bourgain in [@5]. We also establish useful estimates for the linear solution group, the Duhamel forcing term and the inhomogeneous Duhamel term in these spaces. The results of this section are combined with a bilinear estimate in \[7\] to prove local well-posedness of [(\[1.2\])]{} for data $(\phi, f) \in L_x^2 \times H_t^{1/3}$ in the standard KdV setting, ${k}= 1$.
Bourgain’s spaces with a low frequency modification
---------------------------------------------------
\[Df5.1\] Let $f \in {\cal S}'({\mathbb R}^2)$. We say that $f \in X_b$ if $||f||_{X_b} < \infty$, where $||\!\cdot\!||_{X_b}$ is defined by $$\begin{gathered}
\label{5.1}
||f||_{X_b} = \Bigl(\int{\!\!\!}\int (1 + |\lambda - \xi^3|)^{2b}|\hat{f}(\xi, \lambda)|^2d\xi\,d\lambda\Bigr)^{1/2} \\
+ \Bigl(\int{\!\!\!}\int{\nolimits}_{|\xi| < 1} (1 + |\lambda|)^{2\alpha} \hat{f}(\xi, \lambda)|^2d\xi\,d\lambda\Bigr)^{1/2},\end{gathered}$$ where $\frac{1}{2} < \alpha < \frac{2}{3}$ is fixed, and $0 < b < \frac{1}{2}$.
\[Rk5.1\] The space $X_b$ also depends upon the parameter $\alpha$, but we have chosen to suppress this dependence in the notation. This space and the space $Y_b$ below are introduced for studying the case ${k}= 1$ of [(\[1.2\])]{} for data $(\phi, f) \in L_x^2 \times H_t^{1/3}$. A natural extension of $X_b$ for problems with data in $H_x^s \times H_t^{(s + 1)/3}$ may be defined by including the spatial Sobolev weight $(1 + |\xi|)^{2s}$ in the two integrals in [(\[5.1\])]{}. We shall refer to this extension as $X_{s, b}$. Similar comments apply to the space we define next.
\[Df5.2\] Let $f \in {\cal S}'({\mathbb R}^2)$. We say that $f \in Y_b$ if $||f||_{Y_b} < +\infty$, where $||\!\cdot\!||_{Y_b}$ is defined by $$\begin{gathered}
\label{5.2}
||f||_{Y_b} = \Bigl(\int{\!\!\!}\int \frac{|\hat{f}(\xi, \lambda)|^2}{(1 + |\lambda - \xi^3|)^{2b}}d\xi\,d\lambda\Bigr)^{1/2} \\
+ \Bigl(\int{\!\!\!}\int{\nolimits}_{|\xi| < 1} \frac{|\hat{f}(\xi, \lambda)|^2}{(1 + |\lambda|)^{2(1 - \alpha)}}d\xi\,d\lambda\Bigr)^{1/2} \\
+ \biggl(\int \biggl(\int \frac{|\hat{f}(\xi, \lambda)|}{1 + |\lambda - \xi^3|}d\lambda\biggr)^2d\xi\biggr)^{1/2},\end{gathered}$$ where $0 < b < \frac{1}{2}$.
We start off with a useful property of the space $X_b$: stability under multiplication by smooth time cutoffs.
\[Lm5.1\] Let $\theta \in C_0^\infty({\mathbb R})$ and $f \in X_b$. Then, for $b \in (0, 1)$, we have $\theta(t)f(x, t) \in X_b$ and $$\label{5.3}
||\theta f||_{X_b} \leq C||f||_{X_b}.$$
There are two terms in [(\[5.1\])]{} that we must control. We first consider the low frequency term. Note that $\int{\!\!}\int{\nolimits}_{|\xi| \leq 1} |\hat{f}(\xi, \lambda)|^2d\xi\,d\lambda \leq ||f||_{X_b}^2$. Next, $$\int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} |\lambda|^{2\alpha}|\widehat{\theta f}|^2 = \int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} \bigl|D_t^\alpha\bigl(\theta\cdot\tilde{f}(\xi, t)\bigr)\bigr|^2d\xi\,dt,$$ where $\tilde{f}$ denotes the spatial Fourier transform of $f$. We now use $$||D^s{}(\theta v{})||_{L^2} \leq C(||v||_{L^2} + ||D^s v||_{L^2})$$ to get $$\begin{gathered}
\int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} |\lambda|^{2\alpha}|\widehat{\theta f}|^2 \leq C\int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} (|\tilde{f}(\xi, t)|^2 + |D^\alpha\tilde{f}(\xi, t)|)dt\,d\xi \\
\leq C\int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} (1 + |\lambda|)^{2\alpha}|\hat{f}(\xi, \lambda)|^2d\xi\,d\lambda.\end{gathered}$$ We have shown that $$\int{\!\!\!}\int_{|\xi| \leq 1} (1 + |\lambda|)^{2\alpha}|\widehat{\theta f}(\xi, \lambda)|^2d\xi\,d\lambda \leq C\int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} (1 + |\lambda|)^{2\alpha}|\hat{f}(\xi, \lambda)|^2d\xi\,d\lambda.$$
It remains to estimate the other term in [(\[5.1\])]{}. Note that $\widehat{\theta f} = \hat{\theta} *_\lambda \hat{f}$ and that we have to show that, $\forall a \in {\mathbb R}$, $$\int |\hat{f} *_\lambda \hat{\theta}|^2(1 + |\lambda - a|)^{2b}d\lambda \leq C\int |\hat{f}|^2(1 + |\lambda - a|)^{2b}d\lambda,$$ uniformly in $a$. Since $\int |\hat{\theta}|d\lambda \leq C$, we have $$\int |\hat{f} *_\lambda \hat{\theta}|^2 \leq C\int |\hat{f}|^2(1 + |\lambda - a|)^{2b}d\lambda,$$ so we need to handle $$\int |\lambda - a|^{2b}|\hat{f} *_\lambda \hat{\theta}|^2d\lambda = \int |D_t^b(e^{ia-}\theta\tilde{f})|^2dt.$$ The Leibniz rule for fractional derivatives [@10] gives $$||D_t^b(e^{ia-}\tilde{f}\theta) - \theta D_t^b(e^{ia-}\tilde{f}) - D_t^b(\theta)e^{ia-}\tilde{f}||_{L^2} \leq C||\theta||_{L^\infty}||D_t^b(e^{ia-}\tilde{f})||_{L^2}.$$ Since $||D_t^b(\theta)||_{L^\infty} \leq C$ and $||\tilde{f}||_{L^2}$ is in the right-hand side of [(\[5.3\])]{}, we are done.
Group estimates
---------------
The following result supplements Lemma \[Lm4.1\].
\[Lm5.2\] Let $\theta \in C_0^\infty({\mathbb R})$ be a cutoff function adapted to $[-T, T]$, with $T < 1$. For $\phi \in L^2({\mathbb R})$, we have $$\label{5.4}
||\theta(t)S(t)\phi||_{X_b} \leq C\Bigl(\int (1 + |\lambda|)^{2\alpha}|\hat{\theta}(\lambda)|^2d\lambda\Bigr)^{1/2}||\phi||_{L^2}.$$
We write $(\theta(t)S(t)\phi)\widehat{\ \ }(\xi, \lambda) = \hat{\theta}(\lambda - \xi^3)\hat{\phi}(\xi)$, and use this expression in the two terms of the $X_b$ norm. For the low-frequency term, we have $$\int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} |\lambda|^{2\alpha}|\hat{\theta}(\lambda - \xi^3)|^2|\hat{\phi}(\xi)|^2d\xi\,d\lambda = \int{\nolimits}_{|\xi| \leq 1} |\hat{\phi}(\xi)|^2\Bigl(\int |\lambda|^{2\alpha}|\hat{\theta}(\lambda - \xi^3)|^2d\lambda\Bigr)d\xi.$$ We change variables to see that the above expression is equal to $$\begin{gathered}
\int{\nolimits}_{|\xi| \leq 1} |\hat{\phi}(\xi)|^2\Bigl(\int |\lambda + \xi^3|^{2\alpha}|\hat{\theta}(\lambda)|^2d\lambda\Bigr)d\xi \\
\leq C\int_{|\xi| \leq 1} |\hat{\phi}(\xi)|^2\Bigl(\int (1 + |\lambda|)^{2\alpha}|\hat{\theta}(\lambda)|^2d\lambda\Bigr)d\xi,\end{gathered}$$ so the low-frequency term is fine. The remaining term in [(\[5.1\])]{} is $$\begin{gathered}
\int{\!\!\!}\int (1 + |\lambda - \xi^3|)^{2b}|\hat{\theta}(\lambda - \xi^3)|^2|\hat{\phi}(\xi)|^2d\lambda\,d\xi \\
= \int |\hat{\phi}(\xi)|^2\Bigl(\int (1 + |\lambda - \xi^3|)^{2b}|\hat{\theta}(\lambda - \xi^3)|^2d\lambda\Bigr)d\xi,\end{gathered}$$ and we are done since $b < \frac{1}{2}$.
Duhamel forcing term estimate
-----------------------------
We supplement Lemmas \[Lm4.2\] and \[Lm4.3\] concerning the Duhamel forcing term with the following estimate.
\[Lm5.3\] Let $g \in H^{-1/3}({\mathbb R})$ and let $\theta \in C_0^\infty({\mathbb R})$ be a cutoff function. We have $$\label{5.5}
\Bigl|\Bigl|\theta(t){\!}\int_0^t S(t - t')\delta_0(x)g(t')dt'\Bigr|\Bigr|_{X_b} \leq C{||g||_{H^{-1/3}}}.$$
Let $\hat{w}(\xi, \lambda)$ denote the space-time Fourier transform of $\delta_0(x)g(t)$. The multiplier representation of the operator $S(t)$ (see [(\[1.6\])]{}) allows one to show that the object to be estimated may be written as $$\label{5.6}
u(x, t) = \theta(t)\int{\!\!\!}\int e^{ix\xi}\frac{e^{it\lambda} - e^{it\xi^3}}{\lambda - \xi^3}\hat{w}(\xi, \lambda)d\xi\,d\lambda.$$ We make a useful decomposition of this function. Let $\psi \in C_0^\infty({\mathbb R})$ satisfy $\psi = 1$ near $x = 0$ and $\operatorname{supp}\psi \subseteq \{x : |x| < 1\}$. We first break up [(\[5.6\])]{} into two pieces, one near $\lambda - \xi^3 = 0$ and the other far from $\lambda - \xi^3 = 0$, by writing $u = u_1 + u_2$, where $$\label{5.7}
u_1(x, t) = \theta(t)\int{\!\!\!}\int e^{ix\xi}\frac{e^{it\lambda} - e^{it\xi^3}}{\lambda - \xi^3}\psi(\lambda - \xi^3)\hat{w}(\xi, \lambda)d\xi\,d\lambda$$ and $$\label{5.8}
u_2(x, t) = \theta(t)\int{\!\!\!}\int e^{ix\xi}\frac{e^{it\lambda} - e^{it\xi^3}}{\lambda - \xi^3}\bigl[1 - \psi(\lambda - \xi^3)\bigr]\hat{w}(\xi, \lambda)d\xi\,d\lambda.$$ Next, we take the Taylor expansion of the exponential to observe that $$\label{5.9}
u_1(x, t) = \theta(t)\sum_{k = 1}^\infty \frac{i^kt^k}{k!}\int{\!\!\!}\int e^{ix\xi}e^{it\xi^3}\psi(\lambda - \xi^3)(\lambda - \xi^3)^{k - 1}\hat{w}(\xi, \lambda)d\xi\,d\lambda.$$ Let $\theta_k(t) = t^k\theta(t)$, so that $||\theta_k||_{L^2} \leq ||\theta||_{L^2}$ for all $k$; then $\theta_k'(t) = kt^{k - 1}\theta(t) + t^k\theta'(t)$, so that $||\theta_k||_{L^2} + ||\theta_k'||_{L^2} \leq C(1 + |k|)$. Let $\hat{\phi}_k(\xi) = \int \psi(\lambda - \xi^3)(\lambda - \xi^3)^{k - 1}\hat{w}(\xi, \lambda)d\lambda.$ This notation allows us to reexpress $u_1$ as $$\label{5.10}
u_1(x, t) = \sum_{k = 1}^\infty \frac{i^k}{k!}\theta_k(t)\int e^{ix\xi}e^{it\xi^3}\hat{\phi}_k(\xi)d\xi.$$ In light of Lemma \[Lm5.2\], to control $u_1$ as claimed, it suffices to verify that $$\label{5.11}
||\hat{\phi}_k(\xi)||_{L_\xi^2} = \Bigl|\Bigl|\int \psi(\lambda - \xi^3)(\lambda - \xi^3)^{k - 1}\hat{g}(\lambda)d\lambda\Bigr|\Bigr|_{L_\xi^2} \leq C{||g||_{H^{-1/3}}},$$ where we have used $\hat{w}(\xi, \lambda) = \hat{g}(\lambda)$. The support property of $\psi$ shows that $|\hat{\phi}_k(\xi)|$ is controlled by $\int{\nolimits}_{|\lambda - \xi^3| \leq 1} \hat{g}(\lambda)d\lambda$. We break the $L_\xi^2$ norm into a low- and a high-frequency piece. Consider first $$\begin{gathered}
\int{\nolimits}_{|\xi| \leq 2} \Bigl(\int{\nolimits}_{|\lambda - \xi^3| \leq 1} |\hat{g}(\lambda)|d\lambda\Bigr)^2d\xi = \int{\nolimits}_{|\xi| \leq 2} \Bigl(\int{\nolimits}_{\substack{|\lambda - \xi^3| \leq 1 \\ |\lambda| \leq 9{}}} |\hat{g}(\lambda)|d\lambda\Bigr)^2d\xi \\
\leq \int{\nolimits}_{|\xi| \leq 2} \Bigl(\int{\nolimits}_{|\lambda| \leq 9} \frac{|\hat{g}(\lambda)|}{(1 + |\lambda|)^{1/3}}(1 + |\lambda|)^{1/3}d\lambda\Bigr)^2d\xi \leq C{||g||_{H^{-1/3}}}^2.\end{gathered}$$ Next, we consider $$\int{\nolimits}_{|\xi| \geq 2} \Bigl(\int{\nolimits}_{|\lambda - \xi^3| \leq 1} |\hat{g}(\lambda)|d\lambda\Bigr)^2d\xi = \int{\nolimits}_{|\xi| \geq 2} \Bigl(\int{\nolimits}_{\substack{|\lambda - \xi^3| \leq 1 \\ |\lambda| \geq 1}} |\hat{g}(\lambda)|d\lambda\Bigr)^2d\xi.$$ Write $\eta = \xi^3$ and change variables to find that the above expression is equal to $$\label{5.12}
\int{\nolimits}_{|\eta| \geq 8} \Bigl(\int{\nolimits}_{\substack{|\lambda - \eta| \leq 1 \\ |\lambda| \leq 1{}}} |\hat{g}(\lambda)|d\lambda\Bigr)^2\frac{d\eta}{\eta^{2/3}}.$$ Now, by Hölder, $$\Bigl(\int{\nolimits}_{\substack{|\lambda - \eta| \leq 1 \\ |\lambda| \geq 1}} |\hat{g}(\lambda)|d\lambda\Bigr)^2 \leq \biggl\{\int{\nolimits}_{|\lambda - \eta| \leq 1} \biggl[\frac{|\hat{g}(\lambda)|}{(1 + |\lambda|)^{1/3}}\biggr]^{3/2}d\lambda\biggr\}^{4/3}\Bigl\{\int{\nolimits}_{\substack{|\lambda - \eta| \leq 1 \\ |\lambda| \geq 1}} (1 + |\lambda|)d\lambda\Bigr\}^{2/3}.$$ The last expression on the preceding line is comparable to $(1 + |\eta|)^{2/3}$. Going back to [(\[5.10\])]{} leaves $$\int{\nolimits}_{|\eta| \geq 8} \biggl\{\int{\nolimits}_{|\lambda - \eta| \leq 1} \biggl[\frac{|\hat{g}(\lambda)|}{(1 + |\lambda|)^{1/3}}\biggr]^{3/2}d\lambda\biggr\}^{4/3}d\eta.$$ Another application of Hölder, using the constraint on the $\lambda$-integration, proves [(\[5.11\])]{} and therefore $$||u_1||_{X_b} \leq C{||g||_{H^{-1/3}}}.$$
We turn our attention to the term $u_2$. There are two pieces, $$\label{5.13}
u_{2, 1}(x, t) = \theta(t)\int{\!\!\!}\int e^{ix\xi}e^{it\lambda}\frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}\hat{w}(\xi, \lambda)d\xi\,d\lambda$$ and $$\label{5.14}
u_{2, 2}(x, t) = \theta(t)\int{\!\!\!}\int e^{ix\xi}e^{it\xi^3}\frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}\hat{w}(\xi, \lambda)d\xi\,d\lambda,$$ satisfying $u_2 = u_{2, 1} - u_{2, 2}$. The term $u_{2, 2}$ may be handled using Lemma \[Lm5.2\] once we establish that $$\label{5.15}
\biggl|\biggl|\int \frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}\hat{g}(\lambda)d\lambda\biggr|\biggr|_{L_\xi^2} \leq C{||g||_{H^{-1/3}}}.$$ The (square of the) $|\xi| \leq 1$ contribution to the $L_\xi^2$ norm appearing in [(\[5.15\])]{} is controlled by $$\begin{gathered}
\int{\nolimits}_{|\xi| \leq 1} \biggl(\int{\nolimits}_{|\lambda - \xi^3| \geq 1/2} \frac{1}{1 + |\lambda - \xi^3|}|\hat{g}(\lambda)|d\lambda\biggr)^2d\xi \\
\leq \int{\nolimits}_{|\xi| \leq 1} \Bigl(\int{\nolimits}_{|\lambda| \leq 2} |\hat{g}(\lambda)|d\lambda\Bigr)^2d\xi + \int{\nolimits}_{|\xi| \leq 1} \Bigl(\int{\nolimits}_{|\lambda| \geq 2} \frac{1}{1 + |\lambda|}|\hat{g}(\lambda)|d\lambda\Bigr)^2d\xi \\
\leq C{||g||_{H^{-1/3}}}^2.\end{gathered}$$ When $|\xi| \geq 1$ and $|\lambda| \leq \frac{1}{2}$, $|\lambda - \xi^3| \sim |\xi^3|$ and we get $$\int{\nolimits}_{|\xi| \geq 1} \frac{1}{|\xi|^6}\Bigl(\int{\nolimits}_{|\lambda| \leq 1/2} |\hat{g}(\lambda)|d\lambda\Bigr)^2d\xi \leq {||g||_{H^{-1/3}}}^2.$$ When $|\xi| \geq 1$ and $|\lambda| \geq \frac{1}{2}$, we are left with $$\begin{gathered}
\int{\nolimits}_{|\xi| \geq 1} \biggl(\int{\nolimits}_{|\lambda| \geq 1/2} \frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}\hat{g}(\lambda)d\lambda\Bigr)d\xi \\
= \int{\nolimits}_{|\eta| \geq 1} \Bigl(\int{\nolimits}_{|\lambda| \geq 1/2} \frac{1 - \psi(\lambda - \eta)}{\lambda - \eta}\hat{g}(\lambda)d\lambda\Bigr)^2\frac{d\eta}{\eta^{2/3}}.\end{gathered}$$ We now use the fact that $\frac{1}{\eta^{2/3}}$ is an $A_2$ weight [@16] to get that the above expression is no greater than $$C\int{\nolimits}_{|\lambda| \geq 1/2} \frac{|\hat{g}(\lambda)|^2}{|\lambda|^{2/3}}d\lambda \leq C{||g||_{H^{-1/3}}}^2.$$ This completes the treatment of $u_{2, 2}$; all that remains to be considered is $u_{2, 1}$. Lemma \[Lm5.1\] shows that we may ignore the time cutoff $\theta(t)$ in [(\[5.13\])]{}. We shall consider the low-frequency term in [(\[5.1\])]{} first. We therefore look at the expression $$\label{5.16}
\int{\!\!\!}\int{\nolimits}_{|\xi| \leq 1} \frac{|\lambda|^{2\alpha}}{(1 + |\lambda - \xi^3|)^2}|\hat{g}(\lambda)^2d\lambda\,d\xi.$$ Note that $\int{\nolimits}_{|\xi| \leq 1} \frac{d\xi}{(1 + |\lambda - \xi^3|)^2} \leq \frac{C}{1 + |\lambda|^2}$ and [(\[5.16\])]{} is bounded by $$\int \frac{1}{(1 + |\lambda|)^{2(1 - \alpha)}}|\hat{g}(\lambda)|^2d\lambda,$$ which is fine as long as $1 - \alpha > \frac{1}{3}$, i.e., $\alpha < \frac{2}{3}$, which we have assumed in the definition of $X_b$. The other part of the $X_b$ norm is controlled as follows. We look at $$\begin{gathered}
\label{5.17}
\int{\!\!\!}\int (1 + |\lambda - \xi^3|)^{2b}\frac{1}{(1 + |\lambda - \xi^3|)^2}|\hat{g}(\lambda)|^2d\lambda\,d\xi \\
= \int |\hat{g}(\lambda)|^2\biggl(\int \frac{d\xi}{(1 + |\lambda - \xi^3|)^{2(1 - b)}}\biggr)d\lambda.\end{gathered}$$
\[5.18\] Assuming $b < \frac{1}{2}$, we have $$\int \frac{d\xi}{(1 + |\lambda - \xi^3|)^{2(1 - b)}} \leq \frac{C}{(1 + |\lambda|)^{2/3}}.$$
Note that our assumption $b < \frac{1}{2}$ guarantees that $2(1 - b) = 1 + \varepsilon$ for some $\varepsilon > 0$. Therefore, the claim is fine in case $|\lambda| \leq 2$. For $|\lambda| \geq 2$, we write $\eta = \xi^3$ and change variables to get $$\int \frac{d\xi}{(1 + |\lambda - \xi^3|)^{2(1 - b)}} = \int \frac{d\eta}{|\eta|^{2/3}(1 + |\lambda - \eta|)^{1 + \varepsilon}}.$$ The $\eta$-integral is split into three regions.
[.]{}
$|\eta| < \frac{1}{2}|\lambda|$.
Here we have $(1 + |\lambda - \eta|) \sim (1 + |\lambda|)$, so we write $$\int \frac{d\eta}{|\eta|^{2/3}(1 + |\lambda- \eta|)^{1 + \varepsilon}} \leq \frac{1}{(1 + |\lambda|)^{(2/3) + (\varepsilon/2)}}\int \frac{d\eta}{|\eta|^{2/3}(1 + |\eta|)^{(1/3) + (\varepsilon/2)}}$$ to observe the claim.
$|\eta| \sim |\lambda|$.
Here we get $$\frac{1}{|\lambda|^{2/3}}\int{\nolimits}_{|\lambda|/2 \leq |\eta| \leq 2|\lambda|} \frac{d\eta}{(1 + |\lambda - \eta|)^{1 + \varepsilon}} \leq \frac{C}{|\lambda|^{2/3}}.$$
$2|\lambda| < |\eta|$.
In this region, $(1 + |\lambda - \eta|) \sim (1 + |\eta|)$, so we get $$\int{\nolimits}_{|\eta| \geq 2|\lambda|} \frac{d\eta}{|\eta|^{2/3}(1 + |\eta|)^{1 + \varepsilon}} \leq \int{\nolimits}_{|\eta| \geq 2|\lambda|} \frac{d\eta}{(1 + |\eta|)^{1 + \varepsilon + (2/3)}} \leq \frac{C}{(1 + |\lambda|)^{(2/3) + \varepsilon}}.$$
This completes the proof of the claim.
Returning to [(\[5.17\])]{} and using the claim finishes off our estimate of $u_{2, 1}$, and with it the proof of Lemma \[Lm5.3\].
\[Rk5.1’\] The assumption $b < \frac{1}{2}$ is crucial in the proof of the second case of the claim. It was this that forced us to introduce these modified Bourgain spaces.
Inhomogeneous Duhamel term estimates
------------------------------------
This subsection contains two lemmas concerning the inhomogeneous Duhamel term $\int_0^t S(t - t')w(x, t')dt'$. We begin by showing that, for $\theta \in C_0^\infty({\mathbb R})$, the formula $w(x, t) \mapsto \theta(t)\int_0^t S(t - t')w(x, t')dt'$ defines a bounded map $Y_b \rightarrow X_b$. Then we show that a (time-localized) inhomogeneous Duhamel term may be restricted to $\{x = 0\}$ as an $H^{1/3}({\mathbb R}_t)$ function when the inhomogeneity $w \in Y_b$.
\[Lm5.4\] For $w \in Y_b$ and $\theta \in C_0^\infty$, we have that $$\label{5.19}
\Bigl|\Bigl|\theta(t)\int_0^t S(t - t')w(x, t')dt'\Bigr|\Bigr|_{X_b} \leq C||w||_{Y_b}.$$
The expression to be controlled in $X_b$ was considered in [(\[5.6\])]{} during the proof of Lemma \[Lm5.3\]. As in the discussion there, we decompose $u$ into $u_1 + u_{2, 1} -{} u_{2, 2}$ and estimate the terms separately. The $u_1$ term was reexpressed in [(\[5.10\])]{}, from which we see that, to control it appropriately, it suffices to show that $$||\phi_k||_{L^2} \leq ||w||_{Y_b}.$$ The definition of $\hat{\phi}_k(\xi)$, which appeared between [(\[5.9\])]{} and [(\[5.10\])]{}, shows that we may consider $$||\phi_k||_{L^2} \leq \Bigl(\int \Bigl(\int{\nolimits}_{|\lambda - \xi^3| \leq 1} |\hat{w}(\xi, \lambda)|d\lambda\Bigr)^2d\xi\Bigr)^{1/2},$$ and this is bounded by $$C\biggl(\int \biggl(\int \frac{|\hat{w}(\xi, \lambda)|}{1 + |\lambda - \xi^3|}d\lambda\biggr)^2d\xi\biggr)^{1/2},$$ which is a part of the $Y_b$ norm.
We next focus on the first term in [(\[5.1\])]{} for $u_{2, 1}$ and $u_{2, 2}$.
For $u_{2, 2}$, we use Lemma \[Lm5.2\] and the fact that $$\hat{\phi}(\xi) = \int \frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}\hat{w}(\xi, \lambda)d\lambda$$ satisfies $$|\hat{\phi}(\xi)| \leq \int \frac{1}{1 + |\lambda - \xi^3|}|\hat{w}(\xi, \lambda)|d\lambda,$$ so that $||\phi||_{L^2} \leq ||w||_{Y_b}$. For $u_{2, 1}$, we use Lemma \[Lm5.1\] to ignore the time cutoff $\theta(t)$ in [(\[5.13\])]{} and reduce matters to controlling $$\int{\!\!\!}\int \frac{[1 - \psi(\lambda - \xi^3)]^2}{|\lambda - \xi^3|^2}(1 + |\lambda - \xi^3|)^{2b}|\hat{w}(\xi, \lambda)|^2d\xi\,d\lambda.$$ The support properties of $\psi$ tell us that the above quantity is no greater than $$\begin{gathered}
C\int{\!\!\!}\int \frac{1}{(1 + |\lambda - \xi^3|)^{2(1 - b)}}|\hat{w}(\xi, \lambda)|^2d\xi\,d\lambda \\
= C\int{\!\!\!}\int \frac{1}{(1 + |\lambda - \xi^3|)^{2(1 - 2b)}}\,\frac{|\hat{w}(\xi, \lambda)|^2}{(1 + |\lambda - \xi^3|)^{2b}}d\xi\,d\lambda.\end{gathered}$$ Since $1 - 2b > 0$, $(1 + |\lambda - \xi^3|)^{2(1 - 2b)} \geq 1$, so we bound by $||w||_{Y_b}$.
It remains to estimate the low-frequency part of [(\[5.1\])]{}, $$\begin{gathered}
\int{\nolimits}_{|\xi| \leq 1} \int |\lambda|^{2\alpha}\frac{[1 - \psi(\lambda - \xi^3)]^2}{|\lambda - \xi^3|^2}|\hat{w}(\xi, \lambda)|^2d\xi\,d\lambda \\
\leq C\int{\nolimits}_{|\xi| \leq 1} \int \frac{|\lambda|^{2\alpha}}{(1 + |\lambda|)^2}|\hat{w}(\xi, \lambda)|^2d\xi\,d\lambda \\
\leq C\int{\nolimits}_{|\xi| \leq 1} \frac{1}{(1 + |\lambda|)^{2(1 - \alpha)}}|\hat{w}(\xi, \lambda)|^2d\xi\,d\lambda \leq C||w||_{Y_b}.\end{gathered}$$
The inhomogeneous Duhamel term defines “boundary values”.
\[Lm5.5\] Let $h \in Y_b$ and $\theta \in C_0^\infty({\mathbb R})$. We have that $$\Bigl|\Bigl|\theta(t)\int_0^t S(t - t')h(x, t')dt'\Bigr|_{\{x = 0\}}\Bigr|\Bigr|_{H_t^{1/3}} \leq C||h||_{Y_b}.$$
We decompose the object under consideration into $u_1$, $u_{2, 1}$ and $u_{2, 2}$. As before, $u_1$ and $u_{2, 2}$ rely on the estimate for a term of the form $\theta(t)S(t)\phi$ which we established in Lemma \[Lm4.1\] (see [(\[4.(4.5)\])]{} and Remark \[Rk4.(1.5)\]). It remains to estimate $$u_{2, 1}(0, t) = \theta(t)\int{\!\!\!}\int e^{it\lambda}\hat{h}(\xi, \lambda)\frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}d\lambda\,d\xi = \theta(t)\beta(t).$$ By Proposition \[Pn2.8\], $${||\theta\beta||_{H^{1/3}}} \sim {||\theta\beta||_{\dot{H}^{1/3}}} = ||D_t^{1/3}(\theta\beta)||_{L^2}.$$ By the Leibniz rule from [@10], $$||D_t^{1/3}(\theta\beta) - \theta D_t^{1/3}(\beta) - D_t^{1/3}(\theta)\beta||_{L^2} \leq C||\theta||_{L^\infty}||D_t^{1/3}(\beta)||_{L^2}.$$ Also, $||\beta||_{L^6} \leq C||D_t^{1/3}(\beta)||_{L^2}$ and $||D_t^{1/3}(\theta)||_{L^3} \leq C$, so it suffices to show that $$||D_t^{1/3}(\beta)||_{L^2} \leq C||w||_{Y_b}.$$ We have $$D_t^{1/3}(\beta) = \int e^{it\lambda}|\lambda|^{1/3}{\!}\int \hat{h}(\xi, \lambda)\frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}d\xi\,d\lambda,$$ so $$||D_t^{1/3}(\beta)||_{L^2} = \int |\lambda|^{2/3}\biggl|\int \hat{h}(\xi, \lambda)\frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}d\xi\biggr|^2d\lambda.$$ The $\xi$-integral is controlled by $$\begin{gathered}
\biggl|\int \hat{h}(\xi, \lambda)\frac{1 - \psi(\lambda - \xi^3)}{\lambda - \xi^3}d\xi\biggr| \leq \int |\hat{h}(\xi, \lambda)|\frac{1}{1 + |\lambda - \xi^3|}d\xi \\
\leq \int \hat{h}(\xi, \lambda)\frac{1}{(1 + |\lambda - \xi^3|)^b}\,\frac{1}{1 + |\lambda - \xi^3|)^{1 - b}}d\xi \\
\leq \biggl(\int \frac{|\hat{h}(\xi, \lambda)|^2}{(1 + |\lambda - \xi^3|)^{2b}}d\xi\biggr)^{1/2}\biggl(\int \frac{1}{(1 + |\lambda - \xi^3|)^{2(1 - b)}}d\xi\biggr)^{1/2}.\end{gathered}$$ We apply [(\[5.18\])]{}, cancel $|\lambda|^{2/3}$ and bound by $||h||_{Y_b}$ as desired.
Existence and uniqueness results for the homogeneous and inhomogeneous linear quarter-plane problems, with data in Sobolev spaces
=================================================================================================================================
\[6\]
We begin by discussing some spaces of functions of space-time which will be used in our study of the nonlinear problems. Next, we construct and prove estimates on the solutions of the linear homogeneous analogue of [(\[1.2\])]{}. The corresponding construction and estimation of solutions of the linear inhomogeneous problem concludes the section.
Our construction of solutions of [(\[1.1\])]{} relies on a contraction mapping argument for solving the forced initial value problem [(\[1.2\])]{}. This procedure requires us to interpret the traces along $\{t = 0\}$ and $\{x = 0\}$ of the solution of [(\[1.2\])]{} in order to validate the boundary conditions in [(\[7.1\])]{}. The time-localized solutions $w$ of [(\[1.2\])]{} that we construct will have [*good $H_x^s \times H_t^{(s + 1)/3}$ traces*]{} in the sense that, for some $T > 0$, $$\tag{Good Traces}
w \in C\bigl((-T, T); H^s({\mathbb R}_x)\bigr) \cap C\bigl((-\infty, \infty); H^{(s + 1)/3}({\mathbb R}_t)\bigr).$$ The contraction estimate is established in a space closely related to the linearization of [(\[1.2\])]{}. For the general case $k \geq 2$ (with optimizations presented in the modified KdV $k = 2$ and $L^2$ critical $k = 4$ settings), we employ the mixed-norm spaces used in [@10]. These spaces are based on the [*local smoothing effect*]{} $$||\partial_xS(t)\phi||_{L_x^\infty L_t^2} \leq C||\phi||_{L_x^2}$$ and the [*maximal function estimate*]{} $$||S(t)\phi||_{L_x^4L_t^\infty} \leq C||D^{1/4}\phi||_{L_x^2}.$$ Recall from the introduction that the local smoothing effect is closely related to the good traces property (Good Traces), above. In the standard KdV setting $k = 1$, we establish the contraction estimate in the space $X_b$ defined in \[5\].
In this section, we use the results in the previous sections to construct solutions of the homogeneous and inhomogeneous linear analogues of [(\[1.2\])]{}. We also prove a uniqueness result.
Homogeneous solution operator
-----------------------------
We consider the linear homogeneous initial-boundary value problem $$\label{6.1}
\begin{cases}
\partial_tw + \partial_x^3w = 0, & x > 0, t \in (0, T_0) \\
w(x, 0) = \phi(x), & x > 0 \\
w(0, t) = f(t), & t \in [0, T_0],
\end{cases}$$ where $\phi \in H^s({\mathbb R}^+)$, $f \in H^{(s + 1)/3}({\mathbb R}^+)$, $0 \leq s \leq 1$, $w \in C\bigl([0, +\infty); H^{(s + 1)/3}((0, T_0))\bigr) \cap C\bigl([0, T_0]; H^s({\mathbb R}_x^+)\bigr)$. The equation holds in the sense of ${\cal D}'\bigl({\mathbb R}^+ \times (0, T_0)\bigr)$ and the initial value $\phi$ is taken in the sense of $C\bigl([0, +\infty); H^s({\mathbb R}_x^+)\bigr)$, while the ‘lateral value’ $f$ is taken in the sense of $C\bigl([0, +\infty); H^{(s + 1)/3}((0, T_0))\bigr)$. We will split our considerations into the cases $1/2 < s \leq 1$ and $0 \leq s < 1/2$.
\[Th6.1\] Let $1/2 < s \leq 1$. Given $T_0 > 0$, there exists a linear operator $\operatorname{HS}= \operatorname{HS}_{T_0}$ (the homogeneous solution operator) on the subspace of $H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)$ of functions with the property that $f(0) = \phi(0)$ (in the sense of Proposition \[Pn2.3\]) such that $$w = \operatorname{HS}(f, \phi) \in C\bigl((-\infty, +\infty); H^{(s + 1)/3}({\mathbb R}_t)\bigr) \cap C\bigl((-\infty, +\infty); H^s({\mathbb R}_x)\bigr)$$ and $w$ solves [(\[6.1\])]{} in the sense described above. Moreover, $w(x, -)$ and $w(-, t)$ are continuous for each $x$ and $t$ and $w(x, 0) = \phi(x)$ and $w(0, t) = f(t)$ in the sense of Proposition \[Pn2.3\] for $x \geq 0$ and $0 \leq t \leq T_0$. In addition, $w$ satisfies the following estimates: $$\begin{gathered}
\label{6.2}\begin{split}
\sup_{\gamma \in {\mathbb R}} e^{-C|\gamma|}||D_x^{i\gamma}D_x^{s + 1}w||_{L_x^\infty L_t^2} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s} \\
||D_x^s\partial_xw||_{L_x^\infty L_t^2} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s}, \quad s < 1
\end{split} \\
\label{6.3}\sup_{\gamma \in {\mathbb R}} e^{-C|\gamma|}||D_x^{s - 1/4}D_x^{i\gamma}w||_{L_x^4L_t^\infty} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s} \\
\label{6.4}||D_x^sw||_{L_x^5L_t^{10}} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s} \\
\label{6.5}|||w|||_{X_{s, b}} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s}.\end{gathered}$$ (Recall that the space $X_{s, b}$ was defined in Remark \[Rk5.1\].) The constants in all the estimates above depend only on $s$ and $T_0$.
We start out with the construction of $w$. Let $\Psi_1$, $\Psi_2$ and $\Psi_3$ be cut-off functions, all supported on $[-2T_0, 2T_0]$ and identically 1 on $[-T_0, T_0]$, satisfying $\Psi_1.\Psi_2 = \Psi_1$ and $\Psi_2.\Psi_3 = \Psi_2$. Let $\tilde{\phi}$ denote an extension of $\phi$ to all of $\mathbb R$ satisfying ${||\tilde{\phi}||_{H^{s}(\mathbb R)}} \leq C{||\phi||_{H^{s}({\mathbb R}^+)}}$ (see Remark \[Rk2.1\], for instance, for the existence of a linear extension operator). Let $\alpha(t) = S(t)\tilde{\phi}\bigl|_{x = 0}$ and $\tilde{\alpha} = \Psi_1.\alpha$. By [(\[4.4\])]{}, $\tilde{\alpha} \in H^{(s + 1)/3}({\mathbb R}_t)$ and $\tilde{\alpha}(0) = \tilde{\phi}(0) = \phi(0)$. Let $\tilde{f}$ be an extension of $f$ to all of $\mathbb R$ satisfying ${||\tilde{f}||_{H^{(s + 1)/3}(\mathbb R)}} \leq C{||f||_{H^{(s + 1)/3}({\mathbb R}^+)}}$ and let $f_1 = \Psi_1.\tilde{f} - \tilde{\alpha}$. Then, by Propositions \[Pn2.4\] and \[Pn2.6\], we have that $${||f_1||_{H^{(s + 1)/3}(\mathbb R)}} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s},$$ and, given our compatibility condition, we also have $$\label{6.6}
{||f_1||_{H^{(s + 1)/3}_{0}({\mathbb R}^+)}} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s}.$$ Let now $C_A$ be the constant in Proposition \[Pn4.1\], and ${{\mathbb I}}_\alpha$ the Riemann-Liouville fractional integral studied in \[3\]. We define $$\label{6.6(2)}\tilde{h}(t) = \frac{1}{C_A\Gamma(2/3)}{{\mathbb I}}_{-2/3}(\tilde{f}_1)(t), \quad t \in {\mathbb R}^+$$ By Propositions \[Pn3.1\] and \[Pn3.2\], we have that $$\label{6.7}
{||\tilde{h}||_{H^{(s - 1)/3}_{0}({\mathbb R}^+)}} \leq C{||\tilde{f}_1||_{H^{(s + 1)/3}_{0}({\mathbb R}^+)}} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s}.$$ Finally, let $h = \Psi_3.\tilde{h}$. By Propositions \[Pn2.5\], \[Pn2.6\] and \[Pn2.8\], we have (setting $h(t) = 0$ for $t < 0$) $$\label{6.8}
{||h||_{\dot{H}^{(s - 1)/3}_{0}({\mathbb R}^+)}} \simeq {||h||_{H^{(s - 1)/3}({\mathbb R}^+)}} \simeq {||h||_{H^{(s - 1)/3}_{0}(\mathbb R)}} \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s}.$$ We claim that $$\label{6.9}
\Psi_2.{{\mathbb I}}_{2/3}(h) = \frac{1}{C_A\Gamma(2/3)}\tilde{f}_1$$ In fact, we know that ${{\mathbb I}}_{2/3}(\tilde{h}) = \frac{1}{C_A\Gamma(2/3)}\tilde{f}_1$ from the remarks after Definition \[Df3.1\] and density considerations. Hence $\Psi_2.{{\mathbb I}}_{2/3}(\tilde{h}) = \frac{1}{C_A\Gamma(2/3)}\tilde{f}_1$, and so, to verify the claim, all that we need to show is that $\Psi_2{{\mathbb I}}_{2/3}(\tilde{h}) = \Psi_2{{\mathbb I}}_{2/3}(h)$. This is true, by the definition of ${{\mathbb I}}_{2/3}$ and the properties of $\Psi_2$ and $\Psi_3$, for $h \in C_0^\infty({\mathbb R}^+)$, and hence in our case by density considerations.
We now define $$\label{6.10}
w(x, t) = \Psi_2(t)\Bigl\{\int_0^t S(t - t')(\delta_0)(x)h(t')dt' + S(t)\tilde{\phi}(x)\Bigr\}.$$ In view of [(\[6.8\])]{} and Lemmas \[Lm4.1\] and \[Lm4.3\], we see that [(\[6.2\])]{}–[(\[6.4\])]{} hold. [(\[6.5\])]{} holds because of Lemma \[Lm5.2\] and Remark \[Rk5.1\]. The fact that $w \in C\bigl((-\infty, +\infty); H^{(s + 1)/3}({\mathbb R}_t)\bigr) \cap C\bigl((-\infty, +\infty); H^s({\mathbb R}_x$[R]{}\^$?
)\bigr)$ follows also from [(\[6.8\])]{} and Lemmas \[Lm4.1\] and \[Lm4.3\]. The same is true about the continuity statements. The fact that $w(x, 0) = \phi(x)$ for $x \geq 0$ follows from [(\[4.8\])]{} and Proposition \[Pn2.4\], while the fact that $w(0, t) = f(t)$ for $0 \leq t \leq T_0$ follows from Lemma \[Lm4.2\], density, [(\[6.9\])]{}, our definition of $f_1$ and the fact that $\Psi_i \equiv 1$ on $[0, T_0]$. Finally, the fact that the equations in [(\[6.1\])]{} hold follows from [(\[4.7\])]{} and density.
\[Th6.2\] Let $0 \leq s < 1/2$. Given $T_0 > 0$, there exists a linear operator $\operatorname{HS}= \operatorname{HS}_{T_0}$ on $H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)$ such that $$w = \operatorname{HS}(f, \phi) \in C\bigl((-\infty, +\infty); H^{(s + 1)/3}({\mathbb R}_t)\bigr) \cap C\bigl((-\infty, +\infty); H^s({\mathbb R}_x)\bigr),$$ and $w$ solves [(\[6.1\])]{} in the sense described above. Moreover, $w$ satisfies the estimates [(\[6.2\])]{}, [(\[6.4\])]{} and [(\[6.5\])]{} (and [(\[6.3\])]{} if $s \geq 1/4$).
The construction and proof are identical to that of Theorem \[Th6.1\], once one invokes Lemma \[Lm2.3\] and Proposition \[Pn2.6\], so that $H^\alpha_0({\mathbb R}^+) = H^\alpha({\mathbb R}^+)$ for $0 \leq \alpha < 1/2$. This explains the fact that there is no compatibility condition in this range.
\[Rk6.1\] Global (in time) versions of the results in Theorem \[Th6.2\] can be obtained by using the homogeneous Sobolev spaces $\dot{H}^{(s + 1)/3}({\mathbb R}^+)$ and $\dot{H}^{(s + 1)/3}_0({\mathbb R}^+)$, the fact that, for $0 \leq s < 1/2$, $\dot{H}^{(s + 1)/3}({\mathbb R}^+) = \dot{H}^{(s + 1)/3}_0({\mathbb R}^+)$ and the fact that the operators ${{\mathbb I}}_\alpha$ act well on these homogeneous global spaces. For instance, when $s = 0$, given $(f, \phi) \in \dot{H}^{1/3}({\mathbb R}_t^+) \times L^2({\mathbb R}_x^+)$, we can find $w$ in $C\bigl((-\infty, +\infty); \dot{H}^{1/3}({\mathbb R}_t)\bigr) \cap C\bigl((-\infty, +\infty); L^2({\mathbb R}_x)\bigr)$ such that $w(x, 0) = \phi(x)$ and $w(0, t) = f(t)$ for $x, t > 0$, $\partial_tw$v$?
