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1. Introduction {#sec1}
===============
Soil organic C (SOC) and total N (TN) are very important C and N pools in the terrestrial ecosystems \[[@B1], [@B2]\]. As the components of labile C and N pools in soils, dissolved organic C (DOC) and N (DON) and soil ammonium and nitrate N (NH~4~ ^+^-N and NO~3~ ^−^-N) play crucial roles in the biogeochemistry of C and N and in the nutrient transformation \[[@B3]--[@B5]\]. With the context of climatic warming, how SOC, TN, DOC, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N respond is vital to global C and N cycling \[[@B1], [@B2]\]. However, inconsistent results on the responses of these C and N pools to climatic warming have been observed with respect to vegetation types and initial soil characteristics \[[@B2], [@B3], [@B6]--[@B14]\]. For example, He et al. \[[@B2]\] demonstrated that six-year warming (\~1.4°C increase of 10 cm soil temperature) significantly decreased soil C by 129.3 g m^−2^ in a temperate steppe of Inner Mongolia. In contrast, Li et al. \[[@B7]\] found that two-year warming significantly increased SOC in an alpine meadow (\~2.1°C increase of air temperature) but significantly reduced TN in an alpine swamp meadow (\~2.3°C increase of air temperature) on the Tibetan Plateau. Hagedorn et al. \[[@B13]\] indicated that one-growing-season warming (\~4°C increase of 5 cm soil temperature) did not significantly influence DOC. Song et al. \[[@B1]\] pointed out that six-year warming (\~1.2°C increase of 10 cm soil temperature) significantly reduced DOC in a temperate steppe in Inner Mongolia. Biasi et al. \[[@B15]\] indicated that two-year warming (\~0.9°C increase of 5 cm soil temperature) did not have obvious effects on DON, NH~4~ ^+^-N, NO~3~ ^−^-N, and N~min~ in a lichen-rich dwarf shrub tundra in Siberia. Bai et al. \[[@B14]\] stated that experimental warming (\~0.6--6.7°C in soil temperature) had a significant positive effect on N~min~ but not on TN across all biomes. Therefore, how climatic warming acts on C and N cycling still remains unclear.
More than 70% of the Tibetan Plateau is covered with grasslands \[[@B16]\]. The alpine grasslands of this Plateau are one of the systems most sensitive to global change \[[@B17], [@B18]\]. In alpine grasslands, understanding the responses of SOC, DOC, TN, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N to climatic warming are crucial for predicting future changes in soil fertility and C sequestration. The alpine meadow is one of the most typical grasslands types on the Tibetan Plateau being subjected to climatic warming \[[@B19]\]. Information on how these C and N pools along an elevation gradient respond to climatic warming is scarce on the Tibetan Plateau. Here we set up a warming experiment in an alpine meadow at three elevations (i.e., 4313 m, 4513 m, and 4693 m) on the Northern Tibetan Plateau.
The main objective was to investigate the effects of short-term experimental warming on SOC, TN, DOC, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N. Our previous study indicated that short-term experimental warming could not affect soil microbial biomass \[[@B20]\] and soil microbial activity regulated the balances of soil C and N pools in the alpine meadow \[[@B21]\]. We hypothesized that experimental warming may not affect these C and N pools in this study.
2. Materials and Methods {#sec2}
========================
2.1. Study Area, Experimental Design, and Soil Sampling {#sec2.1}
-------------------------------------------------------
A detailed description of the study area, the warming experimental design, the measurements of microclimate factors (including soil temperature and soil moisture), and the soil sampling are given in Fu et al. \[[@B20], [@B22]\].
Briefly, three alpine meadow sites were established at three elevations (i.e., a low (30°30′N, 91°04′E, and 4313 m), mid- (30°31′N, 91°04′E, and 4513 m), and high (30°32′N, 91°03′E, and 4693 m) elevation) at Damxung Grassland Observation Station of Tibet Autonomous Region in China in May 2010.
Annual mean air temperature and precipitation is 1.3°C and \~476.8 mm, respectively \[[@B20], [@B21]\]. The vegetation is*Kobresia*-dominated alpine meadow and roots are mainly concentrated in the topsoil layer (0--20 cm) \[[@B21], [@B22]\]. The soil is classified as sandy loam, with pH of 6.0--6.7, organic matter of 0.3--11.2%, and total N of 0.03--0.49% \[[@B20], [@B22]\].
Open top chambers (OTCs, 3 mm thick polycarbonate) were used to enhance temperature \[[@B22], [@B23]\]. The bottom and top diameters and the height of OTCs were 1.45 m and 1.00 m and 0.40 m, respectively \[[@B20], [@B22]\]. For each site, four OTCs and their paired control plots (1 m × 1 m) were randomly established in May 2010. There was \~3 m distance between plots.
Daily mean soil temperature (*T* ~*s*~) during the study period of July-September in 2011 inside the OTCs increased by 1.26°C, 0.98°C, and 1.37°C at the low, mid-, and high elevation, respectively, compared to control plots \[[@B20]\]. In contrast, experimental warming decreased daily mean soil moisture (SM) by 0.04 m^3^ m^−3^ in all sites \[[@B20]\]. Daily mean *T* ~*s*~ decreased with increasing elevation from the low to high elevation \[[@B20]\].
We collected topsoil samples (0--20 cm depth) inside each plot using a probe 3.0 cm in diameter on July 7, August 9, and September 10, 2011 \[[@B20]\]. Five soil subsamples were randomly sampled and composited into one soil sample for each plot \[[@B20]\]. Subsamples of the fresh soil were used to measure DOC, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N and other subsamples of the fresh soil were air-dried for the measurements of SOC and TN.
2.2. Soil Analysis {#sec2.2}
------------------
A more detailed description of measurements of soil inorganic N (N~min~, i.e., sum of NH~4~ ^+^-N and NO~3~ ^−^-N), DON, and DOC can be found in Fu et al. \[[@B21]\]. Briefly, soil inorganic N in 20 g fresh soil sample was extracted with 100 mL K~2~SO~4~, filtered through 0.45 *μ*m membrane, and analyzed on a LACHAT Quikchem Automated Ion Analyzer. Dissolved organic C and TN (DTN) in another 20 g fresh soil sample was extracted with 100 mL ultrapure water and filtered through 0.45 membrane. The extractable SOC and TN concentrations in the ultrapure water extracts were measured using a Liqui TOC II elementar analyzer (Elementar Liqui TOC, Elementar Co., Hanau, Germany) and a UV-1700 PharmaSpec visible spectrophotometer (220 nm and 275 nm), respectively. We also analyzed dissolved inorganic N (DIN) in the ultrapure water extracts on a LACHAT Quikchem Automated Ion Analyzer. Then DON was calculated as the difference between DTN and DIN. The potassium dichromate method was used to determine SOC \[[@B24]\]. Soil TN was measured on a CN analyzer (Elementar Variomax CN). Soil microbial biomass (MBC) and N (MBN) data were obtained from Fu et al. \[[@B20]\].
2.3. Statistical Analysis {#sec2.3}
-------------------------
In order to examine the elevation effect, repeated-measures ANOVA with experimental warming and elevation as the between subject factors and with sampling date as the within subject factor was performed for a specific soil property (i.e., SOC, TN, DOC, DON, ratio of DOC to DON (DOC/DON), NH~4~ ^+^-N, NO~3~ ^−^-N, ratio of NH~4~ ^+^-N to NO~3~ ^−^-N(NH~4~ ^+^-N/NO~3~ ^−^-N), and N~min~). At each site, repeated-measures ANOVA with experimental warming (i.e., OTCs versus control) as the between subject factor and with sampling date as the within subject factor was conducted for each soil property. Single factor linear regressions were performed between soil properties and *T* ~*s*~, SM, MBC, and MBN. In addition, multiple stepwise regression analyses were conducted for soil properties to examine the relative importance of *T* ~*s*~, SM, MBC, and MBN in affecting the variations of soil properties. All data were examined for normality and homogeneity before analysis and natural logarithm transformations were made if necessary. The level of significance was *P* \< 0.05. All the statistical tests were performed using the SPSS software (version 16.0; SPSS Inc., Chicago, IL).
3. Results {#sec3}
==========
3.1. Effects of Experimental Warming on Soil Properties {#sec3.1}
-------------------------------------------------------
Regardless of experimental warming, elevation had significant effects on SOC (*F* = 183.19, *P* \< 0.001), TN (*F* = 126.38, *P* \< 0.001), DOC (*F* = 26.42, *P* \< 0.001), DON (*F* = 7.08, *P* \< 0.01), NH~4~ ^+^-N(*F* = 71.98, *P* \< 0.001), NH~4~ ^+^-N/NO~3~ ^−^-N(*F* = 14.01, *P* \< 0.001), and N~min~(*F* = 56.29, *P* \< 0.001) across the three sampling dates. In contrast, there were no significant effects of elevation on NO~3~ ^−^-N and DOC/DON. These C and N pools showed similar seasonal dynamics regardless of experimental warming among the three elevations ([Figure 1](#fig1){ref-type="fig"}).
In line with our initial hypothesis, experimental warming had little effects on SOC, TN, DOC, DON, DOC/DON, and NH~4~ ^+^-N/NO~3~ ^−^-N ([Table 1](#tab1){ref-type="table"}). In contrast, the sensitivity of N~min~ to experimental warming increased with increasing elevation ([Table 1](#tab1){ref-type="table"}). In detail, experimental warming significantly decreased N~min~ by 29.2% and 23.5% at the low and mid-elevation, NO~3~ ^−^-N by 36.4%, 29.5% at the low and mid-elevation, and NH~4~ ^+^-N by 16.7% at the mid-elevation across all the three sampling dates, respectively. In contrast, experimental warming had little effects on NO~3~ ^−^-N and N~min~ at the high elevation.
3.2. Relationships between Soil Properties and Environmental Variables and Soil Microbial Biomass {#sec3.2}
-------------------------------------------------------------------------------------------------
Soil organic C, TN, DOC, NH~4~ ^+^-N, NO~3~ ^−^-N, NH~4~ ^+^-N/NO~3~ ^−^-N, and N~min~ were significantly and positively correlated with SM ([Figure 2](#fig2){ref-type="fig"}). In contrast, SOC, TN, DOC, NH~4~ ^+^-N, and NH~4~ ^+^-N/NO~3~ ^−^-N declined with increasing *T* ~*s*~ ([Table 2](#tab2){ref-type="table"}). The negative correlations of *T* ~*s*~ with DON and N~min~ were relatively lower ([Table 2](#tab2){ref-type="table"}). Soil organic C, TN, DOC, DON, NH~4~ ^+^-N, NH~4~ ^+^-N/NO~3~ ^−^-N, and N~min~ increased significantly with increasing MBC and MBN, while NO~3~ ^−^--N only increased significantly with increasing MBN ([Table 2](#tab2){ref-type="table"}). Nitrate N was not related to MBC and *T* ~*s*~ ([Table 2](#tab2){ref-type="table"}), while DON was not correlated with SM (data not shown). In addition, DOC/DON was not correlated with *T* ~*s*~, SM, MBC, and MBN (data not shown).
The multiple stepwise regression analyses were listed in [Table 3](#tab3){ref-type="table"}. Both SOC and TN were simultaneously affected by MBC and *T* ~*s*~, whereas MBC explained more variation of the two soil properties than *T* ~*s*~. Only MBC was included in the multiple regression equations for DOC, DON, and NH~4~ ^+^-N/NO~3~ ^−^-N, while only MBN was included in the regression equation for NO~3~ ^−^-N. Soil microbial biomass C explained the variation of NH~4~ ^+^-N more than SM. Both MBC and MBN were simultaneously and positively correlated with N~min~. In addition, all the five concerned variables were excluded for DOC/DON.
4. Discussion {#sec4}
=============
4.1. Effects of Experimental Warming on SOC, TN, DOC, and DON {#sec4.1}
-------------------------------------------------------------
Recently, some studies showed that short-term (\<3 years) experimental warming had little effects on SOC, TN, DOC, and/or DON in a tallgrass prairie with a silt loam soil (\~2°C increase of 5 cm soil temperature) in USA \[[@B25]\], in a dragon spruce plantation with a mountain brown soil (\~0.6°C increase of 5 cm soil temperature) on the Tibetan Plateau \[[@B8]\], in an alpine treeline with a sandy Ranker and Podzols soil (\~4°C increase of 5 cm soil temperature) in Switzerland \[[@B13]\], and in a lichen-rich dwarf shrub tundra with Gleyic Cryosols soils (\~0.9°C increase of 5 cm soil temperature) in Siberia \[[@B15]\]. However, other studies with long-term (\>3 years) experimental warming indicated that warming significantly increased or decreased SOC, TN, DOC, and/or DON in a temperate steppe with a Calcic Kastanozems soil in Inner Mongolia (\~1.4°C increase of 10 cm soil temperature) \[[@B2]\], in an alpine meadow (\~3°C increase of 5 cm soil temperature) on the Tibetan Plateau \[[@B3]\], and in a temperate steppe with chestnut soil in Inner Mongolia (\~1.2°C increase of 10 cm soil temperature) \[[@B1]\]. Therefore, the insignificant responses of SOC, TN, DOC, and DON to warming ([Table 1](#tab1){ref-type="table"}) may be due to the short period of warming treatment (14--16 months).
A meta-analysis showed that the effects of experimental warming on N~min~, net N mineralization, and nitrification were significantly and positively correlated with raised soil temperature (\~0.6--6.7°C for N~min~, \~0.6--5.5°C for net mineralization, and \~1.3--5.5°C for net nitrification) across all biomes \[[@B14]\]. Similarly, we found that experimental warming-induced change of soil temperature tended to be negatively correlated with that of TN (*R* ^2^ = 0.43, *P* = 0.057) and positively correlated with that of MBN (*R* ^2^ = 0.43, *P* = 0.056) \[[@B20]\]. In addition, MBN was significantly correlated with SOC, TN, DOC, and DON ([Table 2](#tab2){ref-type="table"}). Therefore, the negligible responses of soil C and N pools to experimental warming ([Table 1](#tab1){ref-type="table"}) may be also due to lower warming magnitude in this alpine meadow.
Microbial activity regulates the production of dissolved organic matter \[[@B5], [@B8], [@B26]\] and experimental warming-induced decline in soil moisture may suppress soil microbial activity \[[@B20], [@B27]\]. Similarly, we also found that soil C and N pools increased with increasing soil microbial biomass and soil moisture ([Figure 2](#fig2){ref-type="fig"}, [Table 2](#tab2){ref-type="table"}). Moreover, short-term experimental warming had little effect on soil microbial biomass in this system \[[@B20]\]. Therefore, the negligible responses of SOC, TN, DOC, and DON to short-term experimental warming may be also related to that of soil microbial biomass \[[@B8], [@B20]\]. Moreover, experimental warming-induced soil drying may also suppress the production of DOC and DON \[[@B8], [@B20]\].
4.2. Effects of Experimental Warming on Soil Inorganic N {#sec4.2}
--------------------------------------------------------
Bai et al. \[[@B14]\] demonstrated that experimental warming did not significantly increase net N nitrification in grasslands. Similarly, experimental warming did not increase net N mineralization in an alpine meadow on the Tibetan Plateau \[[@B28]\]. In the same alpine meadow as this study, the finding that experimental warming did not increase ecosystem photosynthesis and aboveground plant biomass \[[@B22]\] also indirectly supported that experimental warming may not increase soil N availability because it has been observed that plant productivity is positively correlated with net N mineralization \[[@B29]\]. Therefore, the negligible or negative effect of experimental warming on soil inorganic N ([Figure 1](#fig1){ref-type="fig"}, [Table 1](#tab1){ref-type="table"}) may result from the suppression of net N mineralization and nitrification under warming.
The suppression of net N mineralization and nitrification may be owing to decreases in soil moisture and microbial activity because N~min~, NH~4~ ^+^-N, and NO~3~ ^−^-N increased significantly with increasing soil moisture and microbial biomass ([Figure 2](#fig2){ref-type="fig"}, [Table 2](#tab2){ref-type="table"}). Similarly, the experimental warming-induced significant reductions or insignificant changes of inorganic N ([Figure 1](#fig1){ref-type="fig"}, [Table 1](#tab1){ref-type="table"}) were also partly attributed to experimental warming-induced decline in soil microbial biomass \[[@B20]\] and soil drying \[[@B10], [@B29], [@B30]\]. This was in line with the finding that the effect of experimental warming on soil moisture was significantly correlated with that on soil nitrification \[[@B14]\]. On the other hand, microbial biomass was more closely related to soil inorganic N than soil moisture ([Table 3](#tab3){ref-type="table"}). This implied that microbial biomass may dominate the variation of soil inorganic N in this study. However, our previous study showed that short-term experimental warming tended to reduce microbial biomass due to soil drying in the same alpine meadow as this study \[[@B20]\]. Therefore, the experimental warming-induced changes of soil inorganic N, net N mineralization, and nitrification may be directly related to that of microbial activity and indirectly related to that of soil moisture.
The different responses of N~min~ to experimental warming among the three elevations across the sampling dates could be attributed to several probable underlying mechanisms. First, DON is high-quality N source for N mineralization \[[@B8], [@B31]\]. This was supported by the positive relationships between DON and N~min~ and NH~4~ ^+^-N and NO~3~ ^−^-N ([Figure 3](#fig3){ref-type="fig"}). DON under warmed plots tended to be decreased by 10.3% at the low elevation and by 28.7% at the mid-elevation but to be increased by 4.4% at the high elevation across all the three sampling dates, compared to control plots. Second, experimental warming-induced different changes in soil microbial biomass N (MBN) among three elevations \[[@B20]\] could partly explain this phenomenon considering that the production of DON and the immobilization of soil inorganic N were regulated by MBN \[[@B3], [@B32], [@B33]\]. This viewpoint was confirmed by the positive correlations between MBN and DON, N~min~, NH~4~ ^+^-N, and NO~3~ ^−^-N ([Table 2](#tab2){ref-type="table"}). Third, the response of soil N availability to warming could be strongly related to the initial conditions \[[@B8], [@B34]\]. In our system, N~min~, DON, and microbial biomass at the high elevation were significantly larger compared to the low and mid-elevation, whilst there were insignificant differences between the latter two \[[@B20]\].
5. Conclusions {#sec5}
==============
In summary, short-term experimental warming had no obvious effects on topsoil organic C, total N, dissolved organic C, and N pools for the alpine meadow in this study. The insignificant responses of these C and N pools to warming may be due to short-term warming treatment, experiment warming-induced soil drying, and lower warming magnitude. In contrast, the response of soil inorganic N to experimental warming differed among the three elevations, which may be attributed to different response trends of dissolved organic N and microbial biomass and different initial soil inorganic N.
This work was funded by the National Natural Science Foundation of China (no. 41171084) and the National Science and Technology Plan Project of China (no. 2011BAC09B03).
Conflict of Interests
=====================
The authors declare that there is no conflict of interests regarding the publication of this paper.
{#fig1}
{#fig2}
{#fig3}
######
Repeated-measures ANOVA (*F* values) for the main and interactive effects of experimental warming (W) and sampling date (D) on soil organic C (SOC), total N (TN), dissolved organic C (DOC), N (DON), ammonium N (NH~4~ ^+^-N), nitrate N (NO~3~ ^−^-N), the ratio of NH~4~ ^+^-N to NO~3~ ^−^-N (NH~4~ ^+^-N/NO~3~ ^−^-N), and soil inorganic N (N~min~, i.e., sum of NH~4~ ^+^-N and NO~3~ ^−^-N) in an alpine meadow on the Tibetan Plateau at three elevations (*n* = 4).
Elevation Model SOC TN DOC DON DOC/DON NO~3~ ^−^-N NH~4~ ^+^-N NH~4~ ^+^-N/NO~3~ ^−^-N N~min~
----------- ------- -------- ------------- ---------- -------- ------------- ------------- ------------- ------------------------- -----------
4313 m W 0.02 1.58 0.00 0.23 0.70 39.02\*\* 4.22 1.38 26.87\*\*
D 0.31 0.26 16.70\*\*\* 3.66 2.68 55.47\*\*\* 10.98\*\* 10.04\*\* 28.71\*\*\*
W × D 1.04 6.87\* 4.13\* 2.51 1.40 6.32\* 3.44 0.49 5.91\*
4513 m W 1.43 0.03 4.07 5.33 4.52 9.90\* 6.45\* 3.01 10.89\*
D 2.62 0.23 94.06\*\*\* 0.99 5.23 57.26\*\*\* 31.90\*\*\* 13.69\*\*\* 51.19\*\*\*
W × D 0.41 3.35 2.32 6.36\* 6.15\* 11.70\*\* 0.63 8.10\*\* 4.39\*
4693 m W 0.40 2.61 0.07 0.09 0.04 0.26 0.00 0.19 0.14
D 1.96 0.12 0.67 7.80\*\* 0.81 20.22\*\*\* 21.83\*\*\* 3.36 29.26\*\*\*
W × D 0.27 3.89 0.33 3.84 0.34 0.12 2.66 0.88 1.47
\*, \*\*, and \*\*\* indicate *P* \< 0.05, *P* \< 0.01, and *P* \< 0.001, respectively, while no asterisk indicates not significant.
######
Single factor linear regressions between soil properties (soil organic C, SOC; total N, TN; dissolved organic C, DOC; dissolved organic N, DON; nitrate N, NO~3~ ^−^-N; ammonium N, NH~4~ ^+^-N; the ratio of NH~4~ ^+^-N to NO~3~ ^−^-N, NH~4~ ^+^-N/NO~3~ ^−^-N; soil inorganic N, N~min~) and soil temperature (*T* ~*s*~), soil microbial biomass C (MBC), and N (MBN) showing regression parameters (slope, constant, *R* ^2^, and *P*). MBC and MBN data were obtained from Fu et al. \[[@B20]\].
----------------------------------------------------------------------------------------------------------------------------------
Independent\ Regression\ SOC TN DOC DON NO~3~ ^−^-N NH~4~ ^+^-N NH~4~ ^+^-N/NO~3~ ^−^-N N~min~
variable parameters
-------------- ------------- --------- --------- --------- -------- ------------- ------------- ------------------------- --------
*T* ~*s*~ Slope −5.29 −0.32 −7.90 −0.53 −0.03 −1.71 −0.43 −1.74
Constant 100.76 6.81 195.37 13.28 5.73 31.38 7.66 37.11
*R* ^2^ 0.63 0.64 0.38 0.21 0.001 0.31 0.41 0.21
*P* \<0.001 \<0.001 \<0.01 0.057 0.93 \<0.05 \<0.01 0.056
MBC Slope 0.05 0.003 0.10 0.01 0.01 0.03 0.004 0.03
Constant 6.46 1.24 46.29 2.89 3.34 −3.20 0.04 0.14
*R* ^2^ 0.76 0.66 0.70 0.51 0.13 0.92 0.47 0.82
*P* \<0.001 \<0.001 \<0.001 \<0.001 0.139 \<0.001 \<0.01 \<0.001
MBN Slope 0.28 0.01 0.68 0.05 0.06 0.17 0.02 0.23
Constant 10.56 1.58 43.22 2.93 1.60 −3.28 0.41 −1.69
*R* ^2^ 0.43 0.30 0.68 0.42 0.39 0.79 0.25 0.88
*P* \<0.01 \<0.05 \<0.001 \<0.01 \<0.01 \<0.001 \<0.05 \<0.001
----------------------------------------------------------------------------------------------------------------------------------
######
Multiple stepwise regression analyses between soil properties and environmental variables (soil temperature, *T* ~*s*~; soil moisture, SM) and soil microbial biomass (microbial biomass C, MBC; microbial biomass N, MBN) in an alpine meadow on the Tibetan Plateau. MBC and MBN data were obtained from Fu et al. \[[@B20]\].
Soil properties Factors Coefficients *R* ^2^ *P*
------------------------- ---------- -------------- --------- ---------
SOC Constant 49.31 0.003
MBC 0.04 0.76 \<0.001
*T* ~*s*~ −2.69 0.10 0.006
TN Constant 4.28 0.001
MBC 0.002 0.66 0.004
*T* ~*s*~ −0.19 0.14 0.006
DOC Constant 46.29 \<0.001
MBC 0.10 0.70 \<0.001
DON Constant 2.89 0.005
MBC 0.01 0.51 0.001
NH~4~ ^+^-N Constant −4.57 \<0.001
MBC 0.02 0.92 \<0.001
SM 22.39 0.05 \<0.001
NO~3~ ^−^-N Constant 1.60 0.22
MBN 0.06 0.39 0.005
N~min~ Constant −2.24 0.085
MBN 0.15 0.88 \<0.001
MBC 0.01 0.05 0.005
NH~4~ ^+^-N/NO~3~ ^−^-N Constant 0.95 0.036
MBC 0.004 0.47 0.002
[^1]: Academic Editor: Felipe Bastida
| {
"pile_set_name": "PubMed Central"
} |
The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper.
Introduction {#s1}
============
Mechanical ventilation (MV) has been used in critical care patients for decades. In spite of its life-saving potential, it has several shortcomings. A number of experimental studies have shown that mechanical ventilation may result in the appearance of inflammatory mediators in the lung [@pone.0114247-Uhlig1] and subsequently in oedema. [@pone.0114247-Dreyfuss1] Ventilator-Induced Lung Injury (VILI) causes macro and microscopic unspecific changes[@pone.0114247-Katzenstein1] similar to those found in patients with Acute Respiratory Distress Syndrome (ARDS). As it happens with ARDS, VILI is basically the result of important changes in the permeability of the alveolar-capillary membrane. [@pone.0114247-Dreyfuss2] The potential of mechanical ventilation for triggering or worsening pulmonary damages has been shown in animal models where the application of non-physiological ventilatory parameters (mostly very high tidal volumes) aggravated the condition of animals with a previously injured lung [@pone.0114247-Corbridge1], and even caused an injury in those without a previous pulmonary pathology. [@pone.0114247-Dreyfuss1] The use of low tidal volumes has proved to be a better approach in ARDS patients, survival being improved in strategies based on its usage. [@pone.0114247-Amato1]--[@pone.0114247-Villar1] Interestingly, recent experimental and clinical work has demonstrated that MV with low tidal volume can induce similar pulmonary changes to those noticed for VILI [@pone.0114247-Cobelens1]--[@pone.0114247-Wolthuis1] and that its appearance may be related to MV exposure time. [@pone.0114247-Hegeman1]
Aquaporins are a family of small transmembrane proteins that help water to move fast, selectively and bi-directionally through lipid bi-layers. [@pone.0114247-Kozono1], [@pone.0114247-Ma1] 13 different types have been identified in mammals, [@pone.0114247-Verkman1] from which the lung is known to express four: AQP-1, in the pulmonary capillary endothelium (especially alveolar), and the visceral pleura; AQP-3, in the tracheal epithelium; AQP-4, in the tracheal and bronchial epithelium; and AQP-5, on type I pneumocyte cells of the alveoli, on the membrane adjoining to the alveolar lumen. [@pone.0114247-King1] Their role in the development and resolution of pulmonary oedema gives rise to controversy, although it does seem to play a part in VILI. [@pone.0114247-Hales1]
This research aimed to verify if MV with low or moderately high tidal volumes (10 ml/Kg) sustained over time results in lung injury, subsequently altering pulmonary water content and microvascular permeability, as observed in VILI, and to objectivize what happens with AQP 1 and 5 expression, both types mainly involved in the formation of lung oedema, under the same ventilation conditions.
Material and Methods {#s2}
====================
1. Ethics statement {#s2a}
-------------------
The project was carried out after approval from the Ethics Committee for Animal Experimentation and Wellbeing of the Research Foundation of Valencia\'s Hospital Clínico Universitario.
2. Animal model and monitoring {#s2b}
------------------------------
A total of 30 rats were anaesthetised by intraperitoneal injection of ketamine 80 mg/kg and xylazine 5 mg/kg. 5 rats (group C or controls) were sacrificed by intravenous injection of 100 mg/Kg thiopental. The rest of the animals (n = 25) were performed a surgical tracheostomy, using a teflon cannula (Surflo, 16G). Rats were randomly allocated into two groups. 12 rats were ventilated for 2 hours (group 2H) with a Harvard Rodent Ventilator, model 683 (Harvard Apparatus) with a tidal volume of 10 ml/kg and a respiratory rate of 90 breaths/minute. 13 rats were ventilated with exactly the same parameters for 4 hours (group 4H). The cervical vascular bundle was dissected, and the right internal jugular vein and the right carotid artery were catheterized to continuously monitor heart rate (HR) and mean arterial pressure (MAP). Peak inspiratory pressure and respiratory system compliance were continuously recorded.
Anaesthesia was maintained by continuous intravenous infusion of ketamine and cisatracurium using dosis of 100 mcg/Kg/min and 2--3 mcg/Kg/min, respectively (20 ml of ketamine 5%, 10 ml of cisatracurium 0,2% and 20 ml of saline solution 0,9% at a rate of approximately 0,1 ml/h in the internal jugular vein). Anesthesia was supplemented, in cases in which it was necessary, by administration of an intravenous bolus of 0.1 ml of the mixture. Gasometric samples were taken in all animals in groups 2H and 4H at the beginning of MV and 30 minutes before the end of MV.
Rats were sacrificed by intravenous injection of sodium thiopental. The left lung was used for the determination of lung water content. The right lung of 6 rats from groups 2H and 4H was used for determining AQP 1 and AQP 5 expression. Lungs were either frozen in liquid nitrogen or paraffin-embedded for immunohistochemical sectioning and marking. 2 rats in group C and 4 rats from groups 2H and 4H were used to establish pulmonary macrovascular permeability.
3. Measuring lung oedema {#s2c}
------------------------
Lungs were dried with filter paper and placed on a Petri dish with known weight to obtain lung wet weight (LWW). They were then placed in a drying chamber at 80°C for 96 hours and their dry weight (LDW) was determined.
Two indicators of the amount of oedema were obtained: Lung WW/DW ratio and the proportion of pulmonary water, expressed in percentages (%~water~). The latter parameter was estimated using this formula: % ~water~ = (LWW - LDW)/LWW \* 100
4. Measuring microvascular permeability {#s2d}
---------------------------------------
Microvascular permeability was quantified using Evans Blue Dye. 0.5 ml Evans Blue was injected intravenously (30 mg/Kg) 30 minutes before sacrificing the animal. Rats were sacrificed by exsanguination from the carotid artery, but saline was simultaneously infused via the jugular vein in the same amount as that of the blood extracted.
After death, the right lung was separated and immersed in formamide (5 ml) and homogenised for 2 min. The resulting suspension was incubated at 37°C/18 h and then centrifuged at 5000xg/30 minutes, and the supernatant was measured. Concentration of Evans Blue in the supernatant was spectrophotometrically determined.
5. Study of aquaporin expression {#s2e}
--------------------------------
### 5.1 Western blot {#s2e1}
Proteins were extracted from previously frozen lungs. A Compartmental Protein Extraction Kit (Chemicon International, Temecula CA) was used. 200--400 mg tissue was homogenised in cold buffer C (1 ml/g tissue) and Ultra Turrax (KA, Staufen, Germany). Two protein fractions were obtained for each sample: cytoplasm and membrane, and they were quantified. Proteins in each fraction (100 mg) were separately run on a Tris-HCl/SDS gel, 8% acrylamide, and they were transferred onto a nitrocellulose membrane (Hybond-ECL, Amersham). After washing the membrane with distilled water, it was blocked with a PBS/Tween solution, 0.2%, with 5% skimmed milk. It was then incubated with the primary antibody during 2 hours at room temperature. The antibodies used were Anti-Rat AQP1 (Alpha Diagnostic, San Antonio, TX) and Anti-Rat AQP5 (Alpha Diagnostic, San Antonio, TX), both with a 2 mg/ml concentration. After several washes with PBS/Tween 0.2%, it was incubated with the secondary antibody Anti-Rabbit IgG (DAKO, Glostrup, Denmark) in 1∶2000 dilution. β-actin expression was detected as an internal control, and relative protein content was analysed using the enhanced chemoluminiscence method.
### 5.2 Real-time polymerase chain reaction with reverse transcriptase {#s2e2}
Lungs were cut with a microtome, three sections being obtained for each sample for total RNA extraction with TRIZOL (Reagent InvitrogenTM Life Technologies) as in the phenol extraction method described by Chomczynsky. [@pone.0114247-Chomczynski1] Microsections were added 1 ml TRIZOL and homogenized (Polytron PT 1200, Kinematica AG) and centrifuged at 10.000 rpm/10 min at 4°C. The supernatant was removed and RNA was precipitated by adding 0.1 volumes of sodium acetate 3 M, 2.5 volumes cold ethanol and 0.5 µl glycogen (20 mg/ml). RNA was centrifuged again, air-dried and resuspended in 20 µl Tris/EDTA buffer. RNA was reversely transcribed to cDNA with Superscript II (Invitrogen), by incubation with reverse transcriptase at 50°C for 30 min, followed by amplification with custom primers (Invitrogen), summarised in [Table 1](#pone-0114247-t001){ref-type="table"}. 35 amplification cycles were completed, with denaturalization at 95°C (30 sec), hybridization (30 sec) (temperatures on [Table 1](#pone-0114247-t001){ref-type="table"}) and extension at 72°C (1 min). Following amplification, RT-PCR products were separated in agarose gels at 1% and bands were viewed by ethidium bromide staining, and quantified by band density scanning using Scion Image (Beta 4.02, Scion Corporation). Results were expressed in relation to the level of β-actin mRNA in the same RNA samples.
10.1371/journal.pone.0114247.t001
###### RT-PCR primer sequences and temperature conditions.
{#pone-0114247-t001-1}
Gene Primer (5′-3′) Primer, counterclockwise (5′--3) T (°C)
--------- ---------------------------- ---------------------------------- --------
AQP1 TCTGGAGGCTGTGGTGGCT AAGTGAGTTCTCGAGCAGGGA 60
AQP5 TGGGTCTTCTGGGTAGGGCCTATTGT GCCGGCTTTGGCACTTGAGATACT 50
β-Actin ATCATGTTTGAGACCTTCAACA CATCTCTTGCTCGAAGTCCA 56
### 5.3 Immunohistochemical study {#s2e3}
Sections (4 µm thickness) from the paraffin-embedded lungs were obtained with the microtome. After the sections were dewaxed and hydrated, autoclave pretreatment (10 min, 121°C) for AQP1 and AQP5 antigen retrieval was performed and the sections were incubated in 1% H2O2 for 30 min at room temperature to block endogenous peroxidase activity. After being washed in PBS, the sections were then preincubated with goat serum albumin for 30 min at 37°C, and subsequently incubated with the primary antibodies against AQP1 (1∶500) and AQP5 (1∶300) for 18 h at 4°C. Then, the sections were washed with PBS and stained with Biotin-labelled goat anti-rabbit IgG for 30 min at 37°C. Intervening washes in PBS again were followed by incubation with Horseradish enzyme labelled streptavidin working solution for 30 min at 37°C. The sections were washed in PBS before application of diaminobenzidine (DAB), then were mounted under coverslip and analyzed under light microscope.