+ \partial_x^3w = 0$ in ${\cal D}'({\mathbb R}^+ \times {\mathbb R}^+)$ and $w$ satisfies the estimate: $$\label{6.11}
\sup_\gamma e^{-C|\gamma|}||D_x^{i\gamma}D_xw||_{L_x^\infty L_t^2} + ||\partial_xw||_{L_x^\infty L_t^2} + ||w||_{L_x^5L_t^{10}} \leq C||(f, \phi)||_{\dot{H}^{1/3} \times L^2}.$$ This follows as in the proof of Theorem \[Th6.2\], leaving out the cut-off functions. Similar results hold on $\dot{H}^{(s + 1)/3}({\mathbb R}_t^+) \times \dot{H}^s({\mathbb R}_x^+)$ for $0 \leq s < 1/2$.
We will now turn to our uniqueness theorem, which will imply that the solutions constructed in Theorems \[Th6.1\] and \[Th6.2\] and Remark \[Rk6.1\] are unique (when restricted to ${\mathbb R}_x^+ \times [0, T_0]$).
\[Th6.3\] Let $w$ be a solution to [(\[6.1\])]{}, with $s = 0$ and $\phi$ and $f$ identically 0. Then $w \equiv 0$ on ${\mathbb R}_x^+ \times [0, T_0]$.
We begin by regularizing our solutions, so that certain identities can be established. First, let $$\tilde{w}(x, t) = \begin{cases}
w(x, t) & (x, t) \in {\mathbb R}^+ \times [0, T_0] \\
0 & (x, t) \not\in {\mathbb R}^+ \times [0, T_0]
\end{cases}$$ and fix $\theta \in C_0^\infty({\mathbb R})$ satisfying $\theta \geq 0$, $\int \theta = 1$ and $\operatorname{supp}\theta \subseteq [-1, -1/2]$. For $\varepsilon, \delta > 0$, define $$\label{6.12}
w_{\varepsilon, \delta}(x, t) = \int{\!\!\!}\int \tilde{w}(y, t')\frac{\theta}{\varepsilon}\biggl(\frac{x - y}{\varepsilon}\biggr){\!\cdot\!}\frac{\theta}{\delta}\biggl(\frac{t - t'}{\delta}\biggr)dy\,dt'.$$ We start out by making a few observations about $w_{\varepsilon, \delta}$. Fix $0 < T < T_0$, and consider only $\delta < T_0 - T$. Suppose that $(x, t) \in {\mathbb R}^+ \times (0, T)$. Then, the integration in the definition of $w_{\varepsilon, \delta}$ takes place on $\{y : \frac{\varepsilon}{2} + x < y < x + \varepsilon\} \times \{t' : \frac{\delta}{2} + t < t' < t + \delta\}$, and hence, for such $(x, t)$, $\tilde{w}(y, t') = w(y, t')$. Thus, since $w_{\varepsilon, \delta} \in C^\infty({\mathbb R} \times {\mathbb R})$, $\partial_tw_{\varepsilon, \delta} + \partial_x^3w_{\varepsilon, \delta} \equiv 0$ on ${\mathbb R}^+ \times (0, T)$. Notice also that $w_{\varepsilon, \delta} \in C\bigl([0, \infty); H^{1/3}((0, T))\bigr) \cap C\bigl([0, T]; L^2({\mathbb R}^+)\bigr)$, uniformly in $(\varepsilon, \delta)$. We will now establish the identity $$\label{6.13}
\partial_t{\!}\int{\nolimits}_{x > x_0} w_{\varepsilon, \delta}^2(x, t)dx = 2\partial_x^2w_{\varepsilon, \delta}(x_0, t)\!\cdot\!w_{\varepsilon, \delta}(x_0, t) - \bigl(\partial_xw_{\varepsilon, \delta}(x_0, t)\bigr)^2$$ for $x_0 \geq 0$ and $0 \leq t \leq T$. In fact, for $\varepsilon$, $\delta$ fixed, $\partial_tw_{\varepsilon, \delta}, \partial_x^3w_{\varepsilon, \delta} \in L^2({\mathbb R}^+)$ for each such fixed $t$, and hence the left-hand side of [(\[6.13\])]{} equals $$2{\!}\int{\nolimits}_{x > x_0} \partial_tw_{\varepsilon, \delta}(x, t)\!\cdot\!w_{\varepsilon, \delta}(x, t)dx = -2{\!}\int_{x > x_0} \partial_x^3w_{\varepsilon, \delta}(x, t)\!\cdot\!w_{\varepsilon, \delta}(x, t)dx.$$ Note that, since $\partial_x^3w_{\varepsilon, \delta}, \partial_x^2w_{\varepsilon, \delta}, \partial_xw_{\varepsilon, \delta}, w_{\varepsilon, \delta} \in L^2({\mathbb R}^+)$, we can certainly find $x_n \rightarrow +\infty$ so that $\partial_x^jw_{\varepsilon, \delta}(x_n, t) \rightarrow 0$ for all $j = 0, 1, 2, 3$. Then we see that the right-hand side above equals $$\begin{gathered}
2\partial_x^2w_{\varepsilon, \delta}(x_0, t)\!\cdot\!w_{\varepsilon, \delta}(x_0, t) + 2{\!}\int{\nolimits}_{x > x_0} \partial_x^2w_{\varepsilon, \delta}(x, t)\!\cdot\!\partial_xw_{\varepsilon, \delta}(x, t)dx \\
= 2\partial_x^2w_{\varepsilon, \delta}(x_0, t)\!\cdot\!w_{\varepsilon, \delta}(x_0, t) - \bigl(\partial_xw_{\varepsilon, \delta}(x_0, t)\bigr)^2,\end{gathered}$$ as claimed. Fix $0 < t_0 \leq T$, and integrate [(\[6.13\])]{} between $0$ and $t_0$ to obtain $$\begin{gathered}
\label{6.14}
\int{\nolimits}_{x > x_0} w_{\varepsilon, \delta}^2(x, t_0)dx - \int{\nolimits}_{x > x_0} w_{\varepsilon, \delta}^2(x, 0)dx \\
= 2{\!}\int_0^{t_0} \partial_x^2w_{\varepsilon, \delta}(x_0, t)\!\cdot\!w_{\varepsilon, \delta}(x_0, t)dt - \int_0^{t_0} \bigl(\partial_xw_{\varepsilon, \delta}(x_0, t)\bigr)^2dt \\
\leq 2\int_0^{t_0} \partial_x^2w_{\varepsilon, \delta}(x_0, t)\!\cdot\!w_{\varepsilon, \delta}(x_0, t)dt.\end{gathered}$$
Fix now $0 < \delta < T_0 - T$, and define $w_\delta(x, t) = \int \tilde{w}(x, t')\frac{\theta}{\delta}\bigl(\frac{t - t'}{\delta}\bigr)dt'$.
\[6.15\] $w_{\varepsilon, \delta}, \partial_xw_{\varepsilon, \delta}, \partial_x^2w_{\varepsilon, \delta} \in C\bigl([0, 1]; L^2([0, T])\bigr)$, uniformly in $\varepsilon > 0$, for $\delta > 0$ fixed. In fact, since $w \in C\bigl([0, 2]; H^{1/3}((0, T_0))\bigr)$, this easily follows for $w_{\varepsilon, \delta}$, and for $\partial_tw_{\varepsilon, \delta}$. By the equation, this also follows for $\partial_x^3w_{\varepsilon, \delta}$. Next, it is easy to check that $\partial_x^2w_{\varepsilon, \delta} \in L^\infty\bigl([0, 1]; L^2([0, T])\bigr)$, uniformly in $\varepsilon$. In fact, let $f \in L^2\bigl([0, T]\bigr)$ satisfy $||f||_{L^2} = 1$, and consider $F(x) = \int_0^T w_{\varepsilon, \delta}(x, t)f(t)dt$. Then, as is well-known, $$F(x_0 + h) + F(x_0 - h) - 2F(x_0) = F''(\overline{x})h^2$$ for some $\overline{x} \in (x_0 - h, x_0 + h)$, for each $h > 0$. Choose $x_0 = 1/2$ and $h = 1/4$ to conclude that $$\Bigl|\int_0^T \partial_x^2w_{\varepsilon, \delta}(\overline{x}, t)f(t)dt\Bigr| \leq C_\delta$$ since $w_{\varepsilon, \delta} \in C\bigl([0, 1]; L^2([0, T])\bigr)$ – but, if we consider any fixed $x \in [0, 1]$, $$\begin{gathered}
\int_0^T \partial_x^2w_{\varepsilon, \delta}(x, t)f(t)dt = \int_0^T \bigl[\partial_x^2w_{\varepsilon, \delta}(x, t) - \partial_x^2w_{\varepsilon, \delta}(\overline{x}, t)\bigr]f(t)dt \\
+ \int_0^T \partial_x^2w_{\varepsilon, \delta}(\overline{x}, t)f(t)dt,\end{gathered}$$ and, using the fact that $\partial_x^3w_{\varepsilon, \delta} \in C\bigl([0, 1]; L^2([0, T])\bigr)$, our claim follows. Once we know this, our estimate on $\partial_x^3w_{\varepsilon, \delta}$ shows that $\partial_x^2w_{\varepsilon, \delta} \in C\bigl([0, 1]; L^2([0, T])\bigr)$, uniformly in $\varepsilon$, and in fact they are equicontinuous in $\varepsilon$. The statement for $\partial_xw_{\varepsilon, \delta}$ follows similarly.
\[6.16\] For any fixed $0 \leq x_0 \leq 1$, $w_{\varepsilon, \delta}(x_0, -) \xrightarrow{\varepsilon \rightarrow 0} w_\delta(x_0, -)$ in $L^2\bigl([0, T]\bigr)$. Note that this is immediate from the definitions and the fact that $w_\delta \in C\bigl([0, 1]; L^2([0, T])\bigr)$ since $w$ is in $C\bigl([0, 1]; L^2([0, T_0])\bigr)$.
\[6.17\] For any fixed $0 \leq x_0 \leq 1$ and $0 \leq t_0 \leq T$, $$\int{\nolimits}_{x > x_0} w_{\varepsilon, \delta}^2(x, t_0)dx \xrightarrow{\varepsilon \rightarrow 0} \int{\nolimits}_{x > x_0} w_\delta^2(x, t_0)dx.$$ This follows easily from the fact that $w_\delta \in C\bigl([0, T]; L^2({\mathbb R}^+)\bigr)$. Now, using [(\[6.14\])]{}–[(\[6.16\])]{}, we see that, for $x_0 \in [0, 1]$, $$\label{6.18}
\int{\nolimits}_{x > x_0} w_\delta^2(x, t_0)dx - \int{\nolimits}_{x > x_0} w_\delta^2(x, 0)dx \leq C_\delta||w_\delta(x_0, -)||_{L^2([0, T])}.$$ Next, note that, as $x_0 \rightarrow 0$, $||w_\delta(x_0, -)||_{L^2([0, T])} \rightarrow ||w_\delta(0, -)||_{L^2([0, T])}$ since $w_\delta \in C\bigl([0, 1]; L^2([0, T])\bigr)$, which follows from $w \in C\bigl([0, 1]; L^2([0, T])\bigr)$. By our assumption and the definition of $w_\delta$, however, $w_\delta(0, -) \equiv 0$ on $[0, T]$. Thus, it is easy to see that [(\[6.18\])]{} yields $$\label{6.19}
\int{\nolimits}_{x > 0} w_\delta^2(x, t_0)dx \leq \int{\nolimits}_{x > 0} w_\delta^2(x, 0)dx.$$ Since, however, $w \in C\bigl([0, T]; L^2({\mathbb R}^+)\bigr)$, as $\delta \rightarrow 0$ we obtain $$\int{\nolimits}_{x > 0} w^2(x, t_0)dx \leq \int{\nolimits}_{x > 0} w^2(x, 0)dx = 0,$$ and hence $w \equiv 0$ on ${\mathbb R}^+ \times [0, T]$ as desired.
Inhomogeneous linear solution operator
--------------------------------------
Next, we turn our attention to constructing solutions to the inhomogeneous linear quarter-plane problem $$\label{6.20}
\begin{cases}
\partial_tw + \partial_x^3w = h, & x > 0, t \in (0, T_0) \\
w(x, 0) = 0, & x > 0 \\
w(0, t) = 0, & t \in [0, T_0].
\end{cases}$$
\[Th6.4\] Assume that $0 \leq s \leq 1$, $s \neq 1/2$ and $h \in L^2_{T_0}H^s({\mathbb R}_x^+)$. Given $T_0$, there exists a linear operator $\operatorname{IHS}= \operatorname{IHS}_{T_0}$ (the inhomogeneous solution operator) such that $$w = \operatorname{IHS}(h) \in C\bigl((-\infty, +\infty); H^{(s + 1)/3}({\mathbb R}_t)\bigr) \cap C\bigl((-\infty, +\infty); H^s({\mathbb R}_x)\bigr),$$ and $w$ solves [(\[6.20\])]{} in the sense that the equation holds in ${\cal D}'\bigl({\mathbb R}^+ \times (0, T_0)\bigr)$, and the ‘lateral values’ are taken in the sense of $C\bigl((-\infty, +\infty); H^{(s + 1)/3}((0, T_0))\bigr)$ and the initial ones in the sense of $C\bigl([0, T_0]; H^s({\mathbb R}_x^+)\bigr)$. (If $s > 1/2$, this also holds in the pointwise sense.) In addition, for $T_0 \leq 1$, $w$ satisfies the following estimates:
[([[.]{}.]{})]{}
\[6.21\] We have $$\sup_t {||w(-, t)||_{H^{s}({\mathbb R}_x)}} \leq CT_0^{\beta(s)}||h||_{L_{T_0}^2H^s({\mathbb R}_x^+)}.$$
\[6.22\] We have $$\sup_x {||w(x, -)||_{H^{(s + 1)/3}({\mathbb R}_t)}} \leq CT_0^{\beta(s)}||h||_{L_{T_0}^2H^s({\mathbb R}_x^+)}.$$
\[6.23\] We have $$\sup_x {||w(x, -)||_{H^{(s + 1)/3}_{0}({\mathbb R}_t^+)}} \leq CT_0^{\beta(s)}||h||_{L_{T_0}^2H^s({\mathbb R}_x^+)}.$$
\[6.24\] The quantities on the left-hand sides of [(\[6.2\])]{}, [(\[6.3\])]{} and [(\[6.4\])]{}, in case $s \geq 1/4$, are controlled by $CT_0^{\beta(s)}||h||_{L_{T_0}^2H^s({\mathbb R}_x^+)}$,
where $\beta(s) = \frac{1}{3} - \frac{s}{6}$.
Let $$w\_1(x, t) = \_0\^t S(t - t’)(x, t’)dt’,$$ where $\tilde{h} \in L^2\bigl((-\infty, +\infty); H^s({\mathbb R}_x)\bigr)$ and $\tilde{h}$ satisfies $$\tilde{h}(x, t) = \begin{cases}
h(x, t), & (x, t) \in {\mathbb R}^+ \times [0, T_0] \\
0, & t > T_0\text{ or }t < 0
\end{cases}$$ and $||\tilde{h}||_{L_t^2H^s({\mathbb R})} \leq C||h||_{L_{T_0}^2H^s({\mathbb R}_x^+)}$. (Moreover, by Remark \[Rk2.1\], we can take $\tilde{h} = E(h)$, where $E$ is a linear extension operator in the $x$ variable.) We know that $\partial_tw_1 + \partial_x^3w_1 = \tilde{h}$ in ${\cal D}'({\mathbb R} \times {\mathbb R})$. We next consider the estimates [(\[6.21\])]{}–[(\[6.24\])]{} for $w_1$. Minkowski’s integral inequality and the corresponding estimates for the group ([(\[4.1\])]{}, [(\[4.2\])]{}, [(\[4.5\])]{}) show that (in the case of [(\[6.21\])]{}, for instance), with $\Psi \equiv 1$ on $[-T_0, T_0]$ and $\operatorname{supp}\Psi \subseteq [-2T_0, 2T_0]$, $$\begin{gathered}
\label{6.25}
\Bigl|\Bigl|\Psi(t){\!}\int_0^t S(t - t')\tilde{h}(x, t')dt'\Bigr|\Bigr|_{H^s({\mathbb R}_x)} \leq \int_{-2T_0}^{2T_0} {||S(t - t')\tilde{h}(x, t')||_{H^{s}({\mathbb R}_x)}}dt' \\
\leq C{\!}\int_0^{T_0} {||h(-, t')||_{H^{s}({\mathbb R}_x^+)}}dt' \leq CT_0^{1/2}||h||_{L_{T_0}^2H^s({\mathbb R}_x^+)}\end{gathered}$$ and, since $\beta(s) \leq 1/2$, $\Psi(t)w_1(x, t)$ satisfies the estimates [(\[6.21\])]{} and [(\[6.24\])]{}. Finally, translation invariance and [(\[4.48\])]{} give [(\[6.22\])]{} and [(\[6.23\])]{} for $\Psi(t)w_1(x, t)$, as well as the correct continuity and trace statements (see Remark \[Rk4.2\]). Next, let $f(t) = \Psi(t)w_1(0, t)$, $T = \max\{2T_0, 1\}$ and $w_2 = \operatorname{HS}_T(f, 0)$, where $\operatorname{HS}_T$ is the operator constructed in Theorems \[Th6.1\] and \[Th6.2\]. (Note that [(\[4.48\])]{} shows that $f \in H^{(s + 1)/3}_0({\mathbb R}^+)$, and hence, for $s > 1/2$, the compatibility condition in Theorem \[6.1\] is satisfied.) Finally, let $w(x, t) = \Psi(t)w_1(x, t) - w_2(x, t)$. Estimate [(\[4.48\])]{}, together with Theorems \[Th6.1\] and \[Th6.2\] and the above estimates for $w_1$, now gives the desired result.
\[Th6.6\] Let $w = \operatorname{IHS}_{T_0}(h)$. Then, if $h \in L_x^{5/4}L_t^{10/9}$, then $$w \in C\bigl((-\infty, +\infty); L^2({\mathbb R}_x)\bigr) \cap C\bigl((-\infty, +\infty); H^{1/3}({\mathbb R}_t)\bigr),$$ ${\frac{\partial w}{\partial x}} \in L_x^\infty L_t^2$, $w \in L_x^5L_t^{10}$ (all with norm control) and $w$ solves [(\[6.20\])]{} in the sense of Theorem \[Th6.4\], with $s = 0$.
Clearly, it suffices to establish the estimates. Let $w_1(x, t) = \int_0^t S(t - t')h(x, t')dt'$. Then, by [(\[4.47\])]{}, $$||w_1||_{L_x^5L_t^{10}} \leq C||h||_{L_x^{5/4}L_t^{10/9}}.$$ To show that ${\frac{\partial w}{\partial x}} \in L_x^\infty L_t^2$, we first note that $${\frac{\partial w}{\partial x}} = {\cal H}D_xw = D_x{\!}\int_0^t S(t - t'){\cal H}(h)(x, t')dt',$$ with $\cal H$ the Hilbert transform on functions in the $x$-variable. Since $\cal H$ is bounded on $L_x^{5/4}L_t^{10/9}$ (see [@15]), it suffices to show that $D_xw \in L_x^\infty L_t^2$. Using [(\[4.16\])]{} and duality reduces matters to checking that each one of the terms in [(\[4.16\])]{} maps $L_x^1L_t^2$ into $L_x^5L_t^{10}$. This, in turn, follows by complex interpolation between the second inequality for $s = 1$ in [(\[4.7\])]{} and the first inequality in [(\[4.11\])]{}, together with translation invariance (to pass from $\delta_0 \otimes h$ to $\delta_{x_0} \otimes h$) and Minkowski’s integral inequality. (The proof also follows from Proposition 2.3 in [@13].) The fact that $w_1 \in C\bigl((-\infty, +\infty); \dot{H}^{1/3}({\mathbb R}_t)\bigr)$ follows from a familiar density argument, together with the inequality $$\label{6.30}{}
||w_1||_{L_x^\infty\dot{H}^{1/3}_t} \leq C||h||_{L_x^{5/4}L_t^{10/9}}.$$ Once again, [(\[6.30\])]{} follows from [(\[4.16\])]{}, duality and the first inequality in [(\[4.7\])]{}, together with translation invariance and Minkowski’s integral equality. The fact that $w_1 \in C\bigl((-\infty, +\infty); L^2({\mathbb R}_x)\bigr)$ follows by duality from [(\[4.5\])]{} with $s = 0$, in the same manner as [(\[4.43\])]{} is established in (3.7) of [@10]. The fact that $H^{1/3}({\mathbb R}_t^+) = H^{1/3}_0({\mathbb R}_t^+)$ (see Proposition \[Pn2.6\]) and the Hardy-Littlewood-Sobolev inequality $$\label{6.31}
||f||_{L^6({\mathbb R})} \leq C||D_t^{1/3}f||_{L^2({\mathbb R})},$$ together with the Leibniz rule (Theorem A.12 in [@10]), now allow us to establish the desired bounds for $\Psi.w_1$. Finally, since $f = \Psi w_1(0, -) \in H^{1/3}_0({\mathbb R}_t^+)$, the corresponding bounds for $w_2$ follow from Theorem \[Th6.2\].
\[Rk6.2\] A global (in time) version of Theorem \[Th6.6\] can be established by using the homogeneous Sobolev space $\dot{H}^{1/3}$, together with Remark \[Rk6.1\] and the proof above, and omitting the cut-off function. We obtain a solution $w$ defined on ${\mathbb R}^+ \times {\mathbb R}^+$+$s?
$ which lies in $$C\bigl((-\infty, +\infty); L^2({\mathbb R}_x)\bigr) \cap C\bigl((-\infty, +\infty); \dot{H}^{1/3}({\mathbb R}_t)\bigr) \cap L_x^5L_t^{10}({\mathbb R} \times {\mathbb R})$$ and satisfies ${\frac{\partial w}{\partial x}} \in L_x^\infty L_t^2$.
The final result of this section is a Bourgain space analogue of Theorem \[Th6.4\]. We show that the inhomogeneous solution operator $\operatorname{IHS}$ sends the inhomgeneity $w \in Y_b$ into $X_b$ functions with well-defined traces along $\{x = 0\}$ and $\{t = 0\}$ as $H_t^{1/3}$ and $L_x^2$ functions.
\[Th6.6’\] Suppose that $h = \tilde{h}\bigr|_{{\mathbb R}_x^+ \times [0, T_0]}$, with $\tilde{h} \in Y_{s, b}$ for some $0 \leq s \leq 1$, $s \neq \frac{1}{2}$. Then $w = \operatorname{IHS}_{T_0}(\tilde{h}{})$ belongs to $C\bigl((-\infty, \infty); H^{(s + 1)/3}({\mathbb R}_t)\bigr) \cap C\bigl((-\infty, \infty); H^s({\mathbb R}_x)\bigr)$, and $w$ solves [(\[6.20\])]{} in the sense of Theorem \[Th6.4\]. Moreover, $w$ satisfies the following estimates: $$\begin{gathered}
\label{6.25'} \sup_t {||w(-, t)||_{H^{s}({\mathbb R}_x)}} \leq C_{T_0}||h||_{Y_{s, b}} \\
\label{6.26'} \sup_x {||w(x, -)||_{H^{(s + 1)/3}({\mathbb R}_t)}} \leq C_{T_0}||h||_{Y_{s, b}} \\
\label{6.27'} \sup_x {||w(x, -)||_{H^{(s + 1)/3}_{0}({\mathbb R}_t)}} \leq C_{T_0}||h||_{Y_{s, b}} \\
\intertext{and}
\label{6.28'} ||w||_{X_{s, b}} \leq C_{T_0}||h||_{Y_{s, b}}.\end{gathered}$$
Lemma \[Lm5.4\] implies [(\[6.28’\])]{}. Lemma \[Lm5.5\] and the results of \[2\] imply [(\[6.25’\])]{}–[(\[6.27’\])]{}.
\[Rk6.3\] Theorem \[Th6.3\] implies the uniqueness of the restriction to ${\mathbb R}^+ \times [0, T_0]$ of the solutions constructed in Theorems \[Th6.4\]–\[Th6.6’\].
\[Rk6.4\] The methods in the previous section also apply, with minor modifications, to the homogeneous and inhomogeneous problems with a transport term $c\partial_xu$, $c \neq 0$. For example, for the homogeneous problem, $$\begin{cases}
\partial_tw + \partial_x^3w + c\partial_xw = 0, & x > 0, t \in (0, T_0) \\
w(x, 0) = \phi(x), & x > 0 \\
w(0, t) = f(t), &
\end{cases}$$ one still introduces the forced initial value problem $$\begin{cases}
\partial_t\tilde{w} + \partial_x^3\tilde{w} + c\partial_x\tilde{w} = \delta_0(x)g(t), & x \in {\mathbb R}, t \in (0, T_0) \\
\tilde{w}(x, 0) = \tilde{\phi}(x), &
\end{cases}$$ where the forcing function $g$ is selected to ensure that $\tilde{w}(0, t) = \tilde{f}(t)$, $t \in (0, T_0)$. To see that this can be done (for $T_0$ small), let $$\tilde{S}(t)\phi(x) = \int e^{i(x\xi + t(\xi^3 + c\xi))}\hat{\phi}(\xi)d\xi$$ and consider the integral equation $$\int_0^t \tilde{S}(t - t')\delta_0(x)g(t')dt'\Bigr|_{\{x = 0\}} = \tilde{f}(t) - \tilde{S}(t)\phi(x)\bigr|_{x = 0} = \Tilde{\Tilde{f}}(t).$$ Using the notation of \[2\], \[3\] and \[4\], the left-hand side becomes $$\int_0^t \frac{1}{(t - t')^{1/3}}A\bigl((t - t')^{2/3}c\bigr)g(t')dt' = A_c(g)(t).$$ Note that $A(0) \neq 0$, and $A$ is differentiable at $0$, since $\int e^{i\xi^3}\xi\,d\xi = \int e^{i\eta}\frac{\eta^{1/3}}{\eta^{2/3}}d\eta$. Thus, it is easy to see that $A_c(g) - A(0)\int_0^t \frac{g(t')dt'}{(t - t')^{1/3}}$ maps $H_0^{-1}({\mathbb R}^+)$ into $H_0^{1/3}({\mathbb R}^+)$ and $L^2({\mathbb R}^+)$ into $H_0^1\bigl((0, T_0]\bigr)$, with norm small in $T_0$. This, combined with the results in \[2\], \[3\] and \[4\], gives the invertibility of $A_c(g)$ from $H_0^{(s - 1)/3{}}\bigl((0, T_0]\bigr)$ onto $H_0^{(s + 1)/3{}}\bigl((0, T_0]\bigr)$ for small $T_0$. The oscillatory integral estimates in \[4\] (for small time) for the multipliers $e^{it\xi^3}$ and $e^{it(\xi^3 + c\xi)}$ are identical, while the estimates in \[5\], in the Bourgain spaces $$\begin{gathered}
\tilde{X}_b = \Bigl\{f \in {\cal S}'({\mathbb R}^2) : \Bigl(\int{\!\!\!}\int (1 + |\lambda - (\xi^3 + c\xi)|)^{2b}|\hat{f}(\xi, \lambda)|^2d\xi\,d\lambda\Bigr)^{1/2} \\
+ \Bigl(\int{\!\!\!}\int{\nolimits}_{|\xi| < 1} (1 + |\lambda|)^{2\alpha}|\hat{f}(\xi, \lambda)|^2d\xi\,d\lambda\Bigr)^{1/2}\Bigr\},\end{gathered}$$ are also identical. Thus, the results in Theorems \[Th6.1\], \[Th6.2\], \[Th6.4\], \[Th6.6\] and \[Th6.6’\] extend to this setting. The uniqueness result Theorem \[Th6.3\] does hold too (with similar proof).
Well-posedness results for the nonlinear problems
=================================================
\[7\]
In this section we will deal with well-posedness results for the nonlinear quarter-plane problem $$\label{7.1}
\begin{cases}
\partial_tu + \partial_x^3u + u^k\partial_xu, & x > 0, t \in [0, T], k \in {\mathbb N} \\
u(x, 0) = \phi(x), & x > 0 \\
u(0, t) = f(t), & t \in [0, T].
\end{cases}$$ Using the solutions to the corresponding linear problems and their estimates, as presented in \[6\], our results will follow from the methods in [@5] and [@10], yielding identical results. To avoid a lengthy discussion, we have decided to detail only certain “highlight” results. The techniques presented in \[6\] and the ones in this section do, however, yield in full the results in [@5] and [@10].
Well-posedness of generalized KdV in mixed-norm spaces
------------------------------------------------------
We start out by discussing the case $k \geq 2$, first presenting a relatively straightforward result which gives the local well-posedness for $\phi \in H^s({\mathbb R}^+)$, $f \in H^{(s + 1)/3}({\mathbb R}^+)$, $1/2 < s \leq 1$ and $k \geq 2$.
\[Th7.1\] If $k \geq 2$ and $1/2 < s \leq 1$, then, given $(f, \phi) \in H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)$ satisfying the compatibility condition $f(0) = \phi(0)$, there exists $$T = T(||(f, \phi)||_{H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)})$$ such that the ‘integral equation’ $$\label{7.2}
w = \operatorname{HS}_1{}(f, \phi) + \operatorname{IHS}_{2T}(\Psi.w^k.\partial_xw),$$ where $\Psi \equiv 1$ on $[-T, T]$ and $\operatorname{supp}\Psi \subseteq [-2T, 2T]$, has a unique fixed point in the space $$B = \bigl\{w \in C\bigl((-\infty, +\infty); H^s({\mathbb R})\bigr) \cap C\bigl((-\infty, +\infty); H^{(s + 1)/3}({\mathbb R})\bigr) : \Lambda(w) < \infty\},$$ where $\Lambda(w) = \max{\nolimits}_{1 \leq i \leq 6} \lambda_i(w)$ for $$\begin{aligned}
\lambda_1(w) & = \sup_x {||w(x, -)||_{H^{(s + 1)/3}(\mathbb R)}}, \\
\lambda_2(w) & = \sup_t {||w(-, t)||_{H^{s}(\mathbb R)}}, \\
\lambda_3(w) & = \sup_\gamma e^{-C|\gamma|}||D_x^{i\gamma}D_x^{s + 1}w||_{L_x^\infty L_t^2} + ||D_x^s\partial_xw||_{L_x^\infty L_t^2} \\
\intertext{(where the second term is added only when $s < 1$),}
\lambda_4(w) & = \sup_\gamma e^{-C|\gamma|}||D_x^{i\gamma}D_xw||_{L_x^\infty L_t^2} + ||\partial_xw||_{L_x^\infty L_t^2,} \\
\lambda_5(w) & = \sup_\gamma e^{-C|\gamma|}||D_x^{s - 1/4}D_x^{i\gamma}w||_{L_x^4L_t^\infty} \\
\intertext{and}
\lambda_6(w) & = \sup_\gamma e^{-C|\gamma|}||D_x^{i\gamma}w||_{L_x^4L_t^\infty}.\end{aligned}$$ The resulting $w$ solves [(\[7.1\])]{} in ${\mathbb R}^+ \times [0, T]$.
We will show that, for $T$ small, the mapping $$M\_[(f, )]{}(w) = \_1(f, ) + \_[2T]{}(.w\^k.\_xw)$$ is a contraction on $B_a = \{w \in B : \Lambda(w) \leq a\}$ for suitable $a$. First note that Theorems \[Th6.1\] and \[Th6.2\] show that $\operatorname{HS}_1(f, \phi) \in B$ and $$\Lambda\bigl(\operatorname{HS}_1(f, \phi)\bigr) \leq C||(f, \phi)||_{H^{(s + 1)/3} \times H^s}.$$ Now Theorem \[Th6.4\] reduces matters to the ‘non-linear estimate’ $$\label{7.2(2)}||\Psi.w^k.\partial_xw||_{L_{2T}^2H^s({\mathbb R})} \leq C\Lambda(w)^{k + 1},$$ which we proceed to establish. The left-hand side of [(\[7.2(2)\])]{} is controlled by $$||\Psi.w^k.\partial_xw||_{L_{2T}^2L_x^2} + ||\Psi.D_x^s(w^k.\partial_xw)||_{L_{2T}^2L_x^2} = I + II.$$ For $I$, we use the bound $||w^{k - 2}||_{L_x^\infty} \leq C{||w||_{H^{s}_{x}}}^{k - 2}$, which follows from Sobolev embedding and the fact that $s > 1/2$, to estimate $$I \leq C\lambda_2(w)^{k - 2}||\Psi.w^2.\partial_xw||_{L_{2T}^2L_x^2} \leq C\lambda_2(w)^{k - 2}\lambda_6(w)^2\lambda_4(w) \leq C\Lambda(w)^{k + 1}.$$ In order to bound $II$, we use the Leibniz rule, Theorem A.8 of [@10], and the chain rule, Theorem A.6 of [@10], to find that $$\begin{gathered}
II \leq ||D_x^s(w^k.\partial_xw)||_{L_t^2L_x^2} \leq ||D_x^s(w^k.\partial_xw) - w^k.D_x^s\partial_xw - D_x^s(w^k)\partial_xw||_{L_x^2L_t^2} \\
+ ||w^kD_x^s\partial_xw||_{L_x^2L_t^2} + ||D_x^s(w^k)\partial_xw||_{L_x^2L_T^2} =: II_1 + II_2 + II_3.\end{gathered}$$ We have $$II_2 \leq C\lambda_2(w)^{k - 2}||w^2.D_x^s\partial_xw||_{L_x^2L_t^2} \leq C\lambda_2(w)^{k - 2}\lambda_6(w)^2\lambda_3(w).$$ For $II_3$, we use Hölder’s inequality to see that $$\begin{gathered}
II_3 \leq ||\partial_xw||_{L_x^{4(s + 1)/s}L_t^{2(s + 1)}}||D_x^s(w^k)||_{L_x^{4(s + 1)/(s + 2)}L_t^{2(s + 1)/s}} \\
\overset{*}{\leq} C||\partial_xw||_{L_x^{4(s + 1)/s}L_t^{2(s + 1)}}||D_x^s(w)||_{L_x^{4(s + 1)}L_t^{2(s + 1)/s}}||w^{k - 1}||_{L_x^4L_t^\infty} \\
C\lambda_2(w)^{k - 2}\lambda_6(w)||\partial_xw||_{L_x^{4(s + 1)/s}L_t^{2(s + 1)}}||D_x^sw||_{L_x^{4(s + 1)}L_t^{2(s + 1)/s}}.\end{gathered}$$ We have used Theorem A.6 of [@10] to justify the inequality marked with a $*$. Note, however, that $$||\partial_xw||_{L_x^{4(s + 1)/s}L_t^{2(s + 1)}} \leq C\lambda_3(w)^\theta\lambda_6(w)^{1 - \theta},$$ where $\theta = 1/(s + 1)$, and $$||D_x^s(w)||_{L_x^{4(s + 1)}L_t^{2(s + 1)/s}} \leq C\lambda_3(w)^{\theta'}\lambda_6(w)^{1 - \theta'},$$ where $\theta' = s/(s + 1)$, by a well-known variant of the three-lines theorem (see, for instance, Lemma 4.2 in Chapter V of [@17]). (In the case of the first inequality, we also need to pass from $D_xw$ to $\partial_xw$, which involves the boundedness of the Hilbert transform in mixed-norm spaces.) The end result of all this is that $II_3 \leq C\Lambda(w)^{k + 1}$. Finally, Theorem A.8 of [@10] shows that $$II_1 \leq C||D_x^s(w^k)||_{L_x^{4(s + 1)/(s + 2)}L_t^{2(s + 1)/s}}||\partial_xw||_{L_x^{4(s + 1)/s}L_t^{2(s + 1)}},$$ and, proceeding as in the proof of the bound for $II_3$, we arrive at [(\[7.2(2)\])]{}.
We now give, for each $k \geq 2$, a precise result, following [@10]. We will carry out the details only in the cases $k = 2$ and $k = 4$.
### The case $k = 2$, modified KdV
\[Th7.2\] For $k = 2$ and $1/4 \leq s < 1/2$, given $(f, \phi) \in H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)$, there exists $$T = T(||(f, \phi)||_{H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)})$$ such that the ‘integral equation’ [(\[7.2\])]{} (for $k = 2$) has a unique fixed point in the space $B$ defined in Theorem \[Th7.1\]. The resulting $w$ solves [(\[7.1\])]{} in ${\mathbb R}^+ \times [0, T]$.
The proof is identical to that of Theorem \[Th7.1\]. The only place where $s > 1/2$ played a role there was in the bound $||w^{k - 2}||_{L_x^\infty L_T^\infty} \leq C\lambda_2(w)^{k - 2}$, which, when $k = 2$, is not needed. Note that, even in the half-plane case, it is known that one cannot take $s < 1/4$ ([@14']). In our proof, this is reflected in the exponent $s - 1/4$ in [(\[4.5\])]{}.
\[Rk7.1\] One can construct solutions in Theorems \[Th7.1\] and \[Th7.2\] for arbitrarily large $T$ by making $||(f, \phi)||_{H^{(s + 1)/3} \times H^s}$ small. We need only replace, for $T > 1$, $\operatorname{HS}_1$ by $\operatorname{HS}_{2T}$.
### The case $k = 4$
We have chosen to do in detail the case $k = 4$ because its proof is slightly simpler, since it does not involve fractional derivatives. (See [@10] and [@13] for proofs in the half-plane case.)
\[Df7.1\] We define $\operatorname{HS}_\infty$ and $\operatorname{IHS}_\infty$ to be the operators arising in Remarks \[Rk6.1\] and \[Rk6.2\], respectively.
\[Th7.3\] For $k = 4$, given $(f, \phi) \in \dot{H}^{1/3}({\mathbb R}^+) \times L^2({\mathbb R}^+)$ such that $$||(f, \phi)||_{\dot{H}^{1/3} \times L^2} \leq \delta$$ (with $\delta > 0$ an absolute constant), the integral equation $$\label{7.3}
w = \operatorname{HS}_\infty(f, \phi) + \operatorname{IHS}_\infty(w^4\partial_xw)$$ has a unique fixed point in the space $$B = \bigl\{w \in C\bigl((-\infty, +\infty); \dot{H}^{1/3}({\mathbb R})\bigr) \cap C\bigl((-\infty, +\infty); L^2({\mathbb R})\bigr) : \Lambda(w) < \infty\},$$ where $\Lambda(w) = \max{\nolimits}_{1 \leq i \leq 4} \lambda_i(w)$ for $$\begin{aligned}
\lambda_1(w) & = \sup_x {||w(x, -)||_{\dot{H}^{1/3}(\mathbb R)}}, \\
\lambda_2(w) & = \sup_t ||w(-, t)||_{L^2({\mathbb R})}, \\
\lambda_3(w) & = ||\partial_xw||_{L_x^\infty L_t^2} \\
\intertext{and}
\lambda_4(w) & = ||w||_{L_x^5L_t^{10}}.\end{aligned}$$ The resulting $w$ solves [(\[7.1\])]{} (for $k = 4$) in ${\mathbb R}^+ \times (0, \infty)$.
Note that [(\[6.11\])]{} shows that $\Lambda\bigl(\operatorname{HS}_\infty(f, \phi)\bigr) \leq C\delta$. Moreover, note that, if $w \in B$, then Hölder’s inequality shows that $w^4\partial_xw \in L_x^{5/4}L_t^{10/9}$. Thus, Remark \[Rk6.2\] shows that $\Lambda\bigl(\operatorname{IHS}_\infty(w^4\partial_xw)\bigr) \leq C\Lambda(w)^5$, and so, if $B_a = \{w \in B : \Lambda(w) \leq a\}$ and $w \in B_a$, we have that $$\Lambda\bigl(\operatorname{HS}_\infty(f, \phi) + \operatorname{IHS}_\infty(w^4\partial_xw)\bigr) \leq C\delta + Ca^5 \leq C\delta + \frac{1}{2}a$$ whenever $Ca^4 < 1/2$. If we now choose $\delta$ so that $C\delta \leq \frac{1}{2}a$, our mapping sends $B_a$ into $B_a$. Similar reasoning gives that it is a contraction, and this establishes the theorem.
\[Th7.4\] For $k = 4$, given $(f, \phi) \in H^{1/3}({\mathbb R}^+) \times L^2({\mathbb R}^+)$, there exists $T = T(f, \phi) < 1$ such that the ‘integral equation’ [(\[7.4\])]{} below has a unique fixed point in the space $B_T$ defined below. The resulting $w$ solves [(\[7.1\])]{} in ${\mathbb R}^+ \times (0, T)$. Here, $$\label{7.4}
w(x, t) = \Psi(t)\operatorname{HS}_1(f, \phi)(x, t) + \operatorname{IHS}_1(\Psi.w^4\partial_xw)(x, t),$$ where $\Psi(t) = 1$ for $|t| \leq T$ and $\operatorname{supp}\Psi \subseteq \{t : |t| < 2T\}$, and $$B_T = \bigl\{w \in C\bigl([-2T, 2T]; L^2({\mathbb R})\bigr) \cap C\bigl((-\infty, +\infty); H^{1/3}((-2T, 2T))\bigr) : \Lambda_T(w) < \infty\},$$ where $\Lambda_T(w) = \max{\nolimits}_{i \leq 4} \lambda_i(w)$ for $$\begin{aligned}
\lambda_1(w) & = \sup_x {||w - \Psi.\operatorname{HS}_1(f, \phi)||_{H^{1/3}((-2T, 2T))}}, \\
\lambda_2(w) & = \sup_t ||w - \Psi.\operatorname{HS}_1(f, \phi)||_{L^2}, \\
\lambda_3(w) & = ||\partial_xw||_{L_x^\infty L_{2T}^2} \\
\intertext{and}
\lambda_4(w) & = ||w||_{L_x^5L_{2T}^{10}}.\end{aligned}$$
The extra ingredients in this proof are the following estimates: Given $(f_0, \phi_0) \in H^{1/3}({\mathbb R}^+) \times L^2({\mathbb R}^+)$, for any $\varepsilon > 0$ there exists $T = T(f_0, \phi_0)$ and $\delta = \delta(f_0, \phi_0)$ such that, if $||(f, \phi) - (f_0, \phi_0)||_{H^{1/3} \times L^2} \leq \delta$, then $$\begin{gathered}
\label{7.5}||\partial_x\operatorname{HS}_1(f, \phi)||_{L_x^\infty L_T^2} < \varepsilon \\
\intertext{ and }
\label{7.6}||\operatorname{HS}_1(f, \phi)||_{L_x^5L_T^{10}} < \varepsilon.\end{gathered}$$ To establish [(\[7.5\])]{}, note that, by [(\[6.2\])]{}, it suffices to show it for $(f_0, \phi_0)$, with $\varepsilon$ replaced by $\varepsilon/2$. Next, note that the corresponding result for $S(t)\tilde{\phi}_0$ is (5.11) in [@10]. We thus have to show that, if $h \in H^{1/3}_0({\mathbb R}^+)$ and $\operatorname{supp}h \subseteq [0, 1]$, then the corresponding estimate holds for $\int_0^t S(t - t')(\delta_0)(x)h(t')dt'$. Pick now $h_j \in C_0^\infty\bigl((0, 1)\bigr)$ satisfying $h_j \rightarrow h$ in $H^{1/3}$. Because of [(\[4.7\])]{} and Propositions \[Pn2.7\] and \[Pn2.8\], it suffices to establish the result for $$w_0(x, t) = \int_0^t S(t - t')(\delta_0)(x)h_{j_0}(t')dt',$$ with $j_0$ fixed large. Since, however, $h_{j_0} \in C_0^\infty\bigl((0, 1)\bigr)$, $${\frac{\partial w_0}{\partial t}}(x, t) = \int_0^t S(t - t')(\delta_0)(x){\frac{\partial h_{j_0}}{\partial t'}}(t')dt',$$ and so $\bigl|\bigl|{\frac{\partial }{\partial x}}{\frac{\partial }{\partial t}}w_0\bigr|\bigr|_{L_x^\infty L_t^2} \leq C_{j_0},$ by [(\[4.7\])]{}. Then, since $w_0(-, 0) \equiv 0$, $$\int_0^T \biggl|{\frac{\partial w_0}{\partial x}}(x, t)\biggr|^2dt \leq \int_0^T \biggl|\int_0^t {\frac{\partial }{\partial t'}}{\frac{\partial }{\partial x}}w_0(x, t')dt'\biggr|^2dt \leq C_{j_0}T^2,$$ and our result follows. Next note that [(\[7.6\])]{} follows from a similar but simpler argument.
Note that [(\[7.5\])]{} and [(\[7.6\])]{} imply that $\Lambda_T\bigl(\Psi.\operatorname{HS}_1(f, \phi)\bigr) \leq \varepsilon$, where $\varepsilon$ is any fixed positive number, for $T$ sufficiently small. Also, note that $$\Lambda_T\bigl(\operatorname{IHS}_1(\Psi.w^4\partial_xw)\bigr) \leq C||\Psi.w^4\partial_xw||_{L_x^{5/4}L_t^{10/9}} + C\varepsilon,$$ by virtue of Theorem \[Th6.6\], and that Hölder’s inequality shows that $||\Psi.w^4\partial_xw||_{L_x^{5/4}L_t^{10/9}}\linebreak \leq \Lambda_T^5(w)$. Thus $$\Lambda_T\bigl(\Psi.\operatorname{HS}_1(f, \phi) + \operatorname{IHS}_1(\Psi.w^4\partial_xw)\bigr) \leq C\varepsilon + C\Lambda_T^5(w),$$ so that, for $a$ satisfying $Ca^4 \leq 1/2$ and $C\varepsilon \leq a/2$, we have that our mapping sends $B_{T, a} = \{w : \Lambda_T(w) \leq a\}$ into itself, and a similar argument yields the contraction property. This establishes Theorem \[Th7.4\].
\[Rk7.2\] In a manner similar to the one used to prove Corollary 2.11 in [@10], working now with the integral equation $$\label{7.7}
w = \operatorname{HS}_1(f, \phi) + \operatorname{IHS}_1(\Psi.w^4\partial_xw),$$ one can show that, for $k = 4$ and $0 < s < 1/2$, [(\[7.1\])]{} is well-posed in $H^{(s + 1)/3} \times H^s$ in an interval $[0, T]$, with $$T = T(||(f, \phi)||_{H^{(s + 1)/3} \times H^s}).$$ Moreover, if $||(f, \phi)||_{H^{(s + 1)/3} \times H^s}$ is small and $0 < s < 1/2$, one can construct solutions for all $T$.
\[Rk7.3\] Following the proof of Theorem 2.6 in [@10] and the ideas used in the proof of Theorem \[Th7.2\], one can show local well-posedness for [(\[7.1\])]{} (for $k = 3$) in $H^{(s + 1)/3} \times H^s$, with $1/12 \leq s < 1/2$. Moreover, following the proofs of Theorems \[Th7.3\] and \[Th7.4\], Remark \[Rk7.2\] and Theorems 2.15 and 2.17 and Corollary 2.18 in [@10], we can extend Theorems \[Th7.3\] and \[Th7.4\] and Remark \[Rk7.2\] to the case of $k > 4$, where the role of $L^2$ is played by $H^{s_k}$ and the role of $H^{1/3}$ is played by $H^{(s_k + 1)/3}$ (where $s_k = \frac{1}{2} - \frac{2}{k}$).
Local well-posedness of KdV using Bourgain’s spaces
---------------------------------------------------
We next turn our attention to the bilinear case, $k = 1$. Here we will obtain results analogous to Bourgain’s in [@5]. We start out with the main bilinear estimate, Appendix 2 in [@5].
\[Lm7.1\] For $v, w \in X_b$, we have, for suitable $b < \frac{1}{2}$ and $\alpha > \frac{1}{2}$, the bilinear estimate $$\label{7.8'}
||\partial_x(vw)||_{Y_b} \leq C||v||_{X_b}||w||_{X_b}.$$
We recall three fundamental estimates. If $\hat{F}_\rho(\xi, \lambda) = \frac{f(\xi, \lambda)}{(1 + |\lambda - \xi^3|)^\rho}$, then, for $\rho > \frac{3}{8}$ and $0 \leq \theta \leq \frac{1}{8}$, we have ([@11']) $$\label{7.9'}
||D_x^\theta F_\rho||_{L_x^4L_t^4} \leq C||f||_{L_\lambda^2}.$$
If $\rho > \frac{1}{4}$, we have $$\label{7.10'}
||D_x^{1/2}F_\rho||_{L_x^4L_t^2} \leq C||f||_{L_\lambda^2}.$$ The estimate [(\[7.10’\])]{} is an interpolant between the local smoothing estimate and a trivial estimate; see [@5].
If $\hat{H}_\rho(\xi, \lambda) = \frac{f(\xi, \lambda)}{(1 + |\lambda|)^\rho}$ with $\rho > \frac{1}{2}$, then Sobolev’s inequality implies $$\label{7.11'}
||H_\rho||_{L_x^2L_t^\infty} \leq C||f||_{L_{\xi\lambda}^2}.$$
To prove [(\[7.8’\])]{}, we estimate the three pieces of the $Y_b$ norm appearing in [(\[5.2\])]{}. Before turning to the analysis of the first piece, we introduce notation related to the $X_b$ norm, allowing us to reexpress [(\[7.8’\])]{} with $L^2$ norms on the right side. Let $\chi = \chi_{[-1, 1]}$ and define $\beta(\xi, \lambda) = (1 + |\lambda - \xi^3|)^b + \chi(\xi)|\lambda|^\alpha$. Introduce $g_1(\xi, \lambda) = \beta(\xi, \lambda)\hat{u}(\xi, \lambda)$ and $g_2(\xi, \lambda) = \beta(\xi, \lambda)\hat{v}(\xi, \lambda)$. Note that $g_1 \in L_{\xi\lambda}^2 \Leftrightarrow u \in X_b$.
By duality, the first term in [(\[5.2\])]{}is appropriately controlled if we show $$\label{7.12'}
\int{\nolimits}_{\substack{\xi = \xi_1 + \xi_2 \\ \lambda = \lambda_1 + \lambda_2}} \frac{d(\xi, \lambda)|\xi|}{(1 + |\lambda - \xi^3|)^b}\frac{\hat{g}_1(\xi_1, \lambda_1)}{\beta(\xi_1, \lambda_1)}\frac{\hat{g}_2(\xi_2, \lambda_2)}{\beta(\xi_2, \lambda_2)} \leq C||d||_{L^2}||g_1||_{L^2}||g_2||_{L^2}.$$ Symmetry allows us to assume that $|\xi_2| \geq |\xi_1|$. Without loss of generality, we may assume $d, g_1, g_2 \geq 0$.
[Case .]{}
$|\xi| \leq 1$.
In this region, [(\[7.12’\])]{} is bounded by $$\int{\nolimits}_{\substack{\xi = \xi_1 + \xi_2 \\ \lambda = \lambda_1 + \lambda_2}} d(\xi, \lambda)\frac{\hat{g}_1(\xi_1, \lambda_1)}{(1 + |\lambda_1 - \xi_1^3|)^b}{}\frac{\hat{g}_2(\xi_2, \lambda_2)}{(1 + |\lambda_2 - \xi_2^3|)^b}.$$ Let $\hat{D}(\xi, \lambda) = d(\xi, \lambda)$ and $\hat{G}_i(\xi, \lambda) = \frac{\hat{g}_i(\xi, \lambda)}{(1 + |\lambda - \xi^3|)^b}$. Fourier transform properties permit us to rewrite the above expression as $\int D.G_1.G_2$, which we bound using Hölder by $||D||_{L_{xt}^2}||G_1||_{L_{xt}^4}||G_2||_{L_{xt}^4}$. We apply [(\[7.9’\])]{} with $\theta = 0$ to the $L_{xt}^4$ norms; this requires assuming $\frac{3}{8} < b$. Note that this case also addresses the second term in [(\[5.2\])]{}
$|\xi| > 1$.
The convolution constraints $\xi = \xi_1 + \xi_2$ and $\lambda = \lambda_1 + \lambda_2$ imply $$\label{7.13'}
M = \max\{|\lambda - \xi^3|, |\lambda_1 - \xi_1^3|, |\lambda_2 - \xi_2^3|\} > |\xi|\,|\xi_1|\,|\xi_2|.$$
[Case .]{}
$|\xi_1| \geq 1$. (Recall that we have assumed $|\xi_2| \geq |\xi_1|$.)
In this case, $|\xi|\,|\xi_1|\,|\xi_2| \geq \frac{1}{2}|\xi|^2$, so the maximum appearing in [(\[7.13’\])]{} is powerful. We consider three subcases of this case.
[Case .]{}
$|\lambda - \xi^3| = M$.
We bound [(\[7.12’\])]{} by $$C{\!}\int{\nolimits}_{\substack{\xi = \xi_1 + \xi_2 \\ \lambda = \lambda_1 + \lambda_2}} d(\xi, \lambda)\frac{\hat{g}_1(\xi_1, \lambda_1)}{(1 + |\lambda_1 - \xi_1^3|)^b}\frac{|\xi_2|^{1 - 2b}\hat{g}_2(\xi_2, \lambda_2)}{(1 + |\lambda_2 - \xi_2^3|)^b}.$$ This may be rewritten as $\int D.G_1.D_x^{1 - 2b}G_2$, which we estimate as $||D||_{L^2}||G_1||_{L^4}||D_x^{1 - 2b}G_2||_{L^4}$. Then [(\[7.9’\])]{} proves [(\[7.8’\])]{} in this case, provided $1 - 2b \leq \frac{1}{8}$ and $\frac{3}{8} < b$; that is, provided $b \geq \frac{7}{16}$. We require henceforth that $b \geq \frac{7}{16}$.
$|\lambda_1 - \xi_1^3| = M$.
We bound [(\[7.12’\])]{} by $$C{\!}\int{\nolimits}_{\substack{\xi = \xi_1 + \xi_2 \\ \lambda = \lambda_1 + \lambda_2}} \frac{|\xi|^{1 - 2b}d(\xi, \lambda)}{(1 + |\lambda - \xi^3|)^b}\hat{g}_1(\xi_1, \lambda_1)\frac{\hat{g}_2(\xi_2, \lambda_2)}{(1 + |\lambda_2 - \xi_2^3|)^b},$$ and this may also be estimated using [(\[7.8’\])]{}.
$|\lambda_2 - \xi_2^3| = M$.
This case is similar.
$|\xi_1| \leq 1$.
We write $|\xi| = |\xi|^{1/2}|\xi|^{1/2} \leq C|\xi|^{1/2}|\xi_2|^{1/2}$ and bound [(\[7.12’\])]{} by $$C{\!}\int{\nolimits}_{\substack{\xi = \xi_1 + \xi_2 \\ \lambda = \lambda_1 + \lambda_2}} \frac{|\xi|^{1/2}d(\xi, \lambda)}{(1 + |\lambda - \xi^3|)^b}\frac{\hat{g}_1(\xi_1, \lambda_1)\chi(\xi_1)}{1 + \chi(\xi_1)|\lambda_1|^\alpha}\frac{|\xi_2|^{1/2}\hat{g}_2(\xi_2, \lambda_2)}{(1 + |\lambda_2 - \xi_2^3|)^b}.$$ This may be reexpressed as $\int{\!\!}\int D_x^{1/2}D.H_\alpha.D_x^{1/2}G_2$, where $\hat{H}_\alpha(\xi, \lambda) = \frac{\hat{g}_1(\xi, \lambda)}{(1 + |\lambda|)^\alpha}$. Applying Hölder, we bound by $C||D_x^{1/2}D||_{L_x^4L_t^2}||H_\alpha||_{L_x^2L_t^\infty}||D_x^{1/2}G_2||_{L_x^4L_t^2}$, which is controlled using [(\[7.10’\])]{} and [(\[7.11’\])]{}, since $\alpha > \frac{1}{2}$ and $b > \frac{1}{4}$.
All that remains is the third piece of the $Y_b$ norm appearing in [(\[5.2\])]{}. Observe that $$\int \biggl(\int \frac{\hat{f}(\xi, \lambda)}{1 + |\lambda - \xi^3|}d\lambda\biggr)^2d\xi = \int \biggl(\int \frac{\hat{f}(\xi, \lambda)}{(1 + |\lambda - \xi^3|)^b}\frac{1}{(1 + |\lambda - \xi^3|)^{1 - b}}d\lambda\biggr)^2d\xi.$$ By Cauchy-Schwarz, this is bounded by $$\int \biggl(\int \frac{|\hat{f}(\xi, \lambda)|^2}{(1 + |\lambda - \xi^3|)^{2b}}d\lambda\biggr)\biggl(\int \frac{1}{(1 + |\lambda - \xi^3|)^{2(1 - b)}}d\lambda\biggr)d\xi.$$ Since $2(1 - b) > 1$, the second $\lambda$-integral is bounded and we reduce matters to controlling the first term in [(\[5.2\])]{}.
The next result establishes a local well-posedness result for the $k = 1$ case of [(\[1.1\])]{} when the data $(f, \phi) \in H_t^{1/3} \times L_x^2$ are sufficiently small.
\[Th7.5\] There exists a $\delta_0 > 0$ such that, if $(f, \phi) \in H_t^{1/3} \times L_x^2$ satisfies $$\label{7.14'}
||(f, \phi)||_{H_t^{1/3} \times L_x^2} \leq \delta_0,$$ then the “integral equation” $$\label{7.15'}
w = \operatorname{HS}_1(f, \phi) + \operatorname{IHS}_1\bigl(\partial_x(w^2/2)\bigr)$$ has a unique fixed point in the space $$\label{7.16'}
C\bigl((-\infty, \infty); H_x^s) \cap C\bigl((-\infty, \infty); H_t^{(s + 1)/3}) \cap X_b{}$$ (for suitable $b < \frac{1}{2}$ and $\alpha > \frac{1}{2}$). The resulting $w$ solves [(\[7.1\])]{} in ${\mathbb R}^+ \times (0, 1)$.
Theorem \[Th6.1\] and Lemmas \[Lm5.2\] and \[Lm5.3\] show that $\operatorname{HS}_1(\phi, f)$ satisfies [(\[7.16’\])]{}. Lemmas \[Lm5.4\] and \[Lm7.1\] allow us to prove the contraction estimate under the condition [(\[7.14’\])]{}.
Note that the above Theorem extends, with almost identical proof, to the case of data $(f, \phi)$ in $H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)$, $0 < s \leq 1$, $s \leq \frac{1}{2}$ (with the compatibility condition $f(0) = \phi(0)$ when $s > \frac{1}{2}$), and $||(f, \phi)||_{H^{(s + 1)/3}({\mathbb R}^+) \times H^s({\mathbb R}^+)} \leq \delta_s$. We just need to use the $X_{s, b}$ spaces in Remark \[Rk5.1\], and show the corresponding estimates.
\[Rk7.4\] There are two possible approaches to eliminating the restriction on the size of $(f, \phi)$. The first one, as in [@5], leads to considering functions on $[-T, T]$ and seeing that, as $T$ is small, a power of $T$ is gained in the above estimates. The other approach is simply to scale things down: $u$ solves $$\partial_tu + \partial_x^3u + u\partial_xu = 0$$ if and only if $u_\lambda(x, t) = \lambda^2u(\lambda x, \lambda^3t)$ does. One can then choose a small $\lambda$ so that the datum $(f_\lambda, \phi_\lambda)$ corresponding to $u_\lambda$ has norm smaller than $\delta_s$. (The resulting $\lambda$ depends only on $s$ and $||(f, \phi)||_{H^{(s + 1)/3} \times H^s}$.) Once this is done, one uses the fact that $u_\lambda$ is defined for $0 < t < 1$, and hence that $u$ is defined for $0 < t < 1/\lambda^3$, to obtain a solution to [(\[7.1\])]{} in ${\mathbb R}^+ \times (0, T)$, with $$T = T(||(f, \phi)||_{H^{(s + 1)/3} \times H^s}).$$
\[Rk7.5\] The results just explained easily extend to equations with drift terms $c\partial_x$ by simply noting that the estimate in Lemma \[Lm7.1\] also holds in the spaces $\tilde{X}_b$ introduced in Remark \[Rk6.4\]. This is because the key estimate [(\[7.13’\])]{} remains unchanged if we replace $\xi^3$, $\xi_1^3$ and $\xi_2^3$ by $\xi^3 + c\xi$, $\xi_1^3 + c\xi_1$ and $\xi_2^3 + c\xi_2$, respectively, under the convolution constraint $\xi = \xi_1 + \xi_2$.
Global well-posedness for $1 \leq k \leq 4$
-------------------------------------------
When $f \equiv 0$, it is easy to see from Theorem \[Th7.5\] and Remark \[Rk7.4\] (using the argument in the proof of [(\[6.14\])]{} to obtain the [*a priori*]{} bound $$||u(-, t)||_{L^2({\mathbb R}^+)} \leq ||u(-, 0)||_{L^2({\mathbb R}^+)}$$ for sufficiently smooth solutions $u$, and an approximation argument using the solutions constructed in Theorem \[Th7.5\]) that, for each $0 < T < \infty$, one can construct solutions as in Theorem \[Th7.5\] (for $s = 0$) for [(\[7.1\])]{} (for $k = 1$) with $\phi \in L^2({\mathbb R})$. In general, we have:
\[Th7.6\] Given $\phi \in L^2({\mathbb R}^+)$, $f \in H^{7/12}({\mathbb R}^+)$ and $T > 0$, the solutions constructed in Remark \[Rk7.4\] (for $s = 0$) can be extended to the interval $(0, T)$.
To obtain the theorem, it suffices to establish the [*a priori*]{} estimate $$\label{7.11}
\sup_{0 \leq t \leq T} ||u(-, t)||_{L^2({\mathbb R}^+)} \leq C_T(||(f, \phi)||_{H^{7/12}({\mathbb R}^+) \times L^2({\mathbb R}^+)}).$$ To obtain this estimate, we use a device used in Proposition 5.4 of [@1]. In fact, let $v$ be the solution to the linear problem $$\label{7.12}
\begin{cases}
\partial_tv + \partial_x^3v = 0 & \text{in }{\mathbb R}^+ \times (0, T) \\
v|_{x = 0} = f & \\
v|_{t = 0} = \phi_0. &
\end{cases}$$ where $\phi_0$ is chosen so that $\phi_0(0) = f(0)$ and ${||\phi_0||_{H^{3/4}(\mathbb R)}} \leq C{||f||_{H^{7/12}}}$, and $v$ is constructed in Theorem \[Th6.1\] (for $s = 3/4$). We will presently show that $v$ satisfies, in addition to the estimates in Theorem \[Th6.1\], the inequality $$\label{7.13}
||\partial_xv||_{L_T^4L_x^\infty} \leq C||(f, \phi_0)||_{H^{7/12} \times H^{3/4}}$$ (here we see the reason for the exponent $\frac{7}{12} = \frac{3/4 + 1}{3}$). Let $w = u - v$, so that $w$ satisfies $$\label{7.14}
\begin{cases}
\partial_tw + \partial_x^3w + \partial_x(w^2/2) + \partial_x(wv) + \partial_x(v^2/2) = 0 \\
w|_{x = 0} = 0 \\
w|_{t = 0} = \phi - \phi_0.
\end{cases}$$ It clearly suffices, in view of Theorem \[Th6.1\], to establish the analogue of [(\[7.11\])]{} for $w$. Multiplying the equation in [(\[7.14\])]{} by $2w$ and integrating by parts in a manner similar to the proof of [(\[6.14\])]{}, and using the boundary conditions in [(\[7.14\])]{}, we obtain: $$\begin{gathered}
\label{7.15}
\int{\nolimits}_{x > 0} w^2(x, t)dx + \int_0^t \partial_xw(0, t')^2dt' \\
\leq \int{\nolimits}_{x \geq 0} (\phi - \phi_0)^2dx - 2{\!}\int_0^t \int{\nolimits}_{x > 0} \partial_x(wv)w - \int_0^t \int{\nolimits}_{x > 0} v\partial_xv.w.\end{gathered}$$ Since $2{\!}\int_0^t\int{\nolimits}_{x > 0} \partial_x(wv)w = \int_0^t \int{\nolimits}_{x > 0} w^2.\partial_xv$, it is easy to see that the right-hand side of [(\[7.15\])]{} is bounded (in view of Theorem \[Th6.1\] and [(\[7.13\])]{}) by $$\begin{gathered}
\frac{1}{2}\sup_{0 < t < T} ||w(-, t)||_{L^2({\mathbb R}^+)}^2 + ||\phi - \phi_0||_{L^2}^2 + C_T(||(f, \phi_0)||_{H^{7/12} \times H^{3/4}}) \\
+ C_T(||(f, \phi_0)||_{H^{7/12} \times H^{3/4}})\Bigl(\int_0^t ||w(-, t')||_{L^2({\mathbb R}_x^+)}^{8/3}dt'\Bigr)^{3/4},\end{gathered}$$ which (upon raising both sides of [(\[7.15\])]{} to the power $4/3$), combined with Gronwall’s inequality, gives the desired bound. To finish the proof, we sketch the argument leading to [(\[7.13\])]{}. In view of Theorem \[Th6.1\] and its proof, and Theorem 2.1 in [@12], it suffices to show that, if $h \in C_0^\infty\bigl((0, 1)\bigr)$ and $w(x, t) = \int_0^t S(t - t')(\delta_0)(x)h(t')dt'$, then we have $$\label{7.16}
||\partial_xw||_{L_t^4L_x^\infty} \leq C{||h||_{\dot{H}^{-1/12}}}.$$ We establish [(\[7.16\])]{} by means of the well-known variant of the three-lines theorem in Lemma 4.2 of Chapter V of [@17], from the estimates $$\begin{gathered}
\label{7.17}||{\cal H}D_x^{i\gamma}D_x^{1 + 1/4}w||_{L_t^4L_x^\infty} \leq Ce^{C|\gamma|}||h||_{L^2} \\
\intertext{and}
\label{7.18}||{\cal H}D_x^{i\gamma}w||_{L_t^4L_x^\infty} \leq Ce^{C|\gamma|}{||h||_{\dot{H}^{-1/12- 1/3}}}.\end{gathered}$$ [(\[7.17\])]{} follows from Proposition 3.5(2) in [@7].
To establish [(\[7.18\])]{}, we need, in view of [(\[4.16\])]{}, to establish the estimate for ${\cal H}D_x^{i\gamma}D_t^{1/12 + 1/3}A(\delta_0 \otimes g)$ and for $${\cal H}D_x^{i\gamma}D_t^{1/12 + 1/3}{\!\!}\int_{-\infty}^{+\infty} S(t - t')(\delta_0)(x)g(t')dt'$$ with $g \in L^2$. For the second estimate, it suffices to establish it for $${\cal H}D_x^{i\gamma}D_x^{1/4}D_x^1{\!}\int_{-\infty}^{+\infty} S(t - t')(\delta_0)(x)g(t')dt'.$$ This, in turn, using the argument in the proof of [(\[4.31\])]{}, reduces to the ‘kernel estimate’ $$\label{7.19}
|H_{x_0}(x, y, t, s)| \leq \frac{C}{|t - s|^{1/2}},$$ where $$H_{x_0}(x, y, t, s) = \int D_x^{i\gamma}{\cal H}D_x^{1 + 1/4}A(x_0 - x, t - t')D_y^{-i\gamma}D_y^{1 + 1/4}A(y - x_0, t' - s)dt'.$$
Note that a calculation like the one preceding [(\[4.33\])]{} gives the formula $$H_{x_0}(x, y, t, s) = \frac{1}{3}{\!}\int e^{-i(x - y)\xi}e^{i(t - s)\xi^3}|\xi|^{1/2}d\xi,$$ and the estimate now follows from Lemma 2.7 in [@12]. In order to estimate ${\cal H}D_x^{i\gamma}D_t^{1/12 + 1/3}A(\delta_0 \otimes g)$, we first estimate $$D_t^{1/12 + 1/3}A(\delta_0 \otimes g) = \int{\!\!\!}\int e^{ix\xi}e^{it\tau}\frac{|\tau|^{1/12 + 1/3}}{\tau - \xi^3}\hat{g}(\tau)d\tau\,d\xi.$$ As in the proof of [(\[4.38\])]{}, we first calculate the integral over $\xi$, and we are reduced to three terms, the first of which is $$\begin{gathered}
C_1{\!}\int e^{it\tau}|\tau|^{1/12 + 1/3}\operatorname{sgn}(x\tau^{1/3})e^{-ix\tau^{1/3}}\hat{g}(\tau)\frac{d\tau}{\tau^{2/3}} \\
= C_1(\operatorname{sgn}x){\!}\int e^{it\tau}e^{-ix\tau^{1/3}}\operatorname{sgn}(\tau^{1/3})\hat{g}(\tau)\frac{d\tau}{|\tau|^{1/4}}.\end{gathered}$$ The desired estimate for this term follows from Theorem 2.5 in [@12]. The remaining two terms can be handled in a similar manner, in the spirit of the above argument and the proof of [(\[4.38\])]{}. For the proof of the estimate for ${\cal H}D_x^{i\gamma}D_t^{1/12 + 1/3}A(\delta_0 \otimes g)$, we again introduce a family of operators $$T_\eta(g)(x, t) = \int_{-\infty}^{+\infty} e^{it\tau}e^{ix\tau^{1/3}\eta}\hat{g}(\tau)\frac{d\tau}{|\tau|^{1/4}},$$ which we easily check satisfies $$\label{7.20}
||T_\eta(g)||_{L_t^4L_x^\infty} \leq C||g||_{L^2},$$ as a consequence of [(\[7.19\])]{}. We then split our operator, as in the proof of [(\[4.39\])]{}, into the sum of three operators $L_i$, $i = 1, 2, 3$. The bounds for $L_1$ and $L_3$ easily follow from [(\[7.20\])]{}. For $L_2$, we use the argument in [(\[4.39\])]{}, together with [(\[7.20\])]{}, to reduce matters to estimating $$\begin{gathered}
\int e^{it\tau}\frac{|\tau|^{i\gamma/3}\operatorname{sgn}(\tau^{1/3})\hat{g}(\tau)}{|\tau|^{1/4}}\biggl(\int e^{ix\tau^{1/3}\eta}\frac{\varphi_2(\eta)}{1 - \eta}d\eta\biggr)d\tau \\
= \int e^{it\tau}|\tau|^{i\gamma/3}\frac{\operatorname{sgn}(\tau^{1/3})}{|\tau|^{1/4}}e^{-ix\tau^{1/3}}\biggl(\int e^{ix\tau^{1/3}\mu}\frac{\varphi_2(1 - \mu)}{\mu}d\mu\biggr)d\tau\end{gathered}$$ – but the integral in parentheses equals $\int \operatorname{sgn}(x\tau^{1/3} - z)\theta(z)dz$ for some $\theta \in {\cal S}({\mathbb R})$, and, if we now use Corollary 2.9 in [@12] to estimate $$T_2(g)(x, t) = \int e^{it\tau}e^{-ix\tau^{1/3}}\operatorname{sgn}(x\tau^{1/3} - z)|\tau|^{i\gamma/3}\operatorname{sgn}(\tau^{1/3})\hat{g}(\tau)\frac{d\tau}{|\tau|^{1/4}}$$ in $L_t^4L_x^\infty$, uniformly in $z$, and Minkowski’s integral inequality, then the proof is finished.
For $k > 1$, it is well-known (see [@3]) that global well-posedness for $\phi$ in $H^1$ does not follow readily from Theorem \[Th7.1\] when $f \not\equiv 0$. (When $f \equiv 0$, the results are completely analogous to the ones obtained in [@10] for the whole upper half-plane, namely, for $k = 2, 3$ there is global well-posedness, and also for $k \geq 4$, provided the $L^2$ norms of the initial data are small enough.) When $f \not\equiv 0$, we can establish:
\[Th7.7\] Given $T > 0$ and $\phi \in H^1({\mathbb R}^+)$, we have:
1. \[Th7.7(i)\] If $f \in H^{11/12}({\mathbb R}^+)$ and $||f||_{L^2({\mathbb R}^+)}$ is sufficiently small, the solution given in Theorem \[Th7.1\] (for $k = 2$ and $s = 1$) extends to the interval $(0, T)$.
2. \[Th7.7(ii)\] If $f \in H^{5/4}({\mathbb R}^+)$ and $||f||_{L^2({\mathbb R}^+)}$ is sufficiently small, the solution given in Theorem \[Th7.1\] (for $k = 3$ and $s = 1$) extends to the interval $(0, T)$.
3. \[Th7.7(iii)\] If $f \in H^{11/12}({\mathbb R}^+)$ and $||f||_{L^2({\mathbb R}^+)}$ and $||\phi||_{L^2({\mathbb R}^+)}$ are sufficiently small, the solution given in Theorem \[Th7.1\] (for $k \geq 4$ and $s = 1$) extends to the interval $(0, T)$.
We will limit ourselves to a sketch of the proof of this result. We start from the following two identities, readily obtained by integration by parts for sufficiently nice solutions (here $w = u - v$, where $v$ solves [(\[7.12\])]{}): $$\begin{gathered}
\label{7.21}
\int{\nolimits}_{x > 0} u^2(x, t)dx + \int_0^t \partial_xu(0, t')^2dt' + 2{\!}\int_0^t \partial_x^2u(0, t')f(t')dt' \\
- \frac{2}{k + 2}\int_0^t f(t')^{k + 2}dt' = \int{\nolimits}_{x > 0} \phi^2(x)dx\end{gathered}$$ and $$\begin{gathered}
\label{7.22}
\int{\nolimits}_{x > 0} \bigl(\partial_xw(x, t)\bigr)^2dx + \int_0^t \bigl(\partial_x^2w(0, t')\bigr)^2dt' + \int_0^t \frac{f^{2k + 2}(t')}{(k + 1)^2}dt' \\
+ \frac{2}{k + 1}\int_0^t \partial_x^2w(0, t')\!\cdot\!f^{k + 1}(t')dt' \\
- 2{\!}\int_0^t\int{\nolimits}_{x > 0} \partial_x^3v\frac{u^{k + 1}}{k + 1} - \frac{2}{(k + 1)(k + 2)}{\!}\int{\nolimits}_{x > 0} u^{k + 2}(x, t)dx \\
+ \frac{2}{(k + 1)(k + 2)}{\!}\int{\nolimits}_{x > 0} \phi^{k + 2}(x)dx = \int{\nolimits}_{x > 0} (\partial_x\phi)^2(x)dx.\end{gathered}$$ From [(\[7.21\])]{} and [(\[7.22\])]{}, together with estimates on $v$, one obtains, under the conditions of Theorem \[Th7.7\], the [*a priori*]{} bound $$\label{7.23}
\sup_{0 < t < T} {||u(-, t)||_{H^{1}({\mathbb R}^+)}} \leq C_T(f, \phi),$$ from which Theorem \[Th7.7\] easily follows. In fact, to obtain [(\[7.23\])]{} in case [(\[Th7.7(i)\])]{}, one notes that $$2{\!}\int_0^t \int{\nolimits}_{x > 0} \partial_x^3v\frac{u^3}{3} = -2{\!}\int_0^t \partial_x^2v(0, t')\frac{f^3(t')}{3}dt' - 2{\!}\int_0^t \int{\nolimits}_{x > 0} \partial_x^2v.\partial_xu.u^2,$$ and that an extension of the argument used to prove [(\[7.13\])]{} gives (with $\phi_0$ chosen so that ${||\phi_0||_{H^{7/4}}} \leq C{||f||_{H^{11/12}}}$) the estimate $$||\partial_x^2v||_{L_T^4L_x^\infty} \leq C||(f, \phi_0)||_{H^{11/12} \times H^{7/4}}.$$ Applying now simple manipulations to these facts and [(\[7.21\])]{} and [(\[7.22\])]{} yields the estimate $$\begin{gathered}
\label{7.24}
\sup_{0 < t < T} ||u(-, t)||_{L^2({\mathbb R}^+)}^2 + \sup_{0 < t < T} ||\partial_xu(-, t)||_{L^2({\mathbb R}^+)}^2 + \int_0^T \bigl(\partial_x^2u(0, t)\bigr)^2dt \\
\leq C + C\!\sup_{0 < t < T} \int{\nolimits}_{x > 0} u^4(x, t)dx + C{\!}\int_0^T |\partial_x^2u(0, t)|\,|f(t)|dt,\end{gathered}$$ where $C = C\bigl(T, (f, \phi)\bigr)$. Recall now the elementary estimate $$||w||_{L^\infty({\mathbb R}^+)} \leq ||w||_{L^2({\mathbb R}^+)}^{1/2}||\partial_xw||_{L^2({\mathbb R}^+)}^{1/2}$$ ($w(0) = 0$) and use it, together with the estimates on $v$, to conclude that $$\begin{gathered}
\sup_{0 < t < T} ||u(-, t)||_{L^2({\mathbb R}^+)}^2 + \sup_{0 < t < T} ||\partial_xu(-, t)||_{L^2({\mathbb R}^+)}^2 + \int_0^T \bigl(\partial_x^2u(0, t)\bigr)^2dt \\
\leq C + C\Bigl(\int_0^T |\partial_x^2u(0, t)|^2\Bigr)^{1/2}||f||_{L^2} + C\Bigl(\sup_{0 < t < T} \int{\nolimits}_{x > 0} u^2\Bigr)^3.\end{gathered}$$ Let now $h(t) = \int_0^T \bigl(\partial_x^2u(0, t)\bigr)^2dt$ and insert [(\[7.21\])]{} into the right-hand side of it. We then obtain that $$h(T) \leq C + Ch(T)^{1/2}||f||_{L^2} + Ch(T)^{3/2}||f||_{L^2}^3.$$ Since $h(0) = 0$ and $h$ is continuous, if $||f||_{L^2}^3$ is small enough, then we obtain an [*a priori*]{} bound for $h(T)$. This in turn yields a bound for $\sup{\nolimits}_{0 < t < T} ||u(-, t)||_{L^2({\mathbb R}^+)}^2$, and from this our [*a priori*]{} bound follows.
The cases dealt with in [(\[Th7.7(ii)\])]{} and [(\[Th7.7(iii)\])]{} are treated similarly. The key difference is that, when the non-linearity is of a higher power, the integration by parts after [(\[7.23\])]{} is not useful, since then $\partial_xu$ appears and forces too high a power on $u$, and hence on $\partial_xu$. This is avoided by using the fact that, when $f \in H^{5/4}({\mathbb R}^+)$, we have the estimate $||\partial_x^3v||_{L_T^4L_x^\infty} < \infty$, which allows the previous argument to be carried out without this integration by parts. This is actually only of interest in case [(\[Th7.7(ii)\])]{}, since, in case [(\[Th7.7(iii)\])]{}, we are assuming that $||\phi||_{L^2({\mathbb R}^+)}$ is small, which allows us to revert to the method used in [(\[Th7.7(i)\])]{}. The details are omitted.
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[^1]: J. E. C. was supported in part by an N. S. F. Postdoctoral Research Fellowship and N. S. F. grant DMS 0100595.
[^2]: C. E. K. was supported in part by N. S. F. Grant DMS 9500725.
[^3]: This improvement was completed by Justin Holmer while this paper was under review.
| 2024-06-22T01:27:04.277712 | https://example.com/article/9447 |
There is something hugely captivating when you come across the ruins of Monkstown Castle in county Meath. I say ruins but essentially all that remains of this 15th century tower house is the north wall, walking around it and looking upwards is unnerving! The landscape around Monkstown does reflect the fact that at one point this must have been a thriving area, three souterrains, a ruined church, and various earthworks in the surrounding fields are evidence of this. The ‘village of Monketon’ as it was described in the 16th century was owned by St. Mary’s Cistercian abbey and was leased to a Lady Eleanor Plunkett following the ‘Suppression’ in 1540; it does not mention the castle persay but does mention a ‘capital mansion’. One hundred years later in 1640 the Civil Survey stated that Edward Dowdall owned 295 acres at ‘Mountowne or Mounketowne’ in Skreen barony, the property included ‘one castle, one water mill, and one church’. The later period of the tower-house is unknown but it was most certainly in remains by 1837 as Samuel Lewis’ ‘A Topographical Dictionary of Ireland’ makes no mention of the castle or even its ruin when discussing Monkstown. The remains of Monkstown may be scant but they most certainly are charming.
GPS: 53.61391, -6.55834
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| 2024-05-24T01:27:04.277712 | https://example.com/article/9796 |
/*
* Copyright (C) 2018 Intel Corporation. All rights reserved.
*
* SPDX-License-Identifier: BSD-3-Clause
*/
#ifdef PROFILING_ON
#include <types.h>
#include <errno.h>
#include <irq.h>
#include <per_cpu.h>
#include <pgtable.h>
#include <vmx.h>
#include <cpuid.h>
#include <vm.h>
#include <sprintf.h>
#include <logmsg.h>
#define DBG_LEVEL_PROFILING 5U
#define DBG_LEVEL_ERR_PROFILING 3U
#define MAJOR_VERSION 1
#define MINOR_VERSION 0
#define LBR_NUM_REGISTERS 32U
#define PERF_OVF_BIT_MASK 0xC0000070000000FULL
#define LVT_PERFCTR_BIT_UNMASK 0xFFFEFFFFU
#define LVT_PERFCTR_BIT_MASK 0x10000U
#define VALID_DEBUGCTL_BIT_MASK 0x1801U
static uint64_t sep_collection_switch;
static uint64_t socwatch_collection_switch;
static bool in_pmu_profiling;
static uint32_t profiling_pmi_irq = IRQ_INVALID;
extern struct irq_desc irq_desc_array[NR_IRQS];
static void profiling_initialize_vmsw(void)
{
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering cpu%d",
__func__, get_pcpu_id());
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
}
/*
* Configure the PMU's for sep/socwatch profiling.
* Initial write of PMU registers.
* Walk through the entries and write the value of the register accordingly.
* Note: current_group is always set to 0, only 1 group is supported.
*/
static void profiling_initialize_pmi(void)
{
uint32_t i, group_id;
struct profiling_msr_op *msrop = NULL;
struct sep_state *ss = &get_cpu_var(profiling_info.s_state);
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering cpu%d",
__func__, get_pcpu_id());
if (ss == NULL) {
dev_dbg(DBG_LEVEL_ERR_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
return;
}
group_id = ss->current_pmi_group_id = 0U;
for (i = 0U; i < MAX_MSR_LIST_NUM; i++) {
msrop = &(ss->pmi_initial_msr_list[group_id][i]);
if (msrop != NULL) {
if (msrop->msr_id == (uint32_t)-1) {
break;
}
if (msrop->msr_id == MSR_IA32_DEBUGCTL) {
ss->guest_debugctl_value = msrop->value;
}
if (msrop->msr_op_type == (uint8_t)MSR_OP_WRITE) {
msr_write(msrop->msr_id, msrop->value);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: MSRWRITE cpu%d, msr_id=0x%x, msr_val=0x%lx",
__func__, get_pcpu_id(), msrop->msr_id, msrop->value);
}
}
}
ss->pmu_state = PMU_SETUP;
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
}
/*
* Enable all the Performance Monitoring Control registers.
*/
static void profiling_enable_pmu(void)
{
uint32_t lvt_perf_ctr;
uint32_t i;
uint32_t group_id;
uint32_t size;
struct profiling_msr_op *msrop = NULL;
struct sep_state *ss = &get_cpu_var(profiling_info.s_state);
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering cpu%d",
__func__, get_pcpu_id());
if (ss == NULL) {
dev_dbg(DBG_LEVEL_ERR_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
return;
}
/* Unmask LAPIC LVT entry for PMC register */
lvt_perf_ctr = (uint32_t) msr_read(MSR_IA32_EXT_APIC_LVT_PMI);
dev_dbg(DBG_LEVEL_PROFILING, "%s: 0x%x, 0x%lx",
__func__, MSR_IA32_EXT_APIC_LVT_PMI, lvt_perf_ctr);
lvt_perf_ctr &= LVT_PERFCTR_BIT_UNMASK;
msr_write(MSR_IA32_EXT_APIC_LVT_PMI, lvt_perf_ctr);
dev_dbg(DBG_LEVEL_PROFILING, "%s: 0x%x, 0x%lx",
__func__, MSR_IA32_EXT_APIC_LVT_PMI, lvt_perf_ctr);
if (ss->guest_debugctl_value != 0U) {
/* Merge the msr vmexit loading list with HV */
if (ss->vmexit_msr_cnt == 0U) {
struct acrn_vcpu *vcpu = get_ever_run_vcpu(get_pcpu_id());
size = sizeof(struct msr_store_entry) * MAX_HV_MSR_LIST_NUM;
(void)memcpy_s(ss->vmexit_msr_list, size, vcpu->arch.msr_area.host, size);
ss->vmexit_msr_cnt = MAX_HV_MSR_LIST_NUM;
ss->vmexit_msr_list[MAX_HV_MSR_LIST_NUM].msr_index = MSR_IA32_DEBUGCTL;
ss->vmexit_msr_list[MAX_HV_MSR_LIST_NUM].value = ss->guest_debugctl_value & VALID_DEBUGCTL_BIT_MASK;
ss->vmexit_msr_cnt++;
exec_vmwrite64(VMX_EXIT_MSR_LOAD_ADDR_FULL, hva2hpa(ss->vmexit_msr_list));
exec_vmwrite32(VMX_EXIT_MSR_LOAD_COUNT, ss->vmexit_msr_cnt);
}
/* VMCS GUEST field */
ss->saved_debugctl_value
= exec_vmread64(VMX_GUEST_IA32_DEBUGCTL_FULL);
exec_vmwrite64(VMX_GUEST_IA32_DEBUGCTL_FULL,
(ss->guest_debugctl_value & VALID_DEBUGCTL_BIT_MASK));
}
group_id = ss->current_pmi_group_id;
for (i = 0U; i < MAX_MSR_LIST_NUM; i++) {
msrop = &(ss->pmi_start_msr_list[group_id][i]);
if (msrop != NULL) {
if (msrop->msr_id == (uint32_t)-1) {
break;
}
if (msrop->msr_op_type == (uint8_t)MSR_OP_WRITE) {
msr_write(msrop->msr_id, msrop->value);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: MSRWRITE cpu%d, msr_id=0x%x, msr_val=0x%lx",
__func__, get_pcpu_id(), msrop->msr_id, msrop->value);
}
}
}
ss->pmu_state = PMU_RUNNING;
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
}
/*
* Disable all Performance Monitoring Control registers
*/
static void profiling_disable_pmu(void)
{
uint32_t lvt_perf_ctr;
uint32_t i;
uint32_t group_id;
struct profiling_msr_op *msrop = NULL;
struct sep_state *ss = &get_cpu_var(profiling_info.s_state);
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering cpu%d",
__func__, get_pcpu_id());
if (ss != NULL) {
if (ss->vmexit_msr_cnt != 0U) {
/* Restore the msr exit loading list of HV */
struct acrn_vcpu *vcpu = get_ever_run_vcpu(get_pcpu_id());
exec_vmwrite64(VMX_EXIT_MSR_LOAD_ADDR_FULL, hva2hpa(vcpu->arch.msr_area.host));
exec_vmwrite32(VMX_EXIT_MSR_LOAD_COUNT, MAX_HV_MSR_LIST_NUM);
ss->vmexit_msr_cnt = 0U;
}
group_id = ss->current_pmi_group_id;
for (i = 0U; i < MAX_MSR_LIST_NUM; i++) {
msrop = &(ss->pmi_stop_msr_list[group_id][i]);
if (msrop != NULL) {
if (msrop->msr_id == (uint32_t)-1) {
break;
}
if (msrop->msr_op_type == (uint8_t)MSR_OP_WRITE) {
msr_write(msrop->msr_id, msrop->value);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: MSRWRITE cpu%d, msr_id=0x%x, msr_val=0x%lx",
__func__, get_pcpu_id(), msrop->msr_id, msrop->value);
}
}
}
/* Mask LAPIC LVT entry for PMC register */
lvt_perf_ctr = (uint32_t) msr_read(MSR_IA32_EXT_APIC_LVT_PMI);
lvt_perf_ctr |= LVT_PERFCTR_BIT_MASK;
msr_write(MSR_IA32_EXT_APIC_LVT_PMI, lvt_perf_ctr);
ss->pmu_state = PMU_SETUP;
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
} else {
dev_dbg(DBG_LEVEL_ERR_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
}
}
/*
* Writes specified size of data into sbuf
*/
static int32_t profiling_sbuf_put_variable(struct shared_buf *sbuf,
uint8_t *data, uint32_t size)
{
uint32_t remaining_space, offset, next_tail;
void *to;
/*
* 1. check for null pointers and non-zero size
* 2. check if enough room available in the buffer
* 2a. if not, drop the sample, increment count of dropped samples,
* return
* 2b. unless overwrite flag is enabled
* 3. Continue if buffer has space for the sample
* 4. Copy sample to buffer
* 4a. Split variable sample to be copied if the sample is going to
* wrap around the buffer
* 4b. Otherwise do a simple copy
* 5. return number of bytes of data put in buffer
*/
if ((sbuf == NULL) || (data == NULL)) {
return -EINVAL;
}
if (size == 0U) {
return 0;
}
stac();
if (sbuf->tail >= sbuf->head) {
remaining_space = sbuf->size - (sbuf->tail - sbuf->head);
} else {
remaining_space = sbuf->head - sbuf->tail;
}
if (size >= remaining_space) {
/* Only (remaining_space - 1) can be written to sbuf.