6. Statistical analysis {#s2f}
-----------------------
Results were expressed as mean ± standard deviation (SD). To compare results between groups, the non-parametric Kruskall-Wallis and Mann-Whitney tests were used. For the analysis of data within each individual group, the Wilconxon test was applied. Regression analyses for the amount of aquaporins and mRNA and determination coefficients (R^2^) were performed. Values of p\<0.05 were assumed to be statistically significant in all cases.
Results {#s3}
=======
1. Pulmonary oedema {#s3a}
-------------------
No significant differences were found between the three groups for the wet weight-dry weight ratio (group C: 4.72±0.04 vs. group 2H: 4.90±0.33 vs. group 4H: 5.23±0.79) or the percentage of pulmonary water (group C: 78.82±0.16 vs. group 2H: 79.52±1.31 vs. group 4H: 80.55±2.50), though an increasing trend was noticed for both parameters ([Fig. 1](#pone-0114247-g001){ref-type="fig"}).
{#pone-0114247-g001}
2. Ventilatory mechanics and hemodynamic parameters {#s3b}
---------------------------------------------------
Peak inspiratory pressure (PIP) progressively rose in both groups (group 2H and group 4H), higher values being found 90 minutes after the start of the experiment in group 2H and at minute 60 in group 4H ([Fig. 2](#pone-0114247-g002){ref-type="fig"}). No differences were found in the cut-off points of the two groups.
{#pone-0114247-g002}
Pulmonary compliance was reduced gradually in both groups, with significance in respect of the initial value as from minute 30 for group 2H and minute 60 in group 4H ([Fig. 3A](#pone-0114247-g003){ref-type="fig"}). No differences were found between the groups in none of the cut-off points. This decrease in compliance correlated with the peak pressure rise, with an R^2^ value of 0.98, p\<0.01 ([Fig. 3B](#pone-0114247-g003){ref-type="fig"}).
{#pone-0114247-g003}
Rats in both groups were hemodynamically stable. No differences were found in mean arterial pressure (group 2H: 97.95 mmHg ±27.75 vs. group 4H: 104.53 mmHg ±27.54), and the same applies to average heart rate values (group 2H: 341.29 bpm ±66.73 vs. group 4H: 306.52 bpm ±78.11). Mean arterial pressure (MAP) dropped in group 2H progressively compared to the baseline as from minute 60, but this also happened in group 4H as from minute 45. Heart rate also decreased after 120 minutes ([Fig. 4](#pone-0114247-g004){ref-type="fig"}).
{#pone-0114247-g004}
3. Gasometric parameters {#s3c}
------------------------
Gasometric results for groups 2H and 4H are summarised in [Table 2](#pone-0114247-t002){ref-type="table"}. No differences were found for pH, pCO~2~, ABE and lactate values within the study groups, and differences between the two groups were not found either. But a tendency towards mixed acidosis in relation to duration of MV was observed. Oxygenation presented a tendency to pO~2~ and pO~2~/FiO~2~ ratio reduction two hours after MV in group 2H, which was slightly more marked in group 4H after 4 hours.
10.1371/journal.pone.0114247.t002
###### Results of arterial blood gas tests in Group 2H (ventilated for 2 hours, 10 ml/Kg) and Group 4H (ventilated for 4 hours, 10 ml/Kg).
{#pone-0114247-t002-2}
Group 2H (2 hours) Group 4H (4 hours)
-------------- -------------------- --------------------------------------------- -------------- ---------------
**pH** 7,29±0,05 7,21±0,07 7,30±0,05 7,23±0,07
**pCO2** 47,96±3,56 56,87±18,04 47,33±8,51 52,84±7,73
**ABE** −3,96±2,02 −6,70±1,61[\*](#nt102){ref-type="table-fn"} −3,70±2,72 −6,26±4,20
**Lac** 2,08±0,62 1,99±0,66 1,79±0,74 1,91±1,24
**pO2** 93,30±17,72 91,56±16,56 97,28±15,76 83,03±24,27
**pO2/FiO2** 444,38±84,62 436,86±79,17 462,78±74,61 395,22±115,30
Values expressed as mean ± standard deviation.
\* p \<0.05 in relation to baseline.
4. Microvascular permeability {#s3d}
-----------------------------
A significant increase in microvascular permeability was not found. Evans Blue absorbance on lung tissue was as follows: 16.08 ng/mg ±2.45 in group C; 25.96 ng/mg ±9.90 in group 2H and 20.39 ng/mg ±2.20 in group 4H.
5. Expression of aquaporins 1 and 5 {#s3e}
-----------------------------------
AQP 1 steady state levels measured by Western blot in membrane and cytoplasm did not show statistically significant differences in relation to duration of MV ([Figs. 5](#pone-0114247-g005){ref-type="fig"} and [6](#pone-0114247-g006){ref-type="fig"}).
{#pone-0114247-g005}
{#pone-0114247-g006}
AQP-5 steady state levels in cytoplasm and membranes was significantly greater in both groups (2H and 4H) vs. the controls. Besides, AQP-5 expression on cytoplasm and membranes was greater in group 4H than in group 2H (p = 0.027 and p = 0.039, respectively) ([Figs. 5](#pone-0114247-g005){ref-type="fig"} and [7](#pone-0114247-g007){ref-type="fig"}). To better characterize these differences in the expression of AQP 5, a regression analysis of both variables was conducted, which provided a coefficient of determination R^2^ = 0.80 (p = 0.008) and R^2^ = 0.90 (p = 0.001) ([Fig. 8](#pone-0114247-g008){ref-type="fig"}).
{#pone-0114247-g007}
{#pone-0114247-g008}
RT-PCR results show a significant increase in the amount of mRNA for AQP-1 in groups 2H and 4H compared to group C. For AQP 5, an increase was found in the amount of mRNA in group 4H compared to group C ([Fig. 9](#pone-0114247-g009){ref-type="fig"}). The regression analysis of the amount of mRNA showed very significant determination coefficients for alveolar AQP 5 and AQP 1 in relation to duration of MV (R^2^ AQP-5 = 0.71 (p\<0.001) and R^2^ AQP-1 = 0.69 (p\<0.001).
{#pone-0114247-g009}
Immunohistochemical lung preparations of AQP-5 show the membranes of type 1 pneumocytes delimiting the alveolar network. The intensity of the staining increases with duration of MV ([Fig. 10](#pone-0114247-g010){ref-type="fig"}). AQP 1 samples show the network of the alveolar capillaries, as AQP-1 is found in endothelial cells and red blood cells but not in the pneumocytes covering the alveolus. In this case, image analysis does not show an increase in dye intensity in relation to MV time ([Fig. 11](#pone-0114247-g011){ref-type="fig"}).
{#pone-0114247-g010}
{#pone-0114247-g011}
Discussion {#s4}
==========
MV with high tidal volumes or without positive end-expiratory pressure (PEEP) may lead to the appearance of inflammatory mediators in the lung via mechanotransduction. [@pone.0114247-Uhlig1], [@pone.0114247-Tremblay1], [@pone.0114247-Bueno1] MV with tidal volumes over 12 ml/kg is associated with a bad prognosis, while \"lung-protective ventilation\" with low tidal volumes (under 10 ml/kg) and PEEP optimization reduces ventilation-induced injuries. [@pone.0114247-Noauthors1]
However, ventilation with low tidal volumes may result in the appearance of an inflammatory response pattern in the lung. In rats ventilated with low pressures (12 cmH~2~O) and 4 cmH~2~O PEEP during 4 hours, increased activity of myeloperoxidase and macrophage inflammatory protein-2 and interleukin-6 has been reported. [@pone.0114247-Cobelens1] Similarly, mild pro-inflammatory changes have been found in tracheal aspirates and blood of children with healthy lungs ventilated for 2 hours for heart surgery. [@pone.0114247-Plotz1] Likewise, 6 ml/Kg tidal volume MV in Wistar rats has been reported to induce a proinflammatory and profibrogenic response in the lung. [@pone.0114247-Caruso1] And in mechanically ventilated mice at 7.5 ml/Kg for 5 hours, rising levels of IL-6, TNF-α and lung water were found. [@pone.0114247-Wolthuis1] Conversely, some trials have demonstrated MV with tidal volumes of 10 ml/kg during 6 hours not to cause an increase in cytokine expression. [@pone.0114247-Altemeier1] Similarly, no increases in cytokines or mediators were found in previously healthy patients undergoing MV after one hour of exposure, even with tidal volumes of 15 ml/Kg. [@pone.0114247-Wrigge1]
Based on our results, we fail to confirm that MV with scarcely injurious parameters during 4 hours causes acute lung damage or changes in pulmonary permeability with an increase in lung water. A mild trend was observed in our experiments, however. Although levels were not measured for any inflammatory mediator, based on previous studies, inflammatory mediators are likely to be increased by MV even with low tidal volumes.
General anaesthesia and the supine position are known to cause pulmonary atelectasis with predominance in the dependent region. [@pone.0114247-Hedenstierna1] These give the lung a heterogeneous appearance in which atelectasis areas co-exist with aired and even overdistended areas and their corresponding transition zones. [@pone.0114247-Dreyfuss2] Besides, the use of low tidal volumes without PEEP can result in the appearance and maintenance of atelectasis in patients under general anaesthesia and muscular relaxation. [@pone.0114247-Wolthuis1] Regular recruitment with frequent deep insufflations during low tidal volume MV has been reported to improve oxygenation without signs of lung injury in mice mechanically ventilated for hours. [@pone.0114247-Allen1] Therefore, this would explain the worsening observed in the oxygenation of our animals as exposure to MV with low tidal volumes and without PEEP increased.
Our animals may have developed atelectasis in dependent areas, causing different degrees of atelectrauma that would explain the degradation in oxygenation seen in the experiment (*see* [Table 2](#pone-0114247-t002){ref-type="table"}), although it was not statistically significant, as well as the fall in pulmonary compliance and the rise in peak inspiratory pressure (*see* [Figs. 2](#pone-0114247-g002){ref-type="fig"} and [3A](#pone-0114247-g003){ref-type="fig"}). The latter parameters correlated linearly with a coefficient of determination R^2^ of 0.98 in group 4H (animals ventilated for 4 hours) ([Fig. 3B](#pone-0114247-g003){ref-type="fig"}).
Although acid-base parameters are well-known reliable indicators of animal wellbeing, they have only been partially evaluated in murine mechanical ventilation models. [@pone.0114247-Cobelens1], [@pone.0114247-Belperio1], [@pone.0114247-Altemeier1], [@pone.0114247-Tremblay1] In our model, ventilated animals in groups 2H and 4H showed a trend towards mixed acidosis but without significance. As a result of the formation of atelectasis and higher pressures, ventilation might have been less effective, which could account for the rise in pCO~2~ levels, although not significantly. The metabolic component of acidosis can have several causes. Metabolic acidosis in mice can be induced by saline administration, [@pone.0114247-Zuurbier1], [@pone.0114247-Wolthuis1] which in our animals was used for maintenance at very low levels. Yet, metabolic acidosis caused by some hemodynamic failure cannot be totally excluded. This is possibly related to poor compensation for losses rather than potential deficits in venous return and secondary low cardiac output, as a result of the thoracic pressure reversal observed in positive pressure MV. [@pone.0114247-Schwarte1] Similarly, heart rate data showed a significant reduction over time from minute 120 of the experiment, although always within the physiological range of rats. [@pone.0114247-Papadimitriou1]
To date, no research group has explored the expression of AQP 1 and AQP 5 jointly in mechanically ventilated rats with low tidal volumes. However, a study conducted in rats ventilated with very high tidal volumes (40 ml/Kg during 4 hours) showed a reduction in AQP 1 expression. The researchers suggested an inflammatory mediator secondary mechanism, as they managed to mitigate the reduction in AQP 1 by administering a cyclooxygenase 2 inhibitor. [@pone.0114247-Jin1] In another trial, based on an animal model of ARDS induced by smoke inhalation, animals were subjected to MV, finding an increase in mRNA for AQP 1. [@pone.0114247-Schmalstieg1] The shortcoming in these studies is the absence of a control group with non-ventilated animals to study AQP expression.
Our experiments show an increase in AQP 5 expression that became more significant as MV exposure was prolonged and, similarly, an increase in mRNA of AQP 5 which was also greater in group 4H compared to non-ventilated animals. These increases were not accompanied by significant variations in lung water content or microvascular permeability. Although an increase in AQP 1 in the lungs was not found, after 4 h of MV, our study did find a significant increase in mRNA. This is likely to be the previous step to AQP 1 synthesis. It is possibly due to the fact that a longer MV period is needed for an increase in AQP 1 on cytoplasm and membranes to be seen with the Western blot. Different factors have been shown to modulate the amount of AQPs, reducing them under a number of pathological conditions and leading to an increase in pulmonary water and oedema. [@pone.0114247-Wang1]--[@pone.0114247-Jiao1] In addition, the fact that lung injury parameters improve when their expression is induced, assigns AQPs a protective mechanism in the occurrence and development of pulmonary oedema. [@pone.0114247-Cao1]--[@pone.0114247-Dong1] Although some studies with genetically modified animals debate the possible relevant role of AQPs in the reabsorption of alveolar water, they prove the importance of these channels in pulmonary permeability. [@pone.0114247-Bai1], [@pone.0114247-Ma1], [@pone.0114247-Song1] Significant changes in lung water or microvascular permeability were not objectivized in our animals. The explanation for this could be that AQPs, according to some authors, only work in situations of stress. [@pone.0114247-Hales1] Further studies are needed to determine the true role of AQP1 and AQP 5 in MV.
To conclude, in our model prolonged MV and tidal volumes of 10 ml/Kg for 4 hours did not result in increased pulmonary water or changes in microvascular permeability, these being mechanisms involved in ventilation-induced lung injury. Our study found an increase in the protein expression of AQP 5 and its mRNA, correlated with exposure time and mechanical ventilation. Likewise, the amount of mRNA for AQP 1 also increased in correlation with MV time. Apparently, AQP 5 and AQP 1 can have a protective effect against MV-induced pulmonary oedema, but more studies are needed to clarify whether these proteins really play a relevant role in mechanically ventilated lungs under different conditions.
The experiment was carried out in the facilities of the Medical School (University of Valencia).
[^1]: **Competing Interests:**The authors have declared that no competing interests exist.
[^2]: Conceived and designed the experiments: GF JGDLA. Performed the experiments: GF MM EP. Analyzed the data: GF JGDLA BS JC JDA FJB. Contributed reagents/materials/analysis tools: JC BS. Wrote the paper: GF JGDLA BS EP.
| {
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Sai Shan
Sai Shan () is a hill behind Mayfair Gardens on Tsing Yi Island, Hong Kong. The hill is east of and beneath the northern peak of Tsing Yi Peak. A village, Sai Shan Village is in the valley between Sai Shan and Tsing Yi Peak. A road, Sai Shan Road between Mayfair Gardens and Hong Kong Institute of Vocational Education (Tsing Yi) is named after the hill.
Category:Tsing Yi
Category:Mountains, peaks and hills of Hong Kong | {
"pile_set_name": "Wikipedia (en)"
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French Priest Jacques Hamel was killed when two attackers slit the throat of the 86-year-old's throat. Credit:AP French President Francois Hollande identified the attackers as Islamist terrorists, and the IS news agency Amaq cited a security source saying the attack was by "soldiers of the Islamic State". Anti-terrorism prosecutors have been assigned to the investigation. French prosecutor Francois Molins said one of the attackers, Adel Kermiche, had been arrested and imprisoned after becoming radicalised and trying to reach Syria to fight for IS. However, he was released by a judge in March and put under house arrest. Later on Tuesday evening, in a televised address to the nation, Mr Hollande said France would defeat terrorism "by persevering".
Priest identified as Father Jacques Hamel (right), 84, was killed by knifemen in a church in France. He did not flag new measures to address the threat, but emphasised the existing ones would be applied to their fullest. "This war will be a long one," he said. "Our country must avoid overreaction, polemics, confusion and suspicion ... It is our unity that will give us strength." Police officers in Normandy following an attack on a church that left a priest dead. Credit:AP Mr Molins said two men carrying blades entered the church during morning Mass about 9.25am and took six people hostage - the priest, three nuns and a couple of parishioners.
Witnesses told Le Figaro the attackers were armed with knives, one was bearded and one was said to have worn a chachia, a traditional woollen north African hat. French President Francois Hollande shakes hands with police and security personnel in Normandy. Credit:AP They shouted "Allahu Akbar" as they entered the church, "corroborated sources" told Le Point. Sister Daniele, a nun who was in the church, told French television she thought "that's it, it's over" when the attackers stormed in. Adel Kermiche, a younger age. Credit:Facebook
"It was at the foot of the altar, they forced [the priest] to kneel and not move – and then we saw the knife in their right hand," she said. "They took to the floor to speak in Arabic … I didn't understand everything they said, but they shouted, 'You Christians, you are oppressing us.' " Adel Khermiche In another interview, she said: "They did a sort of sermon around the altar in Arabic. It's horrific." Sister Daniele escaped while they were attacking the priest. She did not see his murder.
The church where a 84-year-old priest was murdered in an attack in Normandy, France. Credit:AP "I set off running and I stopped the first car I saw. The driver called the police and they arrived very quickly." Police tried to negotiate with the terrorists through a small side door at the back of the church leading to the sacristy. They then tried to enter but were unable to because the attackers used three hostages as a human shield to block the door, Mr Molins said. The two nuns and a parishioner then left the church followed by the terrorists, one of whom was carrying a handgun, Mr Molins said. They headed for the police crying "Allahu Akbar" and were shot down.
One of the attackers had a fake explosive device on his belt and three knives. The other had a timepiece wrapped in aluminium foil in a backpack with a fake explosive. Police then entered the church to search for explosives. None were found. They found the body of the priest, who died of wounds to his chest and throat. Mr Molins said Kermiche, a local teenager born in 1997, had been identified through his fingerprints. In March 2015 he was arrested in Germany trying to get to Syria using his brother's ID. Two months later, he again tried to join IS and this time got as far as Turkey. He was remanded in custody in France, but in March a judge ordered that he instead be kept under house arrest, and he was allowed to leave home for up to four hours a day. The Paris prosecutor appealed against this decision to release him but it was confirmed by an appeal court.
Sid Ahmen Ghlam, a 24-year-old Algerian student who was arrested and imprisoned after planning to attack places of Catholic worship in the Paris region had previously identified the same church as a potential target, Le Figaro reported. The attack comes with the country still on high alert after the Bastille Day massacre in Nice. "I cry out to God with all men of goodwill," said the archbishop of Rouen Dominique Lebrun in a press release issued by the Rouen diocese, in which the church lies. He said there were three victims: Father Hamel and his killers. Three other people were injured, one very seriously. He said he would return from World Youth Day in Poland and "I will be tonight in my diocese with families and the shocked parish community." He called on young people not to give in to violence but to "become apostles of the civilisation of love".
On social media, the "je suis pretre" ("I am priest") hashtag began spreading. Catholics called for Pope Francis to put the slain priest on a fast track for sainthood. Roberto Maroni, president of the Lombard region, said Father Hamel was a "martyr of faith". At the Vatican, a spokesman, the Reverend Federico Lombardi, said that Pope Francis was horrified at the "barbaric killing" of a priest. Mr Hollande said the attack was a "cowardly assassination" by two terrorists. Visiting the church, he said he had spoken to the family of the dead priest and also a parishioner who had been taken hostage. He linked the "despicable terrorist attack" directly to Islamic State, saying "over the past few days and the past few years we have been facing IS, who have declared war against us". "It's not only Catholics targeted, it is all French people," he said.
"We should be part of a 'bloc', a unity that nobody can divide ... the terrorists will stop at nothing if we do not stop them." He praised police and emergency services who, he said, had avoided a higher death toll with their quick intervention. Mr Hollande later met Prime Minister Manuel Valls, Interior Minister Bernard Cazeneuve and Justice Minister Bernard Cazeneuve at the Elysee Palace. The attack drew statements of condemnation from across French society. Dalil Boubakeur, president of the French Council of the Muslim Faith, declared that "Muslims stand together behind the government to defend France and its institutions." The Representative Council of French Jewish Institutions said that the attack "marks a new stage in the spread of terrorism in France".
Right-wing politician Marine Le Pen tweeted the modus operandi led her to "obviously fear another attack by Islamist terrorists". Mr Valls tweeted his "horror at the barbaric attack … the whole of France and all Catholics are wounded. We will stand together." | {
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Q:
How dangerous is it to translate IPs directly via hosts in Windows
Sorry for the inconvenience, as English is not my native.
I use hosts to access some websites as DNS is polluted.
My question is, take www.google.com as an example.
If I am successfully social engineered by an attacker, and changes the translation in hosts into a phishing website.
If I use http, then I am completely screwed, right?
If I use https, then the browser will give a warning, if my PC is not compromised.
For the https case, is it possible that the phishing website just pass a certificate from www.google.com to me to prove it is genuine?
A:
Consider the following statements:
All certificate authorities trusted by your web browser refuse to issue a certificate for examplebank.com to the attacker without proof of domain ownership.
The signing keys of all authorities are securely stored and an unauthorized person cannot issue a certificate to themselves. (See recent Comodo break-in.)
Your web browser correctly checks if the server's SSL certificate is issued by a valid CA, not revoked, valid for use by servers, and issued for the examplebank.com domain.
There is no active malware or a browser bug that causes such checks to be bypassed.
You always open https://examplebank.com, requesting SSL explicitly instead of relying for the website to redirect you.
You actually read the SSL error messages instead of blindly clicking Ignore when you open the website.
If all of the above are true, HTTPS will warn you that you tried to connect to a fake website. However, HTTPS cannot bypass lower-level redirections (such as spoofing examplebank.com by DNS or /etc/hosts), so if you ignore the warnings, your data will be going to the attacker, not to the real bank.
To conclude, yes, it's dangerous.
In response to the edited question:
If you use plain HTTP, you're screwed.
If you use HTTPS, you will receive a big red warning (see first part of the answer).
Every "certificate" has a RSA (sometimes DSA, ECDSA) key pair. The public key of the pair is part of the certificate, while the private key is locked away in the webserver and never sent over the network. Both keys are needed to successfully complete the TLS/SSL handshake.
If the attacker presents a certificate, but does not have the associated private key, they will not be able to decrypt any traffic that goes over TLS. Wikipedia has a description of the TLS handshake.
A:
SSL (HTTPS) will only protect you as long as your client is not compromised.
If someone manages to modify /etc/hosts, he can also manage to modify your browser to not perform the SSL validation of the server you're connecting to, or he can add his fraud server's fake certificate into your system's database of trusted certificates.
If however your client is not compromised and someone manages to redirect your browser to a different IP address (e.g. some kind of DNS-related hack, or cheating you to modify /etc/hosts without anything else), the browser will warn you that something's wrong with the server's certificate, and, provided you don't ignore the warning and proceed, you are safe.
On your second question:
For the https case, is it possible that the phishing website just pass
a certificate from www.google.com to me to prove it is genuine?
No, that is not possible, unless the attacker managed to obtain the server's private key (e.g. by hacking the server itself). Even if a fraud server "passed on" the server's certificate, he will not be able to prove its identity to the client if it does not possess that private key. If he attempted to do that, he will fail and the browser will show a warning.
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/* Copyright 2019 Google Inc. All Rights Reserved.
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import {Polygon} from '/lib/math/polygon2d.js';
import * as moduleInterface from '/lib/module_interface.js';
import * as moduleTicker from '/client/modules/module_ticker.js';
import * as network from '/client/network/network.js';
import * as peerNetwork from '/client/network/peer.js';
import {easyLog} from '/lib/log.js';
import assert from '/lib/assert.js';
import asset from '/client/asset/asset.js';
import conform from '/lib/conform.js';
import inject from '/lib/inject.js';
import * as stateManager from '/client/state/state_manager.js';
import {TitleCard} from '/client/title_card.js';
import * as time from '/client/util/time.js';
import {delay} from '/lib/promise.js';
function createNewContainer(name) {
var newContainer = document.createElement('div');
newContainer.className = 'container';
newContainer.id = 't-' + time.now();
newContainer.setAttribute('moduleName', name);
return newContainer;
}
export const FadeTransition = {
start(container) {
if (container) {
container.style.opacity = 0.001;
document.querySelector('#containers').appendChild(container);
}
},
async perform(oldModule, newModule, deadline) {
if (newModule.name == '_empty') {
// Fading out.. so fade *out* the *old* container.
oldModule.container.style.transition =
'opacity ' + time.until(deadline).toFixed(0) + 'ms';
oldModule.container.style.opacity = 0.0;
} else {
newModule.container.style.transition =
'opacity ' + time.until(deadline).toFixed(0) + 'ms';
newModule.container.style.opacity = 1.0;
}
// TODO(applmak): Maybe wait until css says that the transition is done?
await delay(time.until(deadline));
}
}
export class ClientModule {
constructor(name, path, config, titleCard, deadline, geo, transition) {
// The module name.
this.name = name;
// The path to the main file of this module.
this.path = path;
// The module config.
this.config = config;
// The title card instance for this module.
this.titleCard = titleCard;
// Absolute time when this module is supposed to be visible. Module will
// actually be faded in by deadline + 5000ms.
this.deadline = deadline;
// The wall geometry.
this.geo = geo;
// The transition to use to transition to this module.
this.transition = transition;
// The dom container for the module's content.
this.container = null;
// Module class instance.
this.instance = null;
// Network instance for this module.
this.network = null;
}
// Deserializes from the json serialized form of ModuleDef in the server.
static deserialize(bits) {
if (bits.module.name == '_empty') {
return ClientModule.newEmptyModule(bits.time);
}
return new ClientModule(
bits.module.name,
bits.module.path,
bits.module.config,
new TitleCard(bits.module.credit),
bits.time,
new Polygon(bits.geo),
FadeTransition,
);
}
static newEmptyModule(deadline = 0, transition = FadeTransition) {
return new ClientModule(
'_empty',
'',
{},
new TitleCard({}),
deadline,
new Polygon([{x: 0, y:0}]),
transition
);
}
// Extracted out for testing purposes.
static async loadPath(path) {
return await import(path);
}
async instantiate() {
this.container = createNewContainer(this.name);
if (!this.path) {
return;
}
const INSTANTIATION_ID =
`${this.geo.extents.serialize()}-${this.deadline}`;
this.network = network.forModule(INSTANTIATION_ID);
let openNetwork = this.network.open();
this.stateManager = stateManager.forModule(network, INSTANTIATION_ID);
const fakeEnv = {
asset,
debug: easyLog('wall:module:' + this.name),
game: undefined,
network: openNetwork,
titleCard: this.titleCard.getModuleAPI(),
state: this.stateManager.open(),
wallGeometry: this.geo,
peerNetwork,
assert,
};
try {
const {load} = await ClientModule.loadPath(this.path);
if (!load) {
throw new Error(`${this.name} did not export a 'load' function!`);
}
const {client} = inject(load, fakeEnv);
conform(client, moduleInterface.Client);
this.instance = new client(this.config);
} catch (e) {
// something went very wrong. Wind everything down.!
this.network.close();
this.network = null;
throw e;
}
}
// Returns true if module is still OK.
async willBeShownSoon() {
if (!this.path) {
return;
}
// Prep the container for transition.
// TODO(applmak): Move the transition smarts out of ClientModule.
this.transition.start(this.container);
try {
await this.instance.willBeShownSoon(this.container, this.deadline);
} catch(e) {
this.dispose();
throw e;
}
}
// Returns true if module is still OK.
beginTransitionIn(deadline) {
if (!this.path) {
return;
}
moduleTicker.add(this.name, this.instance);
try {
this.instance.beginFadeIn(deadline);
} catch (e) {
this.dispose();
throw e;
}
}
finishTransitionIn() {
if (!this.path) {
return;
}
this.titleCard.enter();
this.instance.finishFadeIn();
}
beginTransitionOut(deadline) {
if (!this.path) {
return;
}
this.titleCard.exit();
this.instance.beginFadeOut(deadline);
}
finishTransitionOut() {
if (!this.path) {
return;
}
this.instance.finishFadeOut();
}
async performTransition(otherModule, transitionFinishDeadline) {
await this.transition.perform(otherModule, this, transitionFinishDeadline);
}
dispose() {
if (this.container) {
this.container.remove();
this.container = null;
}
if (!this.path) {
return;
}
this.titleCard.exit(); // Just in case.
moduleTicker.remove(this.instance);
if (this.network) {
this.stateManager.close();
this.stateManager = null;
this.network.close();
this.network = null;
}
}
}
| {
"pile_set_name": "Github"
} |
Regeneration of elastic fibers by three-dimensional culture on a collagen scaffold and the addition of latent TGF-β binding protein 4 to improve elastic matrix deposition.
The objective of this study was to investigate the effects of latent TGF-β binding protein 4 (LTBP-4) on elastic fiber regeneration in three-dimensional cultures of human dermal fibroblasts (HDFs). Appropriate collagen scaffold for elastic fiber regeneration was also examined. Collagen sponges cross-linked at 120 °C and composed of small pores (25 μm on average) was favorable for elastic fiber regeneration by HDFs. Addition of LTBP-4, followed by culture for 21 days, accelerated elastic fiber accumulation within the scaffolds. Conditioned scaffolds containing either HDFs or LTBP-4-built mature elastic fibers were implanted between the dermis and the cutaneous muscle of mice. The combined use of HDFs and LTBP-4 resulted in thicker tissues containing elastic fibers. These results indicate that weakly cross-linked collagen sponges can be used as scaffolds for regenerating elastic fibers both in vitro and in vivo, and that the addition of LTBP-4 accelerates the deposition of both elastin and fibrillin-1, and increases cell proliferation. These techniques may be useful for generating cutaneous or cardiovascular tissue equivalents; furthermore, they may serve as a useful method for the three-dimensional analyses of drugs used to treat skin diseases or to examine the microstructure of elastin networks. | {
"pile_set_name": "PubMed Abstracts"
} |
Incredibly big tune by Watermat & TAI, building upon an effective piano groove, turning this from catchy house music to a bigger than life future anthem. It’s got main stage written all over it, without falling for the known big room sounds. This is new and highly creative dance music, Frequency setting the standard for house music to come. HUGE!
Expertly layering rich melodic synths with driving yet enchanting vocals, Warriors climaxes in a euphoric drop that creates an uplifting, progressive anthem suitable for any festival main stage. Alongside Nicky, Volt & State have created an anthem portraying a mantra of never giving up and always fighting for what you believe in which can be related to on a universal level. | {
"pile_set_name": "Pile-CC"
} |
Road study gets Sampson’s attention
Chris Berendt/Sampson IndependentEconomic developer John Swope talks business during Monday night's meeting of the Sampson Board of Commissioners.
Photo
Chris Berendt/Sampson IndependentEconomic developer John Swope talks business during Monday night's meeting of the Sampson Board of Commissioners.
Chris Berendt/Sampson IndependentCounty board chairman Jefferson Strickland, standing, flanked by Commissioners Jarvis McLamb, left, and Albert Kirby, talks about an invitation to a reads impact study announcement in Wayne County and what it could mean to Sampson.
Photo
Chris Berendt/Sampson IndependentCounty board chairman Jefferson Strickland, standing, flanked by Commissioners Jarvis McLamb, left, and Albert Kirby, talks about an invitation to a reads impact study announcement in Wayne County and what it could mean to Sampson.
A road economic impact study in Wayne County has drawn the attention of those in Sampson for its future implications — notably the money and jobs it could bring with it.
The U.S. 117/I-795 economic impact assessment study will be unveiled later this month and the Wayne County Transportation Committee sent invitations out to those in surrounding counties interested in learning about the effect of the growth on “citizens, economy, development patterns and lifestyle.”
Sampson County officials were among those invited.
“Many of you are familiar with the new road from Wilson to Goldsboro with a number designation of 795,” Sampson Board of Commissioners chairman Jefferson Strickland told his fellow board members. “The plan is for that road to continue onto Faison and be in Sampson County at the (Interstate) 40/(N.C.) 403 intersection. One of the first meetings to present some of the faces and facts is going to be held in August, and they’ve asked several members of our community to attend.”
Strickland proposed that Jerol Kivett, chairman of the Sampson County Transportation Advocacy Group (TAG), Commissioners Albert Kirby and Billy Lockamy, as well as John Swope, executive director of the Sampson Economic Development Commission, be in attendance at the Aug. 21 meeting at Lane Tree Conference Center in Goldsboro.
The board agreed unanimously.
Interstate 795 is an interstate spur that follows the U.S. 117 corridor from I-95 near Wilson to U.S. 70 in Goldsboro, a length of about 25 miles. There are no other interstates in the eastern portion of North Carolina, east of I-95 and I-40.
Its connectivity with a portion of I-40 in northern Sampson could prove vastly beneficial, local officials attested.
The extension of I-795 southward along the U.S. 117 corridor would connect cities and industrial centers important to national defense, economic growth and job creation, Joe Daughtery, chairman of the Wayne County Transportation Committee, stated in his correspondence to Sampson County and others.
Daughtery cited the potential of $74 million in business and resident cost savings, $520 million in GRP (gross regional product) and nearly $490 million in additional personal income by 2040.
“Employment is projected to grow faster as well, adding about 220 more jobs on average per year along the corridor when compared to not completing the corridor,” he said.
A recently-concluded U.S. 70 Corridor Commission study evaluated the economic development impacts of completing the four-lane freeway bypass system of highways for U.S. 70 from I-40 in Raleigh to the Morehead City State Ports facility; and the conversion of U.S. 117 to I-795 from Goldsboro to I-40.
A U.S. 117 conversion would mean expansion for that road and an impact for I-40 in Sampson, Swope said at the time the study was initiated.
The study team of Cambridge Systematics and the Sanford Holshouser Economic Development Consulting LLC conducted that analysis and are the same team set to conduct the U.S. 117/I-795 economic impact assessment study.
With the Department of Transportation also in the fold, Swope has alluded to exciting possibilities.
“I-795 would be proposed to connect to I-40 near Faison,” Swope said previously. “That would give us a direct route north to I-95, direct access instead of going (west) on I-40 and then catching I-95 North. They would connect to a new I-795, giving people traveling north and south better access than traveling I-40 to I-95.”
State officials said the completion of the highway improvements, has extensive long-term implications for the economic future of eastern North Carolina and the counties along the corridor.
The U.S. 70 Corridor Commission study found that as many as 1,900 jobs could be created each year for communities that rely on the corridor such as Smithfield, Goldsboro, Kinston, New Bern, Havelock and Morehead City. Among other statistics, $1.2 billion could be added to the GRP, including $900 million in additional personal income, and as much as $56 million saved for existing businesses.
Local officials are hoping those positive effects ultimately extend to Sampson.