* Since if the next_tail equals head, then it is assumed
* that buffer is empty, not full
*/
clac();
return 0;
}
next_tail = sbuf_next_ptr(sbuf->tail, size, sbuf->size);
to = (void *)sbuf + SBUF_HEAD_SIZE + sbuf->tail;
if (next_tail < sbuf->tail) { /* wrap-around */
offset = sbuf->size - sbuf->tail;
(void)memcpy_s(to, offset, data, offset);
/* 2nd part */
to = (void *)sbuf + SBUF_HEAD_SIZE;
if ((size - offset) > 0U) {
(void)memcpy_s(to, size - offset,
data + offset, size - offset);
}
} else {
(void)memcpy_s(to, size, data, size);
}
sbuf->tail = next_tail;
clac();
return (int32_t)size;
}
/*
* Read profiling data and transferred to SOS
* Drop transfer of profiling data if sbuf is full/insufficient and log it
*/
static int32_t profiling_generate_data(int32_t collector, uint32_t type)
{
uint64_t i;
uint32_t remaining_space = 0U;
int32_t ret = 0;
struct data_header pkt_header;
uint64_t payload_size = 0UL;
void *payload = NULL;
struct shared_buf *sbuf = NULL;
struct sep_state *ss = &(get_cpu_var(profiling_info.s_state));
struct sw_msr_op_info *sw_msrop
= &(get_cpu_var(profiling_info.sw_msr_info));
uint64_t rflags;
spinlock_t *sw_lock = NULL;
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering cpu%d",
__func__, get_pcpu_id());
if (collector == COLLECT_PROFILE_DATA) {
sbuf = per_cpu(sbuf, get_pcpu_id())[ACRN_SEP];
if (sbuf == NULL) {
ss->samples_dropped++;
dev_dbg(DBG_LEVEL_PROFILING, "%s: sbuf is NULL exiting cpu%d",
__func__, get_pcpu_id());
return 0;
}
if (ss->pmu_state == PMU_RUNNING) {
stac();
if (sbuf->tail >= sbuf->head) {
remaining_space = sbuf->size
- (sbuf->tail - sbuf->head);
} else {
remaining_space = sbuf->head - sbuf->tail;
}
clac();
/* populate the data header */
pkt_header.tsc = rdtsc();
pkt_header.collector_id = collector;
pkt_header.cpu_id = get_pcpu_id();
pkt_header.data_type = 1U << type;
pkt_header.reserved = MAGIC_NUMBER;
switch (type) {
case CORE_PMU_SAMPLING:
payload_size = CORE_PMU_SAMPLE_SIZE;
payload = &get_cpu_var(profiling_info.p_sample);
break;
case LBR_PMU_SAMPLING:
payload_size = CORE_PMU_SAMPLE_SIZE
+ LBR_PMU_SAMPLE_SIZE;
payload = &get_cpu_var(profiling_info.p_sample);
break;
case VM_SWITCH_TRACING:
payload_size = VM_SWITCH_TRACE_SIZE;
payload = &get_cpu_var(profiling_info.vm_trace);
break;
default:
pr_err("%s: unknown data type %u on cpu %d",
__func__, type, get_pcpu_id());
ret = -1;
break;
}
if (ret == -1) {
return 0;
}
pkt_header.payload_size = payload_size;
if ((uint64_t)remaining_space < (DATA_HEADER_SIZE + payload_size)) {
ss->samples_dropped++;
dev_dbg(DBG_LEVEL_PROFILING,
"%s: not enough space left in sbuf[%d: %d] exiting cpu%d",
__func__, remaining_space,
DATA_HEADER_SIZE + payload_size, get_pcpu_id());
return 0;
}
for (i = 0U; i < (((DATA_HEADER_SIZE - 1U) / SEP_BUF_ENTRY_SIZE) + 1U); i++) {
(void)sbuf_put(sbuf, (uint8_t *)&pkt_header + i * SEP_BUF_ENTRY_SIZE);
}
for (i = 0U; i < (((payload_size - 1U) / SEP_BUF_ENTRY_SIZE) + 1U); i++) {
(void)sbuf_put(sbuf, (uint8_t *)payload + i * SEP_BUF_ENTRY_SIZE);
}
ss->samples_logged++;
}
} else if (collector == COLLECT_POWER_DATA) {
sbuf = per_cpu(sbuf, get_pcpu_id())[ACRN_SOCWATCH];
if (sbuf == NULL) {
dev_dbg(DBG_LEVEL_PROFILING,
"%s: socwatch buffers not initialized?", __func__);
return 0;
}
sw_lock = &(get_cpu_var(profiling_info.sw_lock));
spinlock_irqsave_obtain(sw_lock, &rflags);
stac();
if (sbuf->tail >= sbuf->head) {
remaining_space
= sbuf->size - (sbuf->tail - sbuf->head);
} else {
remaining_space = sbuf->head - sbuf->tail;
}
clac();
/* populate the data header */
pkt_header.tsc = rdtsc();
pkt_header.collector_id = collector;
pkt_header.cpu_id = get_pcpu_id();
pkt_header.data_type = (uint16_t)type;
switch (type) {
case SOCWATCH_MSR_OP:
dev_dbg(DBG_LEVEL_PROFILING,
"%s: generating cstate/pstate sample socwatch cpu %d",
__func__, sw_msrop->cpu_id);
pkt_header.cpu_id = (uint16_t)sw_msrop->cpu_id;
pkt_header.data_type = sw_msrop->sample_id;
payload_size
= ((uint64_t)sw_msrop->valid_entries) * sizeof(uint64_t);
payload = &(sw_msrop->core_msr[0]);
break;
case SOCWATCH_VM_SWITCH_TRACING:
dev_dbg(DBG_LEVEL_PROFILING,
"%s: generating vm-switch sample", __func__);
payload_size = VM_SWITCH_TRACE_SIZE;
payload = &get_cpu_var(profiling_info.vm_trace);
break;
default:
pr_err("%s: unknown data type %u on cpu %d",
__func__, type, get_pcpu_id());
ret = -1;
break;
}
if (ret == -1){
return 0;
}
pkt_header.payload_size = payload_size;
if ((DATA_HEADER_SIZE + payload_size) >= (uint64_t)remaining_space) {
pr_err("%s: not enough space in socwatch buffer on cpu %d",
__func__, get_pcpu_id());
return 0;
}
/* copy header */
(void)profiling_sbuf_put_variable(sbuf,
(uint8_t *)&pkt_header, (uint32_t)DATA_HEADER_SIZE);
/* copy payload */
(void)profiling_sbuf_put_variable(sbuf,
(uint8_t *)payload, (uint32_t)payload_size);
spinlock_irqrestore_release(sw_lock, rflags);
} else {
dev_dbg(DBG_LEVEL_ERR_PROFILING,
"%s: Unknown collector type", __func__);
return 0;
}
return 0;
}
/*
* Performs MSR operations - read, write and clear
*/
static void profiling_handle_msrops(void)
{
uint32_t i, j;
struct profiling_msr_ops_list *my_msr_node
= get_cpu_var(profiling_info.msr_node);
struct sw_msr_op_info *sw_msrop
= &(get_cpu_var(profiling_info.sw_msr_info));
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering cpu%d",
__func__, get_pcpu_id());
if ((my_msr_node == NULL) ||
(my_msr_node->msr_op_state != (int32_t)MSR_OP_REQUESTED)) {
dev_dbg(DBG_LEVEL_PROFILING, "%s: invalid my_msr_node on cpu%d",
__func__, get_pcpu_id());
return;
}
if ((my_msr_node->num_entries == 0U) ||
(my_msr_node->num_entries >= MAX_MSR_LIST_NUM)) {
dev_dbg(DBG_LEVEL_PROFILING,
"%s: invalid num_entries on cpu%d",
__func__, get_pcpu_id());
return;
}
for (i = 0U; i < my_msr_node->num_entries; i++) {
switch (my_msr_node->entries[i].msr_op_type) {
case MSR_OP_READ:
my_msr_node->entries[i].value
= msr_read(my_msr_node->entries[i].msr_id);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: MSRREAD cpu%d, msr_id=0x%x, msr_val=0x%lx",
__func__, get_pcpu_id(), my_msr_node->entries[i].msr_id,
my_msr_node->entries[i].value);
break;
case MSR_OP_READ_CLEAR:
my_msr_node->entries[i].value
= msr_read(my_msr_node->entries[i].msr_id);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: MSRREADCLEAR cpu%d, msr_id=0x%x, msr_val=0x%lx",
__func__, get_pcpu_id(), my_msr_node->entries[i].msr_id,
my_msr_node->entries[i].value);
msr_write(my_msr_node->entries[i].msr_id, 0U);
break;
case MSR_OP_WRITE:
msr_write(my_msr_node->entries[i].msr_id,
my_msr_node->entries[i].value);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: MSRWRITE cpu%d, msr_id=0x%x, msr_val=0x%lx",
__func__, get_pcpu_id(), my_msr_node->entries[i].msr_id,
my_msr_node->entries[i].value);
break;
default:
pr_err("%s: unknown MSR op_type %u on cpu %d",
__func__, my_msr_node->entries[i].msr_op_type,
get_pcpu_id());
break;
}
}
my_msr_node->msr_op_state = (int32_t)MSR_OP_HANDLED;
/* Also generates sample */
if ((my_msr_node->collector_id == COLLECT_POWER_DATA) &&
(sw_msrop != NULL)) {
sw_msrop->cpu_id = get_pcpu_id();
sw_msrop->valid_entries = my_msr_node->num_entries;
/*
* if 'param' is 0, then skip generating a sample since it is
* an immediate MSR read operation.
*/
if (my_msr_node->entries[0].param != 0UL) {
for (j = 0U; j < my_msr_node->num_entries; ++j) {
sw_msrop->core_msr[j]
= my_msr_node->entries[j].value;
/*
* socwatch uses the 'param' field to store the
* sample id needed by socwatch to identify the
* type of sample during post-processing
*/
sw_msrop->sample_id
= my_msr_node->entries[j].param;
}
/* generate sample */
(void)profiling_generate_data(COLLECT_POWER_DATA,
SOCWATCH_MSR_OP);
}
my_msr_node->msr_op_state = (int32_t)MSR_OP_REQUESTED;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
}
/*
* Interrupt handler for performance monitoring interrupts
*/
static void profiling_pmi_handler(uint32_t irq, __unused void *data)
{
uint64_t perf_ovf_status;
uint32_t lvt_perf_ctr;
uint32_t i;
uint32_t group_id;
struct profiling_msr_op *msrop = NULL;
struct pmu_sample *psample = &(get_cpu_var(profiling_info.p_sample));
struct sep_state *ss = &(get_cpu_var(profiling_info.s_state));
if ((ss == NULL) || (psample == NULL)) {
dev_dbg(DBG_LEVEL_ERR_PROFILING, "%s: exiting cpu%d",
__func__, get_pcpu_id());
return;
}
/* Stop all the counters first */
msr_write(MSR_IA32_PERF_GLOBAL_CTRL, 0x0U);
group_id = ss->current_pmi_group_id;
for (i = 0U; i < MAX_MSR_LIST_NUM; i++) {
msrop = &(ss->pmi_entry_msr_list[group_id][i]);
if (msrop != NULL) {
if (msrop->msr_id == (uint32_t)-1) {
break;
}
if (msrop->msr_op_type == (uint8_t)MSR_OP_WRITE) {
msr_write(msrop->msr_id, msrop->value);
}
}
}
ss->total_pmi_count++;
perf_ovf_status = msr_read(MSR_IA32_PERF_GLOBAL_STATUS);
lvt_perf_ctr = (uint32_t)msr_read(MSR_IA32_EXT_APIC_LVT_PMI);
if (perf_ovf_status == 0U) {
goto reconfig;
}
if ((perf_ovf_status & 0x80000000000000FULL) == 0U) {
ss->nofrozen_pmi++;
}
(void)memset(psample, 0U, sizeof(struct pmu_sample));
/* Attribute PMI to guest context */
if ((get_cpu_var(profiling_info.vm_info).vmexit_reason
== VMX_EXIT_REASON_EXTERNAL_INTERRUPT) &&
((uint64_t)get_cpu_var(profiling_info.vm_info).external_vector
== PMI_VECTOR)) {
psample->csample.os_id
= get_cpu_var(profiling_info.vm_info).guest_vm_id;
(void)memset(psample->csample.task, 0U, 16);
psample->csample.cpu_id = get_pcpu_id();
psample->csample.process_id = 0U;
psample->csample.task_id = 0U;
psample->csample.overflow_status = perf_ovf_status;
psample->csample.rip = get_cpu_var(profiling_info.vm_info).guest_rip;
psample->csample.rflags
= (uint32_t)get_cpu_var(profiling_info.vm_info).guest_rflags;
psample->csample.cs
= (uint32_t)get_cpu_var(profiling_info.vm_info).guest_cs;
get_cpu_var(profiling_info.vm_info).vmexit_reason = 0U;
get_cpu_var(profiling_info.vm_info).external_vector = -1;
/* Attribute PMI to hypervisor context */
} else {
psample->csample.os_id = 0xFFFFU;
(void)memcpy_s(psample->csample.task, 16, "VMM\0", 4);
psample->csample.cpu_id = get_pcpu_id();
psample->csample.process_id = 0U;
psample->csample.task_id = 0U;
psample->csample.overflow_status = perf_ovf_status;
psample->csample.rip = irq_desc_array[irq].ctx_rip;
psample->csample.rflags
= (uint32_t)irq_desc_array[irq].ctx_rflags;
psample->csample.cs = (uint32_t)irq_desc_array[irq].ctx_cs;
}
if ((sep_collection_switch &
(1UL << (uint64_t)LBR_PMU_SAMPLING)) > 0UL) {
psample->lsample.lbr_tos = msr_read(MSR_CORE_LASTBRANCH_TOS);
for (i = 0U; i < LBR_NUM_REGISTERS; i++) {
psample->lsample.lbr_from_ip[i]
= msr_read(MSR_CORE_LASTBRANCH_0_FROM_IP + i);
psample->lsample.lbr_to_ip[i]
= msr_read(MSR_CORE_LASTBRANCH_0_TO_IP + i);
}
/* Generate core pmu sample and lbr data */
(void)profiling_generate_data(COLLECT_PROFILE_DATA, LBR_PMU_SAMPLING);
} else {
/* Generate core pmu sample only */
(void)profiling_generate_data(COLLECT_PROFILE_DATA, CORE_PMU_SAMPLING);
}
/* Clear PERF_GLOBAL_OVF_STATUS bits */
msr_write(MSR_IA32_PERF_GLOBAL_OVF_CTRL,
perf_ovf_status & PERF_OVF_BIT_MASK);
ss->valid_pmi_count++;
group_id = ss->current_pmi_group_id;
for (i = 0U; i < MAX_MSR_LIST_NUM; i++) {
msrop = &(ss->pmi_exit_msr_list[group_id][i]);
if (msrop != NULL) {
if (msrop->msr_id == (uint32_t)-1) {
break;
}
if (msrop->msr_op_type == (uint8_t)MSR_OP_WRITE) {
if (msrop->reg_type != (uint8_t)PMU_MSR_DATA) {
if (msrop->msr_id != MSR_IA32_PERF_GLOBAL_CTRL) {
msr_write(msrop->msr_id, msrop->value);
}
}
else {
if (((perf_ovf_status >> msrop->param) & 0x1U) > 0U) {
msr_write(msrop->msr_id, msrop->value);
}
}
}
}
}
reconfig:
if (ss->pmu_state == PMU_RUNNING) {
/* Unmask the interrupt */
lvt_perf_ctr &= LVT_PERFCTR_BIT_UNMASK;
msr_write(MSR_IA32_EXT_APIC_LVT_PMI, lvt_perf_ctr);
group_id = ss->current_pmi_group_id;
for (i = 0U; i < MAX_MSR_LIST_NUM; i++) {
msrop = &(ss->pmi_start_msr_list[group_id][i]);
if (msrop != NULL) {
if (msrop->msr_id == (uint32_t)-1) {
break;
}
if (msrop->msr_op_type == (uint8_t)MSR_OP_WRITE) {
msr_write(msrop->msr_id, msrop->value);
}
}
}
} else {
/* Mask the interrupt */
lvt_perf_ctr |= LVT_PERFCTR_BIT_MASK;
msr_write(MSR_IA32_EXT_APIC_LVT_PMI, lvt_perf_ctr);
}
}
/*
* Initialize sep state and enable PMU counters
*/
static void profiling_start_pmu(void)
{
uint16_t i;
uint16_t pcpu_nums = get_pcpu_nums();
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (in_pmu_profiling) {
return;
}
for (i = 0U; i < pcpu_nums; i++) {
if (per_cpu(profiling_info.s_state, i).pmu_state != PMU_SETUP) {
pr_err("%s: invalid pmu_state %u on cpu%d",
__func__, get_cpu_var(profiling_info.s_state).pmu_state, i);
return;
}
}
for (i = 0U; i < pcpu_nums; i++) {
per_cpu(profiling_info.ipi_cmd, i) = IPI_PMU_START;
per_cpu(profiling_info.s_state, i).samples_logged = 0U;
per_cpu(profiling_info.s_state, i).samples_dropped = 0U;
per_cpu(profiling_info.s_state, i).valid_pmi_count = 0U;
per_cpu(profiling_info.s_state, i).total_pmi_count = 0U;
per_cpu(profiling_info.s_state, i).total_vmexit_count = 0U;
per_cpu(profiling_info.s_state, i).frozen_well = 0U;
per_cpu(profiling_info.s_state, i).frozen_delayed = 0U;
per_cpu(profiling_info.s_state, i).nofrozen_pmi = 0U;
per_cpu(profiling_info.s_state, i).pmu_state = PMU_RUNNING;
}
smp_call_function(get_active_pcpu_bitmap(), profiling_ipi_handler, NULL);
in_pmu_profiling = true;
dev_dbg(DBG_LEVEL_PROFILING, "%s: done", __func__);
}
/*
* Reset sep state and Disable all the PMU counters
*/
static void profiling_stop_pmu(void)
{
uint16_t i;
uint16_t pcpu_nums = get_pcpu_nums();
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (in_pmu_profiling) {
for (i = 0U; i < pcpu_nums; i++) {
per_cpu(profiling_info.ipi_cmd, i) = IPI_PMU_STOP;
if (per_cpu(profiling_info.s_state, i).pmu_state == PMU_RUNNING) {
per_cpu(profiling_info.s_state, i).pmu_state = PMU_SETUP;
}
dev_dbg(DBG_LEVEL_PROFILING,
"%s: pmi_cnt[%d] = total:%u valid=%u, vmexit_cnt=%u",
__func__, i, per_cpu(profiling_info.s_state, i).total_pmi_count,
per_cpu(profiling_info.s_state, i).valid_pmi_count,
per_cpu(profiling_info.s_state, i).total_vmexit_count);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: cpu%d frozen well:%u frozen delayed=%u, nofrozen_pmi=%u",
__func__, i, per_cpu(profiling_info.s_state, i).frozen_well,
per_cpu(profiling_info.s_state, i).frozen_delayed,
per_cpu(profiling_info.s_state, i).nofrozen_pmi);
dev_dbg(DBG_LEVEL_PROFILING,
"%s: cpu%d samples captured:%u samples dropped=%u",
__func__, i, per_cpu(profiling_info.s_state, i).samples_logged,
per_cpu(profiling_info.s_state, i).samples_dropped);
}
smp_call_function(get_active_pcpu_bitmap(), profiling_ipi_handler, NULL);
in_pmu_profiling = false;
dev_dbg(DBG_LEVEL_PROFILING, "%s: done.", __func__);
}
}
/*
* Performs MSR operations on all the CPU's
*/
int32_t profiling_msr_ops_all_cpus(struct acrn_vm *vm, uint64_t addr)
{
uint16_t i;
struct profiling_msr_ops_list msr_list[MAX_PCPU_NUM];
uint16_t pcpu_nums = get_pcpu_nums();
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &msr_list, addr, (uint32_t)pcpu_nums * sizeof(struct profiling_msr_ops_list)) != 0) {
return -EINVAL;
}
for (i = 0U; i < pcpu_nums; i++) {
per_cpu(profiling_info.ipi_cmd, i) = IPI_MSR_OP;
per_cpu(profiling_info.msr_node, i) = &(msr_list[i]);
}
smp_call_function(get_active_pcpu_bitmap(), profiling_ipi_handler, NULL);
if (copy_to_gpa(vm, &msr_list, addr, sizeof(msr_list)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* Generate VM info list
*/
int32_t profiling_vm_list_info(struct acrn_vm *vm, uint64_t addr)
{
struct acrn_vm *tmp_vm;
struct acrn_vcpu *vcpu;
int32_t vm_idx;
uint16_t i, j;
struct profiling_vm_info_list vm_info_list;
uint16_t pcpu_nums = get_pcpu_nums();
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &vm_info_list, addr, sizeof(vm_info_list)) != 0) {
return -EINVAL;
}
vm_idx = 0;
vm_info_list.vm_list[vm_idx].vm_id_num = -1;
(void)memcpy_s((void *)vm_info_list.vm_list[vm_idx].vm_name, 4U, "VMM\0", 4U);
for (i = 0U; i < pcpu_nums; i++) {
vm_info_list.vm_list[vm_idx].cpu_map[i].vcpu_id = i;
vm_info_list.vm_list[vm_idx].cpu_map[i].pcpu_id = i;
vm_info_list.vm_list[vm_idx].cpu_map[i].apic_id
= per_cpu(lapic_id, i);
}
vm_info_list.vm_list[vm_idx].num_vcpus = i;
vm_info_list.num_vms = 1;
for (j = 0U; j < CONFIG_MAX_VM_NUM; j++) {
tmp_vm = get_vm_from_vmid(j);
if (is_poweroff_vm(tmp_vm)) {
break;
}
vm_info_list.num_vms++;
vm_idx++;
vm_info_list.vm_list[vm_idx].vm_id_num = tmp_vm->vm_id;
(void)memcpy_s((void *)vm_info_list.vm_list[vm_idx].uuid,
16U, tmp_vm->uuid, 16U);
snprintf(vm_info_list.vm_list[vm_idx].vm_name, 16U, "vm_%d",
tmp_vm->vm_id, 16U);
vm_info_list.vm_list[vm_idx].num_vcpus = 0;
i = 0U;
foreach_vcpu(i, tmp_vm, vcpu) {
vm_info_list.vm_list[vm_idx].cpu_map[i].vcpu_id
= vcpu->vcpu_id;
vm_info_list.vm_list[vm_idx].cpu_map[i].pcpu_id
= pcpuid_from_vcpu(vcpu);
vm_info_list.vm_list[vm_idx].cpu_map[i].apic_id = 0;
vm_info_list.vm_list[vm_idx].num_vcpus++;
}
}
if (copy_to_gpa(vm, &vm_info_list, addr, sizeof(vm_info_list)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* Sep/socwatch profiling version
*/
int32_t profiling_get_version_info(struct acrn_vm *vm, uint64_t addr)
{
struct profiling_version_info ver_info;
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &ver_info, addr, sizeof(ver_info)) != 0) {
return -EINVAL;
}
ver_info.major = MAJOR_VERSION;
ver_info.minor = MINOR_VERSION;
ver_info.supported_features = (int64_t)
((1U << (uint64_t)CORE_PMU_SAMPLING) |
(1U << (uint64_t)CORE_PMU_COUNTING) |
(1U << (uint64_t)LBR_PMU_SAMPLING) |
(1U << (uint64_t)VM_SWITCH_TRACING));
if (copy_to_gpa(vm, &ver_info, addr, sizeof(ver_info)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* Gets type of profiling - sep/socwatch
*/
int32_t profiling_get_control(struct acrn_vm *vm, uint64_t addr)
{
struct profiling_control prof_control;
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &prof_control, addr, sizeof(prof_control)) != 0) {
return -EINVAL;
}
switch (prof_control.collector_id) {
case COLLECT_PROFILE_DATA:
prof_control.switches = sep_collection_switch;
break;
case COLLECT_POWER_DATA:
break;
default:
pr_err("%s: unknown collector %d",
__func__, prof_control.collector_id);
break;
}
if (copy_to_gpa(vm, &prof_control, addr, sizeof(prof_control)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* Update the profiling type based on control switch
*/
int32_t profiling_set_control(struct acrn_vm *vm, uint64_t addr)
{
uint64_t old_switch;
uint64_t new_switch;
uint16_t i;
uint16_t pcpu_nums = get_pcpu_nums();
struct profiling_control prof_control;
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &prof_control, addr, sizeof(prof_control)) != 0) {
return -EINVAL;
}
switch (prof_control.collector_id) {
case COLLECT_PROFILE_DATA:
old_switch = sep_collection_switch;
new_switch = prof_control.switches;
sep_collection_switch = prof_control.switches;
dev_dbg(DBG_LEVEL_PROFILING,
" old_switch: %lu sep_collection_switch: %lu!",
old_switch, sep_collection_switch);
for (i = 0U; i < (uint16_t)MAX_SEP_FEATURE_ID; i++) {
if (((new_switch ^ old_switch) & (0x1UL << i)) != 0UL) {
switch (i) {
case CORE_PMU_SAMPLING:
case CORE_PMU_COUNTING:
if ((new_switch & (0x1UL << i)) != 0UL) {
profiling_start_pmu();
} else {
profiling_stop_pmu();
}
break;
case LBR_PMU_SAMPLING:
break;
case VM_SWITCH_TRACING:
break;
default:
dev_dbg(DBG_LEVEL_PROFILING,
"%s: feature not supported %u",
__func__, i);
break;
}
}
}
break;
case COLLECT_POWER_DATA:
dev_dbg(DBG_LEVEL_PROFILING,
"%s: configuring socwatch", __func__);
socwatch_collection_switch = prof_control.switches;
dev_dbg(DBG_LEVEL_PROFILING,
"socwatch_collection_switch: %lu!",
socwatch_collection_switch);
if (socwatch_collection_switch != 0UL) {
dev_dbg(DBG_LEVEL_PROFILING,
"%s: socwatch start collection invoked!", __func__);
for (i = 0U; i < (uint16_t)MAX_SOCWATCH_FEATURE_ID; i++) {
if ((socwatch_collection_switch & (0x1UL << i)) != 0UL) {
switch (i) {
case SOCWATCH_COMMAND:
break;
case SOCWATCH_VM_SWITCH_TRACING:
dev_dbg(DBG_LEVEL_PROFILING,
"%s: socwatch vm-switch feature requested!",
__func__);
break;
default:
dev_dbg(DBG_LEVEL_PROFILING,
"%s: socwatch feature not supported %u",
__func__, i);
break;
}
}
}
for (i = 0U; i < pcpu_nums ; i++) {
per_cpu(profiling_info.soc_state, i)
= SW_RUNNING;
}
} else { /* stop socwatch collection */
dev_dbg(DBG_LEVEL_PROFILING,
"%s: socwatch stop collection invoked or collection switch not set!",
__func__);
for (i = 0U; i < pcpu_nums ; i++) {
per_cpu(profiling_info.soc_state, i)
= SW_STOPPED;
}
}
break;
default:
pr_err("%s: unknown collector %d",
__func__, prof_control.collector_id);
break;
}
if (copy_to_gpa(vm, &prof_control, addr, sizeof(prof_control)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* Configure PMI on all cpus
*/
int32_t profiling_configure_pmi(struct acrn_vm *vm, uint64_t addr)
{
uint16_t i;
struct profiling_pmi_config pmi_config;
uint16_t pcpu_nums = get_pcpu_nums();
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &pmi_config, addr, sizeof(pmi_config)) != 0) {
return -EINVAL;
}
for (i = 0U; i < pcpu_nums; i++) {
if (!((per_cpu(profiling_info.s_state, i).pmu_state ==
PMU_INITIALIZED) ||
(per_cpu(profiling_info.s_state, i).pmu_state ==
PMU_SETUP))) {
pr_err("%s: invalid pmu_state %u on cpu%d",
__func__, per_cpu(profiling_info.s_state, i).pmu_state, i);
return -EINVAL;
}
}
if (pmi_config.num_groups == 0U ||
pmi_config.num_groups > MAX_GROUP_NUM) {
pr_err("%s: invalid num_groups %u",
__func__, pmi_config.num_groups);
return -EINVAL;
}
for (i = 0U; i < pcpu_nums; i++) {
per_cpu(profiling_info.ipi_cmd, i) = IPI_PMU_CONFIG;
per_cpu(profiling_info.s_state, i).num_pmi_groups
= pmi_config.num_groups;
(void)memcpy_s((void *)per_cpu(profiling_info.s_state, i).pmi_initial_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM,
(void *)pmi_config.initial_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM);
(void)memcpy_s((void *)per_cpu(profiling_info.s_state, i).pmi_start_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM,
(void *)pmi_config.start_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM);
(void)memcpy_s((void *)per_cpu(profiling_info.s_state, i).pmi_stop_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM,
(void *)pmi_config.stop_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM);
(void)memcpy_s((void *)per_cpu(profiling_info.s_state, i).pmi_entry_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM,
(void *)pmi_config.entry_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM);
(void)memcpy_s((void *)per_cpu(profiling_info.s_state, i).pmi_exit_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM,
(void *)pmi_config.exit_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM*MAX_GROUP_NUM);
}
smp_call_function(get_active_pcpu_bitmap(), profiling_ipi_handler, NULL);
if (copy_to_gpa(vm, &pmi_config, addr, sizeof(pmi_config)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* Configure for VM-switch data on all cpus
*/
int32_t profiling_configure_vmsw(struct acrn_vm *vm, uint64_t addr)
{
uint16_t i;
int32_t ret = 0;
struct profiling_vmsw_config vmsw_config;
uint16_t pcpu_nums = get_pcpu_nums();
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &vmsw_config, addr, sizeof(vmsw_config)) != 0) {
return -EINVAL;
}
switch (vmsw_config.collector_id) {
case COLLECT_PROFILE_DATA:
for (i = 0U; i < pcpu_nums; i++) {
per_cpu(profiling_info.ipi_cmd, i) = IPI_VMSW_CONFIG;
(void)memcpy_s(
(void *)per_cpu(profiling_info.s_state, i).vmsw_initial_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM,
(void *)vmsw_config.initial_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM);
(void)memcpy_s(
(void *)per_cpu(profiling_info.s_state, i).vmsw_entry_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM,
(void *)vmsw_config.entry_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM);
(void)memcpy_s(
(void *)per_cpu(profiling_info.s_state, i).vmsw_exit_msr_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM,
(void *)vmsw_config.exit_list,
sizeof(struct profiling_msr_op)*MAX_MSR_LIST_NUM);
}
smp_call_function(get_active_pcpu_bitmap(), profiling_ipi_handler, NULL);
break;
case COLLECT_POWER_DATA:
break;
default:
pr_err("%s: unknown collector %d",
__func__, vmsw_config.collector_id);
ret = -EINVAL;
break;
}
if (copy_to_gpa(vm, &vmsw_config, addr, sizeof(vmsw_config)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return ret;
}
/*
* Get the physical cpu id
*/
int32_t profiling_get_pcpu_id(struct acrn_vm *vm, uint64_t addr)
{
struct profiling_pcpuid pcpuid;
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &pcpuid, addr, sizeof(pcpuid)) != 0) {
return -EINVAL;
}
cpuid_subleaf(pcpuid.leaf, pcpuid.subleaf, &pcpuid.eax,
&pcpuid.ebx, &pcpuid.ecx, &pcpuid.edx);
if (copy_to_gpa(vm, &pcpuid, addr, sizeof(pcpuid)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* Update collection statictics
*/
int32_t profiling_get_status_info(struct acrn_vm *vm, uint64_t gpa)
{
uint16_t i;
struct profiling_status pstats[MAX_PCPU_NUM];
uint16_t pcpu_nums = get_pcpu_nums();
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
if (copy_from_gpa(vm, &pstats, gpa,
pcpu_nums*sizeof(struct profiling_status)) != 0) {
return -EINVAL;
}
for (i = 0U; i < pcpu_nums; i++) {
pstats[i].samples_logged =
per_cpu(profiling_info.s_state, i).samples_logged;
pstats[i].samples_dropped =
per_cpu(profiling_info.s_state, i).samples_dropped;
}
if (copy_to_gpa(vm, &pstats, gpa,
pcpu_nums*sizeof(struct profiling_status)) != 0) {
return -EINVAL;
}
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
return 0;
}
/*
* IPI interrupt handler function
*/
void profiling_ipi_handler(__unused void *data)
{
switch (get_cpu_var(profiling_info.ipi_cmd)) {
case IPI_PMU_START:
profiling_enable_pmu();
break;
case IPI_PMU_STOP:
profiling_disable_pmu();
break;
case IPI_MSR_OP:
profiling_handle_msrops();
break;
case IPI_PMU_CONFIG:
profiling_initialize_pmi();
break;
case IPI_VMSW_CONFIG:
profiling_initialize_vmsw();
break;
default:
pr_err("%s: unknown IPI command %d on cpu %d",
__func__, get_cpu_var(profiling_info.ipi_cmd), get_pcpu_id());
break;
}
get_cpu_var(profiling_info.ipi_cmd) = IPI_UNKNOWN;
}
/*
* Save the VCPU info on vmenter
*/
void profiling_vmenter_handler(__unused struct acrn_vcpu *vcpu)
{
if (((get_cpu_var(profiling_info.s_state).pmu_state == PMU_RUNNING) &&
((sep_collection_switch &
(1UL << (uint64_t)VM_SWITCH_TRACING)) > 0UL)) ||
((get_cpu_var(profiling_info.soc_state) == SW_RUNNING) &&
((socwatch_collection_switch &
(1UL << (uint64_t)SOCWATCH_VM_SWITCH_TRACING)) > 0UL))) {
get_cpu_var(profiling_info.vm_info).vmenter_tsc = rdtsc();
}
}
/*
* Save the VCPU info on vmexit
*/
void profiling_pre_vmexit_handler(struct acrn_vcpu *vcpu)
{
uint64_t exit_reason = 0UL;
exit_reason = vcpu->arch.exit_reason & 0xFFFFUL;
if ((get_cpu_var(profiling_info.s_state).pmu_state == PMU_RUNNING) ||
(get_cpu_var(profiling_info.soc_state) == SW_RUNNING)) {
get_cpu_var(profiling_info.vm_info).vmexit_tsc = rdtsc();
get_cpu_var(profiling_info.vm_info).vmexit_reason
= exit_reason;
if (exit_reason == VMX_EXIT_REASON_EXTERNAL_INTERRUPT) {
get_cpu_var(profiling_info.vm_info).external_vector
= (int32_t)(exec_vmread(VMX_EXIT_INT_INFO) & 0xFFUL);
} else {
get_cpu_var(profiling_info.vm_info).external_vector = -1;
}
get_cpu_var(profiling_info.vm_info).guest_rip
= vcpu_get_rip(vcpu);
get_cpu_var(profiling_info.vm_info).guest_rflags
= vcpu_get_rflags(vcpu);
get_cpu_var(profiling_info.vm_info).guest_cs
= exec_vmread64(VMX_GUEST_CS_SEL);
get_cpu_var(profiling_info.vm_info).guest_vm_id = (int16_t)vcpu->vm->vm_id;
}
}
/*
* Generate vmexit data
*/
void profiling_post_vmexit_handler(struct acrn_vcpu *vcpu)
{
per_cpu(profiling_info.s_state, pcpuid_from_vcpu(vcpu)).total_vmexit_count++;
if ((get_cpu_var(profiling_info.s_state).pmu_state == PMU_RUNNING) ||
(get_cpu_var(profiling_info.soc_state) == SW_RUNNING)) {
/* Generate vmswitch sample */
if (((sep_collection_switch &
(1UL << (uint64_t)VM_SWITCH_TRACING)) > 0UL) ||
((socwatch_collection_switch &
(1UL << (uint64_t)SOCWATCH_VM_SWITCH_TRACING)) > 0UL)) {
get_cpu_var(profiling_info.vm_trace).os_id
= vcpu->vm->vm_id;
get_cpu_var(profiling_info.vm_trace).vm_enter_tsc
= get_cpu_var(profiling_info.vm_info).vmenter_tsc;
get_cpu_var(profiling_info.vm_trace).vm_exit_tsc
= get_cpu_var(profiling_info.vm_info).vmexit_tsc;
get_cpu_var(profiling_info.vm_trace).vm_exit_reason
= get_cpu_var(profiling_info.vm_info).vmexit_reason;
if ((sep_collection_switch &
(1UL << (uint64_t)VM_SWITCH_TRACING)) > 0UL) {
(void)profiling_generate_data(COLLECT_PROFILE_DATA,
VM_SWITCH_TRACING);
}
if ((socwatch_collection_switch &
(1UL << (uint64_t)SOCWATCH_VM_SWITCH_TRACING)) > 0UL) {
(void)profiling_generate_data(COLLECT_POWER_DATA,
SOCWATCH_VM_SWITCH_TRACING);
}
}
}
}
/*
* Setup PMI irq vector
*/
void profiling_setup(void)
{
uint16_t cpu;
int32_t retval;
dev_dbg(DBG_LEVEL_PROFILING, "%s: entering", __func__);
cpu = get_pcpu_id();
/* support PMI notification, SOS_VM will register all CPU */
if ((cpu == BSP_CPU_ID) && (profiling_pmi_irq == IRQ_INVALID)) {
pr_info("%s: calling request_irq", __func__);
retval = request_irq(PMI_IRQ,
profiling_pmi_handler, NULL, IRQF_NONE);
if (retval < 0) {
pr_err("Failed to add PMI isr");
return;
}
profiling_pmi_irq = (uint32_t)retval;
}
per_cpu(profiling_info.s_state, cpu).valid_pmi_count = 0U;
per_cpu(profiling_info.s_state, cpu).total_pmi_count = 0U;
per_cpu(profiling_info.s_state, cpu).total_vmexit_count = 0U;
per_cpu(profiling_info.s_state, cpu).pmu_state = PMU_INITIALIZED;
per_cpu(profiling_info.s_state, cpu).vmexit_msr_cnt = 0U;
per_cpu(profiling_info.s_state, cpu).samples_logged = 0U;
per_cpu(profiling_info.s_state, cpu).samples_dropped = 0U;
per_cpu(profiling_info.s_state, cpu).frozen_well = 0U;
per_cpu(profiling_info.s_state, cpu).frozen_delayed = 0U;
per_cpu(profiling_info.s_state, cpu).nofrozen_pmi = 0U;
msr_write(MSR_IA32_EXT_APIC_LVT_PMI,
PMI_VECTOR | LVT_PERFCTR_BIT_MASK);
dev_dbg(DBG_LEVEL_PROFILING, "%s: exiting", __func__);
}
#endif
| 2024-02-25T01:27:04.277712 | https://example.com/article/3994 |
Greenwich Maritime Centre
The Greenwich Maritime Centre (GMI) is a part of the University of Greenwich. Established in 1998, it provides a specialist postgraduate and research institute within the large multi-faculty University of Greenwich. The aims of the GMC are to engage in and facilitate scholarly research, to disseminate and publicise research findings, to provide postgraduate teaching, to develop maritime education, to act as a forum for exploration of maritime issues, to serve as a source of expertise for business and government and to provide cost-effective consultancy services. The GMC provides an active centre for studying maritime history and is located in The Old Royal Naval College, Greenwich, across the road from the National Maritime Museum.
External links
Official website
Maritime Centre
Category:Education in the Royal Borough of Greenwich
Category:Maritime colleges in the United Kingdom
Category:Educational institutions established in 1998
Category:1998 establishments in England | 2023-12-21T01:27:04.277712 | https://example.com/article/5892 |
Q:
LD linker: Target address aligning but not address in ROM
I have a program that's resident in flash and will run from flash. Early in the program data segments are copied from flash to ram. I'm using a linker script like (simplified):
.text :
{
*(.text)
} > FLASH
_etext = .;
PROVIDE (etext = .);
.rodata :
{
PROVIDE(__COPY_DATA_START__ = .);
*(.rodata)
} > ram AT>flash
PROVIDE (__SDATA2_START__ = .);
.sdata2 :
{
*(.sdata2)
} > ram AT>flash
PROVIDE (__sbss2_start = . );
.sbss2 : {
*(.sbss2)
. = ALIGN(4)
} > ram AT>flash
PROVIDE (__sbss2_end = . );
PROVIDE (__SBSS2_END__ = .);
.data :
{
*(.data)
*(.gnu.linkonce.d*)
CONSTRUCTORS
*(.eh_frame)
} > ram AT>flash
PROVIDE (__END_COPY__ = .);
I want the sections to be aligned on 4-byte boundaries (architecture is PowerPC 32-bit). Some of the data sections include sub-word items. I'm finding that the ALIGN instruction aligns the VMA address in RAM but doesn't align the LMA. So my copy-to-ram routine fails because the two areas don't correspond byte-for-byte.
My copy routine looks like
r3 = address in flash of _etext
r4 = address in ram of __COPY_DATA_START__
words to copy = (__END_COPY__ - COPY_DATA_START) / 4
while (words to copy)
* r4++ = *r3++
When the loop gets to an aligned bit, the destination points to some pad bytes, but the source data doesn't include the align-padding so the data gets put too early in memory.
I can tell this from the map file because it looks like (contrived example)
.rodata 0x00000000 0xb15 load address 0xfff13000
0x00000000 PROVIDE (__COPY_DATA_START__, .)
.sdata 0x00000b18 0x10 load address 0xfff13b15 <<< origin 0xb18 is aligned but load address hasn't moved on by the padding bytes
Does anyone know the solution to this problem?
Thank you
Chris
A:
I've had some success by using a different form of the "AT" linker script command. If I use
_etext = .;
PROVIDE (etext = .);
.rodata : AT (_etext)
{
... contents of section ...
}
.sdata2 : AT (_etext + SIZEOF(.rodata) + SIZEOF(.gcc_except_table))
{
... contents of section ...
} > ram
.sbss2 : AT (_etext + SIZEOF(.rodata) + SIZEOF(.gcc_except_table) + SIZEOF(.sdata2) )
{
... contents of section ...
. = ALIGN(16);
} > ram
Then it seems to align as I would expect. The SIZEOF( ) + SIZEOF( ) ... string gets pretty long by the end of the file but at least it works.
(Additional info: Normally you wouldn't copy the rodata section into ram because it's read only. On my system the flash can't handle the kind of accesses requured for floating point constants, so I do need to copy it into RAM even though it won't be modified).
| 2023-10-11T01:27:04.277712 | https://example.com/article/6305 |
Obama tightens regulations on fracking. Requires a “water management” plan be filed, disclosure of chemicals used (I’m sure there’s a huge form for this about an inch thick0 and more testing for oil and gas.
In regards to Run Fast, Run Quick Elizabeth Warren, would it be better that this story goes away, and let her just be damaged goods come November? This happening now leaves too much time for someone else to jump in.
A group of 68 House Democrats and one Republican sent a letter to President Barack Obama on Thursday urging him to reconsider an element of the controversial free trade agreement currently being negotiated by the administration. If approved in its current form, the pact would effectively ban “Buy American” policies in government contracting.
Although the deal, known as the Trans-Pacific Partnership, has received relatively little media attention in the United States, it has sparked international friction among consumer groups and environmental activists who worry that terms demanded by the Obama administration will eliminate important public protections. Domestically, however, the deal’s primary source of political tension is from a portion that could ban “Buy American” provisions — a restriction that opponents emphasize would crimp U.S. jobs.
Montana is a strange state. Remember Clinton won it back in 1992 b/c of the Perot vote but recently and it’s not b/c of demographic changes the voters in that state have been more open to voting for Obama then they were Kerry or Gore.
The banning of buy America is a good idea. Free Trade makes all parties better off. Most of the contracts would go to American companies anyways but exposed to foreign competition would keep them more honest. This is not a mark against Obama.
Californian’s flee their state because the Democrat’s policies there have been a disaster. Unfortunely, when they go to the other Western states, they bring their Democrat voting politics with them. That and the influx of immigrants (whether of not they are citizens) fleeing socialism also vote for these same kind of politicians.
Yes, this goes all the way up to Montana. Fortunately, they look next door at North Dakota’s success and are starting to remember who’s policies actually helps the economy.