For years, Swope has sought — and local officials have extended incentives — to attract industries to locate permanently to Exits 348 and 355 off of I-40 in northern Sampson County with mixed success.
Another large interstate would only aid in that pursuit.
“The highest investment value is an interstate,” Swope said last year. “That is what potential investors look for when developing properties. To bring U.S. 117 on as I-795 would be one more strong asset toward improving and strengthening Sampson County’s economy.”
Lockamy said the new road is already getting plenty of use, which bodes well for the counties through which motorists are navigating.
“I traveled that road Saturday evening going into Goldsboro and the traffic was bumper to bumper coming down it,” Lockamy noted. “The traffic is used to it now.”
Chris Berendt can be reached at 910-249-4616. Follow us on twitter @SampsonInd.
Contribute
Comments
All user comments are subject to our Terms of Service. Users may flag inappropriate comments. | {
"pile_set_name": "Pile-CC"
} |
Reminder: Things can go bad even when racing slowly.
Those who enter rallies do so knowing full well there's a solid chance their car might not make it out in one piece. Crashing is just part of the rally game. This YouTube video shows how a handful of rally cars met their doom as they entered one very slick, low-speed corner.
A video shared on YouTube Sunday shows action from last weekend's Śląska Rally in Poland—or more specifically, a handful of rally cars at the rally crashing into a ditch. From the looks of the video, the cars came in hot, but not too hot, from a faster stretch of the rally stage, and were forced to slow down to handle the upcoming corner without going off the course. But because of the stretch of road near the corner is wet and muddy, some of the cars—mostly small European hatchbacks—have trouble making the corner. This, in turn, led to them driving into the ditch next to the course.
Going off a stage in rally happens. The important thing is whether you and the helpful spectators around you manage to push the car right-side-up so you can keep hustling down the course. | {
"pile_set_name": "Pile-CC"
} |
We have learned that our valued colleague and leader John T. Fleming, President and Chief Executive Officer of Superior Beverage Group, his wife Sue, sons Jack and Andrew, and two close friends were involved in an aircraft accident near Cleveland Thursday night. While search and rescue operations are under way, we are focusing our efforts on supporting the families involved. We are working closely with the proper authorities conducting the investigation. We appreciate the efforts of the first responders on the scene. | {
"pile_set_name": "OpenWebText2"
} |
Q:
JavaScript runtime error: Unable to add dynamic content
I'm making a javascript metro app and have some code like this:
<script>
document.writeln(foo());//this line is trouble
</script>
and when I tried to run, it gave me a rather long error:
Unhandled exception at line 20, column 9 in ms-appx://a375ffac-3b69-475a-bd53-ee3c1ccf4c4e/default.html
0x800c001c - JavaScript runtime error: Unable to add dynamic content.
A script attempted to inject dynamic content, or elements previously
modified dynamically, that might be unsafe. For example, using the
innerHTML property to add script or malformed HTML will generate this
exception. Use the toStaticHTML method to filter dynamic content, or
explicitly create elements and attributes with a method such as
createElement. For more information, see
http://go.microsoft.com/fwlink/?LinkID=247104.
How can I get around this?
A:
Windows 8 restricts the content you can set through innerHTML and Writeln, because it's considered unsafe...
The correct way to add content is:
// The untrusted data contains unsafe dynamic content
var unTrustedData = "<img src='http://www.contoso.com/logo.jpg' on-click='calltoUnsafeCode();'/>";
// Safe dynamic content can be added to the DOM without introducing errors
var safeData = window.toStaticHTML(unTrustedData);
// The content of the data is now
// "<img src='http://www.contoso.com/logo.jpg'/>"
// and is safe to add because it was filtered
document.write(safeData);
If your code has some javascript, you can use this function (But microsoft dont recomend it):
MSApp.execUnsafeLocalFunction(function() {
var body = document.getElementsByTagName('body')[0];
body.innerHTML = '<div style="color:' + textColor + '">example</div>';
});
See at:
http://msdn.microsoft.com/en-us/library/windows/apps/Hh767331.aspx
For your case:
MSApp.execUnsafeLocalFunction(function() {
document.writeln(foo());
});
Note that you should only do this if you understand your content is safe; if you don't, I would recommend using the toStaticHTML method.
A:
regarding to the docs I would try :
document.writeln(window.toStaticHTML(foo()));
| {
"pile_set_name": "StackExchange"
} |
Insulin-induced release of plasminogen activator from human blood platelets.
Incubation of washed platelets in Tyrode buffer, pH 7.5, with insulin (200 microU/ml) and CaCl2 (1.2 mM) at 37 degrees C for 3 h resulted in a threefold increase of plasminogen activator activity in the supernatant over the basal level as determined by both the amidolytic assay and the proteolysis of alpha-casein through the formation of plasmin from plasminogen. This plasminogen activator showed no plasmin-like activity and was inhibited by anti-tissue plasminogen activator antibody as well as by type 1 plasminogen activator inhibitor. The substrate specificity and the inhibition of the enzymic activity by various inhibitors indicated that the platelet plasminogen activator (pPA) was related to tissue-type plasminogen activator of relative molecular weight 56,000. Fibrinolytic activity of pPA and its insulin-dependent release were demonstrated by the shortening of euglobulin lysis time and by the clot lysis time of platelet-rich plasma from normal and type I diabetes mellitus patients. Treatment of platelet membranes with insulin also increased the release of pPA. Increased levels of adenosine 3',5'-cyclic monophosphate (cAMP) in platelets by incubation with various agents completely inhibited the insulin-induced release of the activator. On the other hand, inhibition of platelet aggregation by aspirin had no effect on the release of pPA, indicating that the effect of cAMP was not due to the inhibition of platelet aggregation by the nucleotide. | {
"pile_set_name": "PubMed Abstracts"
} |
August 30, 2011
First amendment gives the Press the right to publish news, information and opinions without government interference.
Sixth amendment guarantees that the defendant is tried in a court open to the public before an impartial jury.
The full accommodation of these seemingly over-lapping fundamental rights is rather challenging. The responsibility to establish a balance between the defendant’s right to a fair trial, the media's right to free speech and the public's right to an open court lies squarely on the shoulders of the presiding judge: Michael Pastor, in our case.
There are several measurements that a judge could employ to establish the aforementioned balance in his court. Jury sequestration is one of them.
JURY SEQUESTRATION
Sequestration is the practice of physically keeping the jury together and totally isolated from outside influences during the trial or deliberation stage, or both. This measure is usually taken only for high profile cases, where the massive media coverage may prejudice the jury's verdict, thus, violating the defendant’s six amendment rights.
In its most extreme form, when not in the courtroom hearing the case, jurors are kept under the constant supervision of a guard at an undisclosed location. Their contact with the outsiders including family is eliminated or curtailed. Any outgoing communication, if any allowed, is monitored to ascertain that their communication doesn’t involve the Trial.
It cost the state of California $3 million to sequester OJ Simpson jury for almost 9 months.
Scott Peterson jury was sequestered only during deliberation period for a week. Mark Geragos, Scott Peterson attorney requested full sequestration during the entire trial. Mr. Geragos stated “This gentleman beside me is fighting with one hand tied behind his back. I'm just trying to level the playing field.”Judge Alfred Delucchi denied the total sequestration request, reasoning that “if I was to tell people you can't see your loved ones for five months, you can't watch television, you can't listen to the radio, you're going to be locked away in a hotel somewhere ... it could have a negative effect on people who could get resentful that they've been locked up."JudgeDelucchi remarked that the jurors will be exposed to outside influences regardless and that "the only place this wouldn't happen is if we parked the jury on Mars. We can't do that."
Michael Jackson 2005 Trial was heard by a non-sequestered jury and despite of the intense worldwide coverage of the trial in detriment of Mr. Jackson, jury rendered
a verdict contrary to the media verdict, acquitting him of all 14 counts of charges.
in the court, stating “we would really like the decision to be made based upon
the evidence that is given in this courtroom and the arguments made inside
this courtroom as opposed to what happens on the Nancy Grace Show”
-Michael Flanagan
Judge Pastor asked the prosecution’s stance on the jury sequestration. Deputy Prosecutor David Walgren responded “the court had addressed the issue previously and advised all parties that the court was not inclined to do a sequestering of the jury 24/7. The People were comfortable with the court’s decision. That’s still our position.”
Judge Pastor then declared “at this juncture, I do not feel in any way, shape or form total sequestration of jury is necessary in this case. To have jurors undergo that kind of extraordinary deprivation, quiet frankly, unhealthy to the administration
of justice. I remain confident that jurors follow the law. They follow orders. I feel confident that the jurors understand their responsibility is to follow the evidence and to decide the case on the evidence and not to be influenced by the extraneous materials”. He then advised the defense team to file a motion for his consideration.
On August 18, 2011, Conrad Murray defense team filed a motion requesting jury sequestration. “This is an unusual Trial. There is a reasonable expectation that Dr. Murray’s Trial will be the most publicized in history” stated the motion which then went on to compare Conrad Murray case to Casey Anthony trial. “Television pundits such as Nancy Grace use air time to campaign for the conviction of Ms. Anthony. By feeding on the public anger, Grace’s viewership rose to one and half million per night in June Grace engaged in continuous character assassination with regard to Ms Anthony, the woman she condescendingly referred to as tot mom.”
And then came, in my opinion, highly incendiary and offensive remarks:
“Even if the jurors are instructed not to watch any news coverage, it is unrealistic to expect an unsequestered jury to avoid hearing about the case. Therefore, complete sequestration is necessary to eliminate the high risk of jury contamination. Dr. Murray respectfully asks this court for an order sequestering the jury during the entire trial, including jury deliberations” concluded the defense motion.
On August 25, 2011, Judge Michael Pastor denied the motion to sequester the jury.
Deputy District Attorney David Walgren stated that the prosecution didn’t feel the sequestration was necessary.
“There has to be a level of trust granted to the jurors” ~David Walgren
“Sequestered juries have indicated they have felt like inmates and they feel they were being imprisoned. They are monitored 24/7, they have minimal freedom of movement and they can’t even speak to loved ones without being monitored. Many sequestered jury indicated that they found the sequestration so frustrating, so intimidating and so cruel that it actually interfered with their assessment of the evidence and the law. While I raise the issue of cost, that is not the over-riding consideration. Justice trumps everything" stated judge Michael Pastor.
Ed Chernoff then stated that in Casey Anthony case media pundits offered their interpretation of the evidence and testimonies, acting as a quasi juror. He then requested that the judge ban the Trial from being televised. “I am suggesting that you consider in-court cameras, maybe amend it to prevent that particular problem” Chernoff said.
Judge Pastor responded “by problem, do you mean the exercise of first amendment? The first amendment is one of those cherished fundamental constitutional rights in the United States. That includes the right to comment.
Judge Michael Pastor then denied the motion for jury sequestration: “I expect that the jurors will follow the high road and that means that they will not be in the receipt of or in contact with information regarding this case. I have tremendous faith in the jury system and in the individual promises of jurors. The defense motion is denied."
In summary, Conrad Murray jury won't be sequestered and the Trial will be televised.
PROS OF SEQUESTRING JURY
Preventing exposure of the jurors to prejudicial publicity
Minimizing pressure from public for a particular verdict
Ensuring juror safety from harassment during trial
Promoting a perception of fairness due to no outside influences
CONS OF SEQUESTRING JURY
It is financially costly to the government
If an impartial jury isn’t acquired in the first place then it can’t be maintained by means of sequestering
It doesn't undo prejudice based on pretrial media coverage
It imposes jurors emotional harm if the sequestration period is long
It may be counter to truth-seeking because it:
vCan lead to a non-representative jury because only limited categories
of people are available for a jury that will be sequestered.
vCan cause jurors to rush to judgment to escape sequestration.
vCan cause the jurors to identify with the government (as caretaker) or against the government (as the jury’s jailer).
Marcia Clark on jury sequestration
"When jurors are forced to spend day and night with each other, apart from their families and friends, they become a tribe unto themselves. Because they only have each other for company, and because most people prefer harmony to discord, there’s a natural desire to cooperate, to compromise in order to reach agreement. And they have no safe retreat. If they disagree with their fellow jurors, they can’t go home to a husband, a wife, a friend, where they can regroup and marshal their energies. Make no mistake about it, sequestration is no picnic and I have sympathy and respect for the jurors who put up with that incredible hardship.
We can’t ignore the mental and emotional impact it has on the jurors—an impact that thwarts the whole point of drafting twelve individuals to decide a defendant’s fate"~Marcia Clark, OJ Simpson prosecutor
August 26, 2011
Despite of ardent fan protests and a letter from Michael Jackson Estate Executers,
Global Live Events announced that they are “%100 going ahead”. Yesterday, they announced Ne-Yo as part of their line-up. But would Ne-Yo have agreed to be participate IF he knew that Leonard Rowe is involved in 'Michael Forever Tribute'?
In 2007, LiveNations cancelled Janet Jackson’s Tour. Her dancers had counted on income from the Tour so she reached out to Leonard Rowe asking if he could promote
a 20 concert Tour. “I did not believe that she had the drawing power to tour” Leonard Rowe wrote in his book. He tried his best to convince Michael Jackson to tour as Janet being the opening act but there was no convincing Michael. So Mr. Rowe asked R Kelly to tour with Janet Jackson. R Kelley agreed. Later, Janet thought that R Kelley would steal the spotlight so she changed her mind about touring with R Kelly. Leonard Rowe proceeding planning just an R Kelley Tour. He booked Ne Yo as an opening act for R Kelley. Ultimately, both R Kelley and Ne Yo litigated Leonard Rowe.
Ne-Yo sued Leonard Rowe for breach of contract. Leonard Rowe had dropped Ne-Yo from the Tour without merit. On September 4, 2008, Ne-Yo was awarded $700,320
Fast forward to the present day….
“Latoya was the lead one” said Chris Hunt, President of Global Live Events regarding Jackson Family members backing for ‘Michael Forever Tribute’. Latoya and her company is very much involved & vested in the tribute. Paul Ring, vice president of Ja Tail business development, is also "Head of US Operations, Global Live Events"
Global Live Events CEO, Eric Bute directed Latoya's "Home' song
Ja Tail made a minor change in their website recently. The nature of the change is blaringly evident: to conceal Leonard Rowe involment in 'Michael Forever Tribute'. With his unpleasant history with Rowe, Ne-Yo might have had reservations in performing in the tribute had he known the Rowe connection. So they surreptitiously deleted evidence.
August 24, 2011
"We are %100 going ahead. We will continue to announce names for the line-up.
We are moving forward and now we will try to address issues that have been raised by fans" Global Live Events stated, inviting verified Michael Jackson fanclubs to take part in a conference call on August 30, in which our concerns will be allayed.
We have been Michael Jackson fans and members of fanclubs for our entire lives yet
we are not aware of the "verified fanclub” concept. Do you doubt our fanship? When Mr. Jackson was alive, never once did he limit his communications only to “verified Michael Jackson fanclubs”. We don't hear this utter nonsense from his Estate Executers either. We are ALL verified in the sense that we would walk through fire to make sure that an audacious company doesn’t cheapen Michael Jackson legacy and brand.
We do not want our concerns allayed, we would like them resolved and how can resolution be possible if your very first step towards us is “we are %100 going ahead”?The so-called tribute is taking place during Conrad Murray Trial. Our most pressing concern is the timing. It is futile to elaborate on why the timing is utterly inappropriate
for any decent human-being should be able to connect the dots.
Your invitation to fans is simply a PR stunt in light of adverse media coverage of your event. Your assertion of “we have been listening to the fans” is a bold-faced lie. We started our campaign BECAUSE you refuse to listen to us and consistently delete our comments from your facebook! We learnt from experience and started screen-capping our comments before you delete them. Here is a comment you deleted yesterday:
In a letter dated August 15, 2011, Michael Jackson Estate declared to Global Live Events
"Estate is the only entity that can grant the right to use Michael Jackson’s name, likeness or any of his intellectual property, whether such use is commercial or other purposes. We assume that you do not intend to use any intellectual property controlled by the Estate"
How does your company leap from receiving this communiqué from the Estate Executers
of Michael Jackson to selling tickets to commercialize a brand that is not your property?
Michael Jackson Estate is the single entity who owns and is responsible to protect the integrity of Michael Jackson brand which we believe you are tainting by an exceedingly questionable event marred with negative publicity. Adding insult to injury, you dub this lackluster event as a Michael Jackson “tribute”.Estate Executors communicated with you that “in light of confusion surrounding this ‘event’ we are extremely concerned about Michael’s legacy. We believe Global Live should address our concerns….”
Global Live Events owe Michael Jackson Estate Executers through and through explanation before they proceed. Your failure to seek Estate's approval demonstrates your lack of respect to the very man you are allegedly honoring.Let me remind you that it is your legal and moral obligation to the Estate Executors to resolve every single issue surrounding the event and have their approval before “%100 going ahead”
We realize that your financial interest indeed outweighs integrity. There is nothing decent about exploiting Mr. Jackson’s death for financial gain, doing so during Conrad Murray Trial and exploiting his young children as an advertising tool. We find the exploitation of Michael's children in your terms and conditions document totally abhorrent. Michael Jackson wrote a song about your ilk titled “money”, will that song be in the tribute line up?
Which brings us to another legal issue to be contended with.
Mr. Jackson worked very hard to build one of the most profitable brands of all time. His brand stands for unsurpassed quality and “magic”.There is nothing quality or magical about Michael Forever Tribute which is simply a circus show of has-beens or rookies.
You stated that you have the backing of “overwhelming majority” of the Jackson Family. So what? Jackson Family doesn’t own Michael Jackson brand, his Estate does…solely. Jackson family has no authority to broker Michael image, likeness and songs all of which you declared you will exploit. The Executers clearly communicated to you that you do NOT have their permission to use their intellectual property. Either you intend to violate copyright laws or you are defrauding public by false advertising.
Unless you show willingness to modify terms surrounding Michael Forever Tribute, including but not limited to the timing & unless a representative of Michael Jackson Estate is present, our answer to your conference call is a resounding NO!
We propose that you proceed with the concert but cease and desist the use of Michael Jackson name, likeness & songs. This is a reasonable compromise.
Most of your attendees are fans of the participating artists. Since you are determined to “go ahead” and we are determined not to let that happen with the current terms, why don't we reach an agreement where everyone wins? Our proposal satisfies all parties:
August 22, 2011
Gentlemen, we are writing you once again in regards to the Michael Forever Tribute.
As you know, Michael Jackson worldwide fan community ardently objects and protests the October 2011 tribute. The fans who cherished a very closed-knit relationship with Mr. Jackson would want nothing more than a befitting tribute in his honor…but in due time & organized with utmost care and professionalism.
Under the current circumstances, Michael Forever tribute produces an outcome opposite of what is being marketed. The tribute is simply tasteless, improper, impractical, insensitive and disrespectful. There is no way to resolve the issues we have with this tribute. Since the announcement of this tribute, the fan community has been upset and unable to focus on the upcoming trial. Every day, we wake up hoping for a cancellation and to our dismay, we encounter deafening silence. We've learnt that Michael Forever Tribute facebook is maintained by a ticketing company who doesn't have answers.
Estate Executers had asked you to “address our concerns and those of Michael's loyal fans”. To date, you haven’t communicated with neither the fans nor the Executors of Michael Jackson -you know, the gentelman you are purportedly paying tribute to. If you don’t respect his Estate or his fans then where do you get off monetizing Michael Jackson’s name? You don’t even bother answering simple customer service questions about the event, let alone addressing grave concerns which were made known to you. Yet you proceed to selling tickets nonchalantly. Global Live Events could really benefit from a crash course on business ethics, integrity, professionalism and customer service.
You are prolonging an unpleasant situation to gauge if you could garner enough ticket buyers who are fans of the attending artists. Do you think that the negative media coverage is beneficial for your company reputation or ticket sales?
Since you don't have enough regard for Michael Jackson to cancel out of respect for him, since your corporate aspirations weigh heavier than doing what’s morally right, we propose this compromise: Drop Michael's name and proceed with the concert with the artists you already booked, including the Jacksons. We only request that you don’t use or refer to Mr. Jackson’s name in any shape or form and that the participating artists including the Jacksons don't butcher…I mean attempt to sing Mr. Jackson’s songs.We find this to be a reasonable compromise for all.
We present our offer for your consideration and expect preferably an immediate cancellation or a modification. Look forward to your response as practicable as possible.
August 19, 2011
Thank you for your prompt reaction in regards to the Michael Forever Tribute.
We realize that unlike fans who react with raw emotion, the Estate executors approach matters with composed diplomacy and that there is a legal chain of actions to be followed. The Fan Community is in total agreement with every concern outlined in the letter from the Estate to the Michael Forever Tribute organizers. And whilst we are confident that the Estate will follow through and take the necessary legal actions in the event that the organizers aren’t compliant, we would like to communicate with you our sentiments in regard to some disconcertingissues relevant to the Michael Forever tribute.
Timing: The Fan Community feels that the timing of this event aims to exploit
the Conrad Murray trial. It is exceedingly insensitive, tasteless and improper.
Caliber of artists: We feel that Michael Forever Tribute isn’t a tribute to honor Michael Jackson. It is merely a concert of various artists but the organizers exploit Michael Jackson’s name to garner interest in the event. The participating artists aren’t selected carefully based on the special connection they may have to Mr. Jackson. Rather, Global Live Events extends invitations to any artist who may agree to participate. They are scraping the bottom of the barrel. We feel that the haphazard and sloppy organization so far will not produce a fitting tribute. We would like the official Tribute to come in due time, preferably organized by Michael’s children and sanctioned by his Estate.
Questionable intent: We feel that the intention of the tribute isn’t to pay homage to Michael Jackson but to capitalize on his good name. We don’t feel that a mere concert with mosaic of artists thrown together on the 11th hour is a suitable tribute
Aptitude of Global Live Events: The Company was formed on March 29, 2011. As evidenced by their incompetency so far, we feel that the inexperienced organizers will fall short in organizing a deserving tribute to Michael Jackson.
Paul Ring who is dubbed as "Global Live Events Executive" is also Latoya's employee. This screams conflict of interest. Latoya appears to be the force behind this exploitation of Michael & his children under the guise of a "tribute".
Latoya Jackson 'Starting Over' book, page 340
Global Live Events CEO Eric Bute & Latoya Jackson
Questionable ticketing: We don't get a sense that this tribute is for L.O.V.E.
It is all about money. Fans are required to pledge to charities in addition to the ticket price. Surreptitiously, the organizers use fans’ donations to assert that
the tribute is for a charitable cause. Then why aren’t they donating part of their profits to charities? We don’t even know where the proceedings are going.
Ticketing policy: The organizer declared “If %50 or more of the contracted artists ATTEND OR PERFORM, the concert will take place and NO refunds will be offered”. We believe that the %50 is covered by the Jacksons' appearances and that the announced artists may attend but not necessarily perform. Attending public should receive exactly what the organizers advertised, they shouldn't be short-changed or duped. The promoter aims to cheat the public with fine print. Doing so in Michael's name dishonors Michael's good name & memory.
Gene Simmons:Global Live Events invited someone who not only made public disparaging remarks about Michael but also his children. We feel that the organizer should have been more diligent in carefully selecting artists. We can forgive Mrs. Jackson; due to her age, perhaps she didn’t know who Kiss is or about Gene Simmons remarks but it's hard to believe that Jackson siblings didn’t know about it. We feel that they proceeded despite of the knowledge.
When we TRIED communicating our concerns about Kiss, our voices fell on deaf ears. Promoter deleted our comments from its facebook and tweeted a promotional video nonchalantly. It took a letter from the Estate for them to address this issue. They shut out the very people they are trying to sell tickets to.
After dropping Kiss today from their line-up, the organizer released this statement:
“We have listened to Michael's fans and are grateful to have been alerted to these unfortunate statements by Gene Simmons. Under the circumstances,
we fully agree that even though Kiss is a band Michael admired, we have no choice but to rescind our invitation to them to appear in our tribute”
Whom Global Live Events heard was NOT “Michael’s fans” but a potential lawsuit and the possibility of the Estate Executers throwing a monkey wrench into their event. We are also displeased by their absurd remark that Michael admired Kiss. That is a completely inaccurate nonsense. We do NOT feel right about Global Live Events, we do not trust them, we do not wish to do business with them.
Recent headlines dragged Mr. Jackson’s name in mud so close to the jury selection to the Conrad Murray trial. We feel this may have tainted the potential jury pool. We do not feel that dropping Kiss suffices. The damage is already done. We didn't sense any genuine regret from the statement by Global Live Events.
WE DO NOT ACCEPT THEIR APOLOGY!
Most of the attendees are fans of participating artists. Michael Jackson fans are troubled that his name is used to sell this concert. If they desire to proceed, then they should just market it as a concert event without involving MJ's name into it.
With the upcoming criminal trial, fans would like to focus only on the trial. We find it near impossible to do so because of constant debacles related to this tribute.
It’s Michael Forever Tribute. His mother, siblings and children are involved. The use of Michael Jackson image and likeness is bound to happen.We cordially request that the Estate commence the necessary steps to acertain that this Tribute either doesn’t happen or it doesn’t happen as a Michael Jackson tribute.
We hope that you will attend this matter in a timely manner so that the storm in our community may pass & we may focus on the upcoming Conrad Murray trial.
We, as Michael Jackson's staunch supporters, refuse to support the Michael Forever Tribute, planned by Global Live Events in October, 2011. Even after the removal of Kiss, we feel that the damage is already done. This colossal mistake could have been avoided, had you exerted the diligence required to organize a befitting tribute. You have proven that you will book just any artist who affirms your invitation. This monumental mistake cannot be forgiven, given the magnitude of the damage it caused so close to the criminal trial. Your apology is too little too late and it does not solve the problems we have with this tribute in general.
Since the initial announcement of the event, fans tried communicating with you in regards to our very valid concerns, have we not? Instead of acknowledging, hearing and working together with us, you have deleted “selected” comments from your facebook page, forcing us to form our own facebook Group: Fans Against Michael Forever Tribute.It shouldn't have come to this. Any company who conducts business in Michael Jackson's name should better know that Michael and his fans have cherished a close-knit relationship where we were always heard and communicated with. We refuse to be treated this way by you!
You only addressed the Gene Simmons issue after the Estate's letter. Therefore, the contention that you "listened to Michael's fans" is empty words uttered to save face in the media. Global Live Events rescinded their offer to Kiss only to qualm the media and the Estate. Simply put, the Kiss cancellation is merely a product of the negative media coverage which stood to affect ticket sales and your profit. It was not done out of respect to Michael Jackson. You've no respect for Michael.
The timing of this tribute in the middle of Conrad Murray's trial, ticketing arrangements, faraway location, obscurity over what charities will be receiving the donations, obscurity over who is pocketing the profits, no-guarantee policy of performers.....the issues with this tribute keep piling up, thus, breaking our focus away from the criminal trial. We find this very upsetting. The addition of Gene Simmons, thus, tarnishing Michael Jackson's name was simply the last straw for us. With the damage you caused, it will be us fans having to fix your mistake.
Michael Forever Tribute is not proper at this time for myriad of reasons. We hope we can resolve this matter amicably so that perhaps in the future when a Tribute is planned, you could be part of the production, with more care and diligence.
Understand that we will not rest until this tribute is cancelled. We do NOT care who from the Jackson family is supporting it. We condemn the exploitation of Michael's children & his mother to legitimatize your tribute!!!
We cordially invite you to announce the cancellation of Michael Forever Tribute. | {
"pile_set_name": "Pile-CC"
} |
Quiksilver Technical Figueira da Foz (Portugal), will participate on this year's Kayaksurf & Waveski circuit with two athletes: José Morais (owner of the store) and Gonçalo Duarte (surfkayaker). Meet the team and check the photos. The swell was not so good but was only to present the Team. Both riders belong to the Figueira Kayak Clube. | {
"pile_set_name": "Pile-CC"
} |
Is racial bias built into U.S. immigration law? “The first instance of any kind of visa as we know it for a legal way to come into the system started with the Chinese Exclusion Act of 1884,” according to Jenny Yang, Director of Advocacy and Policy for World Relief’s Refugee and Immigration Program. Scientific data was circulated as evidence that Chinese people were inferior and ought to be kept out. However, immigration law based on race was abolished in 1965. “Still, a lot of reforms are needed.” | {
"pile_set_name": "Pile-CC"
} |
[Rhinoviruses].
Human rhinoviruses (RV) belong to the Picornaviridae and are divided into three species: rhinovirus A, B and C. As causative viruses of upper airway infections (common cold), they possess enormous epidemiological and clinical importance. Furthermore, rhinoviruses are significant pathogens of acute exacerbations of chronic airway diseases such as asthma and chronic obstructive pulmonary disease. Their role as a cofactor in the development of pneumonia and their relevance in critically ill patients is still unclear and the focus of current research. Due to the unspecific clinical symptoms, diagnosis is difficult. Laboratory detection is sophisticated and a distinction between clinically relevant infection and contamination not always possible. Specific therapeutic antiviral strategies against rhinovirus infection do not exist as yet and, due to the large variety of subtypes, the development of vaccines remains a considerable challenge. | {
"pile_set_name": "PubMed Abstracts"
} |
Product Description
Brooke Marks: Sleep Creep
767 MB | 14:29 Video Runtime | Resolution 1920 x 1080
Gallery Size: 31 pictures | 3000 x 2000 pixels
FAN REQUEST COME TO LIFE!
Brooke Marks needs to recharge her modeling batteries, so she requests a power nap from her photographer – the only stipulation is that Brooke needs the A/C on full blast to get restful sleep. Her photographer agrees, after all, who likes sleeping in a sweltering room with no air conditioning? Brooke adjusts the temperature controls and disappears into the bedroom for a power-hour nap.
Unbeknownst to poor Brooke, her photographer plots against her slumber for sinful reasons. Brooke falls into a serene sleep just in time for her photographer to adjust the thermostat to Amazonian heat levels.
As the temperature rises, Brooke’s nap becomes increasingly elusive, she strips off her light cotton lingerie in an effort to find relief from the heat. In her twilight conscious, she poses around the bed, moving covers and pillows in an effort to relax.
Brooke never manages to have a successful sleep, but you’ll enjoy plenty of gratuitous nude napping footage. Follow the camera into the room, between her sheets, and overhead as she sleeps – leading to fully exposed areas of Brooke’s stunning body.
Brooke Marks may never trust a camera crew near her while she sleeps again – so don’t miss this sexy sleepy-fetish download! | {
"pile_set_name": "OpenWebText2"
} |
Q:
Apple rejected an app that for use on non public api where there aren't any non pulic apis
This is the message I got from Apple for rejecting my app:
Your app uses or references the following non-public APIs:
didDetermineState:forRegion:
didEnterRegion:
didExitRegion:
The use of non-public APIs is not permitted on the App Store because it can lead to a poor user experience should these APIs change.
I really don't know what to do as there api are clearly public. Anyone got some advise? It would really help.
A:
I think the public apis you are mentioning about are those in CLLocationManagerDelegate. If it is the case, take didEnterRegion:, for example, the api is actually locationManager:didEnterRegion:. However, Apple mentions didEnterRegion: only. That probably means somewhere in your app, you have declared a method with that exact signature, and it happens to have the same signature with a private api method.
My suggestion is to do a search on your whole project for such methods and rename them.
| {
"pile_set_name": "StackExchange"
} |
// Copyright (c) Microsoft Open Technologies, Inc. All rights reserved. See License.txt in the project root for license information.
namespace System.Data.Entity.TestModels.ProviderAgnosticModel
{
using System;
public enum AllTypesEnum
{
EnumValue0 = 0,
EnumValue1 = 1,
EnumValue2 = 2,
EnumValue3 = 3,
};
public class AllTypes
{
public int Id { get; set; }
public bool BooleanProperty { get; set; }
public byte ByteProperty { get; set; }
public DateTime DateTimeProperty { get; set; }
public decimal DecimalProperty { get; set; }
public double DoubleProperty { get; set; }
public byte[] FixedLengthBinaryProperty { get; set; }
public string FixedLengthStringProperty { get; set; }
public string FixedLengthUnicodeStringProperty { get; set; }
public float FloatProperty { get; set; }
public Guid GuidProperty { get; set; }
public short Int16Property { get; set; }
public int Int32Property { get; set; }
public long Int64Property { get; set; }
public byte[] MaxLengthBinaryProperty { get; set; }
public string MaxLengthStringProperty { get; set; }
public string MaxLengthUnicodeStringProperty { get; set; }
public TimeSpan TimeSpanProperty { get; set; }
public string VariableLengthStringProperty { get; set; }
public byte[] VariableLengthBinaryProperty { get; set; }
public string VariableLengthUnicodeStringProperty { get; set; }
public AllTypesEnum EnumProperty { get; set; }
}
}
| {
"pile_set_name": "Github"
} |
Cardiac ischemia is a condition that results from insufficient oxygenation to heart muscle and may pose an inherent risk in addition to potentially being a precursor to a life threatening event, such as myocardial infarction (MI). Detecting ischemia may be carried out by a variety of methods, some of which are amendable to implantable monitoring devices. Ischemia, and particularly, unstable ischemia, in a patient may be treated in a clinical setting by a variety of modalities.
A patient with severe unstable ischemia may be a candidate for immediate intervention, such as coronary angioplasty or bypass surgery. However, less severe cases may be treated by pharmaceutical methods as well as others. Even with such treatment modalities available, most ischemic events occur initially outside the clinical environment or at a place or time when such clinical assessment and treatment is not immediately available.
For ICD patients experiencing transient ischemia, standard ventricular pacing therapy in order to increase cardiac output is contraindicated as the increased heart rate induced as a result of the pacing will typically increase the oxygen demand on the heart tissue, and particularly the ischemic heart tissue, which may further exacerbate any damage caused by the ischemia. In addition, generally speaking, a paced rhythm is not as mechanically efficient as a normal sinus rhythm, and, as such, the blood flow output may even be further reduced. Thus, typical single chamber ventricle pacing therapy for an ischemic patient may increase oxygen demand of the heart tissue undergoing ischemic trauma and decrease the pumping efficiency of the heart overall or both.
As such, what has been needed are methods and devices for treating a patient with transient ischemia immediately after onset of the ischemia that do not generate a substantial increase in oxygen consumption by the heart. | {
"pile_set_name": "USPTO Backgrounds"
} |
Characterization of the novel HLA-DRB3*03:37 allele by sequencing-based typing.
HLA-DRB3*03:37 differs from HLA-DRB3*03:01:01:01 by one nucleotide substitution in codon 205 in exon 4. | {
"pile_set_name": "PubMed Abstracts"
} |
Q:
Multiplication error in php
I'm building a site where people can exchange coins (site currency) into Bitcoin. The problem I'm having is that for some reason when I multiply the $btcprice with 3 or less the echo is really weird... for your sake this is the code that matters:
<?php
// get 0,01 usd in bitcoins into a variable
$btcprice = file_get_contents('https://blockchain.info/tobtc?currency=USD&value=0.01');
$valueInBTC = 4 * $btcprice;
echo $valueInBTC;
?>
Anything that's 4 or higher will work, but if you try to multiply this with 3 or less it gets weird. For example this:
<?php
// get 0,01 usd in bitcoins into a variable
$btcprice = file_get_contents('https://blockchain.info/tobtc?currency=USD&value=0.01');
$valueInBTC = 3 * $btcprice;
echo $valueInBTC;
?>
Will echo 7.959E-5
I just don't understand what the problem is...