CHARLESTON, W.Va. (AP) — West Virginia’s general tax collections fell below their estimate for the second consecutive month in April, further eroding a potential surplus for the budget year.
The state is counting on $65 million in excess revenue from the current budget year, which ends June 30, to fund the Medicaid health care program. Despite the back-to-back misses, officials continue to predict a surplus.
The state severance tax on coal and other extracted natural resources brought in $16 million less than projected in March and April, though its collections remain up by $13.7 million year-to-date.
“The severance tax is beginning to tread water a little bit, after some significant growth in the beginning of the year,” Muchow said. “I suspect that has to do with lower coal production as well as much lower natural gas prices. There’s also some softness in the coal pricing area, particularly the futures market.”
CHARLESTON, W.Va. — Alpha Natural Resources Inc. has reported a first-quarter net loss of $29.1 million or 13 cents a share on revenue of $1.9 billion.
Facing weak demand for steam coal used by power companies to generate electricity, Alpha announced production cuts in February that will reduce annual output by about 4 million tons.
Kevin Crutchfield, Alpha’s chief executive officer, hinted that even bigger cuts are in the works.
Since the February cuts, “unusually mild winter weather and decade-low natural gas prices have significantly reduced domestic steam coal consumption and driven utility inventories to near record levels,” he said in a prepared statement. “In response coal producers continue to announce plans to reduce production. Alpha plans to introduce additional production adjustments in the near future.”
The changes to be announced will reduce Alpha’s steam coal production by the equivalent of an additional 7 million tons a year, he said.
The market for low-quality metallurgical coal also has weakened so Alpha will reduce production by the equivalent of 500,000 tons a year, Crutchfield said. Metallurgical coal is used in steelmaking.
>snip>
On Tuesday Arch Coal Inc. said “severe weakness” in the U.S. market for steam coal cut into its earnings and prompted it to reduce production.
Regarding Indiana, Lugar has always been very good at voting correctly when it really counted.
Of course, he could vote the wrong way when it didnt matter in order to burnish his own legacy. Most politicians do this. Dem Evan Bayh was a master at this.
But Lugar didnt forsee the Tea Party movement, and was not savvy enough to realize that even meaningless votes FOR Obama’s COTUS picks, for example, would have tremendous impact on his political viability this time around.
It looks like Obama will finish May with a 48 percent approval rating. But since adults include composite racist white b!tches and girls with daddy issues like Julia, he’ll be 1 pt behind Mitt in the horserace polling comprised of registered voters.
“If the selection of Mitt Romney’s running mate were left up to Republican voters, right now the choice would be a tossup between Rick Santorum and Marco Rubio—but not by much.
A Reuters/Ipsos poll released Thursday night showed that Santorum led the pack in a list of 19 running mates, with 18 percent of Republican voters choosing him just slightly over Rubio, who received the support of 17 percent. Behind them, 13 percent liked New Jersey Gov. Chris Christie; the same number preferred former Florida Gov. Jeb Bush”
Democrats were trying to recruit a Republican ex-Congressman to run against Tim Walberg in MI-07. Today he said he wasn’t going to run. That leaves Dems with a single candidate who has raised less than $7,000, $5K of which was a loan. Cook has MI-07 as Likely Republican, but it should be moved to Safe R. One less 2010 seat we have to worry about.
The Indian fiasco really touches a cord in a liberal state like Massachusetts. Filled with ethnic working class white men and women who normally vote Democrat but who are also sensitive to the fact that an elitist like Warren was trying to gaming the very system people like her put in place to the determinant of working class whites who suffer under that very system.
“This takes her biography into a bizarre dimension,” said Larry Sabato, director of the University of Virginia Center for Politics. “It has derailed the effort to define Warren in a voter-friendly way.”
Sabato also said that Warren’s claim that she didn’t list herself as a minority to gain an employment advantage is not believable.
“This is what happens when candidates don’t tell the truth,” he said. “It’s pretty obvious she was using (the minority listing) for career advancement.”
89- Actually, the Tory losses aren’t that bad and seem to be in line for a mid-term over there. The councils are split into staggered elctoral groups, much like our Senate classes. That, and a huge chunk of the Labour gains came at the expense of the Lib Dems. Losses are never anything to crow about, but -400 is not doom and gloom territory in a British council election. Ultimately, Labour will have to convince the nation three years hence that it is a different party. By then, the sting of budget cuts will have passed and hopefully, they will have moved into something of a recovery.
“US President Barack Obama on Friday shrugged off a disappointing Labor Department report on jobs growth, and said he would press Congress to pass “common sense” measures to create employment.
Obama chose to focus on the fact that the rate of unemployment dropped from 8.2 percent from 8.1 percent, not the headline number showing the economy created only a net 115,000 jobs last month, below market expectations.”
Tim V., now that most conservatives have left NY state, I thought I would scan a few headlines to see how the state is doing now that it is quickly becoming a godless liberal utopia. So I randomly pick an Elmira, NY online newspapers, and here are the local news stories:
Marijuana Growing Operation
Suspicious Death in Hornell
Divers find body of girl on lake bottom
Girl On Girl Bullying In The Elmira City School District, Part II
Former Elmira Mom Pleads Not Guilty to Murder
Closing Arguments Friday in Hate Crime Case
Two Men Charged in August Meth Bust
–Sounds like the state is doing just great! Liberalism at work! FORWARD!!
According to an IFOP opinion poll published on Friday, the last day of the campaign, Mr Hollande’s lead had shrunk to 52 per cent with Sarkozy on 48 per cent, suggesting election day could yet spring a surprise.
I am required to officially back Tim V, but since Bitter has been secretly provided the minutes to every Philly A-hole meeting to Team Evangelical in exchange for preferentual afterlife placement, he has earned protected status.
As a point of honor they will both be allowed one parting blow and this battle will be settled in full.
I doubt Sarko will pull it off (he’s angered so many people over there not only due to policies, but his general personality), but if he does, it will be due to 1) an uninspiring opponent, and 2) the slimmest majority of Frenchmen will see the folly of electing a full blown Socialist to guide their nation through a rough economic patch.
Romney has two more grandchildren. 18 now. Son Tagg had twins via a surrogate. Has 6 now, 3 with a surrogate. Cannot quite understand why 3 natural kids is not enough. But not my concern. Welcome to the new little ones!
if yhou do move to the south there is a new backyard game that has become all the rage. It involves taking turns throwing small bags filled with
CORN
into wooden boards that have cut in them a
HOLE
************************************
So do not get offended if you move there and a neighbor comes up and asks you if you would like over to their back yard to play…
(that game) [rhymes with “Torn Mole”]
***********************************
Many outside the south either snicker loudly or get real offended when ask it the want to play (that game). I do wish they would call it Bean Bag Hole Toss or something other than what they call it.
I think Ras is dead wrong on this poll. 7%+ Obama in Montana would be possible given the number of Democrats in the state, but I have yet to talk to one person in the last 3+ years who will even admit to voting for him.
“i don’t think i could live every day in mississippi”
*******************************
Translated to MS speak that would be
(placing back oh hand on forehead)
“Fiddle-de-dee!!. Ah do not reckon I can bear to suffer a-livin’ in Mizzuhzippah ev’ry blessed da-hee!!!”
*******************************
You will be ok, lisab. You can take turns spending each weekend just across the border in TN, then, LA, then AL, etc.
Carol’s Coon
Take one large coon, skin and clean being sure to remove musk glands from legs. Put coon in large roasting pan and cover with water. Put 4 large yellow onions, 2 complete stalks of celery, tops included and salt and pepper to taste. Boil the coon until very tender. Pour off all liquid and set aside. Discard onions and celery.Prepare 1 quart of brown gravy and pour over coon in roasting pan. Place 8-10 large sweet potatoes (already cooked) around coon and cover. Bake at 350 degrees for 1 hour.
Prepare large pot of turnip greens and 3-4 black skillets of cornbread. Place kitchen towel at each place amt and 2 pots of hot water on table because there will be grease from ear to ear on each guest when the bottom of the pan is licked. There is no better way to cook a coon!!
there are jobs in mass, but there is more competition. his last job in massachusetts had 41 applicants. for arkansas there were 9 and in mississippi there were 5. probably because of the number of schools here in massachusetts.
my husband is something called a cisco engineer, they tend to get hired by project not as an employee.
Romneycare is a disaster. But I don’t blame Romney, some of the worst provisions were enacted by the Dems in the legislature over his veto and then continued to be expanded.
“Romney opposed the employer mandate requiring small businesses with 11 or more employees to provide health insurance. In his view, an employer mandate was an unnecessary burden on businesses in the state. Romney believed that the employer mandate would harm low-profit-margin businesses (such as new or struggling businesses) and that it could reduce wages, or distort employment patterns.”
Romney also opposed dental and optical coverage, and he wanted even the poor to pay something. He vetoed the medicaid expansion for children.
Of course later Patrick added an expensive prescription drug benefit and set the state’s share of the premiums way above the level Romney deemed affordable.
Thanks, Mr. Vito. That as close. Good thing he was tanked when he drove up. I was going to leave him face up in the driveway but it’s raining. I left him on his side. Under a tree. In a thunderstorm. He should be fine.
The Washington Post today digs into voter registration numbers that should leave the Barack Obama campaign a bit worried: among black and Hispanic voters ? especially in key states and districts ? voter registration is trending sharply down.?
Consider these numbers: Registration among Hispanics nationwide is down 5 percent. But even more troubling is in key swing states like New Mexico and Florida, where registration is down 28 and 10 percent, respectively.?
The decline in minority registration ?is obviously an area of concern,? said Democratic strategist Simon Rosenberg, president of NDN, a left-leaning think tank.
But he predicted the Obama campaign ?will have enough money and enough focus to mitigate the problem. .?.?. They have five months to get the electorate looking the way they want.?
But?this is why the Obama campaign and Democrats should be severely concerned:?According to that Pew Research Center survey, the 2008 electorate “was the most racially and ethnically diverse in U.S. history, with nearly one-in-four votes cast by non-whites.”?
Two important tables here. First:
[Hispanic black voter registration]
The voter registration for both black and Hispanic voters rose by a combined 7.6 percent in the 2008 election.?
Now this:
[attached image]
That shows how voter registration affected turnout. And in overwhelming numbers, those voters picked Obama. He won the Latino vote 67 percent to John McCain’s 30 percent, and only 5 percent of black voters picked McCain.?
But in a twist, this could also provide the Republican Party, led by its first national Director of Hispanic Outreach, Bettina Inclan, with an opportunity to pounce with its never-before-seen strategy to appeal for the Hispanic vote.?
?I think the more we talk about the issues and the more we have Republicans going into local communities and saying, ?This is what Republicans believe in. This is what Democrats believe in,? Hispanics are going to make decisions for themselves,”
Operation “Bitterpill” now moved up from pale yellow to burnt orange.
**********************************
(Would be higher level, but there is still some thunder storms around)
*****************
I just texted the “mole”…
about 44,000 total early voters.
(but not all 55 counties have provided complete updates to WV SOS yet)
About 4400 Indies.
Rest split about 2 to 1 D to R early voters.
*******************************
No surprises.
Biggest statewide races on the D side.
6 Ds running in primary for 2 SC judge positions.
4 Ds running for Commissioner of Agriculturecounty level
All of the other action involves races at the county level and that varies county by county.
***********************************
Election Day is Tuesday.
*********************************
Sen. Manchin expected to cruise against a primary opponent. I predict Manchin will get 80-85%
The day of making fun of someones ethnicity has ended. When the Polish pope, Pope John Paul II, became pope of the Catholic Church, polish jokes subsided and eventually ended out of respect for him.
The jokes we called “funny” are now taken as RACIST. Although many don’t want to give them up, it makes the person telling the ethnic joke look ignorantly insensitive, especially if you are caucasian. If you want to win elections, you are wise to use restraint in your choice of so called “good humor.”
#297- mnw
Yes,Ras has recently been “generous” to the O Man in his national approval/ disapproval polling,but appears to be right down the middle in his State polling and national head-to-head between Romney and Obama.
Ann Romney should understand that if you want to appear in touch you should take vacations in low income areas like Martha’s Vineyard and try to help the Spanish economy by going on lavish junkets there.
Just in case you’re having difficulty keeping up with all these Composite Americans, George Zimmerman, the son of a Peruvian mestiza, is the embodiment of endemic white racism and the reincarnation of Bull Connor, but Elizabeth Warren, the great-great-great-granddaughter of someone who might possibly have been listed as Cherokee on an application for a marriage license, is a heartwarming testimony to how minorities are shattering the glass ceiling in Harvard Yard. George Zimmerman, redneck; Elizabeth Warren, redskin. Under the Third Reich’s Nuremberg Laws, Ms. Warren would have been classified as Aryan and Mr. Zimmerman as non-Aryan. Now it’s the other way round. Progress! | 2023-09-15T01:27:04.277712 | https://example.com/article/2216 |
Japan Plan to Buy Islands Draws China’s Condemnation
An aerial picture from a P3C of Japan Maritime Self Defense Forces shows the Senkaku Islands, known as the Diaoyu Islands in Chinese and as Senkaku in Japanese, in the East China Sea. Source: The Yomiuri Shimbun via AP Images
(Corrects spelling of island chain’s Chinese name in third
paragraph.)
July 9 (Bloomberg) -- A Japanese government plan to buy
uninhabited islands owned by a private investor provoked
condemnation from China, which also claims it owns the rocky
outcroppings, the latest flare-up in a dispute over territory
and resources in the East China Sea.
Prime Minister Yoshihiko Noda on July 7 said the government
is considering a purchase of the islands, Kyodo News reported.
China’s Foreign Ministry responded with a statement that the
islets belong to China and “can’t be bought or sold.”
The dispute over who controls the islands, known as Senkaku
in Japanese and Diaoyu in Chinese, escalated in April after
Tokyo Governor Shintaro Ishihara said he wanted to use public
money to buy them. Sovereignty over the area, which has undersea
natural gas and oil fields, has been a flash point between the
world’s second- and third-largest economies.
“Clearly the reason why the Senkaku Islands are a big bone
of contention is the potential for resources,” said Jeff
Kingston, head of the Asian Studies program at Temple University
in Tokyo. “Governor Ishihara has caused a headache for the
government and what they’re trying to do is engage in damage
control by getting the islands out of the grips of Ishihara,
who’s trying to politicize this for his own gain.”
Taiwan also claims the isles, which are about 150 miles
(240 kilometers) northeast of its capital, Taipei; 100 miles
northwest of the southernmost island in Japan’s Okinawa
prefecture; and 400 miles southeast of Shanghai. A Taiwan
government spokesperson on July 7 said the plan to buy the
islands is unacceptable, Japanese public broadcaster NHK
reported.
Taiwan, Vietnam
Japan and China are engaged in territorial disputes with
other countries as well. China is squabbling with the
Philippines and Vietnam over islands in the South China Sea,
while Japan and South Korea each claim ownership of rocky islets
that nearly provoked a 2006 naval clash.
Vietnam’s parliament last month passed a maritime law
reasserted sovereignty over the Paracel and Spratly islands and
as many as 200 protesters marched in Hanoi yesterday, calling
for China to leave the area. The Philippines on July 5 filed a
protest against China’s establishment of a city called Sansha
covering several disputed island groups and atolls.
China and members of the Association of South Asian Nations
should continue negotiations over territorial claims in the
South China Sea, U.S. Secretary of State Hillary Clinton said
yesterday in Tokyo. Clinton didn’t comment on the dispute
between China and Japan.
A 2010 collision between a Chinese fishing vessel and
Japanese Coast Guard ships near the Senkaku Islands frayed ties
for months. The two countries have yet to implement a 2008
agreement to jointly develop the area’s undersea natural gas and
oil resources.
“There are many in the government who think that Ishihara
is playing a dangerous game politicizing the Senkaku Islands and
jeopardizing a rapprochement that has been going on,” Temple
University’s Kingston said. “Now the government is in this
embarrassing position of doing this thing they don’t want to do,
knowing that it’s stoking regional tensions.” | 2024-07-08T01:27:04.277712 | https://example.com/article/2855 |
11 year old Marshall was newly listed with Madison Adoption Associates via an orphanage partnership. , He is diagnosed as having post-operative dropsy of the brain (likely post-operative hydrocephalus).
From his file: Marshall has normal mental development. Because he suffers dropsy of the brain, we reported him to the Tomorrow Plan and according to the plan, on Aug.14 2006, he was treated in Children,,…¾‚s Hospital. On Aug.25 2006, he received a ventriculoperitoneal shunt and on Sep.7 2006, he was discharged. He recovered well, then on Feb.26 2009 he received another surgery for the ventriculoperitoneal shunt and was released on Mar.13 2009. At the age of 2 years, he can point out the names of kids, at the age of 3 years, he can imitate to draw simple shapes, can call a yi, at the age of 4-5 years, he can walk and say simple sentences, due to the reason of Obstructive dropsy of brain, he is easy to fall down. now the balance ability is better, the pronunciation is clear, and he is more extrovert, can communicate with others. He can take care of himself, he is cute and polite, will help the younger brothers and sisters in daily time.
Videos available here:
Contact Sara at: sara@madisonadoption.com for more information or to review his file!
MAA Adoption Programs
Madison Adoption Associates currently offers international adoption programs in the countries of China, the Philippines, and Bulgaria. Our programs mostly focus on placing children who have special medical needs. | 2023-10-04T01:27:04.277712 | https://example.com/article/7965 |
NSA Defender Argues That Too Much Transparency Defeats The Purpose Of Democracy
from the oh-really? dept
Transparency is good. Too much transparency defeats the very purpose of democracy.
Madison understood that transparency was not a supreme value that trumped all other concerns. He also participated in the U.S. Constitutional Convention of 1787, the secrecy of whose proceedings was the key to its success. While governments may hide behind closed doors, U.S. democracy was also born behind them.
In the new domain of dataveillance, the form of oversight should vary depending upon the extent to which transparency and opacity are necessary to the new powers authorized. Allowing some form of surveillance is vital to assure the protection of American interests. Conversely, allowing full public disclosure of our sources and methods is dangerous – identifying publicly how we conduct surveillance risks use of that information by terrorists and, in turn, draws a roadmap of which threats are not known. Thus, complete transparency will defeat the very purpose of disclosure and may even make us less secure.
Thank you for reading this Techdirt post. With so many things competing for everyone’s attention these days, we really appreciate you giving us your time. We work hard every day to put quality content out there for our community. Techdirt is one of the few remaining truly independent media outlets. We do not have a giant corporation behind us, and we rely heavily on our community to support us, in an age when advertisers are increasingly uninterested in sponsoring small, independent sites — especially a site like ours that is unwilling to pull punches in its reporting and analysis. While other websites have resorted to paywalls, registration requirements, and increasingly annoying/intrusive advertising, we have always kept Techdirt open and available to anyone. But in order to continue doing so, we need your support. We offer a variety of ways for our readers to support us, from direct donations to special subscriptions and cool merchandise — and every little bit helps. Thank you.
–The Techdirt Team
Paul Rosenzweig, the former Deputy Assistant Secretary for Policy at Homeland Security, was supposed to testify for the House Intelligence Committee about NSA surveillance. The hearing was postponed and Rosenzweig can't make the new date, but he's posted the testimony he intended to give , in which he makes this incredible claim:The details of this claim are, obviously, a lot more nuanced, but it seems like it's built on a false premise: that people are seekingthat the government does. While that may be true in some cases, it's a very extreme minority. Most people are merely arguing that there are specific things that the government does in our name, which (often by law or Constitution) require significantly more transparency. But, Rosenzweig sets up this strawman to suggest that those arguing for greater transparency don't recognize that there can be any secrecy.Right, but at the end of that process, it was made very, very public. Not so with NSA surveillance. So this is a total red herring. Imagine if the US Constitution were not just written in secret, but then kept that way? Furthermore, in retrospect, it's difficult to see why it even made sense for the Constitutional Convention to have been secret in the first place. There's really no reason why the negotiations and debates couldn't have been done publicly.This is the only place where Rosenzweig seems to come close to actually defending his initial statement that "too much transparency defeats the very purpose of democracy," and it's a very, very weak sell. If his initial premise is true, then he appears to be arguing that "the purpose of democracy" is to "protect us from terrorists." That's not true. It's a fundamental error in his analysis. In fact, it can beargued that the opposite is true: we've long agreed that trading lives for freedom is part of the American Way. Patrick Henry argued "give me liberty or give me death." He didn't argue that we needed to give up liberties to protect him from death.Furthermore, it's patently and obviously false that public disclosure of how surveillance is conducted makes those surveillance methods useless. For decades it has been public knowledge that law enforcement can wiretap phone lines. And yet it remains a useful surveillance tool. Yes, some terrorists will figure out ways around it, but (as many people noted), most terrorists were already well aware that any electronic communication could and would be tracked, and they were careful to use other means when possible. Furthermore, the goal of a free society should not be to stop terrorists from any possible way of communicating in secret, but to recognize that this is going to happen no matter what, and to focus on alternative means of policing, intelligence and law enforcement to do our best to protect against it.In the end, I have to think that Patrick Henry's rallying cry of "give me liberty or give me death" is a hell of a lot more American that Rosenzweig's surveillance state apologism of "too much transparency undermines democracy." We should be living in a country that stands behind the first statement and rejects, wholeheartedly, the cowardice and shamefulness of the latter.
Filed Under: democracy, nsa, nsa surveillance, paul rosenzweig, transparency | 2024-03-12T01:27:04.277712 | https://example.com/article/3024 |
/*
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* code can be redistributed and/or modified under the terms of the
* GNU AFFERO GENERAL PUBLIC LICENSE Version 3
* (http://www.fsf.org/licensing/licenses/agpl-3.0.html) as found
* in the associated LICENSE.txt file.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
*/
package org.neo4j.causalclustering.core.replication;
import java.util.ArrayList;
import java.util.List;
import java.util.concurrent.Future;
import java.util.stream.Stream;
import org.neo4j.causalclustering.core.state.machines.dummy.DummyRequest;
import org.neo4j.internal.kernel.api.security.SecurityContext;
import org.neo4j.logging.Log;
import org.neo4j.procedure.Admin;
import org.neo4j.procedure.Context;
import org.neo4j.procedure.Description;
import org.neo4j.procedure.Name;
import org.neo4j.procedure.Procedure;
import static java.lang.Math.toIntExact;
import static org.neo4j.procedure.Mode.DBMS;
@SuppressWarnings( "unused" )
public class ReplicationBenchmarkProcedure
{
@Context
public Replicator replicator;
@Context
public SecurityContext securityContext;
@Context
public Log log;
private static long startTime;
private static List<Worker> workers;
@Admin
@Description( "Start the benchmark." )
@Procedure( name = "dbms.cluster.benchmark.start", mode = DBMS )
public synchronized void start( @Name( "nThreads" ) Long nThreads, @Name( "blockSize" ) Long blockSize )
{
if ( workers != null )
{
throw new IllegalStateException( "Already running." );
}
log.info( "Starting replication benchmark procedure" );
startTime = System.currentTimeMillis();
workers = new ArrayList<>( toIntExact( nThreads ) );
for ( int i = 0; i < nThreads; i++ )
{
Worker worker = new Worker( toIntExact( blockSize ) );
workers.add( worker );
worker.start();
}
}
@Admin
@Description( "Stop a running benchmark." )
@Procedure( name = "dbms.cluster.benchmark.stop", mode = DBMS )
public synchronized Stream<BenchmarkResult> stop() throws InterruptedException
{
if ( workers == null )
{
throw new IllegalStateException( "Not running." );
}
log.info( "Stopping replication benchmark procedure" );
for ( Worker worker : workers )
{
worker.stop();
}
for ( Worker worker : workers )
{
worker.join();
}
long runTime = System.currentTimeMillis() - startTime;
long totalRequests = 0;
long totalBytes = 0;
for ( Worker worker : workers )
{
totalRequests += worker.totalRequests;
totalBytes += worker.totalBytes;
}
workers = null;
return Stream.of( new BenchmarkResult( totalRequests, totalBytes, runTime ) );
}
private class Worker implements Runnable
{
private final int blockSize;
long totalRequests;
long totalBytes;
private Thread t;
private volatile boolean stopped;
Worker( int blockSize )
{
this.blockSize = blockSize;
}
void start()
{
t = new Thread( this );
t.start();
}
@Override
public void run()
{
try
{
while ( !stopped )
{
Future<Object> future = replicator.replicate( new DummyRequest( new byte[blockSize] ), true );
DummyRequest request = (DummyRequest) future.get();
totalRequests++;
totalBytes += request.byteCount();
}
}
catch ( Throwable e )
{
log.error( "Worker exception", e );
}
}
void stop()
{
stopped = true;
}
void join() throws InterruptedException
{
t.join();
}
}
}
| 2023-12-16T01:27:04.277712 | https://example.com/article/9179 |
Learn Python 3 the Hard Way - jscholes
https://learnpythonthehardway.org/python3/
======
crncosta
This guy has a very stranger way to promote his job.
He firstly said that Py3 sucks and he can't teach it... and now he is teaching
it ;-)
[0]
[https://learnpythonthehardway.org/book/nopython3.html](https://learnpythonthehardway.org/book/nopython3.html)
~~~
iodbh
Which turned into a big internet fight, and he changed his mind.
It's good to see people willing to change the way they do things, especially
when that means publicly contradicting their former selves and with such an
intense personality. It's oddly inspiring.
~~~
baldfat
I think Zed was in the majority when it came to Py3. He kind of comes off as a
jerk due to his personality, but I really like his approach and he always
makes me think. I might not agree with him but he certainly is not boring.
Looking at Pandas which is a R like library. Wes wrote his book in Py2 and did
not have any desire for Py3.
I moved from Python mostly to using R, Racket and Haxe for my other side
projects. This infighting just left a bad taste in my mouth and started seeing
greener pastures, which for once in my life were in fact greener. I still love
Python but I don't use it much due to community drama.
~~~
BuckRogers
Don't blame the community for that. Blame Guido and the core development team.
The community at-large weren't rallying for breaking changes to the language.
GvR wanted that, it's "his" language afterall. Of course some of the community
are more conservative and were willing to more quickly fall in line to
goosestep with the core team on Python3. So the tension stems from the Python3
folks having extreme disdain for all the Python2 users and codebases.
I agree with you though, it's what got me looking towards other tech like
Node, Go, Elixir. I can look past it all except for the fact they got 'unicode
by default' wrong. They should simply do what Go does, everything is a
bytestring with assumed encoding as UTF8. What they have today is ridiculous
and needs changed before I could embrace Python3+.
~~~
soperj
There were definitely people wanting unicode support, which was the breaking
feature.
They supported python 2 for years and year after the release of this, don't
know how you can even mention the word goosestep in this context.
~~~
BuckRogers
I can't understand what's going on with the Python community for folks to even
make statements like yours. It has to be an influx of new Python developers
who started on 3.
Python2 has unicode support. Python2 already had (better) async IO with Gevent
(Tornado is also there). There's just nothing there with Python3 except what I
can only describe as propaganda from the Python Software Foundation that has
led to outright ignorance with many users.
_Some_ people wanted "unicode strings by default". Which Python3 does have,
but they even got that wrong. The general consensus on how to handle this
correctly is to make everything a bytestring and assume the encoding as being
UTF8 by default. Then like Python2, it just works.
~~~
int_19h
> The general consensus on how to handle this correctly is to make everything
> a bytestring and assume the encoding as being UTF8 by default.
Whose "general consensus"? It's certainly not the approach adopted by the vast
majority of mainstream general-purpose programming languages out there.
~~~
BuckRogers
You mean most of the mainstream, genpurpose languages in usage today which
were initially designed 20-50 years ago. And those which don't actively look
for opportunities to shoot themselves in the face with sidestepping changes to
break the language? Then no, not that consensus.
But if you were to find any sensible designer of new language with
skyrocketing, runaway popularity- such as Rob Pike, they'll tell you
differently. Or even Guido van Rossum, if he were to be honest with you. While
Pike's colleagues at Bell Labs like Dennis Ritchie may not have designed C
this way for obvious reasons, they did design Go that way.
~~~
int_19h
So now it's the consensus of "sensible designers of new languages". Where
"sensible" is very subjective, and I have a feeling that your definition of it
would basically presuppose agreeing with your conceptual view of strings,
begging the question.
Aside from Go, can you give any other examples? Swift is obviously in the "new
language" category (more so than Go, anyway), and yet it didn't go down that
path.
~~~
BuckRogers
Well, do your research and come to your own conclusions. Most people are going
to agree that UTF8 is the way to go. You can advocate something else, since
you seem to take affront to my opposition to Python3's Microsoft-oriented
implementation.
If you know anything about Swift, it was designed with a primary goal to being
a smooth transition from and interop with ObjC so like other legacy
implementations (such as CPython3), it had sacrifices that limited how
forward-looking it could be.
~~~
int_19h
I'm not at all opposed to UTF-8 as internal encoding for strings. But that's
completely different and orthogonal to what you're talking about, which is
whether strings and byte arrays should be one and the same thing semantically,
and represented by the same type, or by compatible types that are used
interchangeably.
I want my strings to be strings - that is, an object for which it is
_guaranteed_ that enumerating codepoints always succeeds (and, consequently,
any operation that requires valid codepoints, like e.g. case-insensitive
comparison, also succeeds). This is not the case for "just assume a bytearray
is UTF-8 if used in string context", which is why I consider this model broken
on the abstraction level. It's kinda similar to languages that don't
distinguish between strings and numbers, and interpret any numeric-looking
string as number in the appropriate context.
FWIW, the string implementation in Python 3 supports UTF-8 representation. And
it could probably be changed to use that as the primary canonical
representation, only generating other ones if and when they're requested.
~~~
BuckRogers
A default UTF8 string-type has to be allowed to be used interchangeably with
bytestrings since ASCII is a valid subset. Your string type shouldn't be
spellchecking nor checking for complete sentences either. What comes in, comes
in. Validate it elsewhere.
Thus Go's strings don't potentially fail your desire for a guarantee anymore
than anything else would assuming UTF8. They're unicode-by-default, which was
the whole point to Python3 but Go has it too in a more elegant way. That's the
beauty to UTF8 by default, you can pass it valid UTF8 or ASCII since it's a
subset, the context of which it's being received is up to you. If you're
expecting bytes it works, if you're expecting unicode codepoints that works.
There's no reason to get your hands dirty with encodings unless you need to
decode UTF16 etc first. If there is still a concern about data validation,
that's up to you not your string type to throw an exception.
~~~
int_19h
> A default UTF8 string-type has to be allowed to be used interchangeably with
> bytestrings since ASCII is a valid subset.
This only works in one direction. Sure, any valid UTF-8 is a bytestring. But
not every bytestring is valid UTF-8. "Use interchangeably" implies the ability
to substitute in both directions, which violates LSP.
> What comes in, comes in. Validate it elsewhere.
I have a problem with that. It's explicitly against the fail-fast design
philosophy, whereby invalid input should be detected and acted upon as early
as possible. First, because failing early helps identify the true origin of
the error. And second because there's a category of subtle bugs where invalid
input can be combined or processed in ways that make it valid-but-nonsensical,
and as a result there are no reported errors at all, just quiet incorrect
behavior.
Any language that has Unicode strings can handle ASCII just fine, since ASCII
is a strict subset of UTF-8 - that doesn't require the encoding of the strings
to be UTF-8. For languages that use a different encoding, it would mean that
ASCII gets re-encoded into whatever the language uses, but this is largely an
implementation detail.
Of course, if you're reading a source that is not necessarily in any Unicode
encoding (UTF-8 or otherwise), and that may be non-string data, and you just
need to pass the data through - well then, that's exactly what bytestrings are
there for. The fact that you cannot easily mix them with strings (again, even
if they're UTF-8-encoded) is a benefit in this case, because such mixing only
makes sense if the bytestring is itself properly encoded. If it's not, you
just silently get garbage. Using two different types at the input/output
boundary makes it clear what assumptions can be made about every particular
bit of input.
~~~
BuckRogers
I understand your position. This is a longstanding debate within the PL
community, as you know. I've considered that stance before but I have to say
thanks for stating it so well because it's given me pause. I can't say I agree
but you're not "wrong". I agree with the fail-fast concept but disagree that's
the place to do it. A strict fail-fast diehard probably shouldn't even be
using Python, IMO. I don't have anything else useful to add because this is
simply a engineering design philosophy difference. We both think our own
conclusions are better of course but I appreciate you detailing yours. Good
chat, upvoted.
~~~
int_19h
I agree that this is a difference caused by different basic premises, and
irreconcilable without surrendering one of those premises.
And yes, you're right that Python is probably not a good example of
ideologically pure fast-fail in general, simply because of its dynamic typing
- so that part of argument is not really strong in that particular context.
(Side note: don't you find it amusing that between the two languages that
we're discussing here, the one that is statically typed - Go - chose to be
more relaxed about its strings in the type system, while the one that is
dynamically typed - Python - chose to be more strict?)
The key takeaway, I think, is that there is no general consensus on this. As
you say, "this is a longstanding debate within the PL community" (and not just
the topics we touched upon, but the more broad design of strings - there's
also the Ruby take on it, for example, where string is bytes + encoding).
My broader take, encoding aside, is that strings are actually _not
sufficiently_ high-level in most modern languages (including Python). I really
want to get away from the notion of string as a container of anything, even
Unicode code points, and instead treat it as an opaque representation of text
that has various _views_ exposing things like code points, glyphs, bytes in
various encodings etc. But none of those things should be promoted as the
primary view of what a string _is_ \- and, consequently, you shouldn't be able
to write things like `s[i]` or `for ch in s`.
The reason is that I find that the ability to index either bytes or
codepoints, while useful, has this unfortunate trait that it often gives right
results on limited inputs (e.g. ASCII only, or UCS2 only, or no combining
characters) while being wrong in general. When it's accessible via shorthand
"default" syntax that doesn't make it explicit, people use it because that's
what they notice first, and without thinking about what their mode of access
implies. Then they throw inputs that are common for them (e.g. ASCII for
Americans, Latin-1 for Western Europeans), observe that it works correctly,
and conclude that it's correct (even though it's not).
If they are, instead, forced to explicitly spell out access mode - like
`s.get_code_point(i)` and `for ch in s.code_points()` - they have to at least
stop and think what a "code point" even is, how it's different from various
other explicit options that they have there (like `s.get_glyph(i)`), and which
one is more suitable to the task at hand.
And if we assume that all strings are sequences of bytes in UTF-8, the same
point would also apply to those bytes - i.e. I'd still expect `s[i]` to _not_
work, and having to write something like `s.get_byte(i)` or `for b in
s.bytes()` - for all the same reasons.
~~~
BuckRogers
It's worth nothing that I think Python's success and simplicity came from the
ease of use and flexibility. It should have Go's strings. You have a point
there. The type annotations are really jumping the shark too, it's just no
longer the language that once made so much sense.
On the consensus on bytestrings assumed as UTF8, there's only 1 new language
without legacy baggage that has skyrocketing popularity and it has bytestrings
assumed as UTF8. Everyone I've surveyed says that's no coincidence, including
members of the Python core dev team. So that's where I'm seeing consensus on
the string issue. While Python3 has struggled and folks are rightly irritated.
Because some were irresponsible everyone has to pay, that's not really how I
viewed Python's strengths prior to 3.x. Zed said it best but it really was one
of the best examples of how dynamic typing can be fun.
------
Sir_Cmpwn
>I've standardized on this version of Python because it has a new improved
string formatting system that is easier to use than the previous 4 (or 3, I
forget, there were many)
Wait, is this seriously the only advantage you see to Python 3, Zed?
~~~
Vaskivo
Maybe in the context of the book it is a major reason.
Strings are ubiquitous to programming. I'd argue that it's even more for first
time programmers. Zed wanted something that would be easy to use.
(ASCII) Strings formatting is more important to beginners than unicode
support, new style classes by default, iterators in range()/enumerate()/etc. ,
the new division operator, etc.
I haven't recommended his book to beginners because it was stuck in Python 2.
But I have to agree that Python 2 had some stuff that was more "newbie-
friendly" than Python 3
~~~
Sean1708
> But I have to agree that Python 2 had some stuff that was more "newbie-friendly" than Python 3
What stuff, out of interest?
Also I suspect that a _huge_ proportion of newcomer's got very confused as to
why 3/2 == 1.
~~~
Vaskivo
Yes. But that is easy to explain. "It always rounds down"
Of the top of my head come the range/enumerate/zip returns. They are really
useful and needed to teach "pythonic Python". But it's hard to explain that it
doesn't return a list. "It returns an iterator, that is lazy, and you need to
call 'list()' on it to use it as a list..." You get my point.
You fall to a "just do like I told you. You'll get it later." that plagues a
lot of other languages when being taught to newbies.
But I never said that Python 3 is less "newbie-friendly" than Python 2...
~~~
cgriswald
> Yes. But that is easy to explain. "It always rounds down"
The explanation is easy, but it isn't _simple_.
With respect, "It always rounds down" is a terrible explanation. It explains
the apparent behavior of the / operated in Python 2, but it does not really
explain _why_. A better explanation is that the Python is both dynamically-
and strongly-typed and that / does integer division on integers and "true"
division on floats. For the newbie who understands these concepts, this is a
far more useful explanation and metaphor; and for the newbie who doesn't, he
has to learn somewhere, and frankly the / operator is not a bad example.
~~~
webmaven
_> / does integer division on integers and "true" division on floats._
Floats don't really get true division either:
[https://docs.python.org/3/tutorial/floatingpoint.html](https://docs.python.org/3/tutorial/floatingpoint.html)
And as it happens, I once explained a related problem with round() to Zed Shaw
on Twitter:
[https://twitter.com/zedshaw/status/777780480737357824](https://twitter.com/zedshaw/status/777780480737357824)
~~~
amyjess
This is one reason why I go out of my way to avoid floats and instead use
Decimal whenever I need to support non-integral numbers.
(and from playing around with Perl 6, I love how decimal literals are of type
Rat instead of Num; I wish Python decided to do something similar in Python 3)
Edit in response to Zed's question, in 3.6 I always just do:
print(f'{foo:.2f}')
Works with Decimals and floats.
~~~
webmaven
Yeah, I'm pretty sure he'll turn up his nose at that solution as well.
For purposes of teaching the language to a beginner, he wants literals being
rounded or divided to "just work" in a way that is unsurprising to those
beginners, and there isn't any way to achieve that unless the default type of
a number with a decimal point is Decimal rather than float (which isn't at all
likely to happen).
The closest we are likely to get to that ideal is by introducing a Decimal
literal like 0d2.125, riffing off the Hex and Octal literals (eg. 0xDEADB33F,
0o76510).
P.S., unless I am mistaken, you're just truncating the float, not actually
rounding it
------
tbranyen
If this is anything like his Learn C book, I'll pass. Was a waste of money as
he came off incredibly arrogant and fumbled through it.
~~~
dagw
At least the original LPtHW was quite a fundamentally different book from his
learning C book. The C book was aimed at people who knew at least the basics
of programming in some other language and wanted to learn C, while the Python
book was more aimed people who had never programmed at all.
------
diimdeep
Not hard enough. Try
[https://lectures.quantecon.org/py/](https://lectures.quantecon.org/py/)
~~~
happy-go-lucky
Is that for quants? Seems to be good. Thanks for the link.
~~~
ChristianGeek
No kidding. Thorough, too...the PDF for the Python lectures is 862 pages!
~~~
happy-go-lucky
That's great. In fact I submitted it here at
[https://news.ycombinator.com/item?id=13724295](https://news.ycombinator.com/item?id=13724295)
------
alexeiz
Zed lost his credence. It's hard to take him seriously after what he's said in
the past. Besides, the book is rather light on content.
~~~
renesd
It's actually harmful to point newbies towards his work. There are much better
resources that have been proven in practice to work better.
~~~
dfabulich
Such as?
~~~
dtornabene
well, you can go with the _actual python tutorial_ for one. Or the literally
dozens of intro to python books put out by No Starch, O'Reilly, Packt, Wiley,
etc. You can also go with some of the classics like Swaroops' Byte of Python,
or any of the college lecture notes. I hesitate to suggest this, but its worth
saying, the book that Zed shit on to launch his little franchise is still
actually usable (especially just to read the code examples) and was a much
much much better book in terms of pedagogy then his tedious, arrogant
offerings.
~~~
throwaway7645
Yea...flipped through Zed's book. It seemed alright, but Python Programming
for the Absolute Beginner is an amazing piece of work. Crystal clear, and you
get to build fun little text games.
------
dv35z
Related: I love this book's teaching style, and found it very much resonated
with me - starting from zero, step by step, iteratively learning and building
on previous lessons.
Can anyone suggest something similar for learning Scala?
~~~
solaris999
The canonical source for learning Scala from scratch (at least, when I was
learning a couple of years ago) is the Coursera course by Martin Odersky, one
of the language's founders. It appears that the course has grown somewhat, but
you can still find part 1 here:
[https://www.coursera.org/learn/progfun1](https://www.coursera.org/learn/progfun1)
~~~
dv35z
I took the course - unfortunately, and to be honest, it didn't have the
approachability and "fun" of Zed's books. To me - it felt very dry, academic,
and quickly became a chore to complete rather than a joy. I need the version
aimed for "C- python programmer" / newbie rather than "eager CS student" or
"experienced Java dev".
------
oliwarner
You'll either love or hate his style but one thing you should note is that
popular current production distributions are pegged on older versions (eg
Ubuntu 16.04 has Python 3.5, Debian Jessie has 3.4.
If you're a purist and don't want to maintain your own build of Python (or
trust an external PPA), I'd aim at 3.5.
That said, this is about learning... But you'll need to learn not to use
f-strings if you want to use it on a current-generation LTS distribution.
~~~
mixmastamyk
3.6 is in the repos for yakkety as a beta, and upcoming release on zesty.
Unfortunately it will likely not be the default Py 3.x until the "aardvark"
release.
~~~
oliwarner
I'd advise against using 9m support distributions in production though. It's a
super pain in the arse to have to do major upgrades that often.
~~~
mixmastamyk
9m?
~~~
oliwarner
Sorry. Nine months. That's all the non-LTS versions get.
------
happy-go-lucky
_Python 3.x is the present and future of the language_
~~~
throwaway7645
A language I use daily and love, but one that will end up a dead-end I fear
long-term. So much is going the way of speed now.
~~~
crdoconnor
I doubt that. Most of the cited competitors to python are either seriously
flawed (e.g. go) or aren't really competing on the same turf (e.g.
rust/haskell).
~~~
verandaguy
Speaking as someone who really loves Haskell -- let's be real, it's not
serious competition against Python or Rust, same turf or not. It's a fantastic
language for numerical computing and its applications, and for
compilers/parsers, but it's never going to be as easy to use for the layman as
an imperative language.
As someone who's used Go and who has some mixed feelings about it, I'm curious
-- what do you find flawed in it?
~~~
crdoconnor
>what do you find flawed in it?
* Package management
* The weird and approach to exception handling (which leads to overly verbose code)
* Lack of generics (which leads to overly verbose and somewhat hacky code)
* Vastly smaller 3rd party ecosystem
I think it works well for a very small subset of sysops-style problems (small
servers, small command line tools, etc.) especially since it easily compiles
into one small, portable binary, but outside of that it flounders.
~~~
verandaguy
Thanks for following up! Those are some of my gripes with the language too.
The vendoring system/would-be package manager especially has caused me hours
of headaches, and I'm glad to hear I'm not the only one who considers it
broken.
------
siddharthgdas
If you are a complete beginner in python, I would rather suggest this for
python3 - www.openbookproject.net/thinkcs/python/english3e
------
nof
I would basically avoid this simply by reading his idea of what makes good
educational content: tests, repetition, memorization and boring predetermined
projects. If you know anything about educational theory, you will quickly
discover that constructivist education, or constructionism as Seymour Papert
coined, is a way more effective and motivational way to learn computer science
and coding. There are basic understandings of computering which is beyond
specific language, eg loops or logic. You are not doing yourself any favors by
memorizing the entire syntax of a language. This happens while you do personal
and engaging coding projects.
------
jorge-fundido
I tell people to `ipython; %magic`. For all of python's faults, that REPL is
the gold standard and makes for a nice way to learn the language.
------
BuckRogers
Python3 folks act so daft about his Turing-complete comments. ZS knows what
Turing complete is and means. He was clearly trolling, saying in essence, "if
the CPython team can't create interop between CPython2 and 3 code then they
really botched the job.. Python3 bytecode is Turing incomplete. What a fail."
And then people attempt to troll him saying he doesn't know what Turing
complete is. Perhaps they really don't understand what they're even responding
to, that's what it appears. Or it's just a willful attack because they "like
Python3". Unfortunately with Python3 this is what the Python community has
been slowly devolving into, what comes off as a bunch of trolls/kids or
ridiculous adults.