A:
The result you are getting is not an error. It is simply in a formatting you don't expect / know yet. 7.959E-5is exactly the same as 0.00007959 it is just a different way of writing it down. Think of it as 7.959E-5 = 7.959 × (10 ^ (-5)) = 0.00007959. It is called Scientific notation (E notation). In cumputation / science this notation is used, because you can show very large or very small (as in your case) numbers with less digits (it is just shorter to write).
To get the number in other formattings use the php function sprintf().
As you are handling bitcoin values, you shouldn't be formatiing the numbers until just for output. With bitcoins you always deal with very small numbers and you will soon meet precision problems if you try and calculate with formatted floating point numbers.
| {
"pile_set_name": "StackExchange"
} |
Frithy and Chadacre Woods
Frithy and Chadacre Woods is a 28.7 hectare biological Site of Special Scientific Interest (SSSI) in the parishes of Lawshall and Shimpling in Suffolk, England.
Description
Three ancient and semi-natural woods form the SSSI, namely Frithy Wood in Lawshall parish and Ashen Wood and Bavins Wood on the Chadacre Estate in Shimpling parish.
All three woods are of the wet ash (Fraxinus excelsior) / maple (Acer campestre) type, with hazel (Corylus avellana) also present in considerable quantity. There are pedunculate oak (Quercus robur) trees and other tree and shrub species include aspen (Populus tremula), wild cherry (Prunus avium), midland hawthorn (Crataegus laevigata), hornbeam (Carpinus betulus), crab apple (Malus sylvestris), holly (Ilex aquifolium), spindle (Euonymus europaeus) and common dogwood (Cornus sanguinea). The structure of the woods has been greatly influenced by management of the coppice.
The three woods have a diverse woodland floor vegetation, which is dominated by either dog's mercury (Mercurialis perennis) or brambles (Rubus spp.). They contain a number of plants characteristic of woodlands of this type including herb paris (Paris quadrifolia) in Ashen Wood and wood spurge (Euphorbia amygdaloides), woodruff (Galium odoratum), sanicle (Sanicula europaea) and stinking iris (Iris foetidissima) in Frithy Wood. The SSSI lies within the distribution of oxlip (Primula elatior) and all three woods contain this species. There are many other woodland floor plants including early purple orchid (Orchis mascula), twayblade (Neottia ovata), gromwell (Lithospermum officinale) and bluebell (Hyacinthoides non-scriptus).
There are several well-vegetated rides in the group of woods that support a mixture of woodland and meadow plant species and which attract considerable numbers of common butterflies. Frithy Wood also contains an area of pasture which projects into the wood which is partly shaded by a number of standard trees.
The birdlife of Frithy Wood has been recorded in detail with species including the nightingale, European green woodpecker, great spotted woodpecker and lesser spotted woodpecker which breed regularly.
Roe deer, fallow deer and muntjac can also be seen in the woods but they have caused considerable damage to the ground vegetation.
Forest school
Forest school sessions are held in Frithy Wood by permission of the landowners. The 'school' represents an initiative of All Saints Primary School, Lawshall and the Green Light Trust, an environmental and educational charity.
History
Oliver Rackham has stated that "a wood now called The Frith is almost certain to be pre-conquest, from Old English Fyrhp." In a later book he stated that "an Anglo-Saxon (parallel) is fyrth, a wood, which has given rise to many Frith or Frithy Woods."
There is documentary evidence for the existence of Frithy (formerly Frith) Wood back to 1545 and its Saxon name would imply that the wood is much older than that. All three woods are part of ancient woodland and contain broad boundary banks and ditches typical of coppice woods dating from the medieval period or before.
In more recent times in the twentieth century pigs were kept in Frithy Wood and at one time the wood extended as far as The Street.
Newspaper records
On 31 August 1921 it was reported in the Suffolk Free Press that the remains of George Nunn aged 55 of Lawshall were discovered hanging in Frithy Wood. He had been missing for around 4 months since 22 April and was found a short distance from where he lived.
Access
The woods are not private with easy access.
References
Category:Forests and woodlands of Suffolk
Category:Lawshall
Category:Sites of Special Scientific Interest in Suffolk
Category:Sites of Special Scientific Interest notified in 1987 | {
"pile_set_name": "Wikipedia (en)"
} |
<?php
/**
* Specialized implementation of hook_page_manager_task_tasks(). See api-task.html for
* more information.
*/
function page_manager_contact_user_page_manager_tasks() {
if (!module_exists('contact')) {
return;
}
return array(
// This is a 'page' task and will fall under the page admin UI
'task type' => 'page',
'title' => t('User contact'),
'admin title' => t('User contact'),
'admin description' => t('When enabled, this overrides the default Drupal behavior for displaying the user contact form at <em>user/%user/contact</em>. If no variant is selected, the default Drupal user contact form will be used.'),
'admin path' => 'user/%user/contact',
// Callback to add items to the page managertask administration form:
'task admin' => 'page_manager_contact_user_task_admin',
'hook menu alter' => 'page_manager_contact_user_menu_alter',
// This is task uses 'context' handlers and must implement these to give the
// handler data it needs.
'handler type' => 'context', // handler type -- misnamed
'get arguments' => 'page_manager_contact_user_get_arguments',
'get context placeholders' => 'page_manager_contact_user_get_contexts',
// Allow this to be enabled or disabled:
'disabled' => variable_get('page_manager_contact_user_disabled', TRUE),
'enable callback' => 'page_manager_contact_user_enable',
);
}
/**
* Callback defined by page_manager_contact_user_page_manager_tasks().
*
* Alter the user view input so that user view comes to us rather than the
* normal user view process.
*/
function page_manager_contact_user_menu_alter(&$items, $task) {
if (variable_get('page_manager_contact_user_disabled', TRUE)) {
return;
}
// Override the user view handler for our purpose.
if ($items['user/%user/contact']['page callback'] == 'contact_user_page' || variable_get('page_manager_override_anyway', FALSE)) {
$items['user/%user/contact']['page callback'] = 'page_manager_contact_user';
$items['user/%user/contact']['file path'] = $task['path'];
$items['user/%user/contact']['file'] = $task['file'];
}
else {
// automatically disable this task if it cannot be enabled.
variable_set('page_manager_contact_user_disabled', TRUE);
if (!empty($GLOBALS['page_manager_enabling_contact_user'])) {
drupal_set_message(t('Page manager module is unable to enable user/%user/contact because some other module already has overridden with %callback.', array('%callback' => $items['user/%user/contact']['page callback'])), 'error');
}
}
}
/**
* Entry point for our overridden user view.
*
* This function asks its assigned handlers who, if anyone, would like
* to run with it. If no one does, it passes through to Drupal core's
* user view, which is user_page_view().
*/
function page_manager_contact_user($account) {
// Load my task plugin:
$task = page_manager_get_task('contact_user');
// Load the account into a context.
ctools_include('context');
ctools_include('context-task-handler');
$contexts = ctools_context_handler_get_task_contexts($task, '', array($account));
$output = ctools_context_handler_render($task, '', $contexts, array($account->uid));
if ($output !== FALSE) {
return $output;
}
module_load_include('inc', 'contact', 'contact.pages');
$function = 'contact_user_page';
foreach (module_implements('page_manager_override') as $module) {
$call = $module . '_page_manager_override';
if (($rc = $call('contact_user')) && function_exists($rc)) {
$function = $rc;
break;
}
}
// Otherwise, fall back.
return $function($account);
}
/**
* Callback to get arguments provided by this task handler.
*
* Since this is the node view and there is no UI on the arguments, we
* create dummy arguments that contain the needed data.
*/
function page_manager_contact_user_get_arguments($task, $subtask_id) {
return array(
array(
'keyword' => 'user',
'identifier' => t('User being viewed'),
'id' => 1,
'name' => 'uid',
'settings' => array(),
),
);
}
/**
* Callback to get context placeholders provided by this handler.
*/
function page_manager_contact_user_get_contexts($task, $subtask_id) {
return ctools_context_get_placeholders_from_argument(page_manager_contact_user_get_arguments($task, $subtask_id));
}
/**
* Callback to enable/disable the page from the UI.
*/
function page_manager_contact_user_enable($cache, $status) {
variable_set('page_manager_contact_user_disabled', $status);
// Set a global flag so that the menu routine knows it needs
// to set a message if enabling cannot be done.
if (!$status) {
$GLOBALS['page_manager_enabling_contact_user'] = TRUE;
}
}
| {
"pile_set_name": "Github"
} |
Our main objective is to characterize the immunological properties and molecular nature of inappropriate antigens detected on SJL/J reticulum cell sarcoma (RCS) and to define the role of these antigens in tumorogenesis. We plan to demonstrate the presence of inappropriate alloantigens on spontaneous, transplantable and cultured RCS cells by cell mediated and complement cytotoxicity, and by immunofluorescence. Furthermore, biochemical analysis of inappropriate antigens will be examined by immune precipitation of NP40 lysed 35S methionine labeled tumor cells with specific alloantisera and characterization of the molecules by SDS gel electrophoresis. The role of inappropriate antigens in host stimulation will be investigated by examining the in vivo response to inappropriate alloantigenic specificities in both cellular and antibody mediated assays. The mechanism by which the immune response promotes tumor escape from immune destruction will be investigated including the role of antigen-antibody complexes in specific anti-tumor-antigen-reactive cell opsonization, modulation of tumor associated antigens by circulating antibody, direct tumor mediated suppression of antigen-reactive cells and activation of suppressor cells. | {
"pile_set_name": "NIH ExPorter"
} |
Q:
Removal of special characters, a comma separated text, PHP
I got my text variable which is user-specified, normally, user should enter the tags which has to look following:
"food, community, relationship"
but if user type for example
"food;;[]'.'.;@$#community,,,-;,,,relationship"
the script should change it into:
"food, community, relationship".
How can I get this done?
A:
how about:
$str = "-----music,,,,,,,,games;'235@#%@#%media";
$arr = preg_split("/\W+/", $str, -1, PREG_SPLIT_NO_EMPTY);
$str = implode(', ', $arr);
echo $str,"\n";
output:
music, games, 235, media
You could adapt the \W to which characters you need to keep.
| {
"pile_set_name": "StackExchange"
} |
{
"short_name": "React App",
"name": "Create React App Sample",
"icons": [
{
"src": "favicon.ico",
"sizes": "64x64 32x32 24x24 16x16",
"type": "image/x-icon"
}
],
"start_url": "./index.html",
"display": "standalone",
"theme_color": "#000000",
"background_color": "#ffffff"
}
| {
"pile_set_name": "Github"
} |
[The rescue station--a multidisciplinary treatment unit in the hospital].
The creation of integrative organizational structures are seen as an objective requirement of medicine characterized by progress of knowledge and specialisation. For emergency cases the rescue station has stood the test as a multidisciplinary unit of the hospital. This thesis is confirmed by experiences obtained from practical work in the Frankfurt/Oder District Hospital and by discussions in the "Working Group Rescue Station" of the "Society of Emergency Medicine of the GDR." In order to realize the function of the rescue chain as well as the multidisciplinary motivation, intensive quantitative and qualitative promotion of rescue stations is required. | {
"pile_set_name": "PubMed Abstracts"
} |
YA/Teen Book Club
The YA/Teen Book Club is now reading In Other Lands by Sarah Rees Brennan.
“Four years in the life of an unloved English schoolboy who’s invited to a secret magical school and learns that even in fantasyland, real life is messier than books. . . . But over the course of four years training among child soldiers, Elliot, unsurprisingly, grows up. His slow development into a genuinely kind person is entirely satisfying, as is his awakening to his own bisexuality and to the colonialism, sexism, and racism of Borderlands society. . . . A stellar . . . wholly rewarding journey.”
―Kirkus Reviews (starred review)
Pick up a copy of In Other Lands today at Griffin Free and then join us on Wednesday, May 30 at 5:30 PM for a lively discussion. | {
"pile_set_name": "Pile-CC"
} |
Q:
CSS minify and rename with gulp
I've a variable like
var files = {
'foo.css': 'foo.min.css',
'bar.css': 'bar.min.css',
};
What I want the gulp to do for me is to minify the files and then rename for me.
But the tasks is currently written as (for one file)
gulp.task('minify', function () {
gulp.src('foo.css')
.pipe(minify({keepBreaks: true}))
.pipe(concat('foo.min.css'))
.pipe(gulp.dest('./'))
});
How to rewrite so it work with my variable files defined above?
A:
You should be able to select any files you need for your src with a Glob rather than defining them in an object, which should simplify your task. Also, if you want the css files minified into separate files you shouldn't need to concat them.
var gulp = require('gulp');
var minify = require('gulp-minify-css');
var rename = require('gulp-rename');
gulp.task('minify', function () {
gulp.src('./*.css')
.pipe(minify({keepBreaks: true}))
.pipe(rename({
suffix: '.min'
}))
.pipe(gulp.dest('./'))
;
});
gulp.task('default', ['minify'], function() {
});
A:
I tried the earlier answers, but I got a never ending loop because I wasn't ignoring the files that were already minified.
First use this code which is similar to other answers:
//setup minify task
var cssMinifyLocation = ['css/build/*.css', '!css/build/*.min.css'];
gulp.task('minify-css', function() {
return gulp.src(cssMinifyLocation)
.pipe(minifyCss({compatibility: 'ie8', keepBreaks:false}))
.pipe(rename({ suffix: '.min' }))
.pipe(gulp.dest(stylesDestination));
});
Notice the '!css/build/*.min.css' in the src (i.e. var cssMinifyLocation)
//Watch task
gulp.task('default',function() {
gulp.watch(stylesLocation,['styles']);
gulp.watch(cssMinifyLocation,['minify-css']);
});
You have to ignore minified files in both the watch and the task.
| {
"pile_set_name": "StackExchange"
} |
A Lipid Transfer Protein Variant with a Mutant Eight-cysteine Motif Causes Photoperiod-thermo-sensitive Dwarfism in Rice.
Plant height is an important trait for plant architecture patterning and crop yield improvement. Although the pathways involving in gibberellins and brassinosteroid have been well studied, there are still many gaps in the picture of the networks controlling plant height. Here, we revealed that a dominant photoperiod- and thermo-sensitive dwarf mutant is caused by the active role of a mutated gene Ptd1, of which the wild-type gene encodes a non-specific lipid transfer protein (nsLTP). The Ptd1 plants showed severe dwarfism under long-day and low-temperature conditions, but grew nearly normal under short-day and high-temperature conditions; these phenotypic variations were associated with the Ptd1 mRNA level and its protein accumulation. Furthermore, we found that the growth inhibition in Ptd1 might result from the special protein conformation of Ptd1 due to loss of two disulfide bonds in the Eight-cysteine motif (8-CM) that is conserved among nsLTPs. Our findings give new insights into the understanding of the novel function of disulfide bonds in 8-CM, and provide a new strategy for regulation of cell development and plant height, by modifying the amino acid residues involved in protein conformation patterning. | {
"pile_set_name": "PubMed Abstracts"
} |
Comparing alignment methods for inferring the history of the new world lizard genus Mabuya (Squamata: Scincidae).
The rapid increase in the ability to generate molecular data, and the focus on model-based methods for tree reconstruction have greatly advanced the use of phylogenetics in many fields. The recent flurry of new analytical techniques has focused almost solely on tree reconstruction, whereas alignment issues have received far less attention. In this paper, we use a diverse sampling of gene regions from lizards of the genus Mabuya to compare the impact, on phylogeny estimation, of new maximum likelihood alignment algorithms with more widely used methods. Sequences aligned under different optimality criteria are analyzed using partitioned Bayesian analysis with independent models and parameter settings for each gene region, and the most strongly supported phylogenetic hypothesis is then used to test the hypothesis of two colonizations of the New World by African scincid lizards. Our results show that the consistent use of model-based methods in both alignment and tree reconstruction leads to trees with more optimal likelihood scores than the use of independent criteria in alignment and tree reconstruction. We corroborate and extend earlier evidence for two independent colonizations of South America by scincid lizards. Relationships within South American Mabuya are found to be in need of taxonomic revision, specifically complexes under the names M. heathi, M. agilis, and M. bistriata (sensu, M.T. Rodrigues, Papeis Avulsos de Zoologia 41 (2000) 313). | {
"pile_set_name": "PubMed Abstracts"
} |
Hugh Lucas-Tooth
Sir Hugh Vere Huntly Duff Munro-Lucas-Tooth, 1st Baronet (13 January 1903 – 18 November 1985), born and baptised Hugh Vere Huntly Duff Warrand and known as Sir Hugh Vere Huntly Duff Lucas-Tooth, 1st Baronet, from 1920 to 1965, was a Scottish British Conservative politician. Elected to parliament in 1924 at the age of 21, he was the first British MP to have been born in the 20th century.
Family
Warrand's father was Hugh Munro Warrand (8 July 1870 – 11 June 1935, married 24 April 1901), Major in the 3rd Battalion of the Queen's Own Cameron Highlanders, and son of Alexander John Cruikshank Warrand of Bught, Inverness-shire.
Warrand's mother Beatrice Maude Lucas Lucas-Tooth (died 25 June 1944) was a daughter of Sir Robert Lucas-Tooth, 1st Baronet. Warrand's great-grandfather was Robert Tooth, a prominent Australian businessman. His brother Selwyn John Power Warrand (6 February 1904 – 24 May 1941), who married 25 March 1933 to Frena Lingen Crace, daughter of Everard Crace, from Canberra, Australian Capital Territory, by whom he had two children.
Selwyn John Power Warrand was a Commander in the service of the Royal Navy, fought in World War II and was killed in action on board of HMS Hood (51) and his widow remarried in 1947 Henry Richard Charles Humphries. His sister Beatrice Helen Fitzhardinge Warrand (born 1908), married on 27 September 1941 another World War II veteran, Lieutenant Colonel Lyndall Fownes Urwick, Military Cross, Officer of the Order of the British Empire, son of Sir Henry Urwick of Malvern, Worcestershire, Justice of the Peace.
Biography
Warrand was educated at Eton College, and graduated from Balliol College in 1924 with a Bachelor of Arts degree. He adopted the legally changed name Hugh Vere Huntly Duff Lucas-Tooth of Teanich by Royal Licence in 1920 when he gained the recreated baronetcy of his maternal grandfather, the first baronet, whose three sons had died in World War I, being created 1st Baronet Lucas-Tooth, of Bught, County Inverness, in the Baronetage of the United Kingdom on 1 December 1920, with special remainder to the heirs male of the body of his mother.
Lucas-Tooth was first elected to the House of Commons in the 1924 general election as Conservative Member of Parliament for the Isle of Ely from October 1924 to May 1929. Aged 21, he became the youngest MP, known as "Baby of the House". He served as Parliamentary Private Secretary to Arthur Samuel, Secretary for Overseas Trade. Lucas-Tooth was called to the bar in 1933 at Lincoln's Inn entitled to practise as a barrister. He also became a lieutenant colonel in the service of the Queen's Own Cameron Highlanders.
During the 1930s Lucas-Tooth helped established the Lucas-Tooth gymnasium at Tooley Street in south London for the benefit of unemployed men from the Northern coalfields and unemployed areas. A new style of physical exercises helped improve the fitness of these men. It was featured in a British Pathe newsreel in 1938 titled 'Fit – Fitter – Fittest'.
He was defeated in the 1929 general election by the Liberal candidate, James A. de Rothschild. Lucas-Tooth stood again for parliament in the 1945 general election for Hendon South, and was elected, taking his seat in July 1945. He retained the seat in subsequent general elections until 1970 and was Parliamentary Under-Secretary of State for the Home Department between February 1952 and December 1955.
On 3 February 1965 Lucas-Tooth legally changed his name once again by Deed Poll to Hugh Vere Huntly Duff Munro-Lucas-Tooth of Teaninich, to reflect the Scottish lairdship Munro of Teaninich.
He retired from Parliament at the 1970 general election.
Marriage and issue
He married on 10 September 1925 Laetitia Florence Findlay (died 1978), daughter of Sir John Ritchie Findlay, 1st Baronet, of Aberlour; the couple had three children, Laetitia (born 1926), Jennifer (born 1929), and Hugh (born 1932). Hugh succeeded his father as Baronet.
References
External links
Category:1903 births
Category:1985 deaths
Category:People educated at Eton College
Category:Alumni of Balliol College, Oxford
Category:Conservative Party (UK) MPs for English constituencies
Category:Baronets in the Baronetage of the United Kingdom
Category:UK MPs 1924–1929
Category:UK MPs 1945–1950
Category:UK MPs 1950–1951
Category:UK MPs 1951–1955
Category:UK MPs 1955–1959
Category:UK MPs 1959–1964
Category:UK MPs 1964–1966
Category:UK MPs 1966–1970 | {
"pile_set_name": "Wikipedia (en)"
} |
In aged humans, stroke is a major cause of disability for which no neuroprotective measures are available. In animal studies of focal ischemia, short-term hypothermia often reduces infarct size. Nevertheless, efficient neuroprotection requires long-term, regulated lowering of whole-body temperature. Previously, it is reported that post-stroke exposure to hydrogen sulfide (H2S) effectively lowers whole-body temperature and confers neuroprotection in aged animals. Here we report for the first time that the animals exposed to H2S the normal sleep–wake oscillations are replaced by a low-amplitude EEG dominated by a 4-Hz rhythmicactivity, reminiscent of EEG recordings in hibernating animals. In the present study using magnetic resonance imaging, reverse transcriptase polymerase chain reaction, western blotting and immunofluorescence, we characterized the central nervous system response to H2S -induced hypothermia and report, that annexin A1, a major constituent of peripheral leukocytes that is upregulated after stroke, was consistently downregulated in polymorphonuclear cells in the peri-lesional cortex of post-ischemic, aged rat brain after 48 hours of hypothermia induced by exposure to H2S. This might be due to the reduced kinetics of recruitment, adherence and infiltration of PMN cells by H2S -induced hypothermia. Our findings further suggest that, in contrast to monotherapies that have thus far uniformly failed in clinical practice, prolonged hypothermia has pleiotropic effects on brain physiology that may be necessary for effective protection of the brain after stroke. | {
"pile_set_name": "Pile-CC"
} |
Q:
How to install Visual Studio on Ubuntu 20.04?
Can anyone tell how to install Visual Studio and .NET Framework on Ubuntu 20.04?
Is there any way to Install .NET and Visual Studio in Ubuntu 20.04?
A:
Unfortunately Visual Studio does not available for Linux. But you really want' exactly VS - you should try Wine or any Windows VM.
But I recommend for you one of the following options:
Rider (Cross platform IDE from JetBrains)
Visual Studio Code (Very popular solution for developer on any technology)
Mono Develop
Eclipse
| {
"pile_set_name": "StackExchange"
} |
IN THE COURT OF CRIMINAL APPEALS
OF TEXAS
NO. PD-1240-10
DAVID CEPEDA JONES, Appellant
v.
THE STATE OF TEXAS
ON APPELLANT’S PETITION FOR DISCRETIONARY REVIEW
FROM THE FOURTH COURT OF APPEALS
BEXAR COUNTY
Per curiam. Keasler, and Hervey, JJ., dissent.
O R D E R
The petition for discretionary review violates Rule of Appellate Procedure 9.3(b) and
68.4(i) because the original petition is not accompanied by 11 copies and the petition does
not contain a complete copy of the opinion of the court of appeals.
The petition is struck. See Rule of Appellate Procedure 68.6.
The petitioner may redraw the petition. The redrawn petition and copies must be filed
in the Court of Criminal Appeals within thirty days after the date of this Order.
Filed: October 6, 2010
Do Not Publish
| {
"pile_set_name": "FreeLaw"
} |
Get affordable prints and increased versatility. Set up, connect, and print right from your mobile device, and produce high-quality photos and everyday documents. Print, scan, and copy with ease. HP Photo and Document All-in-One Printers are designed for families and other home users who want a device capable of printing everything from documents, email and web pages to rich, bright lab-quality photos - with copy and scan tools too. Dynamic security enabled printer. Intended to be used with cartridges using only HP original electronic circuitry. Cartridges with modified or non-HP electronic circuitry may not work, and those that work today may not work in the future.
Get affordable prints and increased versatility. Set up, connect, and print right from your mobile device, and produce high-quality photos and everyday documents. Print, scan, and copy with ease.
HP Photo and Document All-in-One Printers are designed for families and other home users who want a device capable of printing everything from documents, email and web pages to rich, bright lab-quality photos - with copy and scan tools too.
Dynamic security enabled printer. Intended to be used with cartridges using only HP original electronic circuitry. Cartridges with modified or non-HP electronic circuitry may not work, and those that work today may not work in the future. | {
"pile_set_name": "Pile-CC"
} |
Toto Wolff says Esteban Ocon will be released from his Mercedes deal if he is to sign for another team in 2020.
Ocon has been left watching Formula 1 from the sidelines this year after ending up as the odd one out on a crazy driver merry go round last year.
Article continues under video
The Frenchman had been set to join Renault, until a gentleman's agreement went out the window when the opportunity to sign Daniel Ricciardo arose.
Ocon's previous seat at Racing Point was filled by Lance Stroll and interest from McLaren and Red Bull, with an eye on Toro Rosso, fizzled out as Mercedes would not free him from his contract.
Wolff has regularly spoken of his confidence that Ocon will find a seat on the 2020 grid, and says he would be deserving of a return.
The Silver Arrows chief told Motorsport.com: "Everyone recognises Esteban's talent, and I truly believe he should have a permanent position in Formula 1 because he is one of the best talents of his generation.
"Unfortunately last year we were victims of a very particular market situation.
"We need to make things clear to allow him to pursue his career in a way that respects the investment and support that Mercedes have given him, obviously without closing open doors from those who showed interest in him."
Ocon has once again been linked with Renault, as Nico Hulkenberg's contract is in its final year, and Wolff suggested that his time with Mercedes could be near its end.
Wolff said: "If he is in another team he will be released regardless, he will no longer be a Mercedes driver because if you drive for another team you will be called to give the best for that team." | {
"pile_set_name": "OpenWebText2"
} |
Introduction {#s1}
============
Usher syndrome (USH) is an autosomal recessive disorder characterized by hearing loss (HL), retinitis pigmentosa (RP) and vestibular dysfunction. Three clinical subtypes can be distinguished. USH type 1 (USH1) is the most severe among them because of profound HL, absent vestibular responses, and prepubertal onset RP. USH type 2 (USH2) is characterized by congenital moderate to severe HL, with a high-frequency sloping configuration. The vestibular function is normal and onset of RP is in the first or second decade. The onset of the visual symptoms such as night blindness in USH usually occurs several years later than in USH1. USH type 3 (USH3) is characterized by variable onset of progressive HL, variable onset of RP, and variable impairment of vestibular function (normal to absent) [@pone.0090688-Kimberling1], [@pone.0090688-Yan1].
To date, nine genetic loci for USH1(*USH1B-H*, *J*, and *K*) have been mapped to chromosomes 11q13.5, 11p15.1, 10q22.1, 21q21, 10q21-q22, 17q24-q25, 15q22-q23 (*USH1H* and *J*), and 10p11.21--q21.1 [@pone.0090688-Yan1], [@pone.0090688-Jaworek1], [@pone.0090688-Riazuddin1]. Six of the corresponding genes have been identified: the actin-based motor protein myosin VIIa (*MYO7A*, USH1B) [@pone.0090688-Weil1]; two cadherin-related proteins, cadherin 23 (*CDH23*, USH1D) [@pone.0090688-Bork1] and protocadherin 15 (*PCDH15*, USH1F) [@pone.0090688-Ahmed1]; and two scaffold proteins, harmonin (*USH1C*) [@pone.0090688-Verpy1] and sans (*USH1G*) [@pone.0090688-Mustapha1]; the Ca^2+^- and integrin-binding protein (*CIB2*, USH1J) [@pone.0090688-Riazuddin1]. In Caucasian USH1 patients, previous studies showed that mutations in *MYO7A*, *USH1C*, *CDH23*, *PCDH15*, and *USH1G*, were found in 39--55%, 7--14%, 7--35%, 7--11%, and 0--7%, respectively (the frequency of *CIB2* is still unknown) [@pone.0090688-Ouyang1], [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1]. In Japanese, Nakanishi et al. showed that *MYO7A* and *CDH23* mutations are present in USH1 patients [@pone.0090688-Nakanishi1], however, the frequency is not yet known. In addition, mutations in three corresponding genes (usherin *USH2A* [@pone.0090688-Eudy1], G protein-coupled receptor 98; *GPR98* [@pone.0090688-Weston1], and deafness, autosomal recessive 31; *DFNB31* [@pone.0090688-Aller1]) have been reported so far in USH2, and USH3 is caused by mutations in the clarin 1 (*CLRN1*) [@pone.0090688-Joensuu1] gene.
Comprehensive molecular diagnosis of USH has been hampered both by genetic heterogeneity and the large number of exons for most of the USH genes. The six USH1 genes collectively contain 180 coding exons [@pone.0090688-Riazuddin1], [@pone.0090688-Mustapha1], [@pone.0090688-Ouyang1] the three USH2 genes comprise 175 coding exons [@pone.0090688-Weston1], [@pone.0090688-Aller1], [@pone.0090688-Nakanishi2], and the USH3 gene has five coding exons [@pone.0090688-Joensuu1]. In addition some of these genes are alternatively spliced ([@pone.0090688-Riazuddin1], [@pone.0090688-Ahmed1], [@pone.0090688-Verpy1], [@pone.0090688-Aller1], [@pone.0090688-Joensuu1] and NCBI database: <http://www.ncbi.nlm.nih.gov/nuccore/>). Thus far, large-scale mutation screening has been performed using direct sequence analysis, but that is both time-consuming and expensive. We thought that targeted exon sequencing of selected genes using the Massively Parallel DNA Sequencing (MPS) technology would enable us to systematically tackle previously intractable monogenic disorders and improve molecular diagnosis.
Therefore, in this study, we have conducted genetic analysis using MPS-based genetic screening to find mutations in nine causative USH genes (except *CIB2*) in Japanese USH1 patients.
Results {#s2}
=======
Mutation analysis of the nine USH genes in 17 unrelated USH1 patients revealed 19 different probable pathogenic variants, of which 14 were novel ([Table 1](#pone-0090688-t001){ref-type="table"}).
10.1371/journal.pone.0090688.t001
###### Possible pathogenic variants found in this study.
{#pone-0090688-t001-1}
Gene Mutation type Nucleotide change Amino acid change exon/intron number Domain control (in 384 alleles) SIFT Score PolyPhen Score Reference
---------- --------------- ------------------- ------------------- -------------------- -------------- -------------------------- ------------ ---------------- --------------------------------
*MYO7A* Frameshift c.1623dup p.Lys542GlnfsX5 Exon 14 \- N/A \- \- Le Quesne Stabej et al. (2012)
c.4482_4483insTG p.Trp1495CysfsX55 Exon 34 \- N/A \- \- This study
c.6205_6206delAT p.Ile2069ProfsX6 Exon 45 \- N/A \- \- This study
Nonsense c.1477C\>T p.Gln493X Exon 13 \- N/A \- \- This study
c.1708C\>T p.Arg570X Exon 15 \- N/A \- \- This study
c.2115C\>A p.Cys705X Exon 18 \- N/A \- \- This study
c.6321G\>A p.Trp2107X Exon 46 \- N/A \- \- This study
Missense c.2074G\>A p.Val692Met Exon 17 Motor domain 0 0.09 0.982 This study
c.2311G\>T p.Ala771Ser Exon 20 IQ 2 0.0026 0.01 0.825 Nakanishi et al. (2010)
c.6028G\>A p.Asp2010Asn Exon 44 FERM 2 0 0 0.925 Jacobson et al. (2009)
*CDH23* Frameshift c.3567delG p.Arg1189ArgfsX5 Exon 30 \- N/A \- \- This study
c.5780_5781delCT p.Ser1927Cysfs16 Exon 44 \- N/A \- \- This study
Splicing c.5821-2A\>G ? Intron 44 \- N/A \- \- This study
Nonsense c.6319C\>T p.Arg2107X Exon 48 \- N/A \- \- Nakanishi et al. (2010)
*PCDH15* Splicing c.158-1G\>A ? Intron 3 \- N/A \- \- This study
Nonsense c.1006C\>T p.Arg336X Exon 10 \- N/A \- \- This study
c.2971C\>T p.Arg991X Exon 22 \- N/A \- \- Roux et al. (2006)
c.3337G\>T p.Glu1113X Exon 25 \- N/A \- \- This study
Missense c.3724G\>A p.Val1242Met Exon 28 Cadherin 11 0 0 1 This study
Computer analysis to predict the effect of missense variants on MYO7A protein function was performed with sorting intolerant from tolerant (SIFT; <http://sift.jcvi.org/>), and polymorphism phenotyping (PolyPhen2; <http://genetics.bwh.harvard.edu/pph2/>).
N/A: not applicable.
All mutations were detected in only one patient each and sixteen of the 17 patients (94.1%) carried at least one mutation, while one patient had no mutations. Thirteen of the 16 mutation carriers each had two pathogenic mutations ([Table 2](#pone-0090688-t002){ref-type="table"}).
10.1371/journal.pone.0090688.t002
###### Details of phenotype and genotype of 17 USH1 patients.
{#pone-0090688-t002-2}
Sample No. Age Sex Allele1 Allele2 Hereditary form Onset of night blindness Cataract Hearing Aid Cochlear Implant
--------------------------------------------------------------------------------------------------------------- ----- ----- -------------------------------------------------- -------------------------------------------------- ----------------- -------------------------- ----------- ------------- ------------------
***MYO7A***
1 37 M p.Gln493X p.Trp1495CysfsX55 sporadic 13 no unilateral unilateral
2 41 W p.l2069fsX6 p.l2069fsX6 AR unknown both eyes bilateral no
5 54 M p.Val692Met p.Val692Met AR 5 both eyes no no
6 54 W p.Arg570X p.Arg570X sporadic 6 no no no
8 14 M p.Lys542GlnfsX5 p.Lys542GlnfsX5 sporadic 6 no unilateral unilateral
11 54 M p.Asp2010Asn p.Trp2107X sporadic 13 no no no
17 56 W p.Cys705X p.Cys705X sporadic unknown no no no
***CDH23***
7 12 W p.Arg1189ArglfsX5 p.Arg1189ArglfsX5 sporadic 12 both eyes no bilateral
9 9 M p.Ser1927Cysfs16 c.5821-2A\>G sporadic 8 no unilateral unilateral
15 16 W p.Arg2107X p.Arg2107X sporadic unknown no no no
***PCDH15***
3 47 W p.Glu1113X p.Glu1113X sporadic 5 both eyes no no
16 28 W p.Arg991X p.Arg991X AR 10 no no no
10 62 M p.Arg962Cys unknown sporadic 9 both eyes no no
12 52 M p.Arg336X unknown sporadic 3 no no no
13 51 M p.Val1242Met unknown sporadic 10 no no no
***MYO7A*** [\*](#nt103){ref-type="table-fn"} **^1^** ***/PCDH15*** [\*](#nt103){ref-type="table-fn"} **^2^**
4 21 M p.Ala771Ser[\*](#nt103){ref-type="table-fn"} ^1^ c.158-1G\>A[\*](#nt103){ref-type="table-fn"} ^2^ sporadic 10 no unilateral unilateral
**unknown**
14 64 W unknown unknown sporadic 15 both eyes unilateral no
\*All subjects have congenital deafness and RP.
Nonsense, frame shift, and splice site mutations are all classified as pathogenic, whereas missense mutations are presumed to be probable pathogenic variants based on results of prediction software for evaluation of the pathogenicity of missense variants ([Table 1](#pone-0090688-t001){ref-type="table"}).
Of the 19 probable pathogenic mutations that we found, 17 were detected by MPS. The remaining two (p.Lys542GlnfsX5 in *MYO7A* and c.5821-2A\>G in *CDH23*) were sequenced by direct sequence analysis.
Of our 17 USH patients, seven had *MYO7A* mutations (41.2%), three had *CDH23* mutations (17.6%), and two had *PCDH15* mutations (11.8%). We did not find any probable pathogenic mutations in *USH1C*, *USH1G*, and USH2/3 genes.
Four USH1 patients (Cases \#3, 5, 8, 15) had probable pathogenic mutations in two different USH genes, with one being a biallelic mutation ([Table 3](#pone-0090688-t003){ref-type="table"}). The other heterozygous/homozygous mutations were missense variants. Three of these patients (Cases \#3, 5, 8) presented with earlier RP onset (night blindness) than in the other patients with two pathogenic mutations (Cases \#1, 6, 7, 9, 11, 16) (*p* = 0.007) ([Fig. 1](#pone-0090688-g001){ref-type="fig"}).
{#pone-0090688-g001}
10.1371/journal.pone.0090688.t003
###### The patients with mutations in two different genes.
{#pone-0090688-t003-3}
Sample Genes with two pathogenic mutations Gene with one heterozygous mutation Nucleotide change Amino acid change control SIFT score PolyPhen score Referense
-------- ------------------------------------- ------------------------------------- ------------------- ------------------------------------------ --------- ------------ ---------------- -------------------------
5 *MYO7A* *CDH23* c.C719T p.P240L[\*](#nt104){ref-type="table-fn"} 0.26 0.06 0.999 Wagatsuma et al. (2007)
8 *MYO7A* *CDH23* c.2568C\>G p.Ile856Met 0 0.08 1 This study
15 *CDH15* *USH1C* c.2437T\>G p.Tyr813Asp 0 0.19 0.932 This study
3 *PCDH15* *USH1G* c.28C\>T p.Arg10Trp 0 0.19 1 This study
\*homozygotes.
One patient (Case \#4) had heterozygote mutations in two USH1 genes (p.Ala771Ser in *MYO7A* and c.158-1G\>A in *PCDH15*). His parents and one brother were found to also be carriers for these mutations. Another brother had no variants ([Fig. 2](#pone-0090688-g002){ref-type="fig"}).
{#pone-0090688-g002}
Discussion {#s3}
==========
For USH1, early diagnosis has many immediate and several long-term advantages for patients and their families [@pone.0090688-Kimberling1]. However, diagnosis in childhood, based on a clinical phenotype, has been difficult because patients appear to have only non-syndromic HL in childhood and RP develops in later years. Although early diagnosis is now possible through DNA testing, performing large-scale mutation screening for USH genes in all non-syndromic HL children has been both time-consuming and expensive. Therefore, the availability of MPS, which facilitates comprehensive large-scale mutation screening [@pone.0090688-Miyagawa1] is a very welcome advance.
MPS technology enabled us to detect pathogenic mutations in USH1 patients efficiently, identifying one or two pathogenic/likely pathogenic mutations in 16 of 17 (94.1%) cases. This was comparable to previous direct sequence analysis results such as Bonnet et al. who detected one or two mutations in 24 out of 27 (89%) USH1 patients [@pone.0090688-Bonnet1] and Le Quesne Stabej et al. who detected one or two mutations in 41 out of 47 (87.2%) USH1 patients [@pone.0090688-LeQuesneStabej1].
In addition, MPS assists in the analysis of disease modifiers and digenic inheritance because it simultaneously investigates many causative genes for a specific disease, such as in our case, USH. Previous reports have described several USH cases with pathogenic mutations in two or three different USH genes [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1], [@pone.0090688-Ebermann1]. In our study, four patients had two pathogenic mutations in one gene and missense variants in a different gene ([Table 3](#pone-0090688-t003){ref-type="table"}). We considered the latter to possibly be a disease modifier. For example, *USH1C*:p.Tyr813Asp, which occurred in 0/384 control chromosomes and was predicted to be "probably damaging" by the Polyphen program, was found with a homozygous *CDH23* nonsense mutation (p.Arg2107X) (Case \#15). As for what the variant "modifies", we speculate that for USH1 patients with a disease modifier, RP symptoms such as night blindness show an earlier onset. However, we think that profound HL and the absence of vestibular function in USH1 patients are not affected by modifiers as they are congenital and therefore not progressive.
Ebermann et al. described a USH2 patient with "digenic inheritance." a heterozygous truncating mutation in *GPR98*, and a truncating heterozygous mutation in PDZ domain-containing 7 (*PDZD7*), which is reported to be a cause of USH [@pone.0090688-Ebermann1]. Our USH1 patient (Case \#4) had segregated *MYO7A*:p.Ala771Ser and *PCDH15*:c.158-1G\>A. Molecular analyses in mouse models have shown many interactions among the USH1 proteins [@pone.0090688-Yan1]. In particular, *MYO7A* directly binds to *PCDH15* and both proteins are expressed in an overlapping pattern in hair bundles in a mouse model [@pone.0090688-Senften1]. *PCDH15*:c.158-1G\>A, predicted to alter the splice donor site of intron 3, has been classified as pathogenic. *MYO7A*:p.Ala771Ser is a non-truncating mutation, but was previously reported as disease-causing [@pone.0090688-Nakanishi1]. So, we consider the patient to be the first reported case of *MYO7A*/*PCDH15* digenic inheritance.
However, we should be aware of two limitations of MPS technology. First, the target region of MPS cannot cover all coding exons of USH genes. Actually, the coverage of the target exons was 97.0% in our study. So, it is impossible to detect a mutation in a region which is not covered using this system (Case \#9: c.5821-2A\>G). Secondarily, the MPS system used in this study, is not effective for detecting homo-polymer regions, for example poly C stretch [@pone.0090688-Loman1] (Case \#8: p.Lys542GlnfsX5). In addition, concerning pathogenecity of mutations identified, functional analysis will be necessary to draw the final conclusion in the future.
In UK and US Caucasian USH1 patients, USH1B (*MYO7A*) has been reported as the most common USH1 genetic subtype [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1], while USH1F (*PCDH15*) has been reported as the most common USH1 genetic subtype in North American Ashkenazi Jews [@pone.0090688-BenYosef1]. In Japanese, our study revealed that the most common type was *MYO7A* (41.7%), which was similar to the frequency in the above Caucasian patients (46.8∼55%) [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1]. However, the small number of USH1 patients in our study might have biased the frequency and further large cohort study will be needed in the future.
In addition, most of our detected mutations were novel. We have previously reported genes responsible for deafness in Japanese patients and observed differences in mutation spectrum between Japanese (who are probably representative of other Asian populations) and populations with European ancestry [@pone.0090688-Usami1].
In conclusion, our study was the first report of USH mutation analysis using MPS and the frequency of USH1 genes in Japanese. Mutation screening using MPS has the potential power to quickly identify mutations of many causative genes such as USH while maintaining cost-benefit performance. In addition, the simultaneous mutation analysis of large numbers of genes was useful for detecting mutations in different genes that are possibly disease modifiers or of digenic inheritance.
Materials and Methods {#s4}
=====================
Subjects {#s4a}
--------
We screened 17 Japanese USH1 patients (aged 9 to 64 years): three from autosomal recessive families (non-affected parents and two or more affected siblings), and 14 from sporadic families. There were 9 males and 8 females. None of the subjects had any other noteworthy symptoms. All subjects or next of kin on the behalf of the minors/children gave prior written informed consent for participation in the project, and the Ethical Committee of Shinshu University approved the study and the consent procedure.
Amplicon Library Preparation {#s4b}
----------------------------
An Amplicon library of the target exons was prepared with an Ion AmpliSeq Custom Panel (Applied Biosystems, Life Technologies, Carlsbad, CA) designed with Ion AmpliSeq Designer (<https://www.ampliseq.com/browse.action>) for nine USH genes by using Ion AmpliSeq Library Kit 2.0 (Applied Biosystems, Life Technologies) and Ion Xpress Barcode Adapter 1--16 Kit (Applied Biosystems, Life Technologies) according to the manufacturers\' procedures.
In brief, DNA concentration was measured with Quant-iT dsDNA HS Assay (Invitrogen, Life Technologies) and Qubit Fluorometer (Invitrogen, Life Technologies) and DNA quality was confirmed by agarose gel electrophoresis. 10 ng of each genomic DNA sample was amplified, using Ion AmpliSeq HiFi Master Mix (Applied Biosystems, Life Technologies) and AmpliSeq Custom primer pools, for 2 min at 99°C, followed by 15 two-step cycles of 99°C for 15 sec and 60°C for 4 min, ending with a holding period at 10°C in a PCR thermal cycler (Takara, Shiga, Japan). After the Multiplex PCR amplification, amplified DNA samples were digested with FuPa enzyme at 50°C for 10 min and 55°C for 10 min and the enzyme was successively inactivated for 60°C for 20 min incubation. After digestion, diluted barcode adapter mix including Ion Xpress Barcode Adapter and Ion P1 adaptor were ligated to the end of the digested amplicons with ligase in the kit for 30 min at 22°C and the ligase was successively inactivated at 60°C for 20 min incubation. Adaptor ligated amplicon libraries were purified with the Agencourt AMPure XP system (Beckman Coulter Genomics, Danvers, MA). The amplicon libraries were quantified by using Ion Library Quantitation Kit (Applied Biosystems, Life Technologies) and the StepOne plus realtime PCR system (Applied Biosystems, Life Technologies) according to the manufacturers\' procedures. After quantification, each amplicon library was diluted to 20 pM and the same amount of the 12 libraries for 12 patients were pooled for one sequence reaction.
Emulsion PCR and Sequencing {#s4c}
---------------------------
The emulsion PCR was carried out with the Ion OneTouch System and Ion OneTouch 200 Template Kit v2 (Life Technologies) according to the manufacturer\'s procedure (Publication Part Number 4478371 Rev. B Revision Date 13 June 2012). After the emulsion PCR, template-positive Ion Sphere Particles were enriched with the Dynabeads MyOne Streptavidin C1 Beads (Life Technologies) and washed with Ion OneTouch Wash Solution in the kit. This process were performed using an Ion OneTouch ES system (Life Technologies).
After the Ion Sphere Particle preparation, MPS was performed with an Ion Torrent Personal Genome Machine (PGM) system using the Ion PGM 200 Sequencing Kit and Ion 318 Chip (Life Technologies) according to the manufacturer\'s procedures.
Base Call and Data Analysis {#s4d}
---------------------------
The sequence data were processed with standard Ion Torrent Suite Software and Torrent Server successively mapped to human genome sequence (build GRCh37/hg19) with Torrent Mapping Alignment Program optimized to Ion Torrent data. The average of 562.33 Mb sequences with about 4,300,000 reads was obtained by one Ion 318 chip. The 98.0% sequences were mapped to the human genome and 94% of them were on the target region. Average coverage of depth in the target region was 314.2 and 93.8% of them were over 20 coverage.
After the sequence mapping, the DNA variant regions were piled up with Torrent Variant Caller plug-in software. Selected variant candidates were filtered with the average base QV (minimum average base quality 25), variant frequency (40--60% for heterozygous mutations and 80--100% for homozygous mutations) and coverage of depth (minimum coverage of depth 10). After the filtrations, variant effects were analyzed with the wANNOVAR web site [@pone.0090688-Wang1], [@pone.0090688-Chang1] (<http://wannovar.usc.edu>) including the functional prediction software for missense variants: Sorting Intolerant from Tolerant (SIFT; <http://sift.jcvi.org/>), and Polymorphism Phenotyping (PolyPhen2; <http://genetics.bwh.harvard.edu/pph2/>). The sequencing data was available in the DNA databank of Japan (Accession number: DRA001273).
Algorithm {#s4e}
---------
Missense, nonsense, and splicing variants were selected among the identified variants. Variants were further selected as less than 1% of: 1) the 1000 genome database (<http://www.1000genomes.org/>), 2) the 5400 exome variants (<http://evs.gs.washington.edu/EVS/>), and 3) the in-house control. Candidate mutations were confirmed by Sanger sequencing and the responsible mutations were identified by segregation analysis using samples from family members of the patients. In addition, the cases with heterozygous or no causative mutation were fully sequenced by Sanger sequencing for USH1 genes in order to verify the MPS results.
Direct Sequence Analysis {#s4f}
------------------------
Primers were designed with the Primer 3 plus web server (<http://www.bioinformatics.nl/cgi-bin/primer3plus/primer3plus.cgi>). Each genomic DNA sample (40 ng) was amplified using Ampli Taq Gold (Life Technologies) for 5 min at 94°C, followed by 30 three-step cycles of 94°C for 30 sec, 60°C for 30 sec, and 72°C for 30 sec, with a final extension at 72°C for 5 min, ending with a holding period at 4°C in a PCR thermal cycler (Takara, Shiga, Japan). The PCR products were treated with ExoSAP-IT (GE Healthcare Bio, Buckinghamshire, UK) and by incubation at 37°C for 60 min, and inactivation at 80°C for 15 min. After the products were purified, we performed standard cycle sequencing reaction with ABI Big Dye terminators in an ABI 3130xl sequencer (Life Technologies).
Accession numbers {#s4g}
-----------------
*MYO7A*, \[NM_000260.3\]; *USH1C*, \[NM\_ 153676.3\]; *CDH23*, \[NM\_ 022124.5\]; *PCDH15*, \[NM\_ 033056.3\]; *USH1G*, \[NM\_ 173477.2\]; *USH2A*, \[NM_206933.2\]; *GPR98*, \[NM\_ 032119.3\]; *DFNB31*, \[NM\_ 015404.3\]; *CLRN1*, \[NM\_ 174878.2\]; *PDZD7*, \[NM\_ 001195263.1\].
We thank A. C. Apple-Mathews for help in preparing the manuscript.
[^1]: **Competing Interests:**The authors have declared that no competing interests exist.
[^2]: Conceived and designed the experiments: HY SI SN SU. Performed the experiments: HY SN. Analyzed the data: HY SN SU. Contributed reagents/materials/analysis tools: HY SI SN KK TT YK HS KN KI TI YN KF CO TK HN SU. Wrote the paper: HY SN SU.
| {
"pile_set_name": "PubMed Central"
} |
For Wil Trapp, his goals are more about quality than quantity.
The Columbus Crew SC captain's stunning stoppage-time strike from distance — his second career MLS goal — was the runaway winner for AT&T Goal of the Week for MLS Week 21.
Trapp took a settling touch before a second one to set up a sensational blast from more than 30 yards away that flew underneath the crossbar for the winner in a 3-2 come-from-behind victory over Orlando City SC Saturday night at MAPFRE Stadium.
Trapp took 65 percent of the GOTW vote, with Zlatan Ibrahimovic coming up a distant second at 17 percent for his low, first-time rocket from 16 yards out that nestled inside the far post that proved to be the winner for the LA Galaxy in a 3-1 victory at Philadelphia.
Here’s how the rest of the pack finished up: Darwin Quintero at 13 percent and Sebastian Giovinco and Damir Kreilach at three percent apiece.
Check out the final Week 21 voting results and video of all five nominated goals. | {
"pile_set_name": "OpenWebText2"
} |
---
layout: example
title: Wheat Plot Example
permalink: /examples/wheat-plot/index.html
spec: wheat-plot
image: /examples/img/wheat-plot.png
---
A [wheat plot](http://www.perceptualedge.com/articles/visual_business_intelligence/the_datavis_jitterbug.pdf) is an alternative to standard dot plots and histograms that incorporates aspects of both. The x-coordinate of a point is based on its exact value. The y-coordinate is determined by grouping points into histogram bins, then stacking them based on their rank order within each bin. While not scalable to large numbers of data points, wheat plots allow inspection of (and interaction with) individual points without overplotting. For a related approach, see [beeswarm plots](../beeswarm-plot/).
{% include example spec=page.spec %}
| {
"pile_set_name": "Github"
} |
Q:
can't select all elements with classList API
I'm having a problem selecting all the LI tags when converting jQuery code to HTML5 javascript
code. I have applied the click event to the parent UL, and the click event is being applied to the correct clicked target LI. The class "selected" is also being applied. The problem is that I need all classes to be cleared from the LI tags before the "selected" class is applied, as I only want it applied to the current event target. In jQuery it is simply a matter of removing classes from the LI's, but I am having problems targeting all the LI tags and removing the class in javascript. I suspect the problem is how I am iterating over the node list returned from QuerySelectorAll. I have also tried amongst other things, document.GetElementsByTagName, and iterating over these.
I am getting an "Uncaught TypeError: Cannot read property 'contains' of undefined" on the myFunc function.
I would be very happy if someone could point out my error.
<div id='button'></div>
<ul id='swatches'>
<li></li>
<li></li>
<li></li>
<li></li>
</ul>
The jQuery code
$('li').on('click', function(){
$('li').removeClass('selected');
$(this).toggleClass('selected');
});
Using the classList API
var swatch = document.getElementById('swatches'),
$li = document.querySelectorAll('#swatches li');
swatch.addEventListener('click', myFunc, false);
function myFunc(e){
var target = e.target;
for(var i=0; i<$li.length; i++){
if($li.classList.contains('selected')){
$li.classList.remove('selected');
}
}
if(target.nodeName.toLowerCase() === 'li'){
e.target.classList.toggle('selected');
}
}
A:
I suspect the problem is how I am iterating over the node list returned from QuerySelectorAll.
Yes. You forget the indices. It should be
for (var i=0; i<$li.length; i++)
if ($li[i].classList.contains('selected'))
// ^^^
$li[i].classList.remove('selected');
// ^^^
However, two points:
You don't need to test for contains() before calling remove() unless you need the information explicitly. Trying to remove a class that doesn't exist just does nothing.
You might not need to iterate the whole $li collection on every click. Since there is only one <li> with the .selected class at a time, you might simply store a reference to the currently-selected element, or use
var cur = swatch.querySelector("li.selected");
if (cur) cur.classList.remove('selected');
(which could work with an id as well).
| {
"pile_set_name": "StackExchange"
} |
Michael Bloomberg’s policies as New York City mayor are analyzed by legal and constitutional experts who explain that in their view the 2020 presidential candidate pursued policies detrimental to people of color. Joy Reid and her panel discuss. | {
"pile_set_name": "OpenWebText2"
} |
[Treatment of bladder neoplasm: vesical instillation of BCG vaccine in microdoses].
We administered BCG at microdoses (1 mg) to 34 patients after surgical operation for bladder cancer, from 1981 to 1989. A 9% recurrency rate was observed during a 42 month follow up period. This is not significantly different from that observed with 120 mg doses, which are associated to known complications. | {
"pile_set_name": "PubMed Abstracts"
} |
Helderberg Escarpment
The Helderberg Escarpment, also known as the Helderberg Mountains, is an escarpment and mountain range in eastern New York, United States, roughly west of the city of Albany. The escarpment rises steeply from the Hudson Valley below, with an elevation difference of approximately 700 feet (from 400 to 1,100 feet) over a horizontal distance of approximately 2,000 feet. Much of the escarpment is within John Boyd Thacher State Park, and has views of the Hudson Valley and the Albany area.
Geology
The escarpment is geologically related to three other escarpments, the Niagara Escarpment,
the Black River Escarpment, and the Onondaga Escarpment.
The rocks exposed in the escarpment date back to the Middle Ordovician to Early Devonian.
In 1934 the Schenectady Gazette described how the Tory Cave, one of the limestone caves to be found in the escarpment, routinely had stalagmites of ice in the springtime.
Transmission towers
Most of the Capital District's television stations installed their transmission towers at the escarpment to take advantage of its high ground. In 2003 a tower was built on the highest point of the escarpment, for transmitting digital television signals.
History
Dutch settlers first homesteaded the plateau above the escarpment in the 17th century. Helderberg is a Dutch name meaning "clear mountain".
The Open Space Institute and the Mohawk Hudson Land Conservancy are working to keep escarpment lands from being developed for housing or industrial uses.
Farmers farming land near the escarpment can apply to sell their development rights, to help make sure that land is not developed. In 2003 the Ten Eyck family, owners of the Indian Ladder Farm just below the escarpment, sold the development rights to their farm for $848,000. Two real estate assessment were done, one on the value of the property as a working farm, the other on its value as a potential site for urban development. The Ten Eycks were paid the difference in return for agreeing to keep the property as a working farm. They were the first property owners to sell their development rights in Albany County.
References
Category:Landforms of New York (state)
Category:Escarpments of the United States
Category:Landforms of Albany County, New York
Category:Mountains of Albany County, New York
Category:Mountains of New York (state) | {
"pile_set_name": "Wikipedia (en)"
} |
A nonsurgical approach to low back pain.
Low back pain, a leading cause of disability in the United States, has a significant economic impact not only on lost productivity but also on healthcare expenditures. Approximately a fifth of patients will see multiple physicians in their quest for relief of low back pain. Primary care physicians therefore play a crucial role in the initial approach to these patients. A thorough history and physical examination directed toward the neurologic, orthopedic, and osteopathic evaluation are essential. This article reviews the diagnosis and assessment of pain levels and a triad system of therapy involving cortical, spinal, and peripheral levels. Options include antidepressants, neuroleptics, neurostimulants, and osteopathic manipulative treatment (OMT) (cortical level); opiates, tramadol hydrochloride, and transcutaneous electrical nerve stimulators (spinal level); and nonsteroidal anti-inflammatory drugs, epidural injections, spinal blocks, antispasmodics, physical therapy, muscle relaxants, exercise, and OMT (peripheral level), By choosing a modality directed at each level, the clinician may provide the patient with a pain management program that will maximize the chosen mode of therapy and restore function and mobility. | {
"pile_set_name": "PubMed Abstracts"
} |
The United States has achieved its minimum expectations in the Women's World Cup, and now the U.S. has reached the part of the tournament where a loss is understandable. Its opponent on Tuesday (7 p.m. ET, FOX) is Germany, the No. 1-ranked team in the world, the reigning European champions and the leading scorers at this World Cup. Germany's beatable, but the Americans are going to have a hard time winning.
Germany is widely considered to be a better team than the United States on current form, and based on the less than thrilling style of soccer that the USWNT has played recently, it's a reasonable conclusion to come to. But the fact is, we really don't know who's better. The last time they played was 2013, when the U.S. beat Germany in the Algarve Cup, then drew against the Germans in a friendly two months later. The last time the two teams played in a major tournament was at the 2004 Summer Olympics. They've dodged each other for the last two Olympics and World Cups, and they don't love scheduling each other.
In the quarterfinals, France outplayed Germany for the most part and exposed some of its weaknesses, though the French did it with personnel that the USWNT can't necessarily match like-for-like. A lot of what France did is duplicable, or can be improved upon. In other cases, the U.S. can't follow France's blueprint.
Here's how the United States can pull off the minor upset of Germany, starting with the bad news -- the factors the Americans can't control for.
The U.S. does not have a Amandine Henry or Camille Abily
Germany was outplayed in the center of midfield by two players who are better defensively and better passers than anyone the United States has. Carli Lloyd can score goals, Lauren Holiday is creative and Morgan Brian has no serious holes in her game, but it's impossible for them to duplicate what Henry and Abily did to Germany. The U.S. midfielders can't match their ball-winning and mid-range passing abilities.
The only way for the USWNT to match the attacking, defensive and transitional output of Abily or Henry is to change formations and play three central midfielders, winning the battle with numbers instead of quality. It seems highly unlikely that Jill Ellis is going to do that. Instead, she's just going to hope Lloyd has an outstanding game.
Anja Mittag is unlikely to play that poorly again
The weirdest thing about Germany's first half against France, in which it got trucked and should have gone down by two or three goals, was how awful Mittag was. She's a world-class attacking midfielder, and she was Germany's most consistent player in the tournament up until the quarterfinal match. But she constantly turned the ball over against France, and was substituted at halftime even though she didn't have a serious injury. Germany boss Silvia Neid knew Dzsenifer Marozsán only had 45 good minutes in her, and when Neid put her on at halftime, Mittag was the player she decided to yank.
It would be downright stunning if Mittag was that bad again. This is partially related to the first point, on the U.S. not having defensive midfielders who match France's quality. Even if she lacked sharpness in the same way that she did against France, Mittag would probably look better against the U.S. than she did in that game.
So, that's the bad news. The Americans can't magically generate world-class central midfielders or expect Mittag to have another bad game. But that doesn't mean there's nothing going in their favor. Here's the good news.
Dzsenifer Marozsán, maybe the best player in the world, is doubtful
Lena Goeßling, who started in Marozsán's place against France, is a perfectly decent player. There's nothing wrong with her and she's good enough to be a starter on a World Cup-winning team. Still, the difference between her and Marozsán was glaring, early and often, in the quarterfinals. She had a few turnovers in spots where Marozsán would not have.
Here's an example. A half-second after this capture, France had the ball and was breaking the other way.
Once Marozsán was on, Germany's attack changed significantly. It took less than five minutes for her to create her team's best chance up to that point, and it was from a place where the French probably thought they weren't in any danger. Marozsán is double-teamed here, being shoved into a place where it's hard to make a dangerous pass, and France has players covering both Germany's attackers and dangerous spaces that players could make late runs into. She finds a way to turn away from two defenders and make a pass to set up a great shot anyway.
Goeßling avoids unforced errors and does a good job making safe passes. Marozsán turns situations that would be understandable forced turnovers into scoring chances with ridiculous regularity. She's almost certainly the best attacking or playmaking midfielder in the world, and she's extremely unlikely to start against the United States.
Marozsán came into this tournament with an injury and has been nursing it throughout, and she might have been fine if Germany had beaten France in regulation time. Instead, she had to play an extra 30 minutes on her injured ankle and was having serious trouble walking at the end of the match.
She'll dress, but sitting behind a "break glass in case of emergency" case. Don't expect to see her unless Germany is trailing late in the second half, or gets to extra time. And while that's awful news for neutral fans, it's great news for the Americans.
Megan Rapinoe is almost a Louisa Necib equivalent
Necib, France's left winger, had her best game of the tournament against Germany, and the United States has a similar player in Rapinoe. She's not exactly the same style of silky technician, but functionally, she does the same things. She's a left winger who can help her team get the ball and serves as the primary playmaker. Even if her touches and passes don't look as smooth and effortless as Necib's, they're just as effective. She doesn't turn the ball over easily and she sets up goals with her creativity. If the Germans had a hard time containing Necib, they will also have a hard time containing Rapinoe.
The Americans are as good or better in defense and goal
Wendie Renard and Laura Georges are very good central defenders, but the American pair might be even better. Ever since Julie Johnston's minor hiccup on Australia's goal in the first group stage game, she's been her team's best player. Her partner, Becky Sauerbrunn, hasn't put a foot wrong all tournament. As good as Celia Šašić is, she was kept relatively quiet by Norway and France. There's no reason that the U.S. center backs, who completely shut down Sweden's Lotta Schelin, can't do the same thing.
And then there's the goalkeeper. Even if you think Hope Solo has no business coming anywhere near a U.S. national team, she remains the starter between the sticks, and she's undoubtedly the best in the world. There was a time when Germany's Nadine Angerer had a claim to the throne, but at 36 and with retirement looming for her, that throne is undisputed. It belongs to Solo, period. And she's worlds better than France keeper Sarah Bouhaddi.
After that, there's one big remaining question that it's impossible to come up with an easy answer for.
Can an American winger do what Elodie Thomis did?
Germany left back Tabea Kemme got absolutely torched by France's right winger, Thomis, over and over again. The U.S. might have a Thomis equivalent in Crystal Dunn rising through the ranks, but she's at home. There isn't a clear like-for-like right winger on the U.S. squad.
But that's not to say the Americans don't have a right winger who can beat Kemme like a drum. A younger version of Heather O'Reilly certainly had it in her, and it's yet to be seen if she can find some of that old magic in this tournament. Christen Press certainly has the pace and skill to duplicate Thomis' game, but she hasn't yet played like a true right winger when deployed in that spot. Perhaps, with a bit of direction from her coaching staff, she could terrorize Kemme down that flank like Thomis did.
So what can the USWNT do to beat Germany?
Three big things, one of which is not really tactical.
1. Hope Solo outplaying Nadine Angerer - There's nothing Ellis can do to ensure this, but it's going to be necessary. Even if the U.S. plays a great game and Ellis has the perfect tactical game plan, the Americans aren't winning unless Solo is excellent and Angerer is slightly less than excellent. The U.S. can create more quality shots and restrict Germany's quality shots, but it's not going to stop Germany from getting shots off. Solo has to be great.
2. Stopping build-up from the back - Germany is noted for its possession play and the United States is derided for hoofing the ball aimlessly. But in the quarterfinals, something pretty amazing happened -- France figured out how to turn Germany into hoofers.
The French laid off the central defenders when Germany tried to pass out of the back and took away passing lanes, while the German defenders took the bait. They blasted the ball up the pitch, and France won a lot of 50-50 battles in the air. Germany got the picture eventually and started dropping Goeßling deep to pick up the ball, but France still did a great job of taking passing lanes away and making the Germans bypass midfield.
Nothing we've seen from the Americans indicates that they know how to do this, but their players aren't unskilled or unintelligent. They're certainly capable of duplicating this tactic.
3. Pumping it down the wings - Kemme and right back Leonie Maier are just decent players, and they only get decent support from their wingers. If there's a place the U.S. has an advantage, it's in wide areas. This is the same as the China match, but for completely different reasons. China literally conceded wide areas on purpose to prioritize clogging the middle, but Germany plays a very conventional formation -- defensive wide areas are just a place where its players aren't anything special.
American fans are probably really sick of hearing this, but they are likely to get nowhere if Rapinoe is not excellent. She was the United States' best attacking player in the four games that she played in, and she will probably be the best attacking player again on Tuesday.
Feed Rapinoe. If your right wing matchup looks good, feed her too. Don't allow Germany to build from the back. Pray Solo is at her best. That's the recipe for beating Germany. | {
"pile_set_name": "OpenWebText2"
} |
Association between pediatric asthma care quality and morbidity and English language proficiency in Ohio.
Limited English proficiency can be a barrier to asthma care and is associated with poor outcomes. This study examines whether pediatric patients in Ohio with limited English proficiency experience lower asthma care quality or higher morbidity. We used electronic health records for asthma patients aged 2-17 years from a regional, urban, children's hospital in Ohio during 2011-2015. Community-level demographics were included from U.S. Census data. By using chi-square and t-tests, patients with limited English proficiency and bilingual English-speaking patients were compared with English-only patients. Five asthma outcomes-two quality and three morbidity measures-were modeled using generalized estimating equations. The study included 15 352 (84%) English-only patients, 1744 (10%) patients with limited English proficiency, and 1147 (6%) bilingual patients. Pulmonary function testing (quality measure) and multiple exacerbation visits (morbidity measure) did not differ by language group. Compared with English-only patients, bilingual patients had higher odds of ever having an exacerbation visit (morbidity measure) (adjusted odds ratio [aOR], 1.4; 95% confidence interval [CI], 1.2-1.6) but lower odds of admission to intensive care (morbidity measure) (aOR, 0.3; 95% CI, 0.2-0.7), while patients with limited English proficiency did not differ on either factor. Recommended follow-up after exacerbation (quality measure) was higher for limited English proficiency (aOR, 1.8; 95% CI, 1.4-2.3) and bilingual (aOR, 1.6; 95% CI, 1.3-2.1), compared with English-only patients. In this urban, pediatric population with reliable interpreter services, limited English proficiency was not associated with worse asthma care quality or morbidity. | {
"pile_set_name": "PubMed Abstracts"
} |
In general, customers using an online order processing system may order products using a local computer (e.g., a client) over a connection to a vendor, such as by dialing in over a modem to a computer network, such as the Internet, to the vendor's computer (e.g., server). Typically, the customer can enter in ordering information into a user interface provided by the vendor's order processing software over the connection which is displayed on a visual display of the customer's computer. For example, the customer can begin by entering in the customer's name and address if the customer is interested in a particular product, and the customer can enter in the name and/or model number of the product that the customer is considering ordering. The customer can then receive product information including pricing information, configuration information, and so on.
After receiving this product information over the network connection, the customer can decide whether to place the order or to hold off submitting the order until a later time. If placing the order, the customer can indicate that the customer wishes to submit the order by further manipulating the computer display provided by the vendor's computer. The vendor's order processing software may require the customer to submit additional information, such as a purchase order number and shipping address. After entering this information, the order processing software processes this information and accepts (or rejects) the order. If the order is accepted, the vendor's computer indicates the acceptance and typically provides the customer with verification information, such as a confirmation number or order number, that the customer writes down on a piece of paper or prints out on a printer connected to the customers' local client computer.
If the customer is not sure of the product to be ordered, the customer can request information from the vendor's order processing software, which is then displayed on the customer's client computer as one or more screens of information provided over the network connection by the order processing software. The customer can then read through the displayed screens, or print them out to read the hard copies of the information for comparison with the customer's requirements and needs. If the customer is a business (e.g., wholesaler, distributor, value added reseller or VAR, original equipment manufacturer or OEM, or other business), then the customer can check or compare its own inventory, requests from its customers (e.g., its retail customers) and other information against the information provided by the vendor's computer to determine what products and configurations of those products to order from the vendor. In addition, the customer can use the ordering information (from a display screen or printout) and then enter (e.g., type in at a keyboard or copy and paste using a mouse) this information into an ordering application or other application (e.g., customer's inventory application) that the customer maintains at its own local computer.