~~~
thehardsphere
1\. I'd really like to see proof that the people he was trolling actually
existed, and if they did exist, a coherent explanation of why beginners to
Python needed to be exposed to the arguments of said people through trolling.
2\. Zed can troll people, and that's totally OK, but the "like Python 3"
people can't troll him or counter-troll him, because it's turning the Python
community into trollville. I'm guessing like sort of how Rails is a ghetto.
~~~
vonklaus
> I'd really like to see proof that the people he was trolling actually
> existed
See the user of this parent comment.
~~~
thehardsphere
I have never asserted that Python 3 can never run Python 2. The claim is that
Zed trolled some imaginary people who said this.
------
pnt12
[https://learnpythonthehardway.org/book/nopython3.html](https://learnpythonthehardway.org/book/nopython3.html)
>This document serves as a collection of reasons why beginners should avoid
Python 3 as of November 22nd, 2016.
This is the first thing I get when searching "Learn python3 hard way" in
Google. Maybe it's time to update this page :)
I didn't enjoy the python2 book too much, but I'll give this one a try.
------
PuffinBlue
Knew it was coming, but still kinda annoying _right_ in the middle:
[https://josharcher.uk/categories/lpthw/](https://josharcher.uk/categories/lpthw/)
------
mistaken
The hard way is still the easy way though. Python is simple to learn :)
------
edgartaor
In your opinion which one is better? Learn Python the hard way or Dive into
Python 3
[http://www.diveintopython3.net](http://www.diveintopython3.net)
~~~
Orangeair
A lot of people dislike Zed Shaw's books (the author of Learn ___ the Hard
Way) for various reasons, and he has posted some things online that serious
call into question his credibility (namely, claiming that Python 3 is not
Turing complete).
Dive into Python 3 is a good book. I used it to supplement my CS classes in
early college. There are some other good book suggestions on the sidebar of
[https://www.reddit.com/r/Python/](https://www.reddit.com/r/Python/) . In
particular, I've heard good things about "Automate the Boring Stuff with
Python".
~~~
dtornabene
Its a great book, that still has relevance, amazingly. Theres also the fact
that he feels like its necessary to shit on anyone who disagrees with
him...or, anyone at all actually. The trolling thing is lame, and a total
waste of peoples time, like, for example, when he literally ate something in
the middle of his lecture at Pycon, as if he somehow couldn't find the time to
eat a candy bar in the elevator. I literally worked Pycon, and I can guarantee
you that speakers, and pretty much anyone else, can find the two minutes to
choke down an orange or whatever before the go up to speak. Its his persona,
which he uses to get notoriety, which he uses to get work.
------
crispytx
Learn Python The Hard Way was the first programming book I ever read. Beats
the hell out of codeacademy and all that other shit.
------
systems
is this complete or a work in progress, because if you try to buy, you can
still only buy the 3rd edition (with a free upgrade to 4th edition)
so to be clear, is the online version complete, and only the pdf and videos
are missing, or even the online version is still work in progress
------
oli5679
Does anyone have any advice from where to go after beginner/intermediate
python? I can hack together a program with the functionality I want, but
frequently it's pretty verbose and the architecture gets creaky as the
complexity increases...
~~~
yhoiseth
I'd suggest
[http://www.obeythetestinggoat.com/](http://www.obeythetestinggoat.com/) if
you're looking to use Python for web development.
------
drops
For a beginner who wants to learn Python, which one is better — 2 or 3?
~~~
satysin
3\. When you need to work with a 2 code base the learning curve won't be big
at all. Whereas if you start with 2 and then move to 3 you will have to
unlearn a bunch of stuff which is just a waste of time. Start with 3 and then
learn just the differences in 2 when/if you need them.
~~~
cgriswald
Agreed. Just as a for-instance: In Python 2, the parenthesis on a print call
are optional. In Python 3, they're not. Going from 3 to 2 you probably won't
even notice. Going from 2 to 3... To this day I often fail to type those
parenthesis.
------
pbreit
Would a tutorial like this really be worse if it used realistic situations?
------
IshKebab
I'm not sure I would recommend learning Python to anyone these days. Go is
just so much nicer and almost as easy, and also avoids the inevitable GIL &
speed problems.
~~~
bkbridge
If you are doing AI, machine learning, it's all Python. Other language support
yes, but python is it. Alexa does not support Go.
> [https://www.tensorflow.org/](https://www.tensorflow.org/)
~~~
StreamBright
You mean the API that you are calling is in Python. I think the heavy lifting
is mostly C/C++.
| 2023-12-12T01:27:04.277712 | https://example.com/article/6265 |
As the Indian Railways step up its safety measures following a low-intensity bomb blast in Kanpur-Bhiwani Kalindi Express last Wednesday, senior officials said the Railway Protection Force (RPF) has been directed to intensify their presence at every station of the country. The security officials have also been asked to ensure that Kashmiris, who travel in long-distance trains, are safe. Apparently, the blast took place just after top security officials met the Railway Board in New Delhi.
"The staff have been asked to move around in groups, randomly inspect stations and its peripheries. Combing operations shall be carried out where people will be frisked, luggage scanned and CCTV monitoring shall increase," said a senior RPF officer.
The RPF has formed groups where the sleuths will carry out checks in plain clothes. The RPF commandos will also inspect the stations, especially the important ones where people movement is in large numbers.
"They will also be posted to keep vigil with metal detectors, move around with sniffer dogs and constantly monitor CCTV. Moreover, they will keep watch on history sheeters and pick-pockets at railway stations. This is being done to keep an eye on any unwarranted activity," he said.
"There will be tight security on trains going to the north, especially Delhi and Kashmir," said an RPF officer.
On February 20, a low-intensity blast took place in the toilet of Kanpur-Bhiwani Kalindi Express. The blast took place near Barrajpur station at around 7.10 pm. Another low intensity blast took place in Kashimira in Thane after an unidentified person allegedly threw a plastic ball filled with explosives. | 2023-11-18T01:27:04.277712 | https://example.com/article/3418 |
There is no known underlying genetic defect predisposing patients to develop primary intraocular lymphoma (PIOL). Discovery of genetic factors predisposing to the development of PIOL would be of benefit for early diagnosis, prognostic staging, and development of novel treatments for PIOL. Until recently, genetic approaches to investigate the etiology of cancer have relied upon methods utilizing linkage based on traditional Mendelian inheritance patterns. It is probable that many diseases are a consequence of multiple genetic factors, and are therefore less amenable to study using traditional methods of linkage analysis and positional cloning to isolate single genes. Single nucleotide polymorphisms (SNPs) are the most common sources of variation in the human genome. SNPs are single-base differences in the DNA sequence that can be observed among individuals in a population. A SNP is defined on the basis of a frequency of at least 1% prevalence in one or more populations. SNPs are present throughout the genome at an average frequency of 1/1000 base pairs. We propose to analyze the frequency of SNPs specifically within the coding frames of biologically plausible genes responsible for function of the innate immune system. The interleukins are a specific pathway of interest because previous research has demonstrated derangements in the ratios of interleukins 10 and 6 in the vitreous humor and spinal fluid of patients with PIOL, leading to the hypothesis that altered function or expression of these or other interleukins could permit the development of this rare malignancy. No results have yet been obtained. | 2023-09-17T01:27:04.277712 | https://example.com/article/9329 |
Benchtop lab mixer
Handling up to 15 liters, the Admix BenchMix Model OPLB-400 high-shear benchtop lab mixer provides versatility with multiple high-shear heads, low-speed impellers and props. It is available with 3hp at 12,000rpm, a low-batch level adapter and adjustable beaker clamp. Once satisfactory results are obtained with the mixer, users can accurately scale up to production volumes.
Ecolab technical experts will explore holistic views of dry cleaning and sanitation programs, how to identify and eliminate water sources, existing cleaning and sanitizing solutions, and new waterless technology. | 2023-11-14T01:27:04.277712 | https://example.com/article/8560 |
HomeAway is the world leader in vacation rentals. We offer the largest selection of properties for any travel occasion and every budget. We're committed to helping families and friends find a perfect vacation rental to create unforgettable travel experiences together.
Calypso Beach Towers...West End of PCB...Across the street from Pier Park!!! 1-1807 Calypso is located on the 18th floor in the East Tower in Tower I. This 1 bedroom/bunk/2 bath Condo is very conveniently located across the street from Pier Park. Amazing View of the Beautiful Gulf of Mexico and the Pier. Sleeps 6.
You will absolutely marvel over all of the amenities that Calypso has to offer, from a day of fishing at the pier, which is located right next door to the complex, to the great sunrays, you will enjoy soaking up by the pools. Guests will also be able to enjoy the great work out facility and the lush landscaping that the tiki bar by the pool has to offer.
Calypso is close to everything that matters on a vacation. Walk to restaurants and shopping just across the street at Pier Park and next door to the Pier.
A Picture is Worth a Thousand Words, But a Virtual Walkthrough Speaks for Itself!
Click Here for a 3D Virtual Tour of This Home!
AMENITIES
----------------------
Free Wifi In the Condo
Gulf View Balcony
Washer / Dryer
Full Kitchen
SLEEPING ARRANGEMENTS
--------------------------------------------
Bedroom 1:
- King size bed
- 20 inch Flat Screen TV/DVD VHS combo
Bathroom 1:
-Shower/Tub combination
-Bunks located in the hallway, twin size
Bathroom 2:
- Walk in Shower
Living Room:
-Sleeper Sofa
-Entrance to the balcony with seating including two chairs, side table and lounger.
-32 inch flat screen TV, DVD player, VHS and CD player
Kitchen:
-Dining area has a table for 4 plus 2 bar stools. Place settings available for 8
-Three chairs on the balcony and two glass tables
FREE FUN DETAILS:
We have selected an array of activities that will cater to many interests and age groups. Below you will
find the FREE FUN activities included with your rental. Please note below some of the activities are seasonal. Activities are non-cumulative. Unused admissions will expire daily. FREE FUN is NOT included in winter monthly rentals.
Free Fun Activities:
Ripley's Believe It or Not (one free adult admission)
Gulf Marine World (one free adult admission)
Bay Point Golf (one free round at Meadows Course per unit. Noncumulative. Nontransferable)
Shell Island (one admission)
Explore 360 - Escape Adventure (one free adult admission)
WonderWorks (one free adult admission)
)
Calypso Beach Towers...West End of PCB...Across the street from Pier Park!!! 1-1807 Calypso is located on the 18th floor in the East Tower in Tower I. This 1 bedroom/bunk/2 bath Condo is very conveniently located across the street from Pier Park. Amazing View of the Beautiful Gulf of Mexico and the Pier. Sleeps 6.
You will absolutely marvel over all of the amenities that Calypso has to offer, from a day of fishing at the pier, which is located right next door to the complex, to the great sunrays, you will enjoy soaking up by the pools. Guests will also be able to enjoy the great work out facility and the lush landscaping that the tiki bar by the pool has to offer.
Calypso is close to everything that matters on a vacation. Walk to restaurants and shopping just across the street at Pier Park and next door to the Pier.
A Picture is Worth a Thousand Words, But a Virtual Walkthrough Speaks for Itself!
Click Here for a 3D Virtual Tour of This Home!
AMENITIES
----------------------
Free Wifi In the Condo
Gulf View Balcony
Washer / Dryer
Full Kitchen
SLEEPING ARRANGEMENTS
--------------------------------------------
Bedroom 1:
- King size bed
- 20 inch Flat Screen TV/DVD VHS combo
Bathroom 1:
-Shower/Tub combination
-Bunks located in the hallway, twin size
Bathroom 2:
- Walk in Shower
Living Room:
-Sleeper Sofa
-Entrance to the balcony with seating including two chairs, side table and lounger.
-32 inch flat screen TV, DVD player, VHS and CD player
Kitchen:
-Dining area has a table for 4 plus 2 bar stools. Place settings available for 8
-Three chairs on the balcony and two glass tables
FREE FUN DETAILS:
We have selected an array of activities that will cater to many interests and age groups. Below you will
find the FREE FUN activities included with your rental. Please note below some of the activities are seasonal. Activities are non-cumulative. Unused admissions will expire daily. FREE FUN is NOT included in winter monthly rentals.
Free Fun Activities:
Ripley's Believe It or Not (one free adult admission)
Gulf Marine World (one free adult admission)
Bay Point Golf (one free round at Meadows Course per unit. Noncumulative. Nontransferable)
Shell Island (one admission)
Explore 360 - Escape Adventure (one free adult admission)
WonderWorks (one free adult admission)
)
Calypso Beach Towers...West End of PCB...Across the street from Pier Park!!! 1-1807 Calypso is located on the 18th floor in the East Tower in Tower I. This 1 bedroom/bunk/2 bath Condo is very conveniently located across the street from Pier Park. Amazing View of the Beautiful Gulf of Mexico and the Pier. Sleeps 6.
You will absolutely marvel over all of the amenities that Calypso has to offer, from a day of fishing at the pier, which is located right next door to the complex, to the great sunrays, you will enjoy soaking up by the pools. Guests will also be able to enjoy the great work out facility and the lush landscaping that the tiki bar by the pool has to offer.
Calypso is close to everything that matters on a vacation. Walk to restaurants and shopping just across the street at Pier Park and next door to the Pier.
A Picture is Worth a Thousand Words, But a Virtual Walkthrough Speaks for Itself!
Click Here for a 3D Virtual Tour of This Home!
AMENITIES
----------------------
Free Wifi In the Condo
Gulf View Balcony
Washer / Dryer
Full Kitchen
SLEEPING ARRANGEMENTS
--------------------------------------------
Bedroom 1:
- King size bed
- 20 inch Flat Screen TV/DVD VHS combo
Bathroom 1:
-Shower/Tub combination
-Bunks located in the hallway, twin size
Bathroom 2:
- Walk in Shower
Living Room:
-Sleeper Sofa
-Entrance to the balcony with seating including two chairs, side table and lounger.
-32 inch flat screen TV, DVD player, VHS and CD player
Kitchen:
-Dining area has a table for 4 plus 2 bar stools. Place settings available for 8
-Three chairs on the balcony and two glass tables
FREE FUN DETAILS:
We have selected an array of activities that will cater to many interests and age groups. Below you will
find the FREE FUN activities included with your rental. Please note below some of the activities are seasonal. Activities are non-cumulative. Unused admissions will expire daily. FREE FUN is NOT included in winter monthly rentals.
Free Fun Activities:
Ripley's Believe It or Not (one free adult admission)
Gulf Marine World (one free adult admission)
Bay Point Golf (one free round at Meadows Course per unit. Noncumulative. Nontransferable)
Shell Island (one admission)
Explore 360 - Escape Adventure (one free adult admission)
WonderWorks (one free adult admission)
)
Overview
Details
condo
844
sq. ft.
Sleeps
6
Bedrooms
1
Bathrooms
2
Minimum Stay
2 - 28 nights
About the property
Condo, 1 Bedroom, 2.0 Baths, (Sleeps 6)
Calypso Beach Towers...West End of PCB...Across the street from Pier Park!!! 1-1807 Calypso is located on the 18th floor in the East Tower in Tower I. This 1 bedroom/bunk/2 bath Condo is very conveniently located across the street from Pier Park. Amazing View of the Beautiful Gulf of Mexico and the Pier. Sleeps 6.
You will absolutely marvel over all of the amenities that Calypso has to offer, from a day of fishing at the pier, which is located right next door to the complex, to the great sunrays, you will enjoy soaking up by the pools. Guests will also be able to enjoy the great work out facility and the lush landscaping that the tiki bar by the pool has to offer.
Calypso is close to everything that matters on a vacation. Walk to restaurants and shopping just across the street at Pier Park and next door to the Pier.
A Picture is Worth a Thousand Words, But a Virtual Walkthrough Speaks for Itself!
Click Here for a 3D Virtual Tour of This Home!
AMENITIES
----------------------
Free Wifi In the Condo
Gulf View Balcony
Washer / Dryer
Full Kitchen
SLEEPING ARRANGEMENTS
--------------------------------------------
Bedroom 1:
- King size bed
- 20 inch Flat Screen TV/DVD VHS combo
Bathroom 1:
-Shower/Tub combination
-Bunks located in the hallway, twin size
Bathroom 2:
- Walk in Shower
Living Room:
-Sleeper Sofa
-Entrance to the balcony with seating including two chairs, side table and lounger.
-32 inch flat screen TV, DVD player, VHS and CD player
Kitchen:
-Dining area has a table for 4 plus 2 bar stools. Place settings available for 8
-Three chairs on the balcony and two glass tables
FREE FUN DETAILS:
We have selected an array of activities that will cater to many interests and age groups. Below you will
find the FREE FUN activities included with your rental. Please note below some of the activities are seasonal. Activities are non-cumulative. Unused admissions will expire daily. FREE FUN is NOT included in winter monthly rentals.
2 years in a row
This was our 2nd year staying in this unit. We have no complaints. Plan on staying there again next year.
Submitted: Jul 16, 2017
Stayed: July 2017
Source: HomeAway
Owner's Response: We are glad to hear you had a great vacation. We love the idea of making lasting memories year after year in the condo! We hope to welcome you back again soon as our guest! Price Morgan Vacation Rentals
Great stay in Panama City Beach
Our stay in PCB was fantastic! The condo was beautiful, clean, and in a great location. Whenever we wanted to go to the beach we just went downstairs and when we wanted to go out to eat or shop we walked
Submitted: May 7, 2016
Stayed: May 2016
Source: HomeAway
Owner's Response: Thank you for your review. We are happy to hear you enjoyed the condo and found the location convenient to shopping and restaurants. We look forward to your next trip to PCB
Girls vacation
Owner's Response: Thank you for the review! Calypso is a great location and it is so convenient to walk to shops and restaurants.. right across from Pier Park. We hope to see you again in the near future
Our Panama City Beach vacation rentals provide all the above and more. Known for sandy white beaches, blue-green waters and mild weather, Panama City Beach is the perfect beach vacation destination. The area offers a variety of outdoor activities, including boating, fishing, surfing, swimming, snorkeling, scuba diving and more! But this coastal city also provides way more than sun and surf.
Our Panama City Beach rentals are conveniently located near award-winning restaurants, great shopping, entertainment and attractions. Visit the Shipwreck Island Waterpark, Zoo World or Gulf World Marine Park, and find go karts, arcades and miniature golf. Check out the famous Pier Park, an entertainment complex that has more than 1 million square-feet of boutiques, specialty stores, restaurants and a movie theater.
Nature lovers will want to explore Camp Helen and St. Andrews state parks, featuring hiking, public beaches, wildlife, and native flowers and plants. Both parks provide additional water recreation activities. St. Andrews State Park is also a popular place for birding, biking and camping.
After a fun-filled day, relax in your home away from home. Our vacation rentals are the perfect place to kick back and spend time with loved ones. Whether staying in a condo or beach home, guests will enjoy amenities such as fully-equipped kitchens, private balconies overlooking the Gulf, lagoon-style pools, hot tubs and more.
Explore our PCB rentals and get ready to plan your perfect getaway!
If you'd like to list your property, learn how our Panama City Beach property management services can benefit you.
Photos
Rates & Availability
Available
Unavailable
Taxes and fees are additional
Updated:
Mar 16, 2018
Notes
Major Credit Cards Accepted.Monthly rates show the rental amount of a four week trip.A 15% deposit is required upon confirmation of all reservations.A $44 limited damage waiver will be applied to all bookings in lieu of a security deposit.Local, State & Federal Taxes 13%.Processing Fee $79 per trip.Fall Into Savings Book Now and Save 20%.
Manager's Cancellation Policy
100% refund if canceled at least 60 days before arrival date.
Service Fee fully refunded on cancellations that qualify for 100% refund. | 2024-02-18T01:27:04.277712 | https://example.com/article/3718 |
719, 1018, 1243, 1394, 1471?
-37*c**2 + 484*c - 101
What is the j'th term of 17188152, 34376302, 51564448, 68752590, 85940728, 103128862, 120316992?
-2*j**2 + 17188156*j - 2
What is the s'th term of 175169, 347030, 518891, 690752, 862613?
171861*s + 3308
What is the g'th term of -858155, -1716312, -2574471, -3432632, -4290795, -5148960?
-g**2 - 858154*g
What is the h'th term of 606164, 606128, 606078, 606008, 605912?
-h**3 - h**2 - 26*h + 606192
What is the m'th term of 5459, 4299, 3141, 1985?
m**2 - 1163*m + 6621
What is the t'th term of -423, -1266, -2349, -3672, -5235, -7038?
-120*t**2 - 483*t + 180
What is the j'th term of 11888526, 23777057, 35665586, 47554113, 59442638, 71331161, 83219682?
-j**2 + 11888534*j - 7
What is the c'th term of 21024, 20913, 20804, 20697?
c**2 - 114*c + 21137
What is the c'th term of -4715523, -4715796, -4716083, -4716390, -4716723, -4717088, -4717491?
-c**3 - c**2 - 263*c - 4715258
What is the i'th term of -255023, -255040, -255081, -255158, -255283?
-2*i**3 - 3*i - 255018
What is the k'th term of 2937, 4733, 6529?
1796*k + 1141
What is the c'th term of -81, -318, -533, -570, -273, 514?
26*c**3 - 145*c**2 + 16*c + 22
What is the f'th term of 769, 4034, 12265, 27940, 53537, 91534, 144409?
413*f**3 + 5*f**2 + 359*f - 8
What is the z'th term of 82, 208, 464, 874, 1462, 2252?
4*z**3 + 41*z**2 - 25*z + 62
What is the m'th term of -29326999, -58654012, -87981035, -117308068, -146635111, -175962164, -205289227?
-5*m**2 - 29326998*m + 4
What is the z'th term of 55225382, 55225379, 55225374, 55225367, 55225358, 55225347, 55225334?
-z**2 + 55225383
What is the i'th term of -9186, -18450, -27716, -36984, -46254, -55526, -64800?
-i**2 - 9261*i + 76
What is the u'th term of 239351, 478678, 718005, 957332, 1196659?
239327*u + 24
What is the k'th term of -118732, -118777, -118830, -118873, -118888, -118857?
3*k**3 - 22*k**2 - 118713
What is the x'th term of 11290291, 11290284, 11290263, 11290222, 11290155, 11290056, 11289919, 11289738?
-x**3 - x**2 + 3*x + 11290290
What is the t'th term of 45416, 45342, 45266, 45188, 45108, 45026, 44942?
-t**2 - 71*t + 45488
What is the b'th term of -903091, -901133, -899175?
1958*b - 905049
What is the g'th term of -94423093, -94423091, -94423087, -94423081, -94423073, -94423063?
g**2 - g - 94423093
What is the z'th term of -365, -1678, -3839, -6848, -10705, -15410, -20963?
-424*z**2 - 41*z + 100
What is the a'th term of -3957812, -3957874, -3957978, -3958124?
-21*a**2 + a - 3957792
What is the z'th term of -65369, -130697, -195987, -261239?
19*z**2 - 65385*z - 3
What is the w'th term of 38006, 37958, 37908, 37856, 37802?
-w**2 - 45*w + 38052
What is the x'th term of -2373, -9625, -16867, -24093, -31297?
x**3 - x**2 - 7256*x + 4883
What is the i'th term of -22975, -46890, -70805, -94720, -118635, -142550?
-23915*i + 940
What is the z'th term of 18797, 22083, 25357, 28619?
-6*z**2 + 3304*z + 15499
What is the f'th term of -6497, -11348, -16199, -21050?
-4851*f - 1646
What is the b'th term of -74184, -78160, -82136, -86112, -90088?
-3976*b - 70208
What is the s'th term of -246, -914, -1896, -3090, -4394, -5706, -6924?
17*s**3 - 259*s**2 - 10*s + 6
What is the i'th term of -9676, -9565, -9408, -9199, -8932, -8601, -8200, -7723?
i**3 + 17*i**2 + 53*i - 9747
What is the r'th term of 889527, 3558077, 8005667, 14232303, 22237991, 32022737, 43586547, 56929427?
r**3 + 889514*r**2 + r + 11
What is the c'th term of 3263, 3581, 4443, 6119, 8879, 12993, 18731?
45*c**3 + 2*c**2 - 3*c + 3219
What is the j'th term of 1033, 7923, 26693, 63283, 123633, 213683?
990*j**3 - 40*j + 83
What is the u'th term of -61713, -61617, -61535, -61473, -61437?
-u**3 - u**2 + 106*u - 61817
What is the h'th term of 4508, 5729, 6956, 8189?
3*h**2 + 1212*h + 3293
What is the m'th term of -12681, -24271, -35863, -47457, -59053, -70651, -82251?
-m**2 - 11587*m - 1093
What is the g'th term of -3014229, -3014129, -3013951, -3013689, -3013337, -3012889, -3012339, -3011681?
g**3 + 33*g**2 - 6*g - 3014257
What is the d'th term of 1232, -3065, -7366, -11671, -15980?
-2*d**2 - 4291*d + 5525
What is the a'th term of 8762, 17626, 26604, 35696?
57*a**2 + 8693*a + 12
What is the k'th term of 23394, 23535, 23676, 23817, 23958?
141*k + 23253
What is the b'th term of 6370, 12650, 18930, 25210?
6280*b + 90
What is the d'th term of -33054, -66386, -99718, -133050, -166382, -199714?
-33332*d + 278
What is the h'th term of -20017, -19589, -19161, -18733, -18305, -17877?
428*h - 20445
What is the o'th term of 315631, 631264, 946897, 1262530, 1578163?
315633*o - 2
What is the v'th term of -23656, -23596, -23526, -23440, -23332, -23196, -23026?
v**3 - v**2 + 56*v - 23712
What is the f'th term of -160, -749, -1782, -3259, -5180?
-222*f**2 + 77*f - 15
What is the b'th term of 465143086, 930286173, 1395429260, 1860572347?
465143087*b - 1
What is the p'th term of -2347216, -4694437, -7041658, -9388879, -11736100?
-2347221*p + 5
What is the z'th term of 1049, 1161, 1305, 1481?
16*z**2 + 64*z + 969
What is the o'th term of -48224, -51311, -54398, -57485?
-3087*o - 45137
What is the u'th term of -263050, -263032, -263010, -262990, -262978?
-u**3 + 8*u**2 + u - 263058
What is the c'th term of 66102, 66315, 66528, 66741, 66954?
213*c + 65889
What is the m'th term of 9305061, 18610124, 27915187, 37220250, 46525313?
9305063*m - 2
What is the f'th term of 42695, 85434, 128219, 171050, 213927?
23*f**2 + 42670*f + 2
What is the a'th term of 12593624, 12593622, 12593618, 12593612, 12593604, 12593594?
-a**2 + a + 12593624
What is the y'th term of -704818, -1409517, -2114218, -2818921, -3523626?
-y**2 - 704696*y - 121
What is the p'th term of -2279, -4445, -6605, -8759, -10907, -13049?
3*p**2 - 2175*p - 107
What is the s'th term of 7458, 7480, 7508, 7536, 7558?
-s**3 + 9*s**2 + 2*s + 7448
What is the t'th term of 127261, 127169, 127079, 126991, 126905, 126821, 126739?
t**2 - 95*t + 127355
What is the q'th term of -5541815, -5541814, -5541813, -5541812?
q - 5541816
What is the q'th term of 10245265, 10245267, 10245269, 10245271, 10245273?
2*q + 10245263
What is the w'th term of -770557, -1540987, -2311417?
-770430*w - 127
What is the r'th term of -834195, -1668383, -2502571, -3336759?
-834188*r - 7
What is the l'th term of 108, -800, -1708, -2616, -3524?
-908*l + 1016
What is the h'th term of 24103279, 24103313, 24103347?
34*h + 24103245
What is the g'th term of 155513, 310209, 464905, 619601, 774297, 928993?
154696*g + 817
What is the t'th term of -179, -291, -485, -761, -1119?
-41*t**2 + 11*t - 149
What is the c'th term of 373985256, 373985253, 373985248, 373985241, 373985232, 373985221, 373985208?
-c**2 + 373985257
What is the j'th term of -1252335, -2504412, -3756489, -5008566, -6260643, -7512720?
-1252077*j - 258
What is the x'th term of 236985, 474086, 711189, 948294, 1185401?
x**2 + 237098*x - 114
What is the j'th term of -333, -1020, -1755, -2202, -2025?
56*j**3 - 360*j**2 + j - 30
What is the q'th term of -2800, -3262, -4068, -5218, -6712, -8550, -10732?
-172*q**2 + 54*q - 2682
What is the m'th term of -542313, -542323, -542333, -542343, -542353, -542363?
-10*m - 542303
What is the g'th term of -369, -1460, -3267, -5790?
-358*g**2 - 17*g + 6
What is the q'th term of -197867, -395745, -593613, -791465, -989295, -1187097, -1384865, -1582593?
q**3 - q**2 - 197882*q + 15
What is the u'th term of 339242, 679413, 1019584, 1359755, 1699926?
340171*u - 929
What is the q'th term of -299741, -2397965, -8093141, -19183745, -37468253, -64745141, -102812885, -153469961?
-299746*q**3 - 2*q + 7
What is the y'th term of -794739, -793593, -792459, -791343, -790251, -789189, -788163, -787179?
-y**3 + 1153*y - 795891
What is the t'th term of 178027, 355847, 533667, 711487, 889307?
177820*t + 207
What is the z'th term of 2704, 2308, 1722, 946, -20, -1176, -2522?
-95*z**2 - 111*z + 2910
What is the l'th term of -55530, -111214, -166892, -222564?
3*l**2 - 55693*l + 160
What is the a'th term of -420704, -420756, -420838, -420950, -421092, -421264, -421466?
-15*a**2 - 7*a - 420682
What is the r'th term of 1365222, 5460837, 12286842, 21843237, 34130022?
1365195*r**2 + 30*r - 3
What is the z'th term of -7496, -14714, -21854, -28916, -35900?
39*z**2 - 7335*z - 200
What is the z'th | 2023-12-28T01:27:04.277712 | https://example.com/article/7414 |
The best nature writing from the newspaper, magazine, blog and book authors of the Lone Star State . . .
Thursday, September 25, 2008
How Does Hurricane Conditions Affect Our Wildlife?by Ro Wauer
Hurricane Ike caused severe problems for people all along the upper Gulf Coast. We have all heard agonizing stories about Ike’s impact on human beings. But what about the wildlife, the birds, mammals, butterflies, and other creatures, that did not evacuate or go into a shelter of some sort? The answer is varied, depending upon a large set of circumstances. For instance, many of the more mobile species, such as birds and butterflies, were able to escape, either by flying away or floating away on the storm front. But many of all these creatures undoubtedly succumbed to Hurricane Ike.
Migrating northern birds probably did not enter the area of Ike’s influence, either by staying put out of danger or circling around the storm. Resident species had little choice, however. They simply hunkered down in some semi-protected location, not coming out until the storm passed them by. Mortality was undoubtedly significant. Some of hardest hit birds were some of the larger colonial roosting species such as the herons, egrets and gulls. But once the storm passed them by, the survivors probably did very well because most of those birds possess an omnivorous diet. They are ably to feed on almost any kind of carrion or a variety of dead and dying creatures. This probably is also true for any vultures and raptors that were present after the storm. In fact, there are records of increased numbers of raptors to an area following a storm.
Hummingbirds probably were hardest hit by the storm, for two reasons. First, they are tiny creatures that can be thrown about by heavy winds, and are very likely to be injured. Second, once the storm passes by, nectaring plants, on which hummingbirds depend, would be seriously diminished. And because flowering plants are probably affected by salt water from the storm, the surviving plants cannot flower for several days or weeks or even the following season. Often hummingbirds that do survival the storm perish soon afterwards unless they can find an adequate food supply. That is why hummingbird feeders, loaded with sugar water, are so important immediately after a storm.
And what about the mammals such as the deer, hogs, coyotes, and rodents? The same scenario for the birds might also apply to the mammals. Burrowing rodents could possibly survive in underground cavities that do not get flooded. But the larger mammals that were forced to face the water and wind might be less successful. Yet, most of these creatures are tough and are opportunists; that is how they are able to survive in this human-dominated society. And once the storm is past, the carnivores are likely to do very well. Deer that feed on plants may be more hard pressed, but they too are hardy creatures and are likely to make it even with a reduced food supply.
Butterflies are an interesting group of wildlife. There are records of butterflies suddenly appearing in a place they have never previously been reported, even a hundred miles or more from they known breeding grounds. Butterflies being so light weight and easily blown about, can ride thermals or storm fronts for amazing distances. Although many undoubtedly succumb to a storm, especially those adults that stay put, many escape simply by drifting away. And since most butterflies live only a couple weeks, and are replaced by newly emerging individuals, so long as the butterfly chrysalis survives, more butterflies can be present soon after a storm. But if their nectaring plants may be in short supply, emergence can be postponed. The aftermath of major storms is a fascinating time for wildlife enthusiasts. Birds and butterflies can appear in out-of-range locations for days afterwards. That is why birders and butterfly enthusiasts keep a watchful eye out for surprise species. | 2023-08-27T01:27:04.277712 | https://example.com/article/6736 |
Jim Cooper (footballer)
James Ernest Cooper (born 19 January 1942) is an English footballer who played as a winger in the Football League for Chester, Southport, Blackpool, Mansfield Town and Crewe Alexandra.
References
Category:1942 births
Category:Living people
Category:Sportspeople from Chester
Category:Association football wingers
Category:English footballers
Category:Chester City F.C. players
Category:Southport F.C. players
Category:Blackpool F.C. players
Category:Mansfield Town F.C. players
Category:Crewe Alexandra F.C. players
Category:English Football League players | 2024-04-27T01:27:04.277712 | https://example.com/article/3303 |
Google gave a glimpse of the upcoming Google TV, in a blog post today and has also put up an official Google TV Website. The website shows off lot of great features and abilities of Google TV.
Google has provided a list of content providers for Google TV which has big names like Turner Broadcasting, NBC Universal, HBO and NBA. Google has also partnered with Amazon to provide users access to Amazon’s Video on Demand service.
It’s goal is to bring the entire Internet on to your TV and it does this with some great features:
With a single click search, you can watch anything you want.
Android phone and iPhone can be used as remote control.
You can share what you’re watching, listening, or doing on your phone by sending it to your TV.
On demand videos are available from Netflix and Amazon’s Video On Demand service.
You can watch TV and browse the internet at the same time.
You can record TV shows.
You can create personal radio station and stream music.
You can use your big screen TV as a picture frame with pictures streaming from Picasa, Flickr, and other photo-sharing websites.
YouTube is formatted for a larger screen.
Google TV updates over the air, so that you always have the latest features.
Here’s preview of Google TV: | 2024-05-13T01:27:04.277712 | https://example.com/article/2402 |
Viktor Kozlov (born 10.01.1958, Chelyabinsk), the Russian guitarist, composer and music teacher. Lives and works in Chelyabinsk (Russia). Honored Artist of the Russian Federation (1997), Professor (2000). Winner of the I-st prize of the First Regional Competition of Russian folk-based instruments in Chelyabinsk (1988), winner of the International Competition for Composers (Esztergom - Hungary, 1989), the student of the All-Russian competition of folk instruments (Nizhny Novgorod, 1990) . He returned from 8 years (Chelyabinsk Children's Music School ¹ 2, teacher SH Muhatdinov). In the years 1979-92. studied at the Chelyabinsk College of Music in guitar, parallel, he studied composition in the class YE Halperin. In 1988, he graduated from the Urals State Conservatory (VM Derun). He has participated in many guitar competitions and festivals in Russia and abroad. He gave solo concerts in Moscow, Minsk, Bishkek, Voronezh, Kharkov, St. Petersburg, Chelyabinsk, Yekaterinburg, Tomsk, Novosibirsk, Surgut, etc.
As a composer, the author of original compositions for classical guitar, Viktor Kozlov won a diploma of I degree in Donetsk (1982) and Moscow (1988). In the summer of 1989, his name became known and abroad on the 9th International Guitar Festival in Esztergom (Hungary) Kozlov won the third prize as a composer.
Composing music began at age 12. The first significant pieces of music written in the School of Music String Quartet, Trio for Flute, Viola and Guitar, Piano Variations, "Dance and Dance" for solo guitar. In the future, Viktor Kozlov prefers composing miniatures for solo guitar and guitar trio. Popular comic plays Kozlov: Oriental Dance (1982), "March of the Soldiers" (1985), "Little Detective" (1990), "Dance of the Hunter" (1997), "Kiskina the Hill" (1999). Several essays written by the composer for guitar and orchestra, "Concertino" (1987), "epics and Russian Dance" (1995), "buffoonery" (1997). A special place in his creativity numerous works for children. He published a collection of musical pieces for young guitarists "Little Secrets senorita Guitars / Children's Album of the young guitarist," which in 1999 was recognized by Russian guitar center (Moscow), the best in Russia.
Kozlov published a number of works in Russia, England, Germany, Italy, Poland and Finland. His works are included in their repertoire guitarists N. Komolyatov (Moscow), Vladimir Zhadko (Kiev), T. Volsky (USA), A. Horeb (St. Petersburg), E. Gredyushko (Belarus), S. Dinnigan (England ), the duo "Capriccioso" (Germany), they also perform trio of guitarists Urals (Kozlov, S. Muhatdinov, V. Cowboy) and instrumental duet "Concertino" (Ekaterinburg) and many others. In Chelyabinsk, a musician working with the Chamber Orchestra "Classic", the State Orchestra of Folk Instruments "Malachite", the orchestra of folk instruments Chelyabinsk Higher Music School.
He currently teaches at the Chelyabinsk Higher Music School. PI Tchaikovsky. Among his students are winners of international and national competitions, the International Fellows program "New Names": I. Kulikov, N. Fedorenko, E. Pushkarenko, A. Kiselev, M. Baklanov, D. Ivanchenko.
V Kozlov - the founder of the South Ural guitar school (author programs for all levels of education).
For several years, he is a member and artistic director of the Urals Guitar Trio, which in addition to the very Viktor Kozlov includes Sharif Muhatdinov and Victor Cowboy.
As chairman of the Chelyabinsk Regional Association of Classical guitarists, he was the initiator of the international festivals in Chelyabinsk "Classical guitar in the Urals" (1991). In 1998, at a recording studio «U-Saund» released CD-ROM Kozlov's "Meditation for solo guitar" with works by contemporary composers, and his own compositions. On the CD are recorded as "Black bullfighter", suite for solo guitar (1988), "The Ballad of Helen of Troy" - for solo guitar (1997). | 2024-01-05T01:27:04.277712 | https://example.com/article/3063 |
Est-ce vrai que les Québécois versent à l’État la moitié de leur paie? Que l’on risque d’avoir moins dans nos poches en acceptant une augmentation de salaire ou de faire des heures supplémentaires? Qu’un citoyen sur deux ne paie pas d’impôt? Ces croyances, qui ont la vie dure, sont fausses, expliquent des experts en fiscalité. Voici pourquoi.
Mythe 1 : L’État prend la moitié de notre salaire!
Agrandir l’image (Nouvelle fenêtre) Exemples de messages publiés sur Twitter. Celui de gauche dit « Sept des 10 provinces [dont le Québec] ont maintenant un taux d’impôt sur le revenu de plus de 50 %. C’est du vol, les gouvernements n’ont pas le droit de prendre plus de la moitié du revenu d’un particulier ». Photo : Twitter
Une simple recherche dans les réseaux sociaux montre que la croyance du 50 % d’impôt est entretenue chez bon nombre de personnes.
Une étude de 2016 portant sur la littératie fiscale des Québécois (Nouvelle fenêtre) confirme d'ailleurs que cette idée est bien ancrée dans les mentalités. À la question Est-il vrai que si votre revenu imposable est de 100 000 $, l’impôt sur le revenu s’élève à 50 000 $? , la majorité des personnes sondées, 56 %, répondaient vrai , 26 % faux et 18 % je ne sais pas .
Cette affirmation est fausse. L’impôt combiné du fédéral et du provincial sur un revenu de 100 000 $ est d’environ 29 000 $, soit 29 %.
Pour un revenu imposable de 50 000 $, qui représente le salaire moyen au Québec, l’impôt combiné du fédéral et du provincial est d’environ 10 000 $, soit 20 %.
Donc, contrairement à une idée reçue, et qui est parfois relayée dans l’espace public, le taux moyen d’imposition pour la vaste majorité des contribuables québécois et canadiens est loin du seuil psychologique de 50 %.
La confusion vient peut-être du fait que certains confondent le taux moyen et le taux marginal d’imposition, pensent Luc Godbout, titulaire de la chaire de recherche en fiscalité et en finances publiques à l'Université de Sherbrooke, et Marc Bachand, professeur de fiscalité à l’Université du Québec à Trois-Rivières.
Le taux moyen représente ce que l’on paye à l’État dans les faits : c’est celui-là qui doit vous intéresser. C’est le pourcentage de l’impôt que vous payez par rapport à l’ensemble de votre revenu.
Mais pour calculer le taux moyen, il faut tenir compte du taux marginal, qui augmente par paliers en fonction du revenu; c’est le principe même de l’impôt progressif. Les premières tranches de votre revenu sont imposées à un taux marginal plus bas, et les dernières tranches, à un taux plus élevé.
Je pense que ça existe encore, ce mythe-là. Et j'ai l'impression que c'est basé sur le fait qu’on a un taux marginal d'à peu près 50 % [pour les tranches de revenus les plus élevées] et que certains pensent que ça s’applique à tout. Marc Bachand
En effet, le taux marginal combiné du fédéral et du provincial pour les revenus élevés dépasse 50 %. Mais ce taux ne s’applique pas à tout le revenu gagné. Par exemple, pour quelqu’un qui gagne 200 000 $, le taux marginal de 50,16 % concerne uniquement la portion comprise entre 150 473 $ et 200 000 $. Pour les portions inférieures de son revenu, il faut se référer à chaque palier d’imposition qui les concerne. Entre zéro et 13 228 $, aucun impôt ne s’applique. Ensuite, entre 13 229 $ et 15 531 $, le taux est de 12,53 %. Puis, de 15 532 $ à 44 544 $, le taux est de 27,53 %. Et ainsi de suite.
Ce qui donne au final le taux moyen, qui est celui que le contribuable devra payer dans les faits. Pour un revenu de 200 000 $, c’est 38,9 %.
Bien entendu, des cotisations sociales s’ajoutent à l’impôt que l’État prélève dans vos poches. Les principales cotisations pour les salariés québécois sont celles du Régime des rentes du Québec (RRQ), du Régime québécois d’assurance parentale (RQAP) et de l’assurance-emploi (AE), des programmes dont vous avez profité ou profiterez probablement un jour. Aussi, bon nombre de contribuables jouissent de crédits et de prestations, comme des incitatifs au travail, des remboursements de taxes ou encore des prestations pour enfants.
Lorsque l’on tient compte de tous ces flux monétaires entre les contribuables et le fisc, on obtient la charge fiscale nette, qui est le total de l’impôt et des cotisations, moins les prestations, en pourcentage du revenu brut.
La charge fiscale nette au Québec pour un célibataire sans enfant qui a le salaire moyen (environ 50 000 $) est de 26 %, selon les calculs de la chaire de recherche en fiscalité et en finances publiques de l’Université de Sherbrooke. Pour le même célibataire sans enfant, mais avec un revenu de 100 000 $, la charge fiscale nette passe à 33 % environ.
Le graphique suivant permet de comparer la charge fiscale selon les situations familiales et les revenus, exprimés en pourcentage du salaire moyen (SM).
Cela varie, bien sûr. Tout dépend du revenu et de la situation familiale, soit le fait d’être seul ou en couple, ou d’avoir un, deux, trois ou aucun enfant.
Pour un couple avec un seul salaire de 50 000 $ et deux enfants, la charge fiscale est de -7,5 %. Ce couple reçoit donc plus d’argent de l’État qu’il ne lui en verse. Ce qui vaut au Québec le qualificatif de paradis fiscal pour les jeunes familles, surtout celles à revenus modestes, grâce notamment aux allocations familiales et aux garderies à faible coût.
Ce même couple avec un salaire de 125 000 $ aura une charge fiscale de 29,2 %.
Il est vrai que pour les revenus très élevés, la charge fiscale nette s'approche de la moitié des revenus. Par exemple, pour un célibataire sans enfant gagnant 350 000 $, la charge fiscale dépasse les 45 %. Elle atteint 50 % quand on franchit les 740 000 $.
On pourrait aussi comptabiliser d’autres formes d’imposition, par exemple les taxes municipales que prélèvent les villes, mais il ne s’agit pas dans ce cas d’impôts ou de taxes sur le revenu; par ailleurs, seule une partie des citoyens en paye.