In another conventional approach, a customer can log onto a vendor's web site over the Internet, and view information about products for sale at the web site provided by the vendor's order processing software from the vendor's web server. The customer can select products from displays on the web site for an order and can then submit the order through the web site. The web site then displays a confirmation number to the customer, who can print it out if desired. | {
"pile_set_name": "USPTO Backgrounds"
} |
The Miami Art Museum and Miami Art Central announced last week that they are forming a partnership in presenting exhibitions of original art works to the public. The move comes as plans by the Miami Art Museum move ahead for creation of an expanded museum. In six months, the two organizations plan to evaluate a possible merger. Whatever the outcome, the development means added impetus to the campaign to build a new museum in downtown Miami and heralds expanded relationships between public and private art institutions here.
Playing a key role in the partnership is Ella Fontanals-Cisneros, who founded Miami Art Central with the objective, she says, of stimulating an active dialogue with the community through exhibitions and education programs reflecting the interests of the local community.
The facility of Cuba-born Mrs. Cisneros is in a 1940s building in South Miami formerly occupied by Southern Bell Co., renovated under the direction of Italian architect Alessandro Fiorentino. It features 20,000 square feet of exhibition space on two floors where five major exhibitions per year and special events are staged.
Mrs. Cisneros was interviewed by Miami Today international editor Michael Hayes before the partnership announcement as she prepared special events at Miami Art Central in conjunction with the Art Basel Miami Beach art fair earlier this month. This is an excerpt from the weekly profile article published in Miami Today. To read the entire article in full, order this issue or subscribe to the print edition of Miami Today. | {
"pile_set_name": "Pile-CC"
} |
Atomic Scala - blearyeyed
http://www.atomicscala.com/book
======
thebluesky
Glad to see Bruce Eckel involved. It's interesting to see just how many Scala
books have been cranked out in the last 6-12 months or are currently in
progress.
------
Toshio
<p>You can download the first 25% of the book <strong>here</strong>.</p>
Ummm ... where?
~~~
thebluesky
Seems he forgot the link. Another excellent book for learning Scala is Scala
for the Impatient. The first 9 chapters are free:
<http://horstmann.com/scala/>
~~~
michaels0620
The link is now working.
| {
"pile_set_name": "HackerNews"
} |
Prep for Changing Brake Pad Material
Should I fully sand my rotors if Im changing pad material?
I understand the basics of disc brakes in that a little bit of the pad material imbeds itsself in the rotors as part of the normal process of braking. This would lead me to believe sanding is necessary. The problem is of course that Im a little lazy.
If it matters, I would be coming off EBC Red pads, which they say are a type of organic material, and moving back to the stock Shimano sintered pads.
I originally left the Shimano pads as they were howlingly loud and had ok success with the EBC's. They are starting to wear fast however, and I now have at least 4 brand new sets of the Shimano's laying around, so I figure I'll try them again rather than spending more money.
Frankly I don't think that's necessary. I would suggest simply changing them out for new pads of whatever compound and then breaking them in. Whenever you change brake pads, independent of compound, you must break them in again.
For God's Sake!
Do NOT sand your rotors. Clean them with isopropyl alcohol, wipe dry with a nice clean rag and keep your greasy, KFC-eatin' fingers offa them. Change out the pads, making sure to center them correctly and then go ride your bike.
Well, I know I would need to break in the new pads, but doing that on top of the older material and mixing the 2 is what I was questioning.
The actuall process of breaking in pads is where through application of the brakes the pad material imbeds in the rotor surface gradually getting you up to full braking performance.
What I dont know is: will the new pad material just push out the old with no problem? Or will they mix and decrease braking performance?
It would be highly unusual for the use of one pad material to interfere with the efficacy of another material on a standard metal rotor in such a way as to noticeably affect braking performance, particularly if the rotor were thoroughly cleaned beforehand. That's my opinion. There may be some kind of materials scientist out there who may know about something going on in the meso-scale that I don't who may disagree with what I just said, but I don't think so.
As far as I'm concerned there's no need to do anything to the rotor when switching between different types of pads. I have a set of older Shimano XTs where I switch to the stock metallic pads when riding up at my friends cottage and use organic ones when riding in the city. I just drop the pads in and they work just fine, no need to clean the rotors or pads. I've switched back & forth many times over the years and I've never had any problems.
It would be highly unusual for the use of one pad material to interfere with the efficacy of another material on a standard metal rotor in such a way as to noticeably affect braking performance, particularly if the rotor were thoroughly cleaned beforehand. That's my opinion. There may be some kind of materials scientist out there who may know about something going on in the meso-scale that I don't who may disagree with what I just said, but I don't think so.
All cleaning them with alcohol will do is remove oils, dirt, etc.
IF the previous pad material should in fact be removed to optimize performance, alcohol isn't going to do it.
IF the previous pad material should in fact be removed to optimize performance, alcohol isn't going to do it.
The rotor has micropores in it that may have captured some pad material, maybe several micrograms at most. If you are being told by a manufacturer or dealer someplace that such an infinitesimally small amount of previous material will somehow interfere with the performance of your new brake pads (which it won't), then you probably need to find a new brand of rotor, brake and pad. The bottom line is this: there is no credible reason to believe that removal of previous pad material is necessary unless you have done something highly unusual with your brakes or are using them for some highly unusual application or there is some highly unusual condition that you are not mentioning in this forum. | {
"pile_set_name": "Pile-CC"
} |
The brain of a honeybee is tiny — the size of a pin head — and contains less than a million neurons, compared to the 85 billion in our own brains. Yet with that sliver of brain, bees can do some extraordinary things. They can count and interpret abstract patterns. Most famously, bees have the ability to communicate the location of flowers to other bees in the hive.
When a foraging bee has found a source of nectar and pollen, it can let others in the hive know by performing a peculiar figure-of-eight dance called the waggle dance. The information contained in the waggle dance was first decoded by Austrian biologist Karl von Frisch, who picked up a Nobel Prize for his discovery in 1973. The dance in itself is not as complex as true language, but it’s remarkable in that it’s a symbolic form of communication.
Recently, Hiroyuki Ai at Fukuoka University has made another breakthrough in our understanding of this extraordinary behavior, by investigating the neurons that allow bees to process the dance information. Bees get information from hearing the dance, as well as seeing it. During the dance, bees vibrate their abdomens as they run in a figure-of-eight pattern. These vibrations send out pulses that are picked up by an organ on the antennae called Johnston’s organ. Johnston’s organs are equivalent to our ears.
Ai maintains hives of honeybees on the campus of Fukuoka University. (Incidentally, he says they have monthly meetings to discuss their research with students, after which they have tea parties and eat the honey produced by their bees.) Until recently, there has been very little understanding of how the bee brain deciphers the information encoded in the waggle dance. The reason, he says, is that bees only perform the dance in the hive, and it’s difficult to get them to do it in the laboratory.
It makes sense that the bees pay attention to sound. “In a dark hive, they can’t see the dance,” Ai says. “Honeybees hear the dance.” Honeybees are very sensitive to vibration, so mimicking the noise of a waggle dance can cause bees to journey to the same place indicated by a real dance.
Ai and his team recorded the vibrations made by the waggle dance, simulated the noises and applied the vibrations to the antennae of bees in the lab. This allowed them to track which neurons fired in response to the waggle dance, and follow their route in the insect brain.
The team discovered three different types of “interneurons.” These are connecting neurons that allow communication between different parts of the brain. Ai, along with team members that include Thomas Wachtler at Ludwig-Maximilians University in Munich, Germany, and Hidetoshi Ikeno of the University of Hyogo in Himeji, traced the path of interneurons in the part of the brain concerned with processing sound. They found that the way the interneurons turn on and off is key to encoding information contained in the waggle dance about distance.
This mechanism of turning on and off — in neuroscience it is called “disinhibition” — is similar to one used in other insects. For example, it’s how crickets listen to the songs of other crickets as well as how moths assess the distance from the source of a smell their antennae have picked up. Ai and his team suggest there is a common neural basis in the way these different species do things.
Communication is the key to forming complex societies. It’s what allows the honeybee to perform such extraordinary behaviors. And, naturally, language is a key factor in human success. Intelligence is required for both these things, so does this mean honeybees, with a minuscule brain, are intelligent? It’s a tricky quality to define. One attempt, from the American Psychological Association Task Force on Intelligence, defines it as the ability “to adapt efficiently to the environment and to learn from experience.” Bees are able to do this.
There are six different kinds of dance, for example, and bees are able to learn and change their behavior accordingly. If bees encounter a dead bee at a flower, they change the pattern of dancing they perform back at the hive, suggesting they can perform a risk/benefit analysis.
Both bee and human language are a consequence of intelligence, and research such as Ai’s forces us to rethink what we mean by intelligence. “There might be a common brain mechanism between humans and honeybees,” he says.
What it certainly shows is that you don’t need a big brain to be smart. As with many things, Charles Darwin realized this, writing in 1871: “The brain of an ant is one of the most marvellous atoms of matter in the world, perhaps more so than the brain of man.”
Rowan Hooper is managing editor of New Scientist magazine. He tweets at @rowhoop and his new book, “Superhuman,” is out next year.
KEYWORDS honeybees, bees | {
"pile_set_name": "OpenWebText2"
} |
Cadmium phytoremediation potential of turnip compared with three common high Cd-accumulating plants.
Phytoextraction is a phytoremediation technique used for remediating polluted soils and it greatly relies on the plants' capacities to accumulate contaminants. Turnip is a high cadmium (Cd)-accumulating plant. We compared the Cd tolerance, growth, and Cd accumulation characteristics of two turnip landraces with three additional commonly known high Cd-accumulating species to systematically estimate its Cd phytoremediation potential. Results showed that the turnips could tolerate relatively lower Cd concentrations than other plants. Growth characteristics analyses indicated that the turnips initially grew rapidly and then gradually slowed down, and their photosynthetic parameters indicated that biomass accumulation was easily affected by light. However, the Cd uptake and translocation capacities of the two turnip landraces were higher than those of Phytolacca americana Linn. and Bidens pilosa Linn. but close to that of Brassica napus Linn.. Ultimately, large amounts of Cd accumulated in turnips during early growth and slightly increased as the fleshy roots increased in size. Based on these findings, the present turnip landraces have potential for soil remediation, but additional research is needed before these landraces can be practically used. Moreover, turnips are good candidates for studying the molecular mechanism of high Cd accumulation in plants. | {
"pile_set_name": "PubMed Abstracts"
} |
---
abstract: 'We continue our study of Cartan schemes and their Weyl groupoids. The results in this paper provide an algorithm to determine connected simply connected Cartan schemes of rank three, where the real roots form a finite irreducible root system. The algorithm terminates: Up to equivalence there are exactly 55 such Cartan schemes, and the number of corresponding real roots varies between $6$ and $37$. We identify those Weyl groupoids which appear in the classification of Nichols algebras of diagonal type.'
address:
- 'Michael Cuntz, Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany'
- 'István Heckenberger, Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Hans-Meerwein-Straße, D-35032 Marburg, Germany'
author:
- 'M. Cuntz'
- 'I. Heckenberger'
bibliography:
- 'quantum.bib'
title: Finite Weyl groupoids of rank three
---
Introduction
============
Root systems associated with Cartan matrices are widely studied structures in many areas of mathematics, see [@b-BourLie4-6] for the fundaments. The origins of the theory of root systems go back at least to the study of Lie groups by Lie, Killing and Cartan. The symmetry of the root system is commonly known as its Weyl group. Root systems associated with a family of Cartan matrices appeared first in connection with Lie superalgebras [@a-Kac77 Prop.2.5.6] and with Nichols algebras [@a-Heck06a], [@a-Heck08a]. The corresponding symmetry is not a group but a groupoid, and is called the Weyl groupoid of the root system.
Weyl groupoids of root systems properly generalize Weyl groups. The nice properties of this more general structure have been the main motivation to develop an axiomatic approach to the theory, see [@a-HeckYam08], [@a-CH09a]. In particular, Weyl groupoids are generated by reflections and Coxeter relations, and they satisfy a Matsumoto type theorem [@a-HeckYam08]. To see more clearly the extent of generality it would be desirable to have a classification of finite Weyl groupoids.[^1] However, already the appearance of a large family of examples of Lie superalgebras and Nichols algebras of diagonal type indicated that a classification of finite Weyl groupoids is probably much more complicated than the classification of finite Weyl groups. Additionally, many of the usual classification tools are not available in this context because of the lack of the adjoint action and a positive definite bilinear form.
In previous work, see [@a-CH09b] and [@p-CH09a], we have been able to determine all finite Weyl groupoids of rank two. The result of this classification is surprisingly nice: We found a close relationship to the theory of continued fractions and to cluster algebras of type $A$. The structure of finite rank two Weyl groupoids and the associated root systems has a natural characterization in terms of triangulations of convex polygons by non-intersecting diagonals. In particular, there are infinitely many such groupoids.
At first view there is no reason to assume that the situation for finite Weyl groupoids of rank three would be much different from the rank two case. In this paper we give some theoretical indications which strengthen the opposite point of view. For example in Theorem \[cartan\_6\] we show that the entries of the Cartan matrices in a finite Weyl groupoid cannot be smaller than $-7$. Recall that for Weyl groupoids there is no lower bound for the possible entries of generalized Cartan matrices. Our main achievement in this paper is to provide an algorithm to classify finite Weyl groupoids of rank three. Our algorithm terminates within a short time, and produces a finite list of examples. In the appendix we list the root systems characterizing the Weyl groupoids of the classification: There are $55$ of them which correspond to pairwise non-isomorphic Weyl groupoids. The number of positive roots in these root systems varies between $6$ and $37$. Among our root systems are the usual root systems of type $A_3$, $B_3$, and $C_3$, but for most of the other examples we don’t have yet an explanation.
It is remarkable that the number $37$ has a particular meaning for simplicial arrangements in the real projective plane. An arrangement is the complex generated by a family of straight lines not forming a pencil. The vertices of the complex are the intersection points of the lines, the edges are the segments of the lines between two vertices, and the faces are the connected components of the complement of the set of lines generating the arrangement. An arrangement is called simplicial, if all faces are triangles. Simplicial arrangements have been introduced in [@a-Melchi41]. The classification of simplicial arrangements in the real projective plane is an open problem. The largest known exceptional example is generated by $37$ lines. Grünbaum conjectures that the list given in [@a-Gruenb09] is complete. In our appendix we provide some data of our root systems which can be used to compare Grünbaum’s list with Weyl groupoids. There is an astonishing analogy between the two lists, but more work has to be done to be able to explain the precise relationship. This would be desirable in particular since our classification of finite Weyl groupoids of rank three does not give any evidence for the range of solutions besides the explicit computer calculation.
In order to ensure the termination of our algorithm, besides Theorem \[cartan\_6\] we use a weak convexity property of certain affine hyperplanes, see Theorem \[convex\_diff2\]: We can show that any positive root in an affine hyperplane “next to the origin” is either simple or can can be written as the sum of a simple root and another positive root. Our algorithm finally becomes practicable by the use of Proposition \[pr:suminR\], which can be interpreted as another weak convexity property for affine hyperplanes. It is hard to say which of these theorems are the most valuable because avoiding any of them makes the algorithm impracticable (unless one has some replacement).
The paper is organized as follows. We start with two sections proving the necessary theorems to formulate the algorithm: The results which do not require that the rank is three are in Section \[gen\_res\], the obstructions for rank three in Section \[rk3\_obst\]. We then describe the algorithm in the next section. Finally we summarize the resulting data and make some observations in the last section.
**Acknowledgement.** We would like to thank B. M[ü]{}hlherr for pointing out to us the importance of the number $37$ for simplicial arrangements in the real projective plane.
Cartan schemes and Weyl groupoids {#gen_res}
=================================
We mainly follow the notation in [@a-CH09a; @a-CH09b]. The fundaments of the general theory have been developed in [@a-HeckYam08] using a somewhat different terminology. Let us start by recalling the main definitions.
Let $I$ be a non-empty finite set and $\{{\alpha }_i\,|\,i\in I\}$ the standard basis of ${\mathbb{Z}}^I$. By [@b-Kac90 §1.1] a generalized Cartan matrix ${C}=({c}_{ij})_{i,j\in I}$ is a matrix in ${\mathbb{Z}}^{I\times I}$ such that
1. ${c}_{ii}=2$ and ${c}_{jk}\le 0$ for all $i,j,k\in I$ with $j\not=k$,
2. if $i,j\in I$ and ${c}_{ij}=0$, then ${c}_{ji}=0$.
Let $A$ be a non-empty set, ${\rho }_i : A \to A$ a map for all $i\in I$, and ${C}^a=({c}^a_{jk})_{j,k \in I}$ a generalized Cartan matrix in ${\mathbb{Z}}^{I \times I}$ for all $a\in A$. The quadruple $${\mathcal{C}}= {\mathcal{C}}(I,A,({\rho }_i)_{i \in I}, ({C}^a)_{a \in A})$$ is called a *Cartan scheme* if
1. ${\rho }_i^2 = \id$ for all $i \in I$,
2. ${c}^a_{ij} = {c}^{{\rho }_i(a)}_{ij}$ for all $a\in A$ and $i,j\in I$.
Let ${\mathcal{C}}= {\mathcal{C}}(I,A,({\rho }_i)_{i \in I}, ({C}^a)_{a \in A})$ be a Cartan scheme. For all $i \in I$ and $a \in A$ define ${\sigma }_i^a \in
\operatorname{Aut}({\mathbb{Z}}^I)$ by $$\begin{aligned}
{\sigma }_i^a ({\alpha }_j) = {\alpha }_j - {c}_{ij}^a {\alpha }_i \qquad
\text{for all $j \in I$.}
\label{eq:sia}
\end{aligned}$$ The *Weyl groupoid of* ${\mathcal{C}}$ is the category ${\mathcal{W}}({\mathcal{C}})$ such that ${\mathrm{Ob}}({\mathcal{W}}({\mathcal{C}}))=A$ and the morphisms are compositions of maps ${\sigma }_i^a$ with $i\in I$ and $a\in A$, where ${\sigma }_i^a$ is considered as an element in $\operatorname{Hom}(a,{\rho }_i(a))$. The category ${\mathcal{W}}({\mathcal{C}})$ is a groupoid in the sense that all morphisms are isomorphisms. The set of morphisms of ${\mathcal{W}}({\mathcal{C}})$ is denoted by $\operatorname{Hom}({\mathcal{W}}({\mathcal{C}}))$, and we use the notation $$\Homsfrom{a}=\mathop{\cup }_{b\in A}\operatorname{Hom}(a,b) \quad
\text{(disjoint union)}.$$ For notational convenience we will often neglect upper indices referring to elements of $A$ if they are uniquely determined by the context. For example, the morphism ${\sigma }_{i_1}^{{\rho }_{i_2}\cdots {\rho }_{i_k}(a)}
\cdots \s_{i_{k-1}}^{{\rho }_{i_k(a)}}{\sigma }_{i_k}^a\in \operatorname{Hom}(a,b)$, where $k\in {\mathbb{N}}$, $i_1,\dots,i_k\in I$, and $b={\rho }_{i_1}\cdots {\rho }_{i_k}(a)$, will be denoted by ${\sigma }_{i_1}\cdots {\sigma }_{i_k}^a$ or by ${\mathrm{id}}_b{\sigma }_{i_1}\cdots \s_{i_k}$. The cardinality of $I$ is termed the *rank of* ${\mathcal{W}}({\mathcal{C}})$. A Cartan scheme is called *connected* if its Weyl groupoid is connected, that is, if for all $a,b\in A$ there exists $w\in \operatorname{Hom}(a,b)$. The Cartan scheme is called *simply connected*, if $\operatorname{Hom}(a,a)=\{{\mathrm{id}}_a\}$ for all $a\in A$.
Let ${\mathcal{C}}$ be a Cartan scheme. For all $a\in A$ let $${(R\re)^{a}}=\{ {\mathrm{id}}_a {\sigma }_{i_1}\cdots \s_{i_k}({\alpha }_j)\,|\,
k\in {\mathbb{N}}_0,\,i_1,\dots,i_k,j\in I\}\subset {\mathbb{Z}}^I.$$ The elements of the set ${(R\re)^{a}}$ are called *real roots* (at $a$). The pair $({\mathcal{C}},({(R\re)^{a}})_{a\in A})$ is denoted by ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$. A real root ${\alpha }\in {(R\re)^{a}}$, where $a\in A$, is called positive (resp. negative) if ${\alpha }\in {\mathbb{N}}_0^I$ (resp. ${\alpha }\in -{\mathbb{N}}_0^I$). In contrast to real roots associated to a single generalized Cartan matrix, ${(R\re)^{a}}$ may contain elements which are neither positive nor negative. A good general theory, which is relevant for example for the study of Nichols algebras, can be obtained if ${(R\re)^{a}}$ satisfies additional properties.
Let ${\mathcal{C}}={\mathcal{C}}(I,A,({\rho }_i)_{i\in I},({C}^a)_{a\in A})$ be a Cartan scheme. For all $a\in A$ let $R^a\subset {\mathbb{Z}}^I$, and define $m_{i,j}^a= |R^a \cap (\ndN_0 {\alpha }_i + \ndN_0 {\alpha }_j)|$ for all $i,j\in
I$ and $a\in A$. We say that $${\mathcal{R}}= {\mathcal{R}}({\mathcal{C}}, (R^a)_{a\in A})$$ is a *root system of type* ${\mathcal{C}}$, if it satisfies the following axioms.
1. $R^a=R^a_+\cup - R^a_+$, where $R^a_+=R^a\cap \ndN_0^I$, for all $a\in A$.
2. $R^a\cap \ndZ{\alpha }_i=\{{\alpha }_i,-{\alpha }_i\}$ for all $i\in I$, $a\in A$.
3. ${\sigma }_i^a(R^a) = R^{{\rho }_i(a)}$ for all $i\in I$, $a\in A$.
4. If $i,j\in I$ and $a\in A$ such that $i\not=j$ and $m_{i,j}^a$ is finite, then $({\rho }_i{\rho }_j)^{m_{i,j}^a}(a)=a$.
The axioms (R2) and (R3) are always fulfilled for ${\mathcal{R}}{^\mathrm{re}}$. The root system ${\mathcal{R}}$ is called *finite* if for all $a\in A$ the set $R^a$ is finite. By [@a-CH09a Prop.2.12], if ${\mathcal{R}}$ is a finite root system of type ${\mathcal{C}}$, then ${\mathcal{R}}={\mathcal{R}}{^\mathrm{re}}$, and hence ${\mathcal{R}}{^\mathrm{re}}$ is a root system of type ${\mathcal{C}}$ in that case.
In [@a-CH09a Def.4.3] the concept of an *irreducible* root system of type ${\mathcal{C}}$ was defined. By [@a-CH09a Prop.4.6], if ${\mathcal{C}}$ is a Cartan scheme and ${\mathcal{R}}$ is a finite root system of type ${\mathcal{C}}$, then ${\mathcal{R}}$ is irreducible if and only if for all $a\in A$ the generalized Cartan matrix $C^a$ is indecomposable. If ${\mathcal{C}}$ is also connected, then it suffices to require that there exists $a\in A$ such that $C^a$ is indecomposable.
Let ${\mathcal{C}}={\mathcal{C}}(I,A,({\rho }_i)_{i\in I},({C}^a)_{a\in A})$ be a Cartan scheme. Let $\Gamma $ be a nondirected graph, such that the vertices of $\Gamma $ correspond to the elements of $A$. Assume that for all $i\in I$ and $a\in A$ with ${\rho }_i(a)\not=a$ there is precisely one edge between the vertices $a$ and ${\rho }_i(a)$ with label $i$, and all edges of $\Gamma $ are given in this way. The graph $\Gamma $ is called the *object change diagram* of ${\mathcal{C}}$.
![The object change diagram of a Cartan scheme of rank three (nr. 15 in Table 1)[]{data-label="fig:14posroots"}](wg14){width="6cm"}
In the rest of this section let $\cC={\mathcal{C}}(I,A,({\rho }_i)_{i\in I}, (C^a)_{a\in A})$ be a Cartan scheme such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system. For brevity we will write $R^a$ instead of ${(R\re)^{a}}$ for all $a\in A$. We say that a subgroup $H\subset {\mathbb{Z}}^I$ is a *hyperplane* if ${\mathbb{Z}}^I/H\cong {\mathbb{Z}}$. Then ${\mathrm{rk}}\,H=\#I-1$ is the rank of $H$. Sometimes we will identify ${\mathbb{Z}}^I$ with its image under the canonical embedding ${\mathbb{Z}}^I\to {\mathbb{Q}}\otimes _{\mathbb{Z}}{\mathbb{Z}}^I\cong {\mathbb{Q}}^I$.
\[le:hyperplane\] Let $a\in A$ and let $H\subset {\mathbb{Z}}^I$ be a hyperplane. Suppose that $H$ contains ${\mathrm{rk}}\,H$ linearly independent elements of $R^a$. Let $\mathfrak{n}_H$ be a normal vector of $H$ in ${\mathbb{Q}}^I$ with respect to a scalar product $(\cdot ,\cdot )$ on ${\mathbb{Q}}^I$. If $(\mathfrak{n}_H,{\alpha })\ge 0$ for all ${\alpha }\in R^a_+$, then $H$ contains ${\mathrm{rk}}\,H$ simple roots, and all roots contained in $H$ are linear combinations of these simple roots.
The assumptions imply that any positive root in $H$ is a linear combination of simple roots contained in $H$. Since $R^a=R^a_+\cup -R^a_+$, this implies the claim.
Let $a\in A$ and let $H\subset {\mathbb{Z}}^I$ be a hyperplane. Suppose that $H$ contains ${\mathrm{rk}}\,H$ linearly independent elements of $R^a$. Then there exist $b\in A$ and $w\in \operatorname{Hom}(a,b)$ such that $w(H)$ contains ${\mathrm{rk}}\,H$ simple roots. \[le:hyperplane2\]
Let $(\cdot ,\cdot )$ be a scalar product on ${\mathbb{Q}}^I$. Choose a normal vector $\mathfrak{n}_H$ of $H$ in ${\mathbb{Q}}^I$ with respect to $(\cdot ,\cdot )$. Let $m=\# \{{\alpha }\in R^a_+\,|\,(\mathfrak{n}_H,{\alpha })<0\}$. Since ${\mathcal{R}}\re
({\mathcal{C}})$ is finite, $m$ is a nonnegative integer. We proceed by induction on $m$. If $m=0$, then $H$ contains ${\mathrm{rk}}\,H$ simple roots by Lemma \[le:hyperplane\]. Otherwise let $j\in I$ with $(\mathfrak{n}_H,{\alpha }_j)<0$. Let $a'={\rho }_j(a)$ and $H'=\s_j^a(H)$. Then $\s_j^a(\mathfrak{n}_H)$ is a normal vector of $H'$ with respect to the scalar product $(\cdot ,\cdot )'=
(\s_j^{{\rho }_j(a)}(\cdot ),\s_j^{{\rho }_j(a)}(\cdot ))$. Since $\s_j^a:R^a_+\setminus \{{\alpha }_j\}\to R^{a'}_+\setminus \{{\alpha }_j\}$ is a bijection and $\s_j^a({\alpha }_j)=-{\alpha }_j$, we conclude that $$\begin{aligned}
\# \{\beta \in R^{a'}_+\,|\,(\s^a_j(\mathfrak{n}_H),\beta )'<0\}=
\# \{{\alpha }\in R^a_+\,|\,(\mathfrak{n}_H,{\alpha })<0\}-1.
\end{aligned}$$ By induction hypothesis there exists $b\in A$ and $w'\in \operatorname{Hom}(a',b)$ such that $w'(H')$ contains ${\mathrm{rk}}\,H'={\mathrm{rk}}\,H$ simple roots. Then the claim of the lemma holds for $w=w'\s_j^a$.
The following “volume” functions will be useful for our analysis. Let $k\in {\mathbb{N}}$ with $k\le \#I$. By the Smith normal form there is a unique left ${\mathrm{GL}}({\mathbb{Z}}^I)$-invariant right ${\mathrm{GL}}({\mathbb{Z}}^k)$-invariant function ${\mathrm{Vol}}_k:({\mathbb{Z}}^I)^k\to {\mathbb{Z}}$ such that $$\begin{aligned}
{\mathrm{Vol}}_k(a_1{\alpha }_1,\dots,a_k{\alpha }_k)=|a_1\cdots a_k| \quad
\text{for all $a_1,\dots,a_k\in {\mathbb{Z}}$,}\end{aligned}$$ where $|\cdot |$ denotes absolute value. In particular, if $k=1$ and $\beta \in {\mathbb{Z}}^I\setminus \{0\}$, then $\Vol
_1(\beta )$ is the largest integer $v$ such that $\beta =v\beta '$ for some $\beta '\in {\mathbb{Z}}^I$. Further, if $k=\#I$ and $\beta _1,\dots,\beta _k\in {\mathbb{Z}}^I$, then ${\mathrm{Vol}}_k(\beta _1,\dots,\beta _k)$ is the absolute value of the determinant of the matrix with columns $\beta _1,\dots,\beta _k$.
Let $a\in A$, $k\in \{1,2,\dots,\#I\}$, and let $\beta _1,\dots,\beta _k\in R^a$ be linearly independent elements. We write $V^a(\beta _1,\dots,\beta _k)$ for the unique maximal subgroup $V\subseteq {\mathbb{Z}}^I$ of rank $k$ which contains $\beta _1,\dots,\beta _k$. Then ${\mathbb{Z}}^I/V^a(\beta _1,\dots,\beta _k)$ is free. In particular, $V^a(\beta _1,\dots,\beta _{\#I})={\mathbb{Z}}^I$ for all $a\in A$ and any linearly independent subset $\{\beta _1,\dots,\beta _{\#I}\}$ of $R^a$.
\[de:base\] Let $W\subseteq {\mathbb{Z}}^I$ be a cofree subgroup (that is, ${\mathbb{Z}}^I/W$ is free) of rank $k$. We say that $\{\beta _1,\dots,\beta _k\}$ is a *base for $W$ at $a$*, if $\beta _i\in W$ for all $i\in \{1,\dots,k\}$ and $W\cap R^a\subseteq \sum _{i=1}^k{\mathbb{N}}_0\beta _i\cup
-\sum _{i=1}^k{\mathbb{N}}_0\beta _i$.
Now we discuss the relationship of linearly independent roots in a root system. Recall that ${\mathcal{C}}$ is a Cartan scheme such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system of type ${\mathcal{C}}$.
\[th:genposk\] Let $a\in A$, $k\in \{1,\dots,\#I\}$, and let $\beta _1,\dots,\beta _k\in R^a$ be linearly independent roots. Then there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, and a permutation $\tau $ of $I$ such that $$w(\beta _i)\in {\mathrm{span}}_{\mathbb{Z}}\{{\alpha }_{\tau (1)},
\ldots ,{\alpha }_{\tau (i)}\} \cap R^b_+$$ for all $i\in \{1,\dots,k\}$.
Let $r=\#I$. Since $R^a$ contains $r$ simple roots, any linearly independent subset of $R^a$ can be enlarged to a linearly independent subset of $r$ elements. Hence it suffices to prove the theorem for $k=r$. We proceed by induction on $r$. If $r=1$, then the claim holds.
Assume that $r>1$. Lemma \[le:hyperplane2\] with $H=V^a(\beta _1,\dots,\beta _{r-1})$ tells that there exist $d\in A$ and $v\in \operatorname{Hom}(a,d)$ such that $v(H)$ is spanned by simple roots. By multiplying $v$ from the left with the longest element of ${\mathcal{W}}({\mathcal{C}})$ in the case that $v(\beta _r)\in -{\mathbb{N}}_0^I$, we may even assume that $v(\beta _r)\in {\mathbb{N}}_0^I$. Now let $J$ be the subset of $I$ such that $\#J=r-1$ and ${\alpha }_i\in v(H)$ for all $i\in J$. Consider the restriction ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})|_{J}$ of ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ to the index set $J$, see [@a-CH09a Def. 4.1]. Since $v(\beta _i)\in H$ for all $i\in \{1,\dots,r-1\}$, induction hypothesis provides us with $b\in A$, $u\in \operatorname{Hom}(d,b)$, and a permutation $\tau '$ of $J$ such that $u$ is a product of simple reflections $\s_i$, where $i\in J$, and $$uv(\beta _n)\in
{\mathrm{span}}_{\mathbb{Z}}\{{\alpha }_{\tau '(j_1)}, \ldots ,{\alpha }_{\tau '(j_n)}\}
\cap R^b_+$$ for all $n\in \{1,2,\dots,r-1\}$, where $J=\{j_1,\dots,j_{r-1}\}$. Since $v(\beta _r)\notin v(H)$ and $v(\beta _r)\in {\mathbb{N}}_0^I$, the $i$-th entry of $v(\beta _r)$, where $i\in I\setminus J$, is positive. This entry does not change if we apply $u$. Therefore $uv(\beta _r)\in {\mathbb{N}}_0^I$, and hence the theorem holds with $w=uv\in \operatorname{Hom}(a,b)$ and with $\tau $ the unique permutation with $\tau (n)=\tau '(j_n)$ for all $n\in \{1,\dots,r-1\}$.
\[simple\_rkk\] Let $a\in A$, $k\in \{1,\dots,\#I\}$, and let $\beta _1,\dots,\beta _k\in R^a$ be linearly independent elements. Then $\{\beta _1,\dots,\beta _k\}$ is a base for $V^a(\beta _1,\dots,\beta _k)$ at $a$ if and only if there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, and a permutation $\tau $ of $I$ such that $w(\beta _i)={\alpha }_{\tau (i)}$ for all $i\in \{1,\dots,k\}$. In this case ${\mathrm{Vol}}_k(\beta _1,\dots,\beta _k)=1$.
The if part of the claim holds by definition of a base and by the axioms for root systems.
Let $b,w$ and $\tau $ be as in Theorem \[th:genposk\]. Let $i\in
\{1,\dots,k\}$. The elements $w(\beta _1),\dots,w(\beta _i)$ are linearly independent and are contained in $V^b({\alpha }_{\tau (1)}, \dots ,
{\alpha }_{\tau (i)})$. Thus ${\alpha }_{\tau (i)}$ is a rational linear combination of $w(\beta _1),\dots,w(\beta _i)$. Now by assumption, $\{w(\beta _1),\dots,w(\beta _k)\}$ is a base for $V^b(w(\beta _1),\dots,w(\beta _k))$ at $b$. Hence ${\alpha }_{\tau
(i)}$ is a linear combination of the positive roots $w(\beta _1),\dots,w(\beta _i)$ with nonnegative integer coefficients. This is possible only if $\{w(\beta _1),\dots,w(\beta _i)\}$ contains ${\alpha }_{\tau (i)}$. By induction on $i$ we obtain that ${\alpha }_{\tau (i)}=w(\beta _i)$.
In the special case $k=\#I$ the above corollary tells that the bases of $\ndZ
^I$ at an object $a\in A$ are precisely those subsets which can be obtained as the image, up to a permutation, of the standard basis of ${\mathbb{Z}}^I$ under the action of an element of ${\mathcal{W}}({\mathcal{C}})$.