Des calculs sont aussi parfois effectués pour tenir compte de toutes les sommes que les citoyens-consommateurs versent aux gouvernements au cours de l’année. Par exemple, l’Institut Fraser, un groupe de réflexion de droite, calculait en 2019 que la famille moyenne canadienne verse 44 % de ses revenus en taxes et impôts. Ce calcul tient compte de tous les impôts et cotisations, des taxes à la consommation, des taxes foncières, de l’impôt sur le gain en capital, des tarifs de douane ainsi que des taxes sur l’alcool, le tabac, l’essence et les ressources naturelles et les frais d'immatriculation.
Ce calcul, publicisé lors de la journée de libération fiscale que relaient chaque année les médias, peut contribuer à fausser les perceptions, affirment les deux fiscalistes. L’Institut Fraser présente cette journée, qui survient en juin, comme le moment dans l’année où l’on cesse de travailler pour le gouvernement et où l’on commence à travailler pour soi.
Mais en échange de ça, la famille moyenne reçoit ceci : les enfants vont à l'école, l’autoroute est déneigée, le grand-père malade est soigné à l’hôpital. Mais ça, [l'indice Fraser] ne nous le dit pas , souligne Luc Godbout.
C'est un raccourci qui est dommageable dans l'espace public. Une famille avec deux enfants qui a un revenu de 50 000 $ au Québec, elle ne paie pas d’impôt! Donc, ça en dit beaucoup, ce sont des choix de société. Maintenant, qu'on additionne toutes les formes d'imposition possibles, du prélèvement de l'État, pour arriver à ce genre de calcul là comme l'Institut Fraser le fait, oui, je veux bien. Mais pensons-y, si on n’avait pas d’impôt et qu’on devait payer tous [les services] individuellement, on ne serait pas gagnant. Cet indice fait fi de cette notion-là , soutient quant à lui Marc Bachand.
Une part du mythe, selon Luc Godbout, vient peut-être aussi du fait que sur nos talons de paie, on peut voir plusieurs ponctions sur notre salaire, comme les cotisations au régime de retraite mis en place par l’employeur, les cotisations syndicales, et les contributions aux régimes privés d’assurance santé ou dentaire. Certains vont regarder la différence entre le net et le brut sur leur chèque de paie, et ils vont considérer que tout cela c’est de l’impôt . Mais il est important d’enlever ces éléments de la notion d’impôt, rappelle-t-il.
Mythe 2 : Si je fais plus d’heures ou j’ai un meilleur salaire, je vais changer de tranche d’imposition et donc avoir moins de revenus nets.
Agrandir l’image (Nouvelle fenêtre) Exemples de messages publiés sur Twitter. Celui de droite dit « C’est la façon dont fonctionnent les salaires, tu obtiens une augmentation, tu te retrouves dans la tranche suivante, mais tu as moins [à la fin] parce que tu es en bas de cette tranche ». Photo : Twitter
Contrairement à une idée reçue, les contribuables ont toujours plus dans leurs poches après impôt s’ils gagnent plus d’argent en travaillant.
Encore une fois, ce mythe du changement de tranche d’imposition découle possiblement de la confusion entre le taux marginal et le taux moyen, selon les spécialistes. Certains croient à tort qu’un nouveau taux marginal qui les frappe lors d’une augmentation de salaire s’appliquera à tous leurs revenus, alors qu’il ne touche que la portion gagnée en plus.
Toutefois, le fait que le Québec, à l’instar d’autres États, est généreux en prestations sociales qui ciblent les personnes les moins fortunées a un revers néfaste, expliquent les fiscalistes.
Notamment pour les familles, Luc Godbout parle d’une zone douloureuse aux alentours de 40 000 $ à 50 000 $ de revenus, quand on se met à gagner un peu plus. Ces quelques dollars supplémentaires de revenus bruts font diminuer grandement des prestations sociales, soit les allocations pour enfants, les primes au travail et les remboursements de taxes, notamment. Moins d’une famille sur dix se retrouve dans cette zone.
Dans certaines situations, en tenant compte de tous les impôts et cotisations additionnels et des pertes de prestations, l’État vient chercher 70 % ou même plus sur une légère hausse de revenus.
Pour un couple avec deux enfants qui gagne 40 000 $ et qui veut faire 1000 $ de plus, […] l'État en enlève grosso modo 70 %, soit 700 $. Alors c'est peut-être là aussi, ce fameux sentiment que l'État m'en prend beaucoup , explique Luc Godbout.
Et des fois les gens ne comprennent pas. On a entendu mille fois "Je ne ferai pas d'overtime parce que je vais changer de bracket". […] Ce n'est pas que tu changes de bracket, mais c'est que tu es dans une zone douloureuse, parce que si tu gagnes plus, tu vas payer plus d'impôt, c'est normal, tu vas payer plus de cotisations sociales, c'est normal, et tu vas perdre des prestations, ça aussi c'est normal. Mais les trois ensemble, ça donne une situation douloureuse , poursuit M. Godbout.
C'est le miroir d'avoir une société avec un filet social. Tout ça, c'est un déploiement normal, on ne peut pas avoir le beurre et l'argent du beurre , ajoute pour sa part Marc Bachand.
Le Québec, c’est le paradis fiscal pour les petites familles. On est les meilleurs au monde. Mais après ça, ça amène des taux élevés [sur des petites hausses de revenus], et c'est préoccupant quand même. Ça peut amener des comportements dysfonctionnels par rapport à l'attractivité du travail , reconnaît-il.
Ça contribue peut-être aussi à maintenir ce mythe-là que "Mon Dieu, ça ne vaut pas la peine de travailler, l'État prend trop" , renchérit Luc Godbout.
En 2016, le gouvernement provincial a introduit un bouclier fiscal (Nouvelle fenêtre) , qui permet d’atténuer les effets néfastes d’une petite hausse de revenus par rapport à l’année précédente, chez les contribuables à revenus modestes. Vous gagnez plus et le bouclier vous protège contre la trop grande voracité de l'État sur la petite augmentation de salaire que vous avez eue. Ça fonctionne, mais ce n'est pas magique! , dit Luc Godbout. Pour plusieurs contribuables, le bouclier permet de sauver quelques points de pourcentage sur les prochains dollars gagnés.
Le fait que les retenues à la source dans les systèmes de paie augmentent en fonction du salaire peut aussi contribuer à l’impression que l’impôt prend une part disproportionnée des revenus générés par des heures supplémentaires. Si on a gagné deux fois plus que d’habitude dans une période de paie, le système considère que notre salaire annuel a doublé. C’est pourquoi les retenues sont beaucoup plus élevées. Mais les sommes retenues en trop nous sont remises à la fin de l’année financière après avoir produit une déclaration.
Mythe 3 : La moitié des gens ne paient pas d'impôt
Agrandir l’image (Nouvelle fenêtre) Exemples de messages publiés sur Twitter. Photo : Twitter
Au Québec, parmi tous les contribuables ayant produit une déclaration en 2015, 35,9 % ne payaient pas d’impôt sur le revenu, selon les données de la chaire.
Parmi les contribuables non imposables, il y a notamment ceux qui restent au foyer et sont à la charge de leur conjoint(e) ainsi que les bénéficiaires de prestations de l’État. Il y a aussi les étudiants travaillant à temps partiel ou encore l’été seulement , écrit la chaire dans son bilan de la fiscalité.
Les gens non imposables, c'est d'abord et avant tout parce qu'ils ont de faibles revenus , explique Luc Godbout. Au Québec, environ un tiers des contribuables gagnent moins de 20 000 $.
Chez les moins de 25 ans, la proportion est de 67,3 % de contribuables non imposables. Chez les 65 ans et plus, ce sont 50,7 % qui sont non imposables. Et dans le groupe des 25 à 64 ans, où se situe la vaste majorité des travailleurs, 25,5 % des contribuables sont non imposables.
Ils contribuent quand même parce que ceux qui travaillent paient des cotisations sociales pour des régimes d'assurabilité [RRQ, RQAP et AE], et ils paient des taxes de vente également , précise Luc Godbout.
Lorsqu’on compare les provinces entre elles, certaines, comme l’Alberta (39,2 %) et la Saskatchewan (41,8 %) ont une proportion légèrement plus élevée de contribuables non imposables que le Québec. D’autres comme l’Ontario (34,4 %) et le Manitoba (32,2 %) ont une proportion moindre.
Les 50 % des contribuables les plus nantis supportent quant à eux la quasi-totalité de la charge fiscale des particuliers au Québec, soit 95,3 %. Cette part est similaire en Ontario (96,1 %) et aux États-Unis (95,9 %).
Donc, 96 % de l'impôt est payé par les 50 % les plus riches. Mais quand on compare à l'Ontario, aux États-Unis, ou à la France, on s'aperçoit que c'est de même partout , dit Luc Godbout. | 2024-01-01T01:27:04.277712 | https://example.com/article/1677 |
Bruners of Oklahoma
Bruners of Oklahoma
I've 3 other times to insert a lot of data here and it seems to get sent somewhere elsa or gets lost. Frustrating !! I'll try again
Daniel Bruner of 1753? son of Daniel 1729? in the Tombigbee area of Alabama, married ___ ? 1759? lived at Concharty, located not far from the Tensaw district. alleged to have been a Micco (not a chief)and resident at Concharty (Red Ground) in 1832 w/ 4 males and 4 females in the house. In 1834, he was the administrator for Redmouth, deceased in Coosa co., Al. He voted at Concharty in 1875, 1883, and 1894. Being allowed to vote indicates that he was part Creek indian. His house consisted of:
Betsey 1775?Leonard 1777?Enoch 1779?Albert 1781?Grace 1784? a Grace was at Stone Bluff and Bixby, Ok.. another Grace was born about 1877, daughter of Daniel Bruner and Manana Pinhill #2194 1954--1906 daughter of Abner Pinehill. Manana had married Thomas WILSON (note)first and next Jim Green. Grace's half-brother is John Green #2196 1887--1907. I will note here that the name Manana would be a little difficult for Creek indians to pronounce and they usually gave nicknames that sounded like the real name, - thus "Minnie Wilson". The "Minnie Wilson" and Manana Pinehill also had the same birth year.
Lucinda 1787?Sarah 1789? a Creek censes will indicate that a Sarah shared a house with Rose.
Rose 1740? another wife of Daniel 1729? was not a Creek indian name back in the early 1800s, the same for Grace. Names like Rose and Grace will come into use in nthe very late 1800s as more intermarriages took place.
Ella 1793Jane 1795
James Bruner 1795 wife is Anna Bruner 1800 moved west in 1829 with a Thomas, and a William. Voted at Little River Tulsa in 1875. * NOTE: Little River Tulsa is my tribal town group and were located around Holdenville, Ok. after the Trail Of Tears. They were mainly from Tuckabatchee town but other goups joined them on the Trail and in Oklahoma. The old Alabama Ekonchatte/Concharty was located near to and south west of Tuckabatchee.
Nancy Bruner, 1805 a Cherokee of the Saline district in 1852, joined the Creeks in Trail west. Was with a Daniel and Archie Bruner.
Jacob Bruner 1812?, son of Daniel 1729? married Eliza ___ 1814 and had Richard R. 1832?, Joseph 1834?, David 1840?.
NOTE: many persons add roll numbers to their family list but do not write which Roll they are taking the numbers from, - very confusing, as I have checked a lot of numbers and they are not from the Dawes Roll of 1899?. I use only the roll numbers from the Dawes Roll. a number preceeded by "nb" indicates the New Born roll. The "mc" indicates the later "minor child" roll.
Lewis/Louis/ Loney/ Luney 1817/24 seems to indicate the same person according to the birth year of his children. Creek males were allowed to have as many wives as they could support or handle. All wives did not stay in the same house which depended on the wishes of the first wife as wives had the say-so about the Household. Other wives could live in other small towns nearby. The children did no belong to the father but to the wife who "owned" the children. | 2023-11-13T01:27:04.277712 | https://example.com/article/7885 |
Q:
Is there a reference document that lists and describes all available variables in Capistrano?
I can usually google around and find this kind of thing but I just can't find this one.
What I'm looking for is a list and description for all the variables that I can set in my deploy.rb file in a Rails 3 app with Capistrano 2.
I've found and read these:
https://github.com/leehambley/capistrano-handbook/blob/master/index.markdown
https://github.com/capistrano/capistrano/wiki/2.x-Significant-Configuration-Variables
http://theadmin.org/articles/2010/06/24/capistrano-variables/
But there are some other variables I'm aware of such as :scm_command, and :local_scm_command (found them here in SO) that are not listed there.
I also took a look at gems/capistrano/lib/capistrano/recipes/deploy.rb but the list is still incomplete.
Where is the complete list of capistrano variables?
A:
Fun story, you can set whichever variables you want. The list of variables that actually need to be set and are used depends on the recipes you are using for deployment. When you're using your own custom recipes, you can set and use whatever variables you want. For instance, a particularly ugly part of my deploy config requires knowing which unicorn pid/config each app is using (as there are multiple unicorns handling utility things on this server in addition to the main app), so I have to
set :unicorn_pid, '/var/run/unicorn/rails.pid'
in one of the app config tasks.
Good luck!
| 2024-02-24T01:27:04.277712 | https://example.com/article/7976 |
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Q:
Выбор формы jQuery
Имеется форма, в которой необходимо выбрать условие поиска (искать по фамилии или по номеру карточки), и чтоб при нажатии на кнопку "поиск" под формой загружалась форма с результатом.
В результирующей форме указывались параметры и сохранялись (записывались в базу). Как это сделать без перезагрузки страницы. Понятно, что на аяксе, но как?
Форма выбора параметров поиска
<table width="305" height="161" border="1">
<tr>
<td width="144"><input type="radio" name="radio" id="radio" value="radio" />
Номер карточки</td>
<td width="145"><input type="radio" name="radio2" id="radio2" value="radio2" />
Фамилия</td>
</tr>
<tr>
<td><input type="text" name="textfield" id="textfield" /></td>
<td><input type="text" name="textfield2" id="textfield2" /></td>
</tr>
<tr>
<td colspan="2"><div align="center">
<input type="submit" name="button" id="button" value=" Поиск " />
</div></td>
</tr>
</table>
Форма ввода параметров (результирующая)
<table width="325" border="1">
<tr>
<td width="142">Номер карточки</td>
<td width="167"><input type="text" name="textfield" id="textfield" /></td>
</tr>
<tr>
<td>ФИО</td>
<td><input type="text" name="textfield2" id="textfield2" /></td>
</tr>
<tr>
<td>Пол</td>
<td><select name="select" id="select">
</select>
</td>
</tr>
<tr>
<td>Образование</td>
<td><select name="select2" id="select2">
</select>
</td>
</tr>
<tr>
<td><div align="center">
<input type="submit" name="button" id="button" value="Сохранить" />
</div></td>
<td><div align="center">
<input type="submit" name="button2" id="button2" value="Отменить" />
</div></td>
</tr>
</table>
A:
<head>
<script type="text/javascript" src="http://code.jquery.com/jquery-1.6.2.min.js"></script>
<style type="text/css">
#big_form {
display: none;
}
</style>
</head>
<body>
<table width="305" height="161" border="1">
<form action="/myscript.php" id="small_form">
<tr>
<td width="144"><input type="radio" name="radio" id="radio1" value="radio" />
номер карточки</td>
<td width="145"><input type="radio" name="radio" id="radio2" value="radio2" />
Фамилия</td>
</tr>
<tr>
<td><input type="text" name="textfield1_name" id="textfield1" /></td>
<td><input type="text" name="textfield2_name" id="textfield2" /></td>
</tr>
<tr>
<td colspan="2"><div align="center">
<input type="submit" name="button" id="search_button" value=" Поиск " />
</div></td>
</tr>
</form>
</table>
<table width="325" border="1" id="big_form">
<tr>
<td width="142">Номер карточки</td>
<td width="167"><input type="text" name="textfield" id="textfield" /></td>
</tr>
<tr>
<td>ФИО</td>
<td><input type="text" name="textfield3" id="textfield3" /></td>
</tr>
<tr>
<td>Пол</td>
<td><select name="select" id="select">
</select>
</td>
</tr>
<tr>
<td>Образование</td>
<td><select name="select2" id="select2">
</select>
</td>
</tr>
<tr>
<td><div align="center">
<input type="submit" name="button" id="button" value="Сохранить" />
</div></td>
<td><div align="center">
<input type="submit" name="button2" id="button2" value="Отменить" />
</div></td>
</tr>
</table>
<script type="text/javascript">
$(document).ready(function() {
$("#small_form").submit(function(event) {
event.preventDefault();
var url = $(this).attr("action");
if ($("#radio1").is(':checked')) {
$.post (
url, {
textfield1_name: $("#textfield1").val()
}, function(response) {
//response - это то, что выдаст сервер на такой пост
//запрос, следовательно тут должен быть скрипт вставляющий
//ответы в форму, это делается так:
//$("#textfield3").val("часть ответа");
$("#big_form").fadeIn(1000);//затем отображаем форму
}
);
} else {
$.post (
url, {
textfield1_name: $("#textfield2").val()
}, function(response) {
//аналогично
}
);
}
});
});
</script>
</body>
ПС обратите внимание, что для избежания проблем все элементы должны иметь разные id, в рамках целой страницы, а не одной формы. Плюс, наверно радио-кнопки должны иметь одно имя, т.к. иначе они могут быть нажаты вместе.
| 2023-08-17T01:27:04.277712 | https://example.com/article/4184 |
Cameron Diaz for “The Sweetest Thing”
After being critically lauded in Vanilla Sky, beautiful and luminous Cameron Diaz is back on screen in familiar territory, starring I the sometimes gross-=out screwball romantic comedy, The Sweetest Thing. And as she confides to Paul Fischer, she is having a ball.
Cameron Diaz could think of better things to do some 48 hours after having been a presenter at the Oscars. Occasionally yawning, the pretty Hollywood star laughingly admits to “wondering what I’m doing at this junket” but “schedules are crazy so you just have to grin and bear it.” This time around, Diaz is in a film for the fun of it, an irreverent, often outrageous romantic comedy, The Sweetest Thing, a film that will prompt comparisons to Something about Mary. “No, I just choose, chose it because it was really far for me and I figured I’d take a challenge. Why not”, she offers sarcastically. “I don’t think you do these kinds of movies unless you get it, you know? So yeah I just did it because I wanted to have some fun and I think it’s funny.” Paired with Christina Applegate and the scene-stealing Selma Blair, Diaz stars as sexy and bold Christina Walters who, after years of avoiding meaningful relationships with men, unexpectedly meets her perfect match (Thomas Jane) one night while hanging out with best girlfriends Courtney (Applegate) and Jane (Blair). When she finds out the next morning that he’s suddenly left town, she and Courtney set out to find him on a wild road trip, encountering a series of hilarious misadventures on their journey. Their search ultimately leads them to a surprising discovery and the realization that love is, after all, the sweetest thing.
As in Mary, Diaz has a chance to let her hair down in Sweetest Thing presenting that wacky side to her persona we know and love. “I love my job, so I just felt like it was time after doing a couple of films that were a little more dramatic and serious that I just wanted to have something fun.” Not that those other films WEREN’T fun, “but I just wanted to have fun on film in and basically be myself.” It appears that Hollywood is returning to the kind of frat humour exemplified in the eighties, and Diaz believes that it’s in the air. “I mean you look at what the Farrelly Brothers did and the can of worms they opened up. They did and for the first time such humour was really accepted by the masses. People were like: Oh, my God, I too can laugh at a mentally disabled person that punches somebody in the throat, because we weren’t making fun of those people, we were making fun of people who make fun of them so it was empowering in a way. I think it is in the air and people want to see that and you know we’re not doing anything mean or malicious in this movie after all.” While she admits that The Sweetest Thing has “gross-out elements” Diaz point out that “it has a heart and is soft around the edges.”
One of the ‘themes’ of The Sweetest Thing, is the notion that it is important to adhere to a set of rules when it comes to love. Diaz doesn’t necessarily stick to that in her personal life, she confesses. “I’ve heard a lot about the rules that men are from Mars and women are from Venus and that kind of stuff, but I haven’t gotten to that yet.” As for her own rules, Diaz is straightforward enough. “I think that the rules are no tricks, honesty, communication, treat people the way you want to be treated and unconditional love.” As to whether Cameron follows her own rules, she laughingly confesses that “I try to, you know but rules are made to be broken.”
Diaz remains cagy when discussing her views on dating. Asked whether she has the same fear of commitment as her latest character, the actress begins looking at the trim on the door before begrudgingly responding. “I’m not afraid of commitment. I am a commitment person and commit to everything I’m doing. I’m hopelessly loyal.” she says, half-smilingly.
Even when she is unexcited about doing press, Diaz remains guarded but chirpy. Talk to anyone about working with Cameron and they all say that she is consistently happy and smiling. “I think that’s my nature and it’s also the way I was raised. My mom is the nicest person on the face of the earth, who treats everybody the same and my father is the funniest man who just has the greatest sense of humor and is completely twisted.” This explains where her twisted sense of humour comes from and what accounts to her keeping her life real. As big a star as Diaz is, she still manages to remain grounded.
“I think you are who you are, this is who I’ve always been and I don’t really know how to think differently. I’m sure that I could train myself to do so and there are things that I am changing and working on.” Not that she knows what, exactly. “You never know how other people perceive you. so it’s nice to hear kind things about yourself, but basically it’s just who I am and it’s the same thing as going: Can I afford this dress or should I pay the rent? Oh, I can’t pay the rent even if I buy this dress! Dah! So it’s that mentality that you grow up, so what you are given as a child always remains with you.”
Yet Diaz has also learned to keep her private life ferociously private, and to achieve that, she laughingly confesses, “I just say no thank you and THEN I say ‘get the fuck out of my face’. I handle the situation whatever way it needs to be handled to maintain what is important to me.” Not necessarily going out in disguise. “The disguise thing is really funny because if you get found out it’s so embarrassing”, she laughingly admits.
Diaz has joined the exclusive $20m club and is expected to be paid that salary for Charlie’s Angels 2, which is her next project. “We start training in June and then in August we start to shoot” is all that she’ll say on that project. There’s also that long-awaited Gangs of New York, whose release is being constantly moved. “I know that there’s a rumor that they’re holding the movie because it’s no good, but I thought it was because it was so good and they’re holding it for Oscar consideration at the end of the year.” | 2023-11-24T01:27:04.277712 | https://example.com/article/6059 |
Outside the courthouse where the trial of accused Boston Marathon bomber Dzhokhar Tsarnaev is slowly getting under way, one woman stands a lonely vigil. Her name is Karin Friedemann, and she’s Tsarnaev’s number one fan. Her devotion to the young man she calls “Jahar, the kid” led to a well publicized skirmish last December with one of the victims of the bomb blasts.
She describes herself as “insignificant” in the eyes of the media. And she almost certainly is. But her attitude regarding Muslim terror is not insignificant. In fact, it’s alarmingly popular among the conspiracy fringe.
I set off to find out what makes Friedemann (who also goes by the name Maria Hussain) tick. I asked her why she would devote her time to defending Tsarnaev. She was more than willing to share.
Friedemann: As I told reporters, I am advocating for a fair trial for the kid. Bill of Rights has to apply to the least of us, or else it doesn”t apply to any of us. So far, no evidence has been revealed to the public, so we have to assume he’s innocent, or in any case we have the right to know the truth of what happened because it’s obvious the media and government are making up stories.
I”ve seen this before: people with an ideological agenda cribbing the language of the Innocence Project. “We just want to make sure everyone gets a fair trial.” Great, fine. Who can disagree with that? But then I quoted one of Friedemann’s own blog posts back to her:
Cole: “Jahar seems resigned as a noble Chechen would be, to the fate of Allah.”
That’s about as non-objective a statement as I”ve ever read. Many, many people in the U.S. fight for the rights of the wrongly accused, but you”d never catch them making such a statement. May I ask what your particular bias is? Is it religious? Is it “conspiratorial?” Or do you just like this kid on a basis more personal than political?
Getting ideologues to spout about their bias is as easy as getting a monkey to fling poo.
“If Carto knew one thing, it’s that the people who use the word “sheeple” are themselves the sheeple-iest people there are.”
Friedemann: His family has told supporters that he would rather die than plead guilty to a crime he did not commit, and I believe that this kind of level of personal integrity is part of being a real Muslim, especially in the Chechen interpretation of it.
I have been following FBI railroading of Muslims for over a decade, so I believe it’s more than probable that he is either innocent or else there is FBI involvement. My emotional involvement in the case is, I guess, not only because it’s local but because a whole entire family has grown around it. Every family that has lost a son has now new connections with the other families and their supporters. It’s a very exciting and vibrant community to support prisoners in general, but in this case it’s all live on Twitter so there are so many very young people waking up to the fact that governments lie. For most of them it was a coming of age.
So I had to ask:
Cole: Have you ever encountered a case in which a Muslim, of free will and not FBI or CIA backed, has killed people?
Friedemann: I have not come across it in this country. Muslims generally come here for the freedom. If there is proof of his involvement in the bombing (other than a photo of him on a cell phone) then my next question would be, what is the bigger picture? His brother had been approached by the FBI to become an informant. Traditionally, if you refuse, they destroy your life. This could be that.
And now it gets fun:
Cole: But isn”t there an incompatibility to, on the one hand, the idea that the U.S. government attacks, torments, provokes, and oppresses Muslims”and to then claim, on the other hand, that Muslims never get angry enough to attack back? If it’s true that no Muslim has ever killed of his/her own free will, then isn”t it the logical extension that we needn”t fear repercussions from our policies in the Muslim world? If, for whatever reason (religious, genetic, upbringing, etc.) Muslims can”t murder, then where is the risk to the U.S. when it comes to pursuing a foreign policy of intervention and aggression? Heck, it seems to me that taking the position that Muslims never kill only encourages the type of U.S. foreign and domestic policies you probably despise. I mean, what do we have to fear, right?
Friedemann: Well, do you know of any Muslim that committed a crime?
Cole: I”m asking a theoretical question, Karin. I”ve never known a Hindu who had measles, but all logic and science point to the fact that a Hindu CAN get measles, like any other human. If someone were to argue that a Hindu can”t get measles, my own limited scope of personal, practical experience would be meaningless. Rather, it would be up to the person making the claim to demonstrate why Hindus can”t or don”t get measles. Therefore, when you argue that Muslims don”t kill, the responsibility is on you to explain why. Is it the faith? Is it genetic? Is it their upbringing? Is it some other factor?
Friedemann: I am aware that there is a lot of fighting going on that involves Muslims overseas, but in the USA, I have been following most of these cases very closely, and I have yet to see any act of violence that was successfully perpetrated by a Muslim immigrant, and in almost every case the FBI was involved.
Homeland Security/FBI is to Muslims what the Nazi Gestapo was to Jews. They generally get imprisoned for “thinking about” doing a crime or having a strong opinion about politics, or fund-raising for charities.
Well, there was that one guy who was a military veteran who shot a bunch of soldiers, but he was probably having PTSD and freaked out.
Regarding the Boston bombing suspects, there simply was no motive, no suspicious behavior, and no bomb making materials found. They loved this country and had a lot of friends. They were not mentally deranged. The only organization they had ever been involved with was the FBI, which had been pressuring Tamerlan to become an informant. In many cases, after a Muslim refuses to work for the FBI, they retaliate by destroying their lives. It happens again and again. That’s why it’s wisest to be skeptical.
I”ll be the first to admit, I was having fun at this point. | 2024-07-09T01:27:04.277712 | https://example.com/article/7523 |
Transcutaneous drug delivery by liposomes using fractional laser technology.
Transdermal delivery of hydrophilic peptides remains a challenge due to their poor cellular uptake and transdermal penetration. We hypothesize that combination of a CO2 fractional laser to enhance percutaneous absorption and liposomes as transdermal carriers would improve skin penetration of hydrophilic drugs. NA. Liposomes were prepared using membrane fusion lipid dioleoylphosphatidylethanolamine, and used to deliver 5-carboxyfluorescein (CF) and fluorescein isothiocyanate-conjugated ovalbumin (OVA-FITC) as model hydrophilic peptide drugs. Liposome size was estimated by dynamic light scattering. Liposome uptake into murine macrophage cells and penetration or permeation into Yucatan micropig skin after irradiation by CO2 fractional laser at varying energy levels (laser power and exposure duration) were investigated using Franz cell and fluorescence microscopy. Oxidative damage to the irradiated mouse skin was assessed by electron spin resonance. Size of CF and OVA-FITC encapsulated liposomes was 324 ± 75 nm. Cellular uptake of OVA-FITC delivered by liposomes was 10-fold higher (1,370 relative fluorescence units, RFU) than delivered in solution form (130 RFU). Fractional laser irradiation increased skin permeation rate of CF liposomes (0-10%) and OVA-FITC liposomes (4-40%) in a dose-dependent manner. Although peeling off the stratum corneum facilitated CF liposome penetration at low energy levels (2.69-3.29 J/cm2 ; 10-20 W for 500 μs), drug permeation was similar (7-8%) in peeled or untreated skin at higher laser energy levels (6.06 J/cm2 ; 20 W for 1,500 μs). FITC penetrated deeper in the skin after laser irradiation. However, OH, O2-, and VC reactive oxygen species were generated upon irradiation of the skin with a fractional CO2 laser. Increasing laser power and irradiation, time increased liposome uptake by cells and penetration of peptide drugs across the skin in a dose-dependent manner. High-energy CO2 fractional laser overcomes the rate-limiting barrier function of the stratum corneum. Further investigations are required to establish the safety and efficacy of fractional laser-irradiation assisted delivery of liposome-encapsulated drugs as a transcutaneous drug delivery system. Lasers Surg. Med. 49:525-532, 2017. © 2016 Wiley Periodicals, Inc. | 2024-07-19T01:27:04.277712 | https://example.com/article/5971 |
Q:
Editing Data in an XLS with PHP then importing into mySQL
I am trying to import an XLS file into PHP, where I can then edit the information and import it into mySQL. I have never done anything related to this, so I am having a hard time grasping how to approach it.
I have looked at a few open source projects:
PHP Excel Reader
ExcelRead
PHPExcel
None of these options perfectly fit what I want to do or maybe I just haven't gone deep enough into the documentation.
There are some things that needed to be taken into consideration. The XLS file cannot be converted into any other file format. This is being made for ease-of-access for nontechnical users. The XLS file is a report generated on another website that will have the same format (columns) every time.
For example, every XLS file with have the same amount of columns (this would be A1):
*ID |Email |First Name |Last Name |Paid |Active |State |Country|*
But, there are more columns in the XLS file than what is going to be imported into the DB.
For example, the rows that are being imported (this would be A1):
*ID |Email |First Name |Last Name |Country*
I know one of two ways to do edit the data would be A. Use something like PHPExcel to read in the data, edit it, then send it to the DB or B. Use something like PHPExcel to convert the XLS to CSV, do a raw import into a temp table, edit the data, and insert it into the old table.
I have read a lot of the PHPExcel documentation but, it doesn't have anything on importing into a database and I don't really even know where to start with editing the XLS before or after importing.
I have googled a lot of keywords and mostly found results on how to read/write/preview XLS. I am looking for advice on the best way of doing all of these things in the least and simplest steps.
A:
See this article on using PHP-ExcelReader, in particular the short section titled "Turning the Tables".
Any solution you have will end up looking like this:
Read a row from the XLS (requires an XLS reader)
Modify the data from the row as needed for your database.
Insert modified data into the database.
You seem to have this fixation on "Editing the data". This is just PHP--you get a value from the XLS reader, modify it with PHP code, then insert into the database. There's no intermediate file, you don't modify the XLS--it's just PHP.
This is a super-simple, untested example of the inner loop of the program you need to write. This is just to illustrate the general pattern.
$colsYouWant = array(1,2,3,4,8);
$sql = 'INSERT INTO data (id, email, fname, lname, country) VALUES (?,?,?,?,?)';
$stmt = $pdo->prepare($sql);
$sheet = $excel->sheets[0];
// the excel reader seems to index by 1 instead of 0: be careful!
for ($rowindex=2; $rowindex <= $sheet['numRows']; $rowindex++) {
$xlsRow = $sheet['cells'][$rowindex];
$row = array();
foreach ($colsYouWant as $colindex) {
$row[] = $xlsRow[$colindex];
}
// now let's "edit the row"
// trim all strings
$row = array_map('trim', $row);
// convert id to an integer
$row[0] = (int) $row[0];
// capitalize first and last name
// (use mb_* functions if non-ascii--I don't know spreadsheet's charset)
$row[2] = ucfirst(strtolower($row[2]));
$row[3] = ucfirst(strtolower($row[3]));
// do whatever other normalization you want to $row
// Insert into db:
$stmt->execute($row);
}
| 2023-09-10T01:27:04.277712 | https://example.com/article/3505 |
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Pricing
Algorithm usage is calculated in Algorithmia Credits. The current exchange rate for purchasing new credits is 10,000 credits to $1 USD. This was chosen to translate into 1 credit = 1 second of compute time.
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All algorithms in the marketplace are charged a fee of 1 credit per second (1cr/sec) of execution time on a single dedicated node. The execution time is calculated from the start of the algorithm execution until the algorithm returns.
In addition to the execution charge, algorithm developers may charge a royalty on each algorithm call. This cost-per-call royalty is associated with a specific version of the algorithm and will remain fixed indefinitely. This ability to apply royalties to an algorithm is to reflect the fact that the value of an algorithm is more than just the seconds of computation is uses and is up to each algorithm developer to set.
When an algorithm developer releases a new minor or major version of the algorithm, they have the option to include a pricing change. Make sure to include the version in your algorithm call to ensure a consistent experience.
Algorithms that call other algorithms
Some algorithms build upon other algorithms to create a new service or tool. While this is a powerful way of leveraging the value of multiple algorithms and parallelizing work across the Algorithmia Cluster, such algorithms may incur additional usage costs.
When calling into an algorithm that uses another algorithm internally, you may encounter an additional usage cost at the same 1cr/sec of execution time per core. Additionally, you may incur additional royalty costs if the associated algorithm also charges a royalty. If you are unsure, you can check if the algorithm you are using has the permission set to call into other algorithms as well as the usage history in your account profile. There you will be able to see all charges from algorithm calls. | 2023-11-19T01:27:04.277712 | https://example.com/article/5464 |
(Newser) - Good Samaritan takes a friend to chemo: check. Good Samaritan drives a fellow churchgoer home: check. Good Samaritan arrested and jailed for having crystal meth in his car that turned out to be flakes from a doughnut: Wait, what? This all happened in one day to Daniel Rushing in Orlando in December 2015, and NPR reports the 65-year-old now has a $37,500 settlement from the city after he sued them. Rushing was leaving a 7-Eleven (one being monitored by cops for drug activity, per the Orlando Sentinel) with his church friend when he was pulled over for speeding and another minor infraction; the police officer noticed he had a concealed-weapons permit, confirmed he had a pistol on him, and asked him to step out of the car. He agreed to let his car be searched, and when officers spotted crystals on the floor and tested them, they came up positive for methamphetamine.
"I've never even smoked a cigarette!" he told cops, explaining it was just Krispy Kreme residue, but he was arrested on charges of meth possession while armed and thrown in jail, where he sat for 10 hours before making bail. NPR reports that the cheap drug-testing kits that law enforcement rely on in the field are often inaccurate: A 2016 ProPublica-New York Times probe found false positives often emerge from these kits, with 21% of evidence wrongly determined by Florida cops to be meth. The results of these kits can be marred by everything from weather to human error. In Rushing's case, the cops weren't trained correctly in using the kits, per WHAS. Rushing has no hard feelings and says his goal now is to get his arrest wiped: He's trying to get security work and having a hard time due to his record. | 2023-12-29T01:27:04.277712 | https://example.com/article/8586 |
Imprimi potest
Imprimi potest or imprimi permittitur (Latin for "it can be printed") is a declaration by a major superior of a Roman Catholic religious institute that writings on questions of religion or morals by a member of the institute may be printed. Superiors make such declarations only after censors charged with examining the writings have granted the nihil obstat, a declaration of no objection. Final approval can then be given through the imprimatur ("let it be printed") of the author's bishop or of the bishop of the place of publication.
See also
Index Librorum Prohibitorum
References
External links
Code of Canon Law, The Means of Social Communication and Books in Particular (canons 822-832)
Category:Catholic theology and doctrine
Category:Latin religious words and phrases
Category:Censorship in Christianity
Category:Catholic Church legal terminology
Category:Canon law of religious | 2024-02-26T01:27:04.277712 | https://example.com/article/1613 |
1000 People Fall Ill After "Mud Day" Event in France
The French equivalent of popular sporting event Tough Mudder, called 'Mud Day' has caused unexpected illness with more than 1,000 runners suffering from norovirus following the event. The Mud Day race forces participants to crawl through various obstacles submerged in mud over the course of 8 miles.
It is believed that the illness was contracted from the mud at the event held near Nice as it may have been contaminated with animal faeces. On the day of the event, many runners allegedly complained about the smell of manure on the track. The following day, around 30 people were suffering from vomiting and diarrhoea however this figure skyrocketed in the following days to roughly 1000 participants.
The health agency in the region, PACA has said investigations were underway to determine what caused the outbreak, after the alarming number of complaints and at least one hospitalisation for the illness.
Today at Unlock the Law we look at whether the participants could make a personal injury claim against the organisers for contracting the virus.
Norovirus Compensation Claims
It is common for people to make a norovirus compensation claim after they have contracted the illness on holiday - especially if they have been on a cruise. Norovirus is highly contagious and can spread quickly if not properly contained especially in enclosed areas such as hotels and cruise ships. The virus causes severe sickness and diarrhoea which can sometimes result in hospitalisation.
Can I make a claim if I become sick on holiday?
There are a number of legal provisions designed to protect you if you fall ill on holiday as a result of another party's negligence.
If you booked your holiday through a tour operator based in the UK, most aspects of your holiday will be covered by The Package Travel, Package Holidays and Package Tours Regulations 1992. These regulations mean that the tour operator you booked with is responsible for all the different parts that make up your holiday - including your food, transport and accommodation. This makes it easier for you to make a claim as it is UK law that will apply.
In order to make a claim under the Package Holidays Regulations 1992, you must be able to prove that the tour operator displayed lack of reasonable care and skill in supplying your holiday. This could mean that they did not check the level of health and safety of the resort, or make note of any recent outbreaks of illness. The expected standard however will be considered in relation to the reasonable standard of the country where the accident happened.
How much could i claim for an illness oN holiday?
The amount of compensation you could be awarded will depend on the specific details of you case and the nature of your illness or injury.
For example, if you contracted mild food poisoning whilst on holiday where you experience stomach pain, vomiting and diarrhoea which last for several days, these cases generally settle for between £700 and £3,000.
However, with more severe case of food poisoning which leads to severe toxicosis causing serious pain, vomiting, diarrhoea and fever, which requires admission to hospital may cause serious and continuing conditions such as irritable bowel syndrome. This could have a significant impact on your life and ability and thus would attract a much higher award, even up to around £40,000. | 2024-04-18T01:27:04.277712 | https://example.com/article/5227 |
Programming. Electronics. Open-source. Pseudo-random opinions.
I spent much of this past weekend cleaning and re-organizing a rather daunting collection of stuff in my home office. This process revealed the small gray toolbox that my dad gave me when I was eight or nine years old. The back of the box has a taped-on yellow sticky note that says “Jeff’s Electronics Box” with four components in the corners: an electrolytic capacitor, a ceramic disc capacitor, a resistor with perfectly bent leads, and one AA battery. (This was long before I had any knowledge of or reason to work with surface-mount parts.) It occurred to me when I saw the sticky note that I have come full-circle through a pretty interesting career path.
The Beginning: Amateur Engineer
I remember “electronics” being the first thing that I wanted to do as a hobby and, possibly, as a career. Of course, I had no idea what such a career would entail at the time. Heck, even if I had known what it was like then, the industry has evolved so rapidly that my mental picture would have been completely inaccurate by the time I actually entered the field.
Nevertheless, I remember clearly taking that toolbox full of wires and components and tools to a mid-week “career night” event at an AWANA club that I attended at the time. In fact, I believe that event necessitated the label. Otherwise, the plain toolbox would not have indicated anything significant about my potential career choice. I really wanted to paint the right picture to other attendees.
I developed my interest further between the ages of 10 and 12 building some excellent Graymark kits, including a fun programmable robot that was probably the most complicated kit I had done at the time. My dad got me the version of the kit that included the practice foam breadboard, which allowed you to build the entire circuit in a large-scale elevated form for easy troubleshooting. It was like a debug mode build for hardware, before the days of ubiquitous per-component breakout boards. The only trouble was that it required soldering everything once, then unsoldering or cutting long leads before re-soldering in the final PCB location. I had little interest in doing all of that extra work just to prove to myself that the circuit would behave as expected, and I think I opted to skip a lot of it.
My interest in electronics morphed into a desire to become an amateur radio operator around the time I turned 12, which surprised my parents because I have always been a very quiet person. To this day, I’m not sure why I chose to pick up a hobby that is literally built around communication, but I enjoyed myself and learned a great deal in the process. I let that fall by the wayside after a few years due to other interests.
Step 2: Software Developer
My focus shifted more towards software design and network administration in my early teens, including some adventures with various Linux distributions (before you could get up and running in 10 minutes with the latest Ubuntu LiveCD) and building an 802.11b wireless network in our home to share our EarthLink DSL connection (before you could go to the nearest big-box retail store and buy a router). Ah, those were the days.
I earned my first tech-sector dollars in my mid-teens working for a friend on Goldmine database customizations, a gig that lasted about six months or so before we went our separate ways. A while after this, I slowly built up a personal tech support clientele through word-of-mouth. I even registered a sole proprietorship for myself locally as “JR Network Solutions” (constantly interpreted as “Jr.” instead, much to my chagrin). We got a second landline added to our house for my business number, although the only calls I ever got were solicitations. I still remember talking for an hour to a Verio rep trying to sell me web hosting at ridiculously high prices. (I didn’t sign up for anything.)
My software development career started in earnest after I built a non-trivial ASP-powered dynamic calendar script for a church website, and ended up on the radar of a couple of guys who owned an outsourced IT support company that also dabbled in web design for some of their clients, including the church. The calendar script impressed them enough that they asked if I wanted to do some more in-depth work for them on a project they had going on, and I happily agreed.
I spent a full nine years with that company, delaying my college education by one semester to get started. I continued through five years of classes, my wedding, and then moving across the country to Virginia. They provided a stable but flexible position, allowing me to work around my widely varying class schedules and then remotely from Virginia. My main project was an in-house business management system built in PHP and MySQL, but I also managed the server that project was hosted on, built a distributed asset monitoring system, integrated the management system with their accounting service, built a Windows application for easier scheduling, and even manned the phones for a short time.
Step 3: Electronics Hobbyist
In mid-2011, I started working on the Keyglove project in my spare time after discovering the wonderful world of Arduino. The concept of using simple C++ functions to make an inexpensive but flexible bit of hardware actually do something in the physical world excited me to no end, and it compelled me to begin my adventure back towards hardware. I had tried playing around with PIC16F84 microcontrollers about 10 years prior, but I never managed to achieve the entry-level “blink an LED” project with that platform. The programming interface hadn’t evolved to the level of simplicity that the Arduino provided in 2011.
The Keyglove project required a wireless interface to do what I needed, so I began exploring Bluetooth connectivity options. I tried one module from Broadcom that I literally desoldered from a cheap wireless keyboard and mounted onto a simple custom breakout board that I commissioned from Adam and Matthew over at Wayne and Layne. I managed to make it talk–just barely–but the module was otherwise opaque and ultimately not useful. After further investigation, I finally settled on the comprehensive WT12 module from Bluegiga. With some tips from Adam and Matthew and a shiny new CadSoft EAGLE installation, I churned out my own WT12 module breakout PCB design and had it fabricated by Laen over at OSH Park.
Thanks in no small part to the near plug-and-play experience that Bluegiga’s WT12 module provided, the board worked on the first try, and I was off and running. I wrote a host-side iWRAP firmware control library to work with the WT12 in order to assist with Keyglove integration, and then expanded my breakout line to include a few more of Bluegiga’s modules after many people asked for them. My yak-shaving design project began to grow into a real business.
Step 4: Applications Engineer
I remained in my web design position throughout all of this Arduino experimentation and fledgling hardware design work. However, that changed in mid-2012 when Bluegiga offered me a position doing apps engineering for them. All of my efforts with their products put me on their radar, and they essentially wanted to pay me to do the same things I had done as a hobby. Not a bad deal! The semi-yearly trips to headquarters in Finland provided a fun bonus, too.
My tenure at Bluegiga lasted from 2012 to 2015, through their acquisition by Silicon Labs near the beginning of 2015. Going from a web design and network administration role for an IT company into an applications engineering role for a wireless module company entailed a pretty drastic adjustment for day-to-day activity. However, I enjoyed the challenges and learned an enormous amount by directly supporting customers. There’s nothing like a customer to highlight all of the unanticipated ways to use your product.
Step 5: Firmware Engineer
Answering customer support tickets day after day after week after month after year starts to get old after a while. Despite management’s efforts to let me work on other activities, the support volume wouldn’t allow it on a regular basis. I became more and more eager to get away from “whack-a-mole” ticket management, preferring a more programming-oriented position where I could work on one large project for an extended time.
Cypress Semiconductor offered me such a role as a principal firmware engineer in late 2015, and I accepted. I got to spend the next two years on a long-term software/firmware design project. I even got to define and build the whole thing from the ground up, which is a dream for many engineers. In addition to honing my coding ability, I learned about project management, in-depth test definitions, team code reviews, business auditing processes, and many things that are hard to put into words. I even got to write a detailed user guide for the project. (I blame my appreciation and proclivity for writing on my parents and high school English teacher.)
My time at Cypress allowed for strong growth in some important professional areas, and helped me recover my coding creativity after a bit of a dry spell doing customer support. I thoroughly enjoyed my years there, the work I did, and the team I got to work with. Like my Bluegiga/Silicon Labs stint, I was satisfied (or better!) and not looking for other opportunities. However, that didn’t stop other opportunities from showing up unbidden.
Full Circle: Hardware Engineer
In October of this year, after two years at Cypress, I decided to make yet another transition when I received an offer from BioMech, a smaller, more local company innovating in the motion analytics space. My official role is now Director of Hardware Engineering, and I’m responsible for a few different designs so far. It’s not just the schematic and board designs, in fact, but also the firmware that powers them. My tasks challenge me in all of the most personally satisfying ways. The work is actually very similar to what I did with the Keyglove project for fun in my free time. I just have more of it to do.
I’m now back where I started, but with two decades of personal development and technological evolution on top of it. I get to “do electronics,” as eight-year-old me might have put it, and it usually feels like fun. I’m in a great spot and excited for what the next few years hold.
My dad gets much of the credit for exposing me early to the things that put me on this track. I can trace a pretty clear line back to those formative experiences, and I wouldn’t be in this spot without them. (Not that my mom was less influential, since she homeschooled my brothers and me through most of high school; while she didn’t focus on electronics, she did provide the educational framework for darn near everything I learned.)
Now I have two kids of my own, and I actively look for ways to let them explore new activities. At only six months old, Lucas is still a bit young for anything even remotely career-specific. But Julia, now almost three, enjoys playing with electronics components and jumper wires and solderless breadboards for fun. She even calls downstairs to Mommy that she’s “working on my project!” when we’re told that dinner is ready. Looks like I have to un-set that precedent.
Neither of my kids may choose anything remotely similar to what I did for my career, and that’s fine. Regardless, I hope that they will always feel enabled and encouraged to pursue the things that excite them.
A Child’s Electronics Toolbox was last modified: November 21st, 2017 by Jeff Rowberg
It’s January 1st, 2015, and you know what that means: I have a sudden urge to write. I don’t know exactly why this always happens, but it’s pretty predictable. A few big things happened this year, or at least began happening. I’ll go through them one by one.
in the last many months, I’ve gone full-bore on my Keyglove project right up until exhibiting it at Open Hardware Summit and Maker Faire in New York right at the end of September, followed immediately by an unplanned but very fortuitous job change to Bluegiga Technologies, which involved a week in Atlanta, then two weeks in Finland, then another week in Chicago, all in October. Wow. | 2024-05-27T01:27:04.277712 | https://example.com/article/3983 |
There are twin scoops today that suggest a new direction in the Mueller investigation. The AP broke the report that Mueller’s team interviewed Tom Barrack — who on top of being an actual billionaire (unlike Trump), one of his closest friends, and the guy who recommended he hire Paul Manafort, was his Inauguration Committee Chair — in December.
One of the people who spoke to AP said the questioning focused entirely on two officials from Trump’s campaign who have been indicted by Mueller: Trump’s former campaign chairman, Paul Manafort, and Manafort’s onetime deputy, Rick Gates. Gates agreed to plead guilty to federal conspiracy and false-statement charges in February and began cooperating with investigators. A second person with knowledge of the Barrack interview said the questioning was broader, including financial matters about the campaign, the transition and Trump’s inauguration in January 2017.
Rick Gates, who served as Deputy Chair of the inauguration, flipped in late February.
In early April, the press reported that multiple oligarchs were being questioned about inauguration donations by Mueller.
Investigators are asking whether wealthy Russians illegally funneled cash donations directly or indirectly into Donald Trump’s presidential campaign and inauguration.
Yesterday, NYT confirmed that the oligarch stopped in NY was Viktor Vekselberg. In addition to the inauguration, Vekselberg attended the RT dinner attended by Mike Flynn, and ran a corrupt Cypriot bank with Wilbur Ross.
Federal agents working with Mr. Mueller stopped Mr. Vekselberg, a billionaire businessman, at a New York-area airport this year, searched his electronic devices and questioned him, according to people familiar with the matter. They confronted him after he stepped off a private plane about two months ago, according to one of the people. [snip] Vekselberg also attended a December 2015 dinner in Russia where Michael T. Flynn, Mr. Trump’s first national security adviser, was also among the guests and sat beside Mr. Putin. The dinner was hosted by RT, the English-language television news network financed by the Kremlin. [snip] Another potential area of interest for Mr. Mueller is Mr. Vekselberg’s business in Cyprus, the Mediterranean nation considered a magnet for Russian money. Mr. Vekselberg has controlled a company that has been the largest single shareholder in the Bank of Cyprus. Around the same time that Mr. Vekselberg was investing in the bank, Mr. Trump’s future commerce secretary, Wilbur L. Ross, was its vice chairman.
Remember, Barrack raised double money for the inauguration than a normal take. And as of earlier this year, Trump still hadn’t donated the money, as promised.
In late September, the committee announced that it had donated $3 million to multiple groups involved in hurricane relief efforts in the Gulf Coast, Florida and the Caribbean. An undetermined amount of funds were allocated to redecorating the White House and Vice President Mike Pence’s home in Washington, rather than charitable efforts. Barrack, chairman of the inaugural committee, said details about the committee’s donations to charity would be released in November. Yet the deadline passed without further financial information being disclosed. A spokesman for Barrack declined to comment on the report’s delay or allegations that the committee mismanaged funds under his leadership.
So that money went … somewhere.
Update: My use of “honing” instead of “homing” has set off quite the debate. I’ve changed it to move discussion back to the topic at hand. Thanks to all who weighed in. | 2024-02-25T01:27:04.277712 | https://example.com/article/1398 |
Oral health is critically important to children's overall health and represents the largest unmet health need for children. With the Surgeon General's 2000 report on oral health, there has been a growing awareness of the need to increase access to services and address racial/ethnic disparities in both service use and oral health status. Despite states' considerable efforts to address oral health and a few recent reports attempting to review selected state policies, little is known about the degree to which state policies affect children's oral health. The goal of the proposed study is to assess whether variations in state policies are related to children's oral health conditions and care utilization for children ages 1-17 years. The specific aims include: 1) To examine variations in state oral health policies in 2006. 2) To examine whether state oral health policies in 2006 are associated with state-level children's oral health and dental care utilization in 2007. 3)To examine whether state oral health policies in 2006 have an independent effect on children's oral health in 2007 after adjusting for individual child, family and state characteristics. Data for the proposed study come from: the 2007 National Survey of Children's Health (NSCH), the 2007 American Community Survey (ACS) conducted by the US Census, and from 2006 policy data compiled by the American Dental Association (ADA), the Children's Dental Health Project (CDHP), and the Association of State and Territorial Dental Directors (ASTDD) in collaboration with the Centers for Disease Control and Prevention (CDC). T-tests will be used to assess variations in the number and extent of state policies across states (Aim 1). Multivariable regression models will be constructed to consider relations between state policies with state- level oral health status and care use, conditioned on state characteristics (Aim 2). Multilevel regression models will be used to assess whether state policies have an independent effect on children's oral health after adjusting for individual child, family, and state characteristics. Age-specific policies will be examined for age subgroups (1-5, 6-11, and 12-17 years) (Aim 3). The proposed work will be the first study to link state policies to service use and children's oral health status, which supports NIDCR's Strategic Goal 1 (objective I-2: to increase the Institute's commitment to basic and applied research in the behavioral and social sciences) and Goal IV (objective IV-1: to identify the full range of factors that contribute to oral health inequality). Findings will inform prevention programs and policies that address children's oral health status and the emerging Healthy People 2020 oral health objectives. Our findings will also suggest whether selected provisions under Health Care Reform should be prioritized. | 2024-01-26T01:27:04.277712 | https://example.com/article/7152 |
MGL Ch. 140 Sec. 131C
Transporting of firearms in a vehicle
Section 131C. (a) No person carrying a loaded firearm under a Class A license issued under section 131 or 131F shall carry the same in a vehicle unless such firearm while carried therein is under the direct control of such person. Whoever violates the provisions of this subsection shall be punished by a fine of $500.
(b) No person carrying a firearm under a Class B license issued under section 131 or 131F shall possess the same in a vehicle unless such weapon is unloaded and contained within the locked trunk of such vehicle or in a locked case or other secure container. Whoever violates the provisions of this subsection shall be punished by a fine of $500.
(c) No person possessing a large capacity rifle or shotgun under a Class A or Class B license issued under section 131 or 131F shall possess the same in a vehicle unless such weapon is unloaded and contained within the locked trunk of such vehicle or in a locked case or other secure container. Whoever violates the provisions of this subsection shall be punished by a fine of not less than $500 nor more than $5,000.
(d) The provisions of this section shall not apply to (i) any officer, agent or employee of the commonwealth or any state or the United States; (ii) any member of the military or other service of any state or of the United States; (iii) any duly authorized law enforcement officer, agent or employee of any municipality of the commonwealth; provided, however, that any such person described in clauses (i) to (iii), inclusive, is authorized by a competent authority to carry or possess the weapon so carried or possessed and is acting within the scope of his duties.
(e) A conviction of a violation of this section shall be reported forthwith by the court or magistrate to the licensing authority who shall immediately revoke the card or license of the person so convicted. No new such card or license may be issued to any such person until one year after the date of revocation. | 2023-12-28T01:27:04.277712 | https://example.com/article/9320 |
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Carlos Molina del Rio is a Madrid-based games developer and founder of independent studio 89bits. After years of working at Telefonica creating mobile infrastructure for one of Spain’s most important telecom companies, he decided to start his own games and entertainment company to combine gaming and live sporting events with the mobile experience. Read about his experience in launching a new entertainment category in fantasy sports management.
Today, there is an unanswered question many mobile gaming developers are struggling to answer.
What makes a successful game?
When trying to feed the equation for a successful game, many developers and analysts simply accept the disparity between success and failure. We see, therefore it is – some games are just more popular than others and you don’t know what works until you test it.
'We help developers to battle the competitiveness of today’s mobile games market.'– Oliver ClarkTweet Me
Oliver Clark examined the benefits of using ID-based mobile data to find the right users during his Casual Connect Asia 2015 lecture. Oliver advises developers to “capture information that can lead you to make sensible decisions about targeting. Targeting is key.” For more, see the video below.
As big gamedev events are becoming quite rare in Kyiv, Ukraine, game developers themselves are organizing informal gatherings to still share experience and discuss their ongoing and/or fresh games. As for gamejams, Ukrainian devs have already got the taste of these, and just-for-fun projects become award-winning hits — think of Party Hard, for instance, who won the Critics’ Choice award at Casual Connect Europe 2015 Indie Showcase. So the CEO of a Kyiv-based studio of Gestalt Games, Andriy Tykhonchuk, and his wife Olena decided to organize a 48-hours gamedev challenge of INDIE|48 that took place in April 2015 at the G13 project studio.
“I came up with this idea after seeing a YouTube video of some Scandinavian devs doing something similar. I felt like participating in an event of this type too! But accidentally did too much and organized one. Why 48 hours? I think it’s standard time for this type of events. You cannot do much in one day, and 3 days is a lot”, Andriy explains.
The G13 project studio in Kyiv has become kinda home for over 40 developers for 48 hours
Of course he did some research before organizing INDIE|48, and discovered that no one in Ukraine is really doing this exact type of hackathon events, focused entirely on games. However, there are IT competitions like, for example, the Golden Byte contest, where there is a games nomination.
While Andriy carried the burden of all organizational work, his wife Olena helped a lot during the event itself. “We were doing this for the first time. We’re actually just a small indie company of 5 people”, he shares. “The hardest part was to find sponsors. Things are tight with this in our country.”
The hardest part was to find sponsors. Things are tight with this in our country.Tweet Me
Nevertheless, Unity Technologies and the “Liberation” NGO agreed to support the event for aspiring developers for this first time. “I really want to believe that INDIE|48 will become a tradition and gain support of big companies. While we’ll go on developing the indie gamedev hangout”, Andriy adds.
GestaltGames organized this event after not discovering any other games-focused hackathons in Ukraine.
Crocodile, Sleep, Sport
The task was to create a playable game within the 48-hours timeframe. No pre-made assets were allowed, except for sound — but this meant the team could not qualify for the Best Sound nomination.
Crocodile, Sleep, Sport — these were the keywords chosen by the judges, Tatem Games‘ CEO Igor Karev and Alexander Shtachenko from iLogos. The keywords needed to be incorporated in the game in whatever way the devs considered appropriate.
The countdown and the keywords were projected on the screen.
Day 1: Survivability Test
From the initial 19 teams who wanted to participate, 14 had actually arrived, and only 13 survived till Day 3. Most participants were from Kyiv, though some have made a long way from other Ukrainian cities specifically for the gamejam.
Andriy reminded the rules, announced the keywords — and started the countdown! The teams, who were at first sitting at their tables like good schoolchildren at their first lesson, start brainstorming and sketching stuff, gradually moving to all coziest corners of the studio. The best time to walk around and just peek over the shoulder and overhear bits of creative discussions!
Brainstorming ideas wasn’t the easiest task, as well as crocodile, sleep and sport weren’t the easiest keywords.
This first stage seemed the most tense, since the keywords weren’t the easiest ones to implement and not all teams were happy with this choice.
The myth of game developers being “night owls” operating on buckets of coffee and energy drinks has been partly busted at INDIE|48. Surpsingly many teams chose the option of sleep over an allnighter. Nevertheless, those who felt better working at night were free to do so — a gamejam is not an army, so there were no limitations on sleep/work schedules. By nap time most of the teams already came up with some intriguing sketches — that, however, did not reveal their ideas completely.
Most teams had a basic concept by the end of Day 1.
Day 2: Implementation
Day 2 has been about pure work: initial ideas have been shaped, and needed to be brought to life. By this time the teams had already communicated with each other for a while, and chats became more frequent. The coffee machine-and-cookies area became the space of networking and sharing overall impressions. For some people the gamejam happened to be a test for balancing work and hobbies: one of the devs admitted that “7 days a week making games feels like too much”. What is more, for some participants INDIE|48 was the first time of dealing with games. In one of the teams the programmer was there for the sake of challenging himself in a gamejam, and he brought friends just to keep company — and one of the guys happened to be skilled in writing music and therefore useful.
Making games is both work and a hobby for many participants of the INDIE48 gamejam.
Day 3: The Variety of crocodiles, sports and dreams
On Day 3 you could already see drafts turning into actual games: the art became distinctive, and one could try to follow gameplay if they were shameless enough to peek over the devs’ shoulders for long.
As opposed to the popular belief that in Slavic countries 90% of work is done in the last 10% of time, there was no panic or rush even in the last minutes of the 48-hours gamemaking challenge.
As Andriy the organizer initially said, 48 hours was more or less enough for creating a playable product.
The crocodile happened to be the antagonist in the majority of the games, though some teams gave the reptile a chance to be the hero and not the villain.
Will at least someone make the crocodile a hero and not the villain?
The Empairish team presented a game called Of Crocs And Humans, where you play as an ex-sportsman with the hobby of collecting crocodiles’ eggs. Not an easy task, considering that sleepy female crocodiles attack the sportsman if he gets too noisy at night.
A retired sportsman who steals crocodile eggs as a hobby appears in the game Of Crocs And Humans by Empairish.Don’t make too much noise at night – female crocs are sleeping and will eat anyone who wakes them up.
They said – There Is No Team Name, and just called their team this way. And named their creation Yellow Bed: crocodiles here are haunting people in their sleep, and need to be destroyed with a saw. When the sleeper, that is — the player, loses the battle, everything ends with a yellow bed. Does this need an explanation why? 😀
If you don’t defeat the crocodiles in a nightmare, they’ll scare you enough for your bed to become yellow.The Yellow Bed game had a clear explanation of controls.
Finally, the poor crocodiles got some positive exposure! In Revolution Fist’s project CrocoRun a circus-show crocodile trained as a sportsman wants to escape. He gets this chance when the handler falls asleep, but then luck gets bad: the human wakes up while the crocodile tries to snatch the key. Playing as the crocodile, you need to chase the handler, and bite him 3 times to win the game.
In CrocoRun you play as a crocodile who uses his chance to escape a circus.The handler wakes up and runs away! Chase him and bite 3 times to win the game.
The creation of ZdarovaBanditu, with cute pixel graphics and made with GameMaker, was presented as The Bed. In this game the protagonist falls asleep in his room, and in a dream a witch asks him to help her get home, because a creepy creature gets in her way. Defeating it, you get the boxing gloves, that you’ll need to fight the final boss — a boxing crocodile.
Help the witch get home by fighting the evil creatures that are on her way in a game called The Bed by ZdarovaBanditu.The final boss is a boxing crocodile.
During the presentation part of the gamejam, Andriy Tykhonchuk asked the audience to choose their favorite by applauding, the one who gets the loudest support wins. But since this small gamedev hangout turned out to be supportive towards each other, and no one was left without their dose of appreciation, it wasn’t an easy task for Andriy and judges from Tatem Games and iLogos to define who got most. Eventually, the People’s Choice award was given to the Renegades team, the authors of Joe vs Crocodiles. Here you act as Joe the baseball player who needs to get home and save his sleeping son from crocodiles, since the kid is afraid of them. The fighting happens during a baseball match — shoot crocodiles with balls or just smash with the bat.
The Renegades team welcomed one of the members right there at INDIE|48, and managed to make a game playable on iPad, and anyone from the audience could try it on the tablet.
Joe is a baseball player who fights crocodiles because his son is afraid of them.Smash the crocodiles with the bat or shoot with the balls.
A company of university friends who names themselves AnyKey used the keywords in BloodyBet – in some country people enjoy betting on others who dare to walk on swamps around sleeping crocodiles. In this game you only see the protagonist’s two legs, and it is them you control, each one separately. Just don’t make waves — they wake the crocodiles up, and you end as their food. If you don’t — you get a drink as a reward for an accomplished level, and move on to the next one. Surprise! The drink makes your legs shaky, and the challenge gets harder.
Control the protagonist’s legs and don’t make waves as you walk between sleeping crocodiles- otherwise you lose the bet and the game!Someone just got eaten.
And these guys, the organizers say, could have won, but forgot to add sound. Anyway, the Best Gameplay and Best Idea awards went home with the Two Squares & Triangle team for CROCODIE. These devs said that their primary purpose at the gamejam was to create something fun. Their game of the “survival crocodile boating” genre, as they called it, features an abstract country’s national sport of crocodile-back riding. The animals need to eat in order not to fall asleep. They consume fish as they move along the river, and the “jockey” can knock flying birds down — and feed them to their crocodile as well. CROCODIE can be played both as single- and multiplayer: one gamer controls the “jockey”, the other one plays for the crocodile.
The genre is survival crocodile boating, as the developers explained.The multiplayer version of CROCODIE makes it possible to race together with a friend – one controls the “jockey”, the other one moves the crocodile.Need to kill some time? Move endlessly between sleeping crocodiles in a canoe, all this accompanied by an electronic tune.The Garinich Game team managed to create the game even despite numerous technical issues.
The Garinich Game team came all the way from the city of Cherkasy. They say there was only one person actually working on the game, while the other two were there just to make a team of three. Despite not having an artist and Unity crashing halfway the event, the guys decided to “make at least something”, which was presented as Disco Amazonka: an endless timekiller game with a catchy electronic tune, where you need to move a canoe carefully between some sleeping crocodiles.
The Best Idea winners, Rebel Dev Team, discovered their coolest artist wasn’t old enough to participate in INDIE|48 (all participants needed to be at least 18), so the art for their game Z.O.Z.H was made by another team member. And again, the crocodiles got some positive features here, These guys created a trippy world of drinkers and drug addicts, one of which is hanging upside down.
A good crocodile tries to bring some sports to the world of drinkers and drug addicts. The Z.O.Z.H abbreviation in Russian stands for “healthy way of living”
This is all a dream of a crocodile who wants to bring some sport to this crazy place. You can get help from a fat fairy who, as the authors say, obviously loves sports. Items are collected throughout the game, and in the end are used to assemble a device to escape the dream. As for the genre, the game is a platformer, but the world around you spins, adding some more physical challenge.
A fat fairy helps you create the device to escape this dream.
“A mix of all that can be played in one’s free time” was how WeAreGroot defined the genre of their game Y.A.I.G 48, which is a dream of a sleeping fat crocodile who wants to become fit. He walks around a dark gym trying to steal weight plates from barbels to bring home and work out there, and fights enemies trying to stop him.
A crocodile in this game is creeping around a dark gym in order to steal some equipment to work out at home.A relaxing level has been added to this game with an overall tense atmosphere.
Tap The Sheep game doesn’t have any reference to crocs, sleep or sport in the title, but the authors, a 3-programmers team of Drunk Elephant Games, proved this impression wrong! Their game is for people who need to calm down and fall asleep. Control the four legs of a crocodile heading towards his bed, and count sheep on your way. Better slowly, since the faster you walk, the more you wake up, while you shouldn’t.
You need to fall asleep while playing this game, it’s been designed for this purpose!
As well as you shouldn’t reach the bed: you need to be already asleep by this time. The developers said that for the crocodile they used inverse kinematics, not just animation. The game has no music, but the presentation was accompanied by the developers’ singing a popular lullaby from a kids’ TV show.
You can direct the crocodile into water instead of the bed – he will swim steering with his tail.
And Steel Midnight Finish chose Python to make the game of Caligo (“mist” in Latin), instead of the initially planned C++ that they eventually considered too complicated. The story is about a boy tortured by nightmares. His dad gives him a toy crocodile to scare bad things away in the realm of dreams. In addition to an uncommon programming decision, the game art isn’t traditionally cartoonish and bright, but on the contrary, gives some ambient and, as the devs explain, a surreal feel.
Ambient and surreal vibes instead of colorful cartoons made the Caligo game stand out.And again, the crocodile is a positive character here.
Cool Art + Catchy Sound = Winner
And the winner is… Diversido, a team from Kyiv with their game BillaBong, where you play as an aborigine kid trying to walk on a swamp not to wake up sleeping crocodiles. They became the absolute winners of the gamejam, also getting the awards for Best Art and Best Sound.
Creating a decent UI was one of Diversido’s key purposes.
Diversido’s product manager and developer Valerii Minenko created a catchy tune that the main character whistles as she walks among the reptiles: after the team presented their game, you could hear guys whistling that same tune for a while. Valerii shares more about BillaBong.
“You cannot do many things with a sleeping someone. We found just one – wake them up!”
“Every game is a combination of mechanics and setting, it’s a world where the player needs to do something. My formula of a good game is that gameplay and setting should perfectly fit each other. If we create a game about crocodiles — the player must not ask himself why it is exactly crocodiles but not puppies or, for example, Gummi Bears”, Valerii explains.
Since the keywords were “crocodile”, “sleep” and “sport”, Valerii and his colleague Anya started brainstorming around the idea of sleeping crocodiles and tried to make them an essential part of the gameplay. “You cannot do many things with a sleeping someone. We found just one – wake them up!”, he comments. This became the base of the gameplay — the crocodiles sleep and somebody wakes them up.
The idea of making something small but complete resulted in a game that won 3 awards.
“We focused on creating a small but complete project. We didn’t develop much of functionality, but tried to keep the quality of our work perfect. Also, we tried to add to the project not only basic gameplay, but necessary supporting functionality as well – like UI and sounds”.
“I think the biggest challenge was to plan our work in a way that if someone had a look at it, he wouldn’t feel like something is missing. I hope we managed this.”
The Diversido team were using Unity 5, since this is what they work with on a daily basis in their company of Diversido Mobile. Valerii adds that they still haven’t made many projects with the freshest version of Unity, so were also interested in playing with the new engine features.
INDIE|48 became a good teambuilding opportunity for the Diversido Mobile studio.
For their team the gamejam turned out an excellent teambuilding opportunity: much better than investigating bars together, Valerii says. “I feel that we have become closer during the event. Hope this will be useful for our future work. Also I now know what our performance is when we are working with passion. It is very high!”
Now I know what our performance is when we are working with passion.Tweet Me
Diversido haven’t yet decided what to do with the BillaBong game project conceived at INDIE|48. Valerii shared that they’re currently preparing a few projects for release and would rather focus on that. Nevertheless, BillaBong has been added to their website, and they show it to all their friends.
Seven Summits Studio is an award-winning independent game development company based out of Hyderabad, India. The studio was founded in 2013 by a group of passionate individuals who strive to create impactful experiences through video games.
Petite is an ambient experience that narrates a woman’s story while focusing on key incidents that happen in her life. Every level is a new situation, and each memory you unlock is a unique one, depending on the emotions you choose.
In recent years DFC Intelligence has focused on segmenting the diverse base of game consumer types. The most important trend that is emerging in the game market is the growth of consumers that play on multiple platforms. For example, almost all console players also play on PC to some extent. Increasingly both console and PC gamers are playing on mobile devices.
The following interview is provided by TechnologyAdvice, an Inc. 5000 company that connects buyers and sellers of business technology through meaningful relationships.
Gil Shoham, CEO of mobile advertising technology platform Supersonic, spoke with TechnologyAdvice host Clark Buckner about their recent Series B Funding, current trends in the mobile advertising space, and the role of big data.
Traplight Games worked on technology that would give a new kind of creative power to gamers and bring user-generated content to mobile devices in a way never seen before.
Talk about doing a 360. When Traplight Games started in 2010, they began by publishing their own in-house game The Hero. However, after that, they quickly turned into a full-time work-for-hire enterprise — working on projects for companies such as Redlynx, Supercell, and Tuokio.
Girls and Warplanes (Russian – Храброе Звено) is the 8th project of the Minsk-based studio of Neskinsoft. It all started from a small experiment in the genre of action. Even though the company has got some experience of creating dynamic games for the midcore audience, they admit they still have room for improvement. Their previous title, Беги, Вова, Беги (Run, Vova, Run) has been praised by the players, but, despite thousands of positive reviews, in terms of monetization the product was far from even covering the development expenses. “In order not to fall into the same trap again, we decided to take a sneak peek on the solutions of more successful colleagues from the Asian market”, Sergei Neskin, the CEO and co-founderof Neskinsoft explains. | 2024-01-12T01:27:04.277712 | https://example.com/article/1804 |
/* ====================================================================
* Copyright (c) 1999-2001 Carnegie Mellon University. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* This work was supported in part by funding from the Defense Advanced
* Research Projects Agency and the National Science Foundation of the
* United States of America, and the CMU Sphinx Speech Consortium.
*
* THIS SOFTWARE IS PROVIDED BY CARNEGIE MELLON UNIVERSITY ``AS IS'' AND
* ANY EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CARNEGIE MELLON UNIVERSITY
* NOR ITS EMPLOYEES BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* ====================================================================
*
*/
/*
* prim_type.h -- Primitive types; more machine-independent.
*
* **********************************************
* CMU ARPA Speech Project
*
* Copyright (c) 1999 Carnegie Mellon University.
* ALL RIGHTS RESERVED.
* **********************************************
*
* HISTORY
*
* 12-Mar-1999 M K Ravishankar (rkm@cs.cmu.edu) at Carnegie Mellon
* Added arraysize_t, point_t, fpoint_t.
*
* 01-Feb-1999 M K Ravishankar (rkm@cs.cmu.edu) at Carnegie Mellon
* Added anytype_t.
*
* 08-31-95 M K Ravishankar (rkm@cs.cmu.edu) at Carnegie Mellon
* Created.
*/
#ifndef _LIBUTIL_PRIM_TYPE_H_
#define _LIBUTIL_PRIM_TYPE_H_
typedef int int32;
typedef short int16;
typedef char int8;
typedef unsigned int uint32;
typedef unsigned short uint16;
typedef unsigned char uint8;
typedef float float32;
typedef double float64;
typedef union anytype_s {
void *ptr; /* User defined data types at this ptr */
int32 int32;
uint32 uint32;
float32 float32;
float64 float64;
} anytype_t;
/* Useful constants */
#define MAX_INT32 ((int32) 0x7fffffff)
#define MAX_INT16 ((int16) 0x00007fff)
#define MAX_INT8 ((int8) 0x0000007f)
#define MAX_NEG_INT32 ((int32) 0x80000000)
#define MAX_NEG_INT16 ((int16) 0xffff8000)
#define MAX_NEG_INT8 ((int8) 0xffffff80)
#define MAX_UINT32 ((uint32) 0xffffffff)
#define MAX_UINT16 ((uint16) 0x0000ffff)
#define MAX_UINT8 ((uint8) 0x000000ff)
/* The following are approximate; IEEE floating point standards might quibble! */
#define MAX_POS_FLOAT32 3.4e+38f
#define MIN_POS_FLOAT32 1.2e-38f /* But not 0 */
#define MAX_POS_FLOAT64 1.8e+307
#define MIN_POS_FLOAT64 2.2e-308
/* Will the following really work?? */
#define MAX_NEG_FLOAT32 ((float32) (-MAX_POS_FLOAT32))
#define MIN_NEG_FLOAT32 ((float32) (-MIN_POS_FLOAT32))
#define MAX_NEG_FLOAT64 ((float64) (-MAX_POS_FLOAT64))
#define MIN_NEG_FLOAT64 ((float64) (-MIN_POS_FLOAT64))
#endif
| 2024-01-17T01:27:04.277712 | https://example.com/article/3439 |
Q:
2007-06-17 09:05:34.813 - date format needs conversion
Need this format: 2007-06-17 09:05:34.813 modified in MS Access to be like this:
mm/dd/yyy hh:nn:ss AM/PM
Tried this in my Access query:
"newdate": Format([newdate],"yyyy/mm/dd hh:nn:ss")
but it's not working.
A:
Source format is not a date, so your formula doesn't work. You need to remove number after dot:
Format(Left([newdate],InStr(1,[newdate],".")-1),"yyyy/mm/dd hh:nn:ss AMPM")
| 2023-08-22T01:27:04.277712 | https://example.com/article/2591 |
Q:
Visual Studio Code で C++ のデバッグ時にブレークポイントが無視される
Visual Studio Code に C/C++ for Visual Studio Code の 拡張機能を入れてコードを書いているところ、以下の不具合が発生します。
1.デバッグのサイドバーで変数が何も表示されない。
2.ブレークポイントを設定しても反応しない。
原因は何でしょうか。
コンパイラはg++を使用しています。
最適化されているとの指摘がありましたが、g++には-O0のオプションをつけています。
これでは最適化させないのに不十分なのでしょうか？
ソースファイルは、
#include <iostream>
using namespace std;
int main(){
cout<<"hello world"<<endl;
int a=10;//<--ここにブレークポイント
int i;
cin>>i;
cout<<"hello world 2"<<endl;
return 0;
}
tasks.jsonは
{
"version": "2.0.0",
"tasks": [
{
"label": "C++ Build",
"type": "shell",
"command": "g++",
"args": [
"-O0",
"-g",
"${file}",
"-o",
"${cwd}\\${fileBasenameNoExtension}"
],
"group": {
"kind": "build",
"isDefault": true
},
"problemMatcher": []
}
]
}
launch.jsonは、
{
"version": "0.2.0",
"configurations": [
{
"name": "(Windows) Launch",
"type": "cppvsdbg",
"request": "launch",
"program": "${cwd}\\${fileBasenameNoExtension}.exe",
"args": [],
"stopAtEntry": false,
"cwd": "${workspaceFolder}",
"environment": [],
"externalConsole": true,
"logging": {
"trace" : true,
}
}
]
}
launch.jsonを以下のように書き換えることで解決しました。
{
// IntelliSense を使用して利用可能な属性を学べます。
// 既存の属性の説明をホバーして表示します。
// 詳細情報は次を確認してください: https://go.microsoft.com/fwlink/?linkid=830387
"version": "0.2.0",
"configurations": [
{
"name": "(gdb) Launch",
"type": "cppdbg",
"request": "launch",
"program": "${workspaceRoot}/${fileBasenameNoExtension}.exe",
"args": [],
"stopAtEntry": false,
"cwd": "${workspaceFolder}",
"environment": [],
"externalConsole": true,
"MIMode": "gdb",
"miDebuggerPath": "C:/MinGW/bin/gdb.exe",
"setupCommands": [
{
"description": "Enable pretty-printing for gdb",
"text": "-enable-pretty-printing",
"ignoreFailures": true
}
]
}
]
A:
解決しました。
launch.jsonに誤りがありました。
{
"version": "0.2.0",
"configurations": [
{
"name": "(gdb) Launch",
"type": "cppdbg",
"request": "launch",
"program": "${workspaceRoot}/${fileBasenameNoExtension}.exe",
"args": [],
"stopAtEntry": false,
"cwd": "${workspaceFolder}",
"environment": [],
"externalConsole": true,
"MIMode": "gdb",
"miDebuggerPath": "C:/MinGW/bin/gdb.exe",
"setupCommands": [
{
"description": "Enable pretty-printing for gdb",
"text": "-enable-pretty-printing",
"ignoreFailures": true
}
]
}
]
| 2024-06-24T01:27:04.277712 | https://example.com/article/3212 |
REPLY {#h0.0}
=====
Our commentary "After All, Only Millions?" ([@B1]) highlighted that, in contrast to a recent scaling law-based estimate of global microbial diversity of a trillion species-level operational taxonomic units ([@B2]), the decreasing frequencies of novel 16S rRNA gene sequences recovered by high-throughput sequencing ([@B3], [@B4]) is suggesting that global microbial diversity might well be saturated at a few million. No one knows even the order of magnitude of *Bacteria* and *Archaea* species numbers that ongoing surveys will ultimately yield. Acknowledging that such a census can never be truly completed, it will make a difference for many microbiologists whether we assume for our next experiments that, in addition to each species of higher plants and animals, we also need to consider either just a few hundred or a million unique microbial species in each microbiome.
We are well aware that the short-read 16S rRNA sequence repositories already contain around 1 × 10e7 different sequences, many of those only recorded once or twice. Rather than arguing that a significant part of these short sequences may be erroneous, we would like to reiterate that an accurate census should be based on long (nearly complete), high-quality 16S rRNA sequences ([@B3], [@B4]). Furthermore, the simple identity-based thresholds of operational taxonomic units do not record monophyly, which is a fundamental basis for the species definition of *Bacteria* and *Archaea*.
We certainly agree with our colleagues Jay Lennon and Kenneth Locey ([@B5]) that the census should include more ecosystems and that the number of candidate phyla is high ([@B3]), reflecting the deep divergence and long evolutionary history of *Bacteria* and *Archaea*. Yet, we disagree with their prediction of the extent of the rare biosphere. Our contrasting hypotheses will be brought to a test in a future in which novel sequencing technologies will provide long, error-free, and nonchimeric sequences. And even then, the debate on the global number of species of *Bacteria* and *Archaea* will continue since this relevant question cannot be resolved solely based on comparative 16S rRNA sequence analysis.
This is a response to a letter by Lennon and Locey (http://dx.doi.org/10.1128/mBio.01298-16).
**Citation** Amann R, Rossello-Mora R. 2016. Reply to "The Underestimation of Global Microbial Diversity". mBio 7(5):e01623-16. doi:10.1128/mBio.01623-16.
[^1]: **Editor** Margaret J. McFall-Ngai, University of Hawaii
| 2024-03-02T01:27:04.277712 | https://example.com/article/6016 |
Topping a year of uncertainty and mostly silence from HP, Cnet has broken the story of LG's pending acquisition of the entire WebOS (former Palm) Global Business Unit, including patents, employees, and source code. Surprisingly, the rejuvenated WebOS will be used not to power any of LG's smartphones (where the company is a firmly entrenched Android supporter) or a new line of tablets but rather its expanding line of Smart TVs.
Rumors have swirled for the better part of the past six months of LG's interest in WebOS. Currently, LG offers a line of Android/Google TV-based Smart LED HDTVs as well as lower-end line of proprietary NetCast SmartTVs with the usual assortment of Netflix and other streaming apps baked into the sets' firmware.
The Verge has published an excellent insiders look into the "death of Palm and webOS." The well researched article looks back at Palm's efforts to revive the platform and companies fortunes in the last five years of its existence.
The piece, which includes quotes and commentary from a number of former Palm employees and engineers, primarily focuses on the efforts of building and launching webOS and the ensuing struggle to market.
History has proven that tossing out a familiar platform that prints money for your business and starting anew isn't easy: just ask Apple and Microsoft, whose next-generation desktop operating systems in the 1990s (codenamed "Copland" and "Cairo," respectively) floundered aimlessly for years before being replaced with other initiatives. The politics of a mobile platform are no different. The entire process can quickly devolve into a holy war, it turns out, never mind the risk of alienating your users and third-party developers — the very people by whom any platform is ultimately made or broken.
CRN has posted excerpts of a new interview with HP CEO Meg Whitman in which she reveals some insight regarding her stance on the future of WebOS.
On slide # 10 of the multi-page spread, Whitman firmly states that HP "(has) to have a tablet offering. We will be back in that business. We're coming back into the market with a Windows 8 tablet, first on an x86 chip and then maybe on an ARM chip. We'll see."
Slide #13 and #14 discuss HP's message to the remaining people on the WebOS team and the rest of high-profile departures, some of which we have recently covered. Whitman says that "This has been a very rocky period for the former Palm team/WebOS team that we built. And this was not a happy set of occurrences over the last six to eight months. So we have lost some people." She surprisingly even states that "Between August and November, there was no plan."
The Verge has posted an interview with Jon Rubinstein, freshly-departed from HP. Some of the highlights discussed in the surprisingly frank interview include the timeline previously set in place for Rubinstein's departure from HP (12 to 24 months). According to the interview, Ruby was planning on leaving HP even prior to the TouchPad launch. He politely refused to discuss the "things that didn't work out the way everyone expected" aside from the CEO churn during his not-quite 2-year tenure with HP (Hurd, Lesjak, Apotheker, Whitman). He also states that that "HP wasn't in good enough shape on its own to be able to support the effort", speaking in terms of the capital outlay needed to perfect WebOS and its accompanying hardware and ecosystem.
Long-time PIC readers may recall the story of former Palm CEO Ed Colligan plucking Rubinstein out of his semi-retirement poolside in Mexico (illustrated in this article from 2007) and it's to this tranquil destination that Ruby has returned for "some time off". The "Podfather" is still using his HP Veer and expressed no desire to head north and try to rectify the problems at RIM.
Culminating many months of silence from the former Palm CEO, All Things D is reporting that Jon Rubinstein is leaving Hewlett Packard, effectively shutting the book on one of the last vestiges of the old Palm guard at the company. This news comes just two days after HP's announcement of their WebOS open-source timeline.
The All Things D article goes on to state that Rubinstein has "no immediate plans" and the departure comes on the heels of his fulfillment of a 12-24 month commitment to stay onboard with HP in the aftermath of the Palm acquisition in 2010.
The article concludes with report that Rubinstein's departure is no great surprise, as he had not been seen on HP grounds after last summer's groundbreaking decision by ex-CEO Leo Apotheker to discontinue HP's WebOS hardware products.
HP today made a number of announcements regarding its plans to open source the WebOS operating system. HP has released a detailed schedule for releasing components of the OS with the full source available by September.
In addition, the company has released version 2.0 of the Enyo developer tool. Enyo 2.0 enables developers to write a single application that works across mobile devices and desktop web browsers, from the webOS, iOS and Android platforms to the Internet Explorer and Firefox browsers – and more. The source code for Enyo is available today, giving the open source community immediate access to the application framework for webOS.
HP has released new round of webOS updates for the HP TouchPad, Pre 2 and even the officially unreleased Pre 3 smartphone. The free updates are available now as on device over the air downloads.
webOS v3.0.5TouchPad users will be receiving webOS 3.0.5. This TouchPad update offers users faster switching in Calendar views, IM presence indicators and faster scrolling in Email, support for HTTP Live Streaming, the ability to easily toggle auto-correction on or off, and an option you can set so that a period will be inserted when you press the space bar twice. Further details can be found here.
The dust has not even settled on today's mega-announcement from HP to open-source WebOS and we already have some new info straight from the mouth of CEO Meg Whitman and board member Marc Andreessen (of Netscape fame) regarding a possible return to WebOS hardware in the future from HP.
The Verge conducted a sit-down interview in with Whitman and Andreessen earlier today about the future of WebOS, both as an ongoing open-sourced project and as the possible basis for future HP Tablet hardware.
For the time being, only a few excerpts from the full interview have been posted. In short, Whitman stated that yes, HP would indeed be revisiting WebOS tablet hardware but stopped short of committing to it in 2012 or later. She went on to state that the team is going to be reorganized in "a quite different direction than we've been taking it in the past". Presumably this will be a much sleeker, highly-competitive piece of hardware compared to HP's mediocre TouchPad that was seemingly launched as a barely-updated response to the 18 month-old first-generation iPad.
HP has just posted a press release detailing its decision on its future plans for the webOS platform. In short, the company plans to open source the webOS software but is noncommittal on any future hardware plans.
HP says they will make the underlying code of webOS available under an open source license. Their desire is for developers, partners, HP engineers and other hardware manufacturers to work on the project to deliver ongoing enhancements and new versions. HP also will contribute ENYO, the application framework for webOS, to the community in the near future along with a plan for the remaining components of the user space.
"webOS is the only platform designed from the ground up to be mobile, cloud-connected and scalable," said Meg Whitman, HP president and chief executive officer. "By contributing this innovation, HP unleashes the creativity of the open source community to advance a new generation of applications and devices."
Every time HP announces a new update to their WebOS devices, the community breathes a collective sigh of relief that their devices are continuing to be useful and supported. So this week's news that a WebOS system update for both the TouchPad and the Pre 2 is definitely reason to smile.
First off, WebOSInternals has tweeted the news that select Pre 2 owners are reporting WebOS 2.2.4 is starting to trickle out. Skype support for non-VZW Pre 2 handsets is the main focus of this update, along with Bluetooth MAP support and sync improvements to the core PIM apps.
Coming as something of a surprise this late Thursday evening, Precentral brings word of the breaking news that that HP CEO Meg Whitman has scheduled an all-hands meeting for Friday, December 9th. At approximately 10:30AM PST, the fate of WebOS in the hands of HP should finally be made clear.
Last week, Whitman told a French newspaper that a decision would be reached within the "next two weeks", though few expected an announcement this soon. Prior to this event, it was exactly one month ago at another all hands on meeting when HP decided to do take more time to determine the fate of the platform.
Just when you thought it was safe to start your holiday shopping for an Android or iOS-based tablet, HP has announced a curious return of the fire sale TouchPads, albeit as a slightly less attractive offering than what was offered during the original August blowout.
Beginning December 11th at 7PM Eastern time, HP will make a limited quantity of refurbish 16GB and 32GB TouchPads available through their eBay store. In addition to the two tablet SKUs at the previous $99 and $149 price points, HP will be offering a bundle consisting of a case, TouchStone charging dock, and Bluetooth wireless keyboard for $79.The timing for this clearance sale is new especially intriguing in light of the announcement expected for Friday, December 9th on the fate of WebOS. Thankfully, the purchase of a companion HP PC is not required.
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DEVOTION duvet cover (satin cotton) Jade-005
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Vandyck DEVOTION white duvet cover (SABB18105) with a pattern of ferns and twigs of color Jade-005, green. The back of the cover is uni colored for a playful cover. Made from 100% satin cotton. Instop strip with large bottle neck.
DEVOTION duvet cover (satin cotton) Misty Blue-109
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Vandyck DEVOTION white duvet cover (SABB18105) with a pattern of ferns and twigs of color Misty Blue-109, blue. The back of the cover is uni colored for a playful cover. Made from 100% satin cotton. Instop strip with large bottle neck. | 2024-06-13T01:27:04.277712 | https://example.com/article/8353 |