In [@p-CH09a] the notion of an ${\mathcal{F}}$-sequence was given, and it was used to explain the structure of root systems of rank two. Consider on ${\mathbb{N}}_0^2$ the total ordering $\le _{\mathbb{Q}}$, where $(a_1,a_2)\le _{\mathbb{Q}}(b_1,b_2)$ if and only if $a_1 b_2\le a_2 b_1$. A finite sequence $(v_1,\dots ,v_n)$ of vectors in ${\mathbb{N}}_0^2$ is an ${\mathcal{F}}$-sequence if and only if $v_1<_{\mathbb{Q}}v_2
<_{\mathbb{Q}}\cdots <_{\mathbb{Q}}v_n$ and one of the following holds.
- $n=2$, $v_1=(0,1)$, and $v_2=(1,0)$.
- $n>2$ and there exists $i\in \{2,3,\dots,n-1\}$ such that $v_i=v_{i-1}+v_{i+1}$ and $(v_1,\dots,v_{i-1}.v_{i+1},\dots,v_n)$ is an ${\mathcal{F}}$-sequence.
In particular, any ${\mathcal{F}}$-sequence of length $\ge 3$ contains $(1,1)$.
\[pr:R=Fseq\] [@p-CH09a Prop.3.7] Let ${\mathcal{C}}$ be a Cartan scheme of rank two. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system. Then for any $a\in A$ the set $R^a_+$ ordered by $\le _\QQ$ is an ${\mathcal{F}}$-sequence.
\[pr:sumoftwo\] [@p-CH09a Cor. 3.8] Let ${\mathcal{C}}$ be a Cartan scheme of rank two. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system. Let $a\in A$ and let $\beta \in R^a_+$. Then either $\beta $ is simple or it is the sum of two positive roots.
\[co:r2conv\] Let $a\in A$, $n\in {\mathbb{N}}$, and let ${\alpha },\beta \in R^a$ such that $\beta -n{\alpha }\in R^a$. Assume that $\{{\alpha },\beta -n{\alpha }\}$ is a base for $V^a({\alpha },\beta )$ at $a$. Then $\beta -k{\alpha }\in R^a$ for all $k\in \{1,2,\dots ,n\}$.
By Corollary \[simple\_rkk\] there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, and $i,j\in I$ such that $w({\alpha })={\alpha }_i$, $w(\beta -n{\alpha })={\alpha }_j$. Then $n{\alpha }_i+{\alpha }_j=w(\beta )\in R^b_+$. Hence $(n-k){\alpha }_i+{\alpha }_j\in R^b$ for all $k\in \{1,2,\dots,n\}$ by Proposition \[pr:sumoftwo\] and (R2). This yields the claim of the corollary.
\[co:cij\] Let $a\in A$, $k\in {\mathbb{Z}}$, and $i,j\in I$ such that $i\not=j$. Then ${\alpha }_j+k{\alpha }_i\in R^a$ if and only if $0\le k\le -c^a_{i j}$,
Axiom (R1) tells that ${\alpha }_j+k{\alpha }_i\notin R^a$ if $k<0$. Since $c^{{\rho }_i(a)}_{i j}=c^a_{i j}$ by (C2), Axiom (R3) gives that $\al
_j-c^a_{i j}{\alpha }_i=\sigma _i^{{\rho }_i(a)}({\alpha }_j)\in R^a$ and that ${\alpha }_j+k{\alpha }_i\notin R^a$ if $k>-c^a_{i j}$. Finally, if $0<k<-c^a_{i j}$ then ${\alpha }_j+k{\alpha }_i\in R^a$ by Corollary \[co:r2conv\] for ${\alpha }={\alpha }_i$, $\beta ={\alpha }_j-c^a_{i j}{\alpha }_i$, and $n=-c^a_{i j}$.
Proposition \[pr:sumoftwo\] implies another important fact.
\[root\_is\_sum\] Let ${\mathcal{C}}$ be a Cartan scheme. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system of type ${\mathcal{C}}$. Let $a\in A$ and ${\alpha }\in R^a_+$. Then either ${\alpha }$ is simple, or it is the sum of two positive roots.
Assume that ${\alpha }$ is not simple. Let $i\in I$, $b\in A$, and $w\in \operatorname{Hom}(b,a)$ such that ${\alpha }=w({\alpha }_i)$. Then $\ell(w)>0$. We may assume that for all $j\in I$, $b'\in A$, and $w'\in \operatorname{Hom}(b',a)$ with $w'(\alpha_j)={\alpha }$ we have $\ell(w')\ge\ell(w)$. Since $w(\alpha_i)\in {\mathbb{N}}_0^I$, we obtain that $\ell(w\s_i)>\ell(w)$ [@a-HeckYam08 Cor. 3]. Therefore, there is a $j\in I\setminus \{i\}$ with $\ell(w\s_j)<\ell(w)$. Let $w=w_1w_2$ such that $\ell(w)=\ell(w_1)+\ell(w_2)$, $\ell(w_1)$ minimal and $w_2=\ldots \s_i\s_j\s_i\s_j^b$. Assume that $w_2=\s_i\cdots \s_i\s_j^b$ — the case $w_2=\s_j\cdots \s_i \s_j^b$ can be treated similarly. The length of $w_1$ is minimal, thus $\ell(w_1\s_j)>\ell(w_1)$, and $\ell(w)=\ell(w_1)+\ell(w_2)$ yields that $\ell(w_1\s_i)>\ell(w_1)$. Using once more [@a-HeckYam08 Cor. 3] we conclude that $$\begin{aligned}
\label{eq:twopos}
w_1(\alpha_i)\in {\mathbb{N}}_0^I,\quad w_1(\alpha_j)\in {\mathbb{N}}_0^I.\end{aligned}$$ Let $\beta=w_2(\alpha_i)$. Then $\beta \in \NN_0 \alpha_i+\NN_0 \alpha_j$, since $\ell (w_2\s_i)>\ell (w_2)$. Moreover, $\beta $ is not simple. Indeed, $\alpha=w(\alpha_i)=w_1(\beta)$, so $\beta$ is not simple, since $\ell(w_1)<\ell(w)$ and $\ell(w)$ was chosen of minimal length. By Proposition \[pr:sumoftwo\] we conclude that $\beta$ is the sum of two positive roots $\beta_1$, $\beta_2\in {\mathbb{N}}_0{\alpha }_i+{\mathbb{N}}_0{\alpha }_j$. It remains to check that $w_1(\beta_1)$, $w_1(\beta_2)$ are positive. But this follows from .
Obstructions for Weyl groupoids of rank three {#rk3_obst}
=============================================
In this section we analyze the structure of finite Weyl groupoids of rank three. Let ${\mathcal{C}}$ be a Cartan scheme of rank three, and assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type ${\mathcal{C}}$. In this case a hyperplane in ${\mathbb{Z}}^I$ is the same as a cofree subgroup of rank two, which will be called a *plane* in the sequel. For simplicity we will take $I=\{1,2,3\}$, and we write $R^a$ for the set of positive real roots at $a\in A$.
Recall the definition of the functions ${\mathrm{Vol}}_k$, where $k\in \{1,2,3\}$, from the previous section. As noted, for three elements ${\alpha },\beta,\gamma\in\ZZ^3$ we have ${\mathrm{Vol}}_3(\alpha,\beta,\gamma )=1$ if and only if $\{\alpha,\beta,\gamma\}$ is a basis of ${\mathbb{Z}}^3$. Also, we will heavily use the notion of a base, see Definition \[de:base\].
\[rootmultiple\] Let $a\in A$ and $\alpha,\beta \in R^a$. Assume that ${\alpha }\not=\pm \beta $ and that $\{{\alpha },\beta\}$ is not a base for $V^a({\alpha },\beta )$ at $a$. Then there exist $k,l\in {\mathbb{N}}$ and $\delta \in R^a$ such that $\beta -k{\alpha }=l\delta $ and $\{{\alpha },\delta \}$ is a base for $V^a({\alpha },\beta )$ at $a$.
The claim without the relation $k>0$ is a special case of Theorem \[th:genposk\]. The relation $\beta \not=\delta $ follows from the assumption that $\{{\alpha },\beta \}$ is not a base for $V^a({\alpha },\beta )$ at $a$.
Let $a\in A$ and $\alpha,\beta \in R^a$ such that ${\alpha }\not=\pm \beta $. Then $\{{\alpha },\beta \}$ is a base for $V^a(\al, \beta )$ if and only if ${\mathrm{Vol}}_2({\alpha },\beta )=1$ and ${\alpha }-\beta \notin R^a$. \[le:base2\]
Assume first that $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$. By Corollary \[simple\_rkk\] we may assume that ${\alpha }$ and $\beta $ are simple roots. Therefore ${\mathrm{Vol}}_2({\alpha },\beta )=1$ and ${\alpha }-\beta \notin R^a$.
Conversely, assume that ${\mathrm{Vol}}_2({\alpha },\beta )=1$, ${\alpha }-\beta \notin R^a$, and that $\{{\alpha },\beta \}$ is not a base for $V^a({\alpha },\beta )$ at $a$. Let $k,l,\delta $ as in Lemma \[rootmultiple\]. Then $$1={\mathrm{Vol}}_2({\alpha },\beta )={\mathrm{Vol}}_2({\alpha },\beta -k{\alpha })=l{\mathrm{Vol}}_2({\alpha },\delta ).$$ Hence $l=1$, and $\{{\alpha },\delta \}=\{{\alpha },\beta -k{\alpha }\}$ is a base for $V^a({\alpha },\beta )$ at $a$. Then $\beta -{\alpha }\in R^a$ by Corollary \[co:r2conv\] and since $k>0$. This gives the desired contradiction to the assumption ${\alpha }-\beta \notin R^a$.
Recall that a semigroup ordering $<$ on a commutative semigroup $(S,+)$ is a total ordering such that for all $s,t,u\in S$ with $s<t$ the relations $s+u<t+u$ hold. For example, the lexicographic ordering on ${\mathbb{Z}}^I$ induced by any total ordering on $I$ is a semigroup ordering.
\[posrootssemigroup\] Let $a\in A$, and let $V\subset {\mathbb{Z}}^I$ be a plane containing at least two positive roots of $R^a$. Let $<$ be a semigroup ordering on ${\mathbb{Z}}^I$ such that $0<\gamma $ for all $\gamma \in R^a_+$, and let ${\alpha },\beta $ denote the two smallest elements in $V\cap R^a_+$ with respect to $<$. Then $\{{\alpha },\beta \}$ is a base for $V$ at $a$.
Let ${\alpha }$ be the smallest element of $V\cap R^a_+$ with respect to $<$, and let $\beta $ be the smallest element of $V\cap (R^a_+\setminus \{{\alpha }\})$. Then $V=V^a(\al, \beta )$ by (R2). By Lemma \[rootmultiple\] there exists $\delta \in V\cap
R^a$ such that $\{{\alpha },\delta \}$ is a base for $V$ at $a$. First suppose that $\delta <0$. Let $m\in {\mathbb{N}}_0$ be the smallest integer with $\delta +(m+1){\alpha }\notin R^a$. Then $\delta +n{\alpha }<0$ for all $n\in {\mathbb{N}}_0$ with $n\le m$. Indeed, this holds for $n=0$ by assumption. By induction on $n$ we obtain from $\delta +n{\alpha }<0$ and the choice of ${\alpha }$ that $\delta +n{\alpha }<-{\alpha }$, since $\delta $ and ${\alpha }$ are not collinear. Hence $\delta +(n+1){\alpha }<0$. We conclude that $-(\delta +m{\alpha })>0$. Moreover, $\{{\alpha },-(\delta +m{\alpha })\}$ is a base for $V$ at $a$ by Lemma \[le:base2\] and the choice of $m$. Therefore, by replacing $\{{\alpha },\delta \}$ by $\{{\alpha },-(\delta +m{\alpha })\}$, we may assume that $\delta >0$. Since $\beta >0$, we conclude that $\beta =k{\alpha }+l\delta $ for some $k,l\in
{\mathbb{N}}_0$. Since $\beta $ is not a multiple of ${\alpha }$, this implies that $\beta =\delta $ or $\beta >\delta $. Then the choice of $\beta $ and the positivity of $\delta $ yield that $\delta =\beta $, that is, $\{{\alpha },\beta \}$ is a base for $V$ at $a$.
\[le:badroots\] Let $k\in {\mathbb{N}}_{\ge 2}$, $a\in A$, ${\alpha }\in R^a_+$, and $\beta \in {\mathbb{Z}}^I$ such that ${\alpha }$ and $\beta $ are not collinear and ${\alpha }+k\beta \in R^a$. Assume that ${\mathrm{Vol}}_2({\alpha },\beta )=1$ and that $(-{\mathbb{N}}{\alpha }+{\mathbb{Z}}\beta )
\cap {\mathbb{N}}_0^I=\emptyset $. Then $\beta \in R^a$ and ${\alpha }+l\beta \in R^a$ for all $l\in \{1,2,\dots,k\}$.
We prove the claim indirectly. Assume that $\beta \notin R^a$. By Lemma \[posrootssemigroup\] there exists a base $\{\gamma _1,\gamma
_2\}$ for $V^a({\alpha },\beta )$ at $a$ such that $\gamma _1,\gamma _2\in R^a_+$. The assumptions of the lemma imply that there exist $m_1,l_1\in {\mathbb{N}}_0$ and $m_2,l_2\in {\mathbb{Z}}$ such that $\gamma _1=m_1{\alpha }+m_2\beta $, $\gamma _2=l_1{\alpha }+l_2\beta $. Since $\beta \notin R^a$, we obtain that $m_1\ge 1$ and $m_2\ge 1$. Therefore relations ${\alpha },{\alpha }+k\beta \in R^a_+$ imply that $\{{\alpha },{\alpha }+k\beta \}=\{\gamma _1,\gamma _2\}$. The latter is a contradiction to ${\mathrm{Vol}}_2(\gamma _1,\gamma _2)=1$ and ${\mathrm{Vol}}_2({\alpha },{\alpha }+k\beta )=k>1$. Thus $\beta \in R^a$. By Lemma \[rootmultiple\] we obtain that $\{\beta ,{\alpha }-m\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$ for some $m\in {\mathbb{N}}_0$. Then Corollary \[co:r2conv\] and the assumption that ${\alpha }+k\beta \in R^a$ imply the last claim of the lemma.
We say that a subset $S$ of ${\mathbb{Z}}^3$ is *convex*, if any rational convex linear combination of elements of $S$ is either in $S$ or not in ${\mathbb{Z}}^3$. We start with a simple example.
\[le:square\] Let $a\in A$. Assume that $c^a_{12}=0$.
\(1) Let $k_1,k_2\in {\mathbb{Z}}$. Then ${\alpha }_3+k_1{\alpha }_1+k_2{\alpha }_2\in R^a$ if and only if $0\le k_1\le -c^a_{13}$ and $0\le k_2\le -c^a_{23}$.
\(2) Let $\gamma \in ({\alpha }_3+{\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)\cap R^a$. Then $\gamma -{\alpha }_1\in R^a$ or $\gamma +{\alpha }_1\in R^a$. Similarly $\gamma -{\alpha }_2\in R^a$ or $\gamma +{\alpha }_2\in R^a$.
\(1) The assumption $c^a_{12}=0$ implies that $c^{{\rho }_1(a)}_{23}=c^a_{23}$, see [@a-CH09a Lemma4.5]. Applying ${\sigma }_1^{{\rho }_1(a)}$, ${\sigma }_2^{{\rho }_2(a)}$, and ${\sigma }_1{\sigma }_2^{{\rho }_2{\rho }_1(a)}$ to ${\alpha }_3$ we conclude that ${\alpha }_3-c^a_{13}{\alpha }_1$, ${\alpha }_3-c^a_{23}{\alpha }_2$, ${\alpha }_3-c^a_{13}\al
_1-c^a_{23}{\alpha }_2\in R^a_+$. Thus Lemma \[le:badroots\] implies that ${\alpha }_3+m_1{\alpha }_1+m_2{\alpha }_2\in R^a$ for all $m_1,m_2\in {\mathbb{Z}}$ with $0\le m_1\le -c^a_{13}$ and $0\le m_2\le -c^a_{23}$. Further, (R1) gives that ${\alpha }_3+k_1{\alpha }_1+k_2{\alpha }_2\notin R^a$ if $k_1<0$ or $k_2<0$. Applying again the simple reflections ${\sigma }_1$ and ${\sigma }_2$, a similar argument proves the remaining part of the claim. Observe that the proof does not use the fact that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is irreducible.
\(2) Since $c^a_{12}=0$, the irreducibility of ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ yields that $c^a_{13},c^a_{23}<0$ by [@a-CH09a Def.4.5, Prop.4.6]. Hence the claim follows from (1).
\[pr:suminR\] Let $a\in A$ and let $\gamma _1,\gamma _2,\gamma _3\in R^a$. Assume that ${\mathrm{Vol}}_3(\gamma _1,\gamma _2,\gamma _3)=1$ and that $\gamma _1-\gamma _2,\gamma _1-\gamma _3\notin R^a$. Then $\gamma _1+\gamma _2\in R^a$ or $\gamma _1+\gamma _3\in R^a$.
Since $\gamma _1-\gamma _2\notin R^a$ and ${\mathrm{Vol}}_3(\gamma _1,\gamma
_2,\gamma _3)=1$, Theorem \[th:genposk\] and Lemma \[le:base2\] imply that there exists $b\in A$, $w\in \operatorname{Hom}(a,b)$ and $i_1,i_2,i_3\in I$ such that $w(\gamma _1)={\alpha }_{i_1}$, $w(\gamma _2)={\alpha }_{i_2}$, and $w(\gamma _3)={\alpha }_{i_3}+k_1{\alpha }_{i_1}+k_2{\alpha }_{i_2}$ for some $k_1,k_2\in {\mathbb{N}}_0$. Assume that $\gamma _1+\gamma _2\notin R^a$. Then $c^b_{i_1i_2}=0$. Since $\gamma _3-\gamma _1\notin R^a$, Lemma \[le:square\](2) with $\gamma =w(\gamma _3)$ gives that $\gamma _3+\gamma _1\in R^a$. This proves the claim.
\[le:root\_diffs1\] Assume that $R^a\cap ({\mathbb{N}}_0{\alpha }_1+{\mathbb{N}}_0{\alpha }_2)$ contains at most $4$ positive roots.
\(1) The set $S_3:=({\alpha }_3+{\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)\cap R^a$ is convex.
\(2) Let $\gamma \in S_3$. Then $\gamma ={\alpha }_3$ or $\gamma -{\alpha }_1\in R^a$ or $\gamma -{\alpha }_2\in R^a$.
Consider the roots of the form $w^{-1}({\alpha }_3)\in R^a$, where $w\in \Homsfrom{a}$ is a product of reflections ${\sigma }_1^b$, ${\sigma }_2^b$ with $b\in A$. All of these roots belong to $S_3$. Using Lemma \[le:badroots\] the claims of the lemma can be checked case by case, similarly to the proof of Lemma \[le:square\].
The lemma can be proven by elementary calculations, since all nonsimple positive roots in $({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)\cap R^a$ are of the form say ${\alpha }_1+k{\alpha }_2$, $k\in {\mathbb{N}}$. We will see in Theorem \[th:class\] that the classification of connected Cartan schemes of rank three admitting a finite irreducible root system has a finite set of solutions. Thus it is possible to check the claim of the lemma for any such Cartan scheme. Using computer calculations one obtains that the lemma holds without any restriction on the (finite) cardinality of $R^a\cap ({\mathbb{N}}_0{\alpha }_1+{\mathbb{N}}_0{\alpha }_2)$.
\[le:root\_diffs2\] Let ${\alpha },\beta ,\gamma \in R^a$ such that ${\mathrm{Vol}}_3({\alpha },\beta ,\gamma )=1$. Assume that ${\alpha }-\beta $, $\beta -\gamma $, ${\alpha }-\gamma \notin R^a$ and that $\{{\alpha },\beta ,\gamma \}$ is not a base for ${\mathbb{Z}}^I$ at $a$. Then the following hold.
\(1) There exist $w\in \Homsfrom{a}$ and $n_1,n_2\in {\mathbb{N}}$ such that $w({\alpha })$, $w(\beta )$, and $w(\gamma -n_1{\alpha }-n_2\beta )$ are simple roots.
\(2) None of the vectors ${\alpha }-k\beta $, ${\alpha }-k\gamma $, $\beta -k{\alpha }$, $\beta -k\gamma $, $\gamma -k{\alpha }$, $\gamma -k\beta $, where $k\in {\mathbb{N}}$, is contained in $R^a$.
\(3) ${\alpha }+\beta $, ${\alpha }+\gamma $, $\beta +\gamma \in R^a$.
\(4) One of the sets $\{{\alpha }+2\beta ,\beta +2\gamma ,\gamma +2{\alpha }\}$ and $\{2{\alpha }+\beta ,2\beta +\gamma ,2\gamma +{\alpha }\}$ is contained in $R^a$, the other one has trivial intersection with $R^a$.
\(5) None of the vectors $\gamma -{\alpha }-k\beta $, $\gamma -k{\alpha }-\beta $, $\beta -\gamma -k{\alpha }$, $\beta -k\gamma -{\alpha }$, ${\alpha }-\beta -k\gamma $, ${\alpha }-k\beta -\gamma $, where $k\in {\mathbb{N}}_0$, is contained in $R^a$.
\(6) Assume that ${\alpha }+2\beta \in R^a$. Let $k\in {\mathbb{N}}$ such that ${\alpha }+k\beta \in R^a$, ${\alpha }+(k+1)\beta \notin R^a$. Let ${\alpha }'={\alpha }+k\beta $, $\beta '=-\beta $, $\gamma '=\gamma +\beta $. Then ${\mathrm{Vol}}_3({\alpha }',\beta ',\gamma ')=1$, $\{{\alpha }',\beta ',\gamma '\}$ is not a base for ${\mathbb{Z}}^I$ at $a$, and none of ${\alpha }'-\beta '$, ${\alpha }'-\gamma '$, $\beta '-\gamma '$ is contained in $R^a$.
\(7) None of the vectors ${\alpha }+3\beta $, $\beta +3\gamma $, $\gamma +3{\alpha }$, $3{\alpha }+\beta $, $3\beta +\gamma $, $3\gamma +{\alpha }$ is contained in $R^a$. In particular, $k=2$ holds in (6).
\(1) By Theorem \[th:genposk\] there exist $m_1,m_2,n_1,n_2,n_3\in \ndN
_0$, $i_1,i_2,i_3\in I$, and $w\in \Homsfrom{a}$, such that $w({\alpha })={\alpha }_{i_1}$, $w(\beta )=m_1{\alpha }_{i_1}+m_2{\alpha }_{i_2}$, and $w(\gamma )=n_1{\alpha }_{i_1}+n_2{\alpha }_{i_2}+n_3{\alpha }_{i_3}$. Since $\det w\in
\{\pm 1\}$ and ${\mathrm{Vol}}_3({\alpha },\beta ,\gamma )=1$, this implies that $m_2=n_3=1$. Further, $\beta -{\alpha }\notin R^a$, and hence $w(\beta )={\alpha }_{i_2}$ by Corollary \[co:cij\]. Since $\{{\alpha },\beta ,\gamma \}$ is not a base for ${\mathbb{Z}}^I$ at $a$, we conclude that $w(\gamma )\not={\alpha }_{i_3}$. Then Corollary \[co:cij\] and the assumptions $\gamma -{\alpha }$, $\gamma -\beta
\notin R^a$ imply that $w(\gamma )\notin {\alpha }_{i_3}+{\mathbb{N}}_0{\alpha }_{i_1}$ and $w(\gamma )\notin {\alpha }_{i_3}+{\mathbb{N}}_0{\alpha }_{i_2}$. Thus the claim is proven.
\(2) By (1), $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$. Thus ${\alpha }-k\beta \notin R^a$ for all $k\in {\mathbb{N}}$. The remaining claims follow by symmetry.
\(3) Suppose that ${\alpha }+\beta \notin R^a$. By (1) there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, $i_1,i_2,i_3\in I$ and $n_1,n_2\in {\mathbb{N}}$ such that $w({\alpha })={\alpha }_{i_1}$, $w(\beta )={\alpha }_{i_2}$, and $w(\gamma )={\alpha }_{i_3}+n_1{\alpha }_{i_1}+n_2{\alpha }_{i_2}\in R^b_+$. By Theorem \[root\_is\_sum\] there exist $n'_1,n'_2\in {\mathbb{N}}_0$ such that $n'_1\le n_1$, $n'_2\le n_2$, $n'_1+n'_2<n_1+n_2$, and $${\alpha }_{i_3}+n'_1{\alpha }_{i_1}+n'_2{\alpha }_{i_2}\in R^b_+,\quad
(n_1-n'_1){\alpha }_{i_1}+(n_2-n'_2){\alpha }_{i_2}\in R^b_+.$$ Since ${\alpha }+\beta \notin R^a$, Proposition \[pr:R=Fseq\] yields that $R^b_+\cap
{\mathrm{span}}_{\mathbb{Z}}\{{\alpha }_{i_1},{\alpha }_{i_2}\}=\{{\alpha }_{i_1},{\alpha }_{i_2}\}$. Thus $\gamma -{\alpha }\in R^a$ or $\gamma -\beta \in R^a$. This is a contradiction to the assumption of the lemma. Hence ${\alpha }+\beta \in R^a$. By symmetry we obtain that ${\alpha }+\gamma $, $\beta +\gamma \in R^a$.
\(4) Suppose that ${\alpha }+2\beta $, $2{\alpha }+\beta \notin R^a$. By (1) the set $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$, and ${\alpha }+\beta \in R^a$ by (3). Then Proposition \[pr:R=Fseq\] implies that $R^a\cap {\mathrm{span}}_{\mathbb{Z}}\{{\alpha },\beta \}=\{\pm {\alpha },\pm \beta ,\pm ({\alpha }+\beta
)\}$. Thus (1) and Lemma \[le:root\_diffs1\](2) give that $\gamma -{\alpha }\in
R^a$ or $\gamma -\beta \in R^a$, a contradiction to the initial assumption of the lemma. Hence by symmetry each of the sets $\{{\alpha }+2\beta ,2\al
+\beta \}$, $\{{\alpha }+2\gamma ,2{\alpha }+\gamma \}$, $\{\beta +2\gamma ,2\beta
+\gamma \}$ contains at least one element of $R^a$.
Assume now that $\gamma +2{\alpha }$, $\gamma +2\beta \in R^a$. By changing the object via (1) we may assume that ${\alpha }$, $\beta $, and $\gamma -n_1{\alpha }-n_2\beta $ are simple roots for some $n_1,n_2\in {\mathbb{N}}$. Then Lemma \[le:badroots\] applies to $\gamma +2{\alpha }\in R^a_+$ and $\beta -{\alpha }$, and tells that $\beta
-{\alpha }\in R^a$. This gives a contradiction.
By the previous two paragraphs we conclude that if $\gamma +2{\alpha }\in R^a$, then $\gamma +2\beta \notin R^a$, and hence $\beta +2\gamma \in R^a$. Similarly, we also obtain that ${\alpha }+2\beta \in R^a$. By symmetry this implies (4).
\(5) By symmetry it suffices to prove that $\gamma -({\alpha }+k\beta )\notin R^a$ for all $k\in {\mathbb{N}}_0$. For $k=0$ the claim holds by assumption.
First we prove that $\gamma -({\alpha }+2\beta )\notin R^a$. By (3) we know that $\gamma +{\alpha }$, ${\alpha }+\beta \in R^a$, and $\gamma -\beta \notin R^a$ by assumption. Since ${\mathrm{Vol}}_2(\gamma +{\alpha },{\alpha }+\beta )=1$, Lemma \[le:base2\] gives that $\{\gamma +{\alpha }, {\alpha }+\beta \}$ is a base for $V^a(\gamma +{\alpha },{\alpha }+\beta )$ at $a$. Since $\gamma -({\alpha }+2\beta )=(\gamma +{\alpha })
-2({\alpha }+\beta )$, we conclude that $\gamma -({\alpha }+2\beta )\notin R^a$.
Now let $k\in {\mathbb{N}}$. Assume that $\gamma -({\alpha }+k\beta )\in R^a$ and that $k$ is minimal with this property. Let ${\alpha }'=-{\alpha }$, $\beta '=-\beta $, $\gamma '=\gamma -({\alpha }+k\beta )$. Then ${\alpha }',\beta ',\gamma '\in R^a$ with ${\mathrm{Vol}}_3({\alpha }',\beta ',\gamma ')=1$. Moreover, ${\alpha }'-\beta '\notin
R^a$ by assumption, ${\alpha }'-\gamma '=-(\gamma -k\beta )\notin R^a$ by (2), and $\beta '-\gamma '=-(\gamma -{\alpha }-(k-1)\beta )\notin R^a$ by the minimality of $k$. Further, $\{{\alpha }',\beta ',\gamma '\}$ is not a base for $R^a$, since $\gamma =\gamma '-{\alpha }'-k\beta '$. Hence Claim (3) holds for $\al
',\beta ',\gamma '$. In particular, $$\gamma '+\beta '=\gamma -({\alpha }+(k+1)\beta )\in R^a.$$ This and the previous paragraph imply that $k\ge 3$.
We distinguish two cases depending on the parity of $k$. First assume that $k$ is even. Let ${\alpha }'=\gamma +{\alpha }$ and $\beta '=-({\alpha }+k/2\beta )$. Then ${\mathrm{Vol}}_2({\alpha }',\beta ')=1$ and ${\alpha }'+2\beta '=\gamma -({\alpha }+k\beta )\in R^a$. Lemma \[le:badroots\] applied to ${\alpha }',\beta '$ gives that $\gamma
-k/2\beta ={\alpha }'+\beta '\in R^a$, which contradicts (2).
Finally, the case of odd $k$ can be excluded similarly by considering $V^a(\gamma +{\alpha },\gamma -({\alpha }+(k+1)\beta ))$.
\(6) We get ${\mathrm{Vol}}_3({\alpha }',\beta ',\gamma ')=1$ since ${\mathrm{Vol}}_3({\alpha },\beta ,\gamma )=1$ and ${\mathrm{Vol}}_3$ is invariant under the right action of ${\mathrm{GL}}({\mathbb{Z}}^3)$. Further, $\beta '-\gamma '=-(2\beta +\gamma )\notin R^a$ by (4), and ${\alpha }'-\gamma '\notin R^a$ by (5). Finally, $({\alpha }',\beta ',\gamma ')$ is not a base for ${\mathbb{Z}}^I$ at $a$, since $R^a\ni \gamma -n_1{\alpha }-n_2\beta =\gamma '-n_1{\alpha }'+(1+n_2-kn_1)\beta '$, where $n_1,n_2\in {\mathbb{N}}$ are as in (1).
\(7) We prove that $\gamma +3{\alpha }\notin R^a$. The rest follows by symmetry. If $2{\alpha }+\beta \in R^a$, then $\gamma +2{\alpha }\notin R^a$ by (4), and hence $\gamma +3{\alpha }\notin R^a$. Otherwise ${\alpha }+2\beta ,\gamma +2{\alpha }\in R^a$ by (4). Let $k$, ${\alpha }'$, $\beta '$, $\gamma '$ be as in (6). Then (6) and (3) give that $R^a\ni \gamma '+{\alpha }'=\gamma +{\alpha }+(k+1)\beta $. Since $\gamma +{\alpha }\in
R^a$, Lemma \[le:badroots\] implies that $\gamma +{\alpha }+2\beta \in R^a$. Let $w$ be as in (1). If $\gamma +3{\alpha }\in R^a$, then Lemma \[le:badroots\] for the vectors $w(\gamma +{\alpha }+2\beta )$ and $w({\alpha }-\beta )$ implies that $w({\alpha }-\beta )\in R^a$, a contradiction. Thus $\gamma +3{\alpha }\notin R^a$.
Recall that $\cC$ is a Cartan scheme of rank three and ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$.
\[root\_diffs\] Let $a\in A$ and ${\alpha },\beta,\gamma\in R^a$. If ${\mathrm{Vol}}_3({\alpha },\beta,\gamma)=1$ and none of $\alpha-\beta$, $\alpha-\gamma$, $\beta-\gamma$ are contained in $R^a$, then $\{{\alpha },\beta,\gamma \}$ is a base for ${\mathbb{Z}}^I$ at $a$.
Assume to the contrary that $\{{\alpha },\beta ,\gamma \}$ is not a base for ${\mathbb{Z}}^I$ at $a$. Exchanging ${\alpha }$ and $\beta $ if necessary, by Lemma \[le:root\_diffs2\](4) we may assume that ${\alpha }+2\beta \in R^a$. By Lemma \[le:root\_diffs2\](6),(7) the triple $({\alpha }+2\beta
,-\beta , \gamma +\beta )$ satisfies the assumptions of Lemma \[le:root\_diffs2\], and $({\alpha }+2\beta )+2(-\beta )={\alpha }\in R^a$. Hence $2{\alpha }+3\beta =2({\alpha }+2\beta )+(-\beta )\notin R^a$ by Lemma \[le:root\_diffs2\](4). Thus $V^a({\alpha },\beta )\cap R^a=\{\pm {\alpha },
\pm ({\alpha }+\beta ),\pm ({\alpha }+2\beta ), \pm \beta \}$ by Proposition \[pr:R=Fseq\], and hence, using Lemma \[le:root\_diffs2\](1), we obtain from Lemma \[le:root\_diffs1\](2) that $\gamma -{\alpha }\in R^a$ or $\gamma -\beta \in R^a$. This is a contradiction to our initial assumption, and hence $\{{\alpha },\beta ,\gamma \}$ is a base for ${\mathbb{Z}}^I$ at $a$.
\[convex\_diff2\] Let $a\in A$ and $\gamma _1,\gamma _2,{\alpha }\in R^a$. Assume that $\{\gamma _1,\gamma _2\}$ is a base for $V^a(\gamma _1,\gamma _2)$ at $a$ and that ${\mathrm{Vol}}_3(\gamma _1,\gamma _2,{\alpha })=1$. Then either $\{\gamma _1,\gamma _2,{\alpha }\}$ is a base for ${\mathbb{Z}}^I$ at $a$, or one of ${\alpha }-\gamma _1$, $\al-\gamma _2$ is contained in $R^a$.
For the proof of Theorem \[th:class\] we need a bound for the entries of the Cartan matrices of ${\mathcal{C}}$. To get this bound we use the following.
\[le:someroots\] Let $a\in A$.
\(1) At most one of $c^a_{12}$, $c^a_{13}$, $c^a_{23}$ is zero.
\(2) ${\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$.
\(3) Let $k\in {\mathbb{Z}}$. Then $k{\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$ if and only if $k_1\le k\le k_2$, where $$\begin{aligned}
k_1=
\begin{cases}
0 & \text{if $c^a_{23}<0$,}\\
1 & \text{if $c^a_{23}=0$,}
\end{cases}
\quad
k_2=
\begin{cases}
-c^a_{12}-c^a_{13} & \text{if $c^{{\rho }_1(a)}_{23}<0$,}\\
-c^a_{12}-c^a_{13}-1 & \text{if $c^{{\rho }_1(a)}_{23}=0$.}
\end{cases}
\end{aligned}$$
\(4) We have $2{\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$ if and only if either $c^a_{12}+c^a_{13}\le -3$ or $c^a_{12}+c^a_{13}=-2$, $c^{\rfl
_1(a)}_{23}<0$.
\(5) Assume that $$\begin{aligned}
\#(R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2))\ge 5.
\label{eq:Rbig}
\end{aligned}$$ Then there exist $k\in {\mathbb{N}}_0$ such that $k{\alpha }_1+2{\alpha }_2+{\alpha }_3\in R^a$. Let $k_0$ be the smallest among all such $k$. Then $k_0$ is given by the following. $$\begin{aligned}
\begin{cases}
0 & \text{if $c^a_{23}\le -2$,}\\
1 & \text{if $-1\le c^a_{23}\le 0$,
$c^a_{21}+c^a_{23}\le -2$, $c^{{\rho }_2(a)}_{13}<0$,}\\
1 & \text{if $-1\le c^a_{23}\le 0$,
$c^a_{21}+c^a_{23}\le -3$, $c^{{\rho }_2(a)}_{13}=0$,}\\
2 & \text{if $c^a_{21}=c^a_{23}=-1$, $c^{{\rho }_2(a)}_{13}=0$,}\\
2 & \text{if $c^a_{21}=-1$, $c^a_{23}=0$, $c^{{\rho }_2(a)}_{13}\le -2$,}\\
3 & \text{if $c^a_{21}=-1$, $c^a_{23}=0$, $c^{{\rho }_2(a)}_{13}=-1$,
$c^{{\rho }_2(a)}_{12}\le -3$,}\\
3 & \text{if $c^a_{21}=-1$, $c^a_{23}=0$, $c^{{\rho }_2(a)}_{13}=-1$,
$c^{{\rho }_2(a)}_{12}=-2$, $c^{{\rho }_1{\rho }_2(a)}_{23}<0$,}\\
4 & \text{otherwise.}
\end{cases}
\end{aligned}$$ Further, if $c^a_{13}=0$ then $k_0\le 2$.
We may assume that ${\mathcal{C}}$ is connected. Then, since ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is irreducible, Claim (1) holds by [@a-CH09a Def.4.5, Prop.4.6].
\(2) The claim is invariant under permutation of $I$. Thus by (1) we may assume that $c^a_{23}\not=0$. Hence ${\alpha }_2+{\alpha }_3\in
R^a$. Assume first that $c^a_{13}=0$. Then $c^{{\rho }_1(a)}_{13}=0$ by (C2), $c^{{\rho }_1(a)}_{23}\not=0$ by (1), and ${\alpha }_2+{\alpha }_3\in R^{{\rho }_1(a)}_+$. Hence $\s^{{\rho }_1(a)}_1({\alpha }_2+{\alpha }_3)=-c^a_{12}{\alpha }_1+{\alpha }_2+{\alpha }_3\in
R^a$. Therefore (2) holds by Lemma \[le:badroots\] for ${\alpha }={\alpha }_2+{\alpha }_3$ and $\beta ={\alpha }_1$.
Assume now that $c^a_{13}\not=0$. By symmetry and the previous paragraph we may also assume that $c^a_{12},c^a_{23}\not=0$. Let $b={\rho }_1(a)$. If $c^b_{23}=0$ then ${\alpha }_1+{\alpha }_2+{\alpha }_3\in R^b$ by the previous paragraph. Then $$R^a\ni \s^b_1({\alpha }_1+{\alpha }_2+{\alpha }_3)
=(-c^a_{12}-c^a_{13}-1){\alpha }_1+{\alpha }_2+{\alpha }_3,$$ and the coefficient of ${\alpha }_1$ is positive. Further, ${\alpha }_2+{\alpha }_3\in R^a$, and hence (2) holds in this case by Lemma \[le:badroots\]. Finally, if $c^b_{23}\not=0$, then ${\alpha }_2+\al
_3\in R^b_+$, and hence $(-c^a_{12}-c^a_{13}){\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$. Since $-c^a_{12}-c^a_{13}>0$, (2) follows again from Lemma \[le:badroots\].
\(3) If $c^a_{23}<0$, then ${\alpha }_2+{\alpha }_3\in R^a$ and $-k{\alpha }_1+{\alpha }_2+{\alpha }_3\notin R^a$ for all $k\in {\mathbb{N}}$. If $c^a_{23}=0$, then ${\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$ by (2), and $-k{\alpha }_1+{\alpha }_2+{\alpha }_3\notin R^a$ for all $k\in {\mathbb{N}}_0$. Applying the same argument to $R^{{\rho }_1(a)}$ and using the reflection $\s^{{\rho }_1(a)}_1$ and Lemma \[le:badroots\] gives the claim.
\(4) This follows immediately from (3).
\(5) The first case follows from Corollary \[co:cij\] and the second and third cases are obtained from (4) by interchanging the elements $1$ and $2$ of $I$. We also obtain that if $k_0$ exists then $k_0\ge 2$ in all other cases. By and Proposition \[pr:R=Fseq\] we conclude that ${\alpha }_1+{\alpha }_2\in R^a$. Then $c^a_{21}<0$ by Corollary \[co:cij\], and hence we are left with calculating $k_0$ if $-1\le c^a_{23}\le 0$, $c^a_{21}+c^a_{23}=-2$, $c^{{\rho }_2(a)}_{13}=0$, or $c^a_{21}=-1$, $c^a_{23}=0$. By (1), if $c^{{\rho }_2(a)}_{13}=0$ then $c^{{\rho }_2(a)}_{23}\not=0$, and hence $c^a_{23}<0$ by (C2). Thus we have to consider the elements $k{\alpha }_1+2{\alpha }_2+{\alpha }_3$, where $k\ge 2$, under the assumption that $$\begin{aligned}
c^a_{21}=c^a_{23}=-1, \, c^{{\rho }_2(a)}_{13}=0 \quad \text{or}\quad
c^a_{21}=-1,\, c^a_{23}=0.
\label{eq:ccond1}
\end{aligned}$$ Since $c^a_{21}=-1$, Condition gives that $$c^{{\rho }_2(a)}_{12}\le -2,$$ see [@a-CH09a Lemma4.8]. Further, the first set of equations in implies that $c^{{\rho }_1{\rho }_2(a)}_{13}=0$, and hence $c^{{\rho }_1{\rho }_2(a)}_{23}<0$ by (1). Since ${\sigma }_2^a(2{\alpha }_1+2{\alpha }_2+{\alpha }_3)=2{\alpha }_1+{\alpha }_3-c^a_{23}\al
_2$, the first set of equations in and (4) imply that $k_0=2$. Similarly, Corollary \[co:cij\] tells that $k_0=2$ under the second set of conditions in if and only if $c^{{\rho }_2(a)}_{13}\le -2$.
It remains to consider the situation for $$\begin{aligned}
c^a_{21}=-1,\,c^a_{23}=0,\,c^{{\rho }_2(a)}_{13}=-1.
\label{eq:ccond2}
\end{aligned}$$ Indeed, equation $c^a_{23}=0$ implies that $c^{{\rho }_2(a)}_{23}=0$ by (C2), and hence $c^{{\rho }_2(a)}_{13}<0$ by (1), Assuming we obtain that ${\sigma }_2^a(3{\alpha }_1+2{\alpha }_2+{\alpha }_3)=3{\alpha }_1+{\alpha }_2+{\alpha }_3$, and hence (3) implies that $k_0=3$ if and only if the corresponding conditions in (5) are valid.
The rest follows by looking at $\sigma _1 \sigma _2^a(4{\alpha }_1+2{\alpha }_2+\al
_3)$ and is left to the reader. The last claim holds since $c^a_{13}=0$ implies that $c^a_{23}\not=0$ by (1). The assumption $\#(R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2))\ge 5$ is needed to exclude the case $c^a_{21}=-1$, $c^{{\rho }_2(a)}_{12}=-2$, $c^{{\rho }_1\rfl
_2(a)}_{21}=-1$, where $R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)=\{{\alpha }_2,{\alpha }_1+{\alpha }_2,
2{\alpha }_1+{\alpha }_2,{\alpha }_1\}$, by using Proposition \[pr:R=Fseq\] and Corollary \[co:cij\], see also the proof of [@a-CH09a Lemma4.8].
\[cartan\_6\] Let $\cC$ be a Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}$ is a finite irreducible root system of type $\cC$. Then all entries of the Cartan matrices of $\cC$ are greater or equal to $-7$.
It can be assumed that ${\mathcal{C}}$ is connected. We prove the theorem indirectly. To do so we may assume that $a\in A$ such that $c^a_{12}\le -8$. Then Proposition \[pr:R=Fseq\] implies that $\# (R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2))\ge 5$. By Lemma \[le:someroots\] there exists $k_0\in \{0,1,2,3,4\}$ such that ${\alpha }:=k_0{\alpha }_1+2{\alpha }_2+{\alpha }_3\in R^a_+$ and ${\alpha }-{\alpha }_1\notin R^a$. By Lemma \[le:base2\] and the choice of $k_0$ the set $\{{\alpha },{\alpha }_1\}$ is a base for $V^a({\alpha },{\alpha }_1)$ at $a$. Corollary \[simple\_rkk\] implies that there exists a root $\gamma \in R^a$ such that $\{{\alpha },{\alpha }_1,\gamma \}$ is a base for ${\mathbb{Z}}^I$ at $a$. Let $d\in A$, $w\in \operatorname{Hom}(a,d)$, and $i_1,i_2,i_3\in I$ such that $w({\alpha })={\alpha }_{i_1}$, $w({\alpha }_1)={\alpha }_{i_2}$, $w(\gamma )={\alpha }_{i_3}$.
Let $b={\rho }_1(a)$. Again by Lemma \[le:someroots\] there exists $k_1\in \{0,1,2,3,4\}$ such that $\beta :=k_1{\alpha }_1+2{\alpha }_2+{\alpha }_3\in R^b_+$. Thus $$R^a_+\ni \s_1^b(\beta )=(-k_1-2c^a_{12}-c^a_{13}){\alpha }_1+2{\alpha }_2+\al
_3.$$ Further, $$-k_1-2c^a_{12}-c^a_{13}-k_0>-c^a_{12}$$ since $k_0\le 2$ if $c^a_{13}=0$. Hence ${\alpha }_{i_1}+(1-c^a_{12}){\alpha }_{i_2}
\in R^d$, that is, $c^d_{i_2 i_1}<c^a_{1 2}\le -8$. We conclude that there exists no lower bound for the entries of the Cartan matrices of ${\mathcal{C}}$, which is a contradiction to the finiteness of ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$. This proves the theorem.
The bound in the theorem is not sharp. After completing the classification one can check that the entries of the Cartan matrices of ${\mathcal{C}}$ are always at least $-6$. The entry $-6$ appears for example in the Cartan scheme corresponding to the root system with number $53$, see Corollary \[co:cij\].
\[Euler\_char\] Let ${\mathcal{C}}$ be an irreducible connected simply connected Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system of type ${\mathcal{C}}$. Let $e$ be the number of vertices, $k$ the number of edges, and $f$ the number of ($2$-dimensional) faces of the object change diagram of ${\mathcal{C}}$. Then $e-k+f=2$.
Vertices of the object change diagram correspond to elements of $A$. Since ${\mathcal{C}}$ is connected and ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is finite, the set $A$ is finite. Consider the equivalence relation on $I\times A$, where $(i,a)$ is equivalent to $(j,b)$ for some $i,j\in I$ and $a,b\in A$, if and only if $i=j$ and $b\in \{a,{\rho }_i(a)\}$. (This is also known as the pushout of $I\times A$ along the bijections ${\mathrm{id}}:I\times A\to I\times A$ and ${\rho }:I\times A\to I\times A$, $(i,a)\mapsto (i,{\rho }_i(a))$.) Since ${\mathcal{C}}$ is simply connected, ${\rho }_i(a)\not=a$ for all $i\in I$ and $a\in A$. Then edges of the object change diagram correspond to equivalence classes in $I\times A$. Faces of the object change diagram can be defined as equivalence classes of triples $(i,j,a)\in I\times I\times A\setminus
\{(i,i,a)\,|\,i\in I,a\in A\}$, where $(i,j,a)$ and $(i',j',b)$ are equivalent for some $i,j,i',j'\in I$ and $a,b\in A$ if and only if $\{i,j\}=\{i',j'\}$ and $b\in \{({\rho }_j{\rho }_i)^m(a),
{\rho }_i({\rho }_j{\rho }_i)^m(a)\,|\,m\in {\mathbb{N}}_0\}$. Since ${\mathcal{C}}$ is simply connected, (R4) implies that the face corresponding to a triple $(i,j,a)$ is a polygon with $2m_{i,j}^a$ vertices.
For each face choose a triangulation by non-intersecting diagonals. Let $d$ be the total number of diagonals arising this way. Now consider the following two-dimensional simplicial complex $C$: The $0$-simplices are the objects. The $1$-simplices are the edges and the chosen diagonals of the faces of the object change diagram. The $2$-simplices are the $f+d$ triangles. Clearly, each edge is contained in precisely two triangles. By [@b-tomDieck91 Ch.III, (3.3), 2,3] the geometric realization $X$ of $C$ is a closed $2$-dimensional surface without boundary. The space $X$ is connected and compact.
Any two morphisms of ${\mathcal{W}}({\mathcal{C}})$ with same source and target are equal because ${\mathcal{C}}$ is simply connected. By [@a-CH09a Thm.2.6] this equality follows from the Coxeter relations. A Coxeter relation means for the object change diagram that for the corresponding face and vertex the two paths along the sides of the face towards the opposite vertex yield the same morphism. Hence diagonals can be interpreted as representatives of paths in a face between two vertices, and then all loops in $C$ become homotopic to the trivial loop. Hence $X$ is simply connected and therefore homeomorphic to a two-dimensional sphere by [@b-tomDieck91 Ch.III, Satz 6.9]. Its Euler characteristic is $2=e-(k+d)+(f+d)=e-k+f$.
\[re:planesandfaces\] Assume that ${\mathcal{C}}$ is connected and simply connected, and let $a\in A$. Then any pair of opposite $2$-dimensional faces of the object change diagram can be interpreed as a plane in ${\mathbb{Z}}^I$ containing at least two positive roots ${\alpha },\beta \in R^a_+$. Indeed, let $b\in A$ and $i_1,i_2\in I$ with $i_1\not=i_2$. Since ${\mathcal{C}}$ is connected and simply connected, there exists a unique $w\in \operatorname{Hom}(a,b)$. Then $V^a(w^{-1}({\alpha }_{i_1}),w^{-1}({\alpha }_{i_2}))$ is a plane in ${\mathbb{Z}}^I$ containing at least two positive roots. One can easily check that this plane is independent of the choice of the representative of the face determined by $(i_1,i_2,b)\in I\times I\times A$. Further, let $w_0\in \operatorname{Hom}(b,d)$, where $d\in A$, be the longest element in ${\mathrm{Hom}(b,{\mathcal{W}}({\mathcal{C}}))}$. Let $j_1,j_2\in I$ such that $w_0({\alpha }_{i_n})=-{\alpha }_{j_n}$ for $n=1,2$. Then $(j_1,j_2,d)$ determines the plane $$V^a( (w_0w)^{-1}({\alpha }_{j_1}),(w_0w)^{-1}({\alpha }_{j_2}))=
V^a(w^{-1}({\alpha }_{i_1}),w^{-1}({\alpha }_{i_2})).$$ This way we attached to any pair of ($2$-dimensional) opposite faces of the object change diagram a plane containing at least two positive roots.
![The object change diagram of the last root system of rank three[]{data-label="fig:37posroots"}](wg37){width="9cm"}
Let $<$ be a semigroup ordering on ${\mathbb{Z}}^I$ such that $0<\gamma $ for all $\gamma \in R^a_+$. Let ${\alpha },\beta \in R^a_+$ with ${\alpha }\not=\beta $, and assume that ${\alpha }$ and $\beta $ are the smallest elements in $R^a_+\cap
V^a({\alpha },\beta )$ with respect to $<$. Then $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$ by Lemma \[posrootssemigroup\]. By Corollary \[simple\_rkk\] there exists $b\in A$ and $w\in \operatorname{Hom}(a,b)$ such that $w({\alpha }),w(\beta )\in R^b_+$ are simple roots. Hence any plane in ${\mathbb{Z}}^I$ containing at least two elements of $R^a_+$ can be obtained by the construction in the previous paragraph.
It remains to show that different pairs of opposite faces give rise to different planes. This follows from the fact that for any $b\in A$ and $i_1,i_2\in I$ with $i_1\not=i_2$ the conditions $$d\in A,\ u\in \operatorname{Hom}(b,d),\ j_1,j_2\in I,\
u({\alpha }_{i_1})={\alpha }_{j_1},\ u({\alpha }_{i_2})={\alpha }_{j_2}$$ have precisely two solutions: $u={\mathrm{id}}_b$ on the one side, and $u=w_0w_{i_1i_2}$ on the other side, where $w_{i_1i_2}=\cdots \s_{i_1}\s_{i_2}\s_{i_1}{\mathrm{id}}_b\in {\mathrm{Hom}(b,{\mathcal{W}}({\mathcal{C}}))}$ is the longest product of reflections ${\sigma }_{i_1}$, ${\sigma }_{i_2}$, and $w_0$ is an appropriate longest element of ${\mathcal{W}}({\mathcal{C}})$. The latter follows from the fact that $u$ has to map the base $\{\al
_{i_1},{\alpha }_{i_2},{\alpha }_{i_3}\}$ for ${\mathbb{Z}}^I$ at $b$, where $I=\{i_1,i_2,i_3\}$, to another base, and any base consisting of two simple roots can be extended precisely in two ways to a base of ${\mathbb{Z}}^I$: by adding the third simple root or by adding a uniquely determined negative root.
It follows from the construction and by [@a-CH09b Lemma 6.4] that the faces corresponding to a plane $V^a({\alpha },\beta )$, where ${\alpha },\beta \in R^a_+$ with ${\alpha }\not=\beta $, have as many edges as the cardinality of $V^a({\alpha },\beta )\cap R^a$ (or twice the cardinality of $V^a({\alpha },\beta )\cap R^a_+$).
\[sum\_rank2\] Let $\cC$ be a connected simply connected Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$. Let $a\in A$ and let $M$ be the set of planes containing at least two elements of $R^a_+$. Then $$\sum_{V\in M} \#(V\cap R^a_+) = 3(\# M-1).$$
Let $e,k,f$ be as in Proposition \[Euler\_char\]. Then $\#M=f/2$ by Remark \[re:planesandfaces\]. For any vertex $b\in A$ there are three edges starting at $b$, and any edge is bounded by two vertices. Hence counting vertices in two different ways one obtains that $3e=2k$. Proposition \[Euler\_char\] gives that $e-k+f=2$. Hence $2k = 3e = 3(2-f+k)$, that is, $k=3f-6$.
Any plane $V$ corresponds to a face which is a polygon consisting of $2\# (V\cap R^a_+)$ edges, see Remark \[re:planesandfaces\]. Summing up the edges twice over all planes (that is summing up over all faces of the object change diagram), each edge is counted twice. Hence $$2 \sum_{V\in M} 2\#(V\cap R^a_+) = 2k = 2(3f-6),$$ which is the formula claimed in the theorem.
\[ex\_square\] Let $\cC$ be a connected simply connected Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$. Then there exists an object $a\in A$ and $\alpha,\beta,\gamma\in R^a_+$ such that $\{\alpha,\beta,\gamma\}=\{\al_1,\al_2,\al_3\}$ and $$\label{square_hexagon}
\#(V^a(\alpha,\beta)\cap R^a_+)=2, \quad
\#(V^a(\alpha,\gamma)\cap R^a_+)=3.$$ Further $\alpha+\gamma, \beta +\gamma , \alpha+\beta+\gamma\in R^a_+$.
Let $M$ be as in Thm. \[sum\_rank2\]. Let $a$ be any object and assume $\#(V\cap R^a_+)>2$ for all $V\in M$, then $\sum_{V\in M} \#(V\cap R^a_+) \ge 3\# M$ contradicting Thm. \[sum\_rank2\]. Hence for all objects $a$ there exists a plane $V$ with $\#(V\cap R^a_+)=2$. Now consider the object change diagram and count the number of faces: Let $2q_i$ be the number of faces with $2i$ edges. Then Thm. \[sum\_rank2\] translates to $$\label{thm_trans}
\sum_{i\ge 2} i q_i = -3+3\sum_{i\ge 2} q_i.$$ Assume that there exists no object adjacent to a square and a hexagon. Since ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is irreducible, no two squares have a common edge, see Lemma \[le:someroots\](1). Look at the edges ending in vertices of squares, and count each edge once for both polygons adjacent to it. One checks that there are at least twice as many edges adjacent to a polygon with at least $8$ vertices as edges of squares. This gives that $$\sum_{i\ge 4} 2i \cdot 2q_i \ge 2\cdot 4\cdot 2q_2.$$ By Equation we then have $-3+3\sum_{i\ge 2}q_i\ge 4q_2+2q_2+3q_3$, that is, $q_2 < \sum_{i\ge 4}q_i$. But then in average each face has more than $6$ edges which contradicts Thm. \[sum\_rank2\]. Hence there is an object $a$ such that there exist $\alpha,\beta,\gamma\in R^a_+$ as above satisfying Equation . We have $\alpha+\gamma, \beta +\gamma , \alpha+\beta+\gamma\in R^a_+$ by Lemma \[le:someroots\](1),(2) and Corollary \[co:cij\].
The classification {#sec:class}
==================
In this section we explain the classification of connected simply connected Cartan schemes of rank three such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system. We formulate the main result in Theorem \[th:class\]. The proof of Theorem \[th:class\] is performed using computer calculations based on results of the previous sections. Our algorithm described below is sufficiently powerful: The implementation in $C$ terminates within a few hours on a usual computer. Removing any of the theorems, the calculations would take at least several weeks.
\(1) Let $\cC$ be a connected Cartan scheme of rank three with $I=\{1,2,3\}$. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$. Then there exists an object $a\in A$ and a linear map $\tau \in \operatorname{Aut}({\mathbb{Z}}^I)$ such that $\tau ({\alpha }_i)\in \{{\alpha }_1,{\alpha }_2,{\alpha }_3\}$ for all $i\in I$ and $\tau (R^a_+)$ is one of the sets listed in Appendix \[ap:rs\]. Moreover, $\tau (R^a_+)$ with this property is uniquely determined.
\(2) Let $R$ be one of the $55$ subsets of ${\mathbb{Z}}^3$ appearing in Appendix \[ap:rs\]. There exists up to equivalence a unique connected simply connected Cartan scheme ${\mathcal{C}}(I,A,({\rho }_i)_{i\in I},(C^a)_{a\in A})$ such that $R\cup -R$ is the set of real roots $R^a$ in an object $a\in A$. Moreover ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC
$. \[th:class\]
Let $<$ be the lexicographic ordering on ${\mathbb{Z}}^3$ such that $\al_3<\al_2<\al_1$. Then ${\alpha }>0$ for any ${\alpha }\in {\mathbb{N}}_0^3\setminus \{0\}$.
Let ${\mathcal{C}}$ be a connected Cartan scheme with $I=\{1,2,3\}$. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type ${\mathcal{C}}$. Let $a\in A$. By Theorem \[root\_is\_sum\] we may construct $R^a_+$ inductively by starting with $R^a_+=\{{\alpha }_3,{\alpha }_2,{\alpha }_1\}$, and appending in each step a sum of a pair of positive roots which is greater than all roots in $R^a_+$ we already have. During this process, we keep track of all planes containing at least two positive roots, and the positive roots on them. Lemma \[posrootssemigroup\] implies that for any known root ${\alpha }$ and new root $\beta $ either $V^a({\alpha },\beta )$ contains no other known positive roots, or $\beta $ is not part of the unique base for $V^a({\alpha },\beta )$ at $a$ consisting of positive roots. In the first case the roots ${\alpha },\beta $ generate a new plane. It can happen that ${\mathrm{Vol}}_2({\alpha },\beta )>1$, and then $\{{\alpha },\beta \}$ is not a base for $V^a({\alpha },\beta )$ at $a$, but we don’t care about that. In the second case the known roots in $V^a({\alpha },\beta )\cap R^a_+$ together with $\beta $ have to form an $\cF$-sequence by Proposition \[pr:R=Fseq\].
Sometimes, by some theorem (see the details below) we know that it is not possible to add more positive roots to a plane. Then we can mark it as “finished”.
Remark that to obtain a finite number of root systems as output, we have to ensure that we compute only irreducible systems since there are infinitely many inequivalent reducible root systems of rank two. Hence starting with $\{{\alpha }_3,{\alpha }_2,{\alpha }_1\}$ will not work. However, by Corollary \[ex\_square\], starting with $\{{\alpha }_3,{\alpha }_2,\al_2+\al_3,{\alpha }_1,\al_1+\al_2,\al_1+\al_2+\al_3\}$ will still yield at least one root system for each desired Cartan scheme (notice that any roots one would want to add are lexicographically greater).
In this section, we will call [*root system fragment*]{} (or [*rsf*]{}) the following set of data associated to a set of positive roots $R$ in construction:
- normal vectors for the planes with at least two positive roots
- labels of positive roots on these planes
- Cartan entries corresponding to the root systems of the planes
- an array of flags for finished planes
- the sum $s_R$ of $\#(V\cap R)$ over all planes $V$ with at least two positive roots, see Theorem \[sum\_rank2\]
- for each root $r\in R$ the list of planes it belongs to.
These data can be obtained directly from $R$, but the calculation is faster if we continuously update them.
We divide the algorithm into three parts. The main part is Algorithm 4.4, see below.
The first part updates a root system fragment to a new root and uses Theorems \[root\_diffs\] and \[cartan\_6\] to possibly refuse doing so:
[**Algorithm ..**]{} [**AppendRoot**]{}($\alpha$,$B$,$\tilde B$,$\hat\alpha$)\
[*Append a root to an rsf*]{}.\
[**Input:**]{} a root $\alpha$, an rsf $B$, an empty rsf $\tilde B$, a root $\hat\alpha$.\
[**Output:**]{} $\begin{cases}
0: & \mbox{if } \alpha \mbox{ may be appended, new rsf is then in } \tilde B, \\
1: & \mbox{if } \alpha \mbox{ may not be appended}, \\
2: & \mbox{if $\alpha \in R^a_+$ implies the existence of
$\beta \in R^a_+$}\\
& \mbox{with $\hat\alpha<\beta <\alpha $.}
\end{cases}$\
[**.**]{}
Let $r$ be the number of planes containing at least two elements of $R$. For documentation purposes let $V_1,\dots,V_r$ denote these planes. For any $i\in \{1,\dots,r\}$ let $v_i$ be a normal vector for $V_i$, and let $R_i$ be the $\cF$-sequence of $V_i\cap R$. Set $i \leftarrow 1$, $g \leftarrow 1$, $c\leftarrow [\:]$, $p \leftarrow [\:]$, $d\leftarrow\{\:\}$. During the algorithm $c$ will be an ordered subset of $\{1,\dots,r\}$, $p$ a corresponding list of “positions”, and $d$ a subset of $R$.
\[A1\_2\] If $i\le r$ and $g\ne 0$, then compute the scalar product $g:=(\alpha , v_i)$. (Then $g=\det ({\alpha },\gamma _1,\gamma _2)
=\pm {\mathrm{Vol}}_3({\alpha },\gamma _1,\gamma _2)$, where $\{\gamma _1,\gamma _2\}$ is the basis of $V_i$ consisting of positive roots.) Otherwise go to Step \[A1\_6\].
\[A1\_3\] If $g=0$ then do the following: If $V_i$ is not finished yet, then check if ${\alpha }$ extends $R_i$ to a new ${\mathcal{F}}$-sequence. If yes, add the roots of $R_i$ to $d$, append $i$ to $c$, append the position of the insertion of ${\alpha }$ in $R_i$ to $p$, let $g \leftarrow 1$, and go to Step 5.
If $g^2=1$, then use Corollary \[convex\_diff2\]: Let $\gamma_1$ and $\gamma_2$ be the beginning and the end of the $\cF
$-sequence $R_i$, respectively. (Then $\{\gamma _1,\gamma _2\}$ is a base for $V_i$ at $a$). Let $\delta_1 \leftarrow \alpha - \gamma_1$, $\delta_2 \leftarrow \alpha - \gamma_2$. If $\delta_1,\delta _2\notin R$, then return $1$ if $\delta
_1,\delta _2 \le \hat {\alpha }$ and return $2$ otherwise.
Set $i \leftarrow i+1$ and go to Step \[A1\_2\].
\[A1\_6\] If there is no objection appending $\alpha$ so far, i.e. $g \ne 0$, then copy $B$ to $\tilde B$ and include $\alpha$ into $\tilde B$: use $c,p$ to extend existing ${\mathcal{F}}$-sequences, and use (the complement of) $d$ to create new planes. Finally, apply Theorem \[cartan\_6\]: If there is a Cartan entry lesser than $-7$ then return 1, else return 0. If $g=0$ then return 2.
The second part looks for small roots which we must include in any case. The function is based on Proposition \[pr:suminR\]. This is a strong restriction during the process.
[**Algorithm ..**]{} [**RequiredRoot**]{}($R$,$B$,$\hat\alpha$)\
[*Find a smallest required root under the assumption that all roots $\le \hat
{\alpha }$ are known*]{}.\
[**Input:**]{} $R$ a set of roots, $B$ an rsf for $R$, $\hat \alpha $ a root.\
[**Output:**]{} $\begin{cases}
0 & \mbox{if we cannot determine such a root}, \\
1,\varepsilon & \mbox{if we have found a small missing root $\varepsilon $
with $\varepsilon >\hat \alpha $},\\
2 & \mbox{if the given configuration is impossible}.
\end{cases}$\
[**.**]{}
Initialize the return value $f \leftarrow 0$.
\[A2\_0\] We use the same notation as in Algo. 4.2, step 1. For all $\gamma _1$ in $R$ and all $(j,k)\in \{1,\dots,r\}\times \{1,\dots,r\}$ such that $j\not=k$, $\gamma _1\in R_j\cap R_k$, and both $R_j,R_k$ contain two elements, let $\gamma _2,\gamma _3\in R$ such that $R_j=\{\gamma _1,\gamma _2\}$, $R_k=\{\gamma _1,\gamma _3\}$. If ${\mathrm{Vol}}_3(\gamma _1,\gamma _2,\gamma _3) = 1$, then do Steps \[A2\_a\] to \[A2\_b\].
\[A2\_a\] $\xi_2 \leftarrow \gamma_1+\gamma_2$, $\xi_3 \leftarrow \gamma_1+\gamma_3$.
If $\hat\alpha \ge \xi_2$: If $\hat\alpha \ge \xi_3$ or plane $V_k$ is already finished, then return 2. If $f=0$ or $\varepsilon > \xi_3$, then $\varepsilon \leftarrow \xi_3$, $f\leftarrow 1$. Go to Step \[A2\_0\] and continue loop.
If $\hat\alpha \ge \xi_3$: If plane $V_j$ is already finished, then return 2. If $f=0$ or $\varepsilon > \xi_2$, then $\varepsilon \leftarrow \xi_2$, $f\leftarrow 1$.
\[A2\_b\] Go to Step \[A2\_0\] and continue loop.
Return $f,\varepsilon$.
Finally, we resursively add roots to a set, update the rsf and include required roots:
[**Algorithm ..**]{} [**CompleteRootSystem**]{}($R$,$B$,$\hat\alpha$,$u$,$\beta$)\
[*\[mainalg\]Collects potential new roots, appends them and calls itself again*]{}.\
[**Input:**]{} $R$ a set of roots, $B$ an rsf for $R$, $\hat\alpha$ a lower bound for new roots, $u$ a flag, $\beta$ a vector which is necessarily a root if $u=$ True.\
[**Output:**]{} Root systems containing $R$.\
[**.**]{} \[A3\]
Check Theorem \[sum\_rank2\]: If $s_R = 3(r-1)$, where $r$ is the number of planes containing at least two positive roots, then output $R$ (and continue). We have found a potential root system.
If we have no required root yet, i.e. $u=$ False, then\
$f,\varepsilon:=$RequiredRoot$(R,B,\hat{\alpha })$. If $f=1$, then we have found a required root; we call CompleteRootSystem($R,B,\hat\alpha, True, \varepsilon$) and terminate. If $f=2$, then terminate.
Potential new roots will be collected in $Y\leftarrow \{\:\}$; $\tilde B$ will be the new rsf.
For all planes $V_i$ of $B$ which are not finished, do Steps \[A3\_a\] to \[A3\_b\].
\[A3\_a\] $\nu \leftarrow 0$.
For $\zeta$ in the set of roots that may be added to the plane $V_i$ such that $\zeta> \hat\alpha$, do the following:
- set $\nu \leftarrow \nu+1$.
- If $\zeta \notin Y$, then $Y \leftarrow Y \cup \{\zeta\}$. If moreover $u=$ False or $\beta > \zeta$, then
- $y \leftarrow$ AppendRoot($\zeta,B,\tilde B,\hat\alpha$);
- if $y = 0$ then CompleteRootSystem($R\cup\{\zeta\},\tilde B,\zeta ,
u, \beta$).
- if $y = 1$ then $\nu \leftarrow \nu-1$.
\[A3\_b\] If $\nu = 0$, then mark $V_i$ as finished in $\tilde B$.
if $u =$ True and AppendRoot($\beta,B,\tilde B,\hat\alpha$) = 0, then call\
CompleteRootSystem($R\cup\{\beta\},\tilde B,\beta, \textrm{False},
\beta$).\
Terminate the function call.
Note that we only used necessary conditions for root systems, so after the computation we still need to check which of the sets are indeed root systems. A short program in [Magma]{} confirms that Algorithm 4.4 yields only root systems, for instance using this algorithm:
[**Algorithm ..**]{} [**RootSystemsForAllObjects**]{}($R$)\
[*Returns the root systems for all objects if $R=R^a_+$ determines a Cartan scheme ${\mathcal{C}}$ such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is an irreducible root system*]{}.\
[**Input:**]{} $R$ the set of positive roots at one object.\
[**Output:**]{} the set of root systems at all objects, or $\{\}$ if $R$ does not yield a Cartan scheme as desired.\
[**.**]{} \[A4\]
$N \leftarrow [R]$, $M \leftarrow \{\}$.
While $|N| > 0$, do steps \[begwhile\] to \[endwhile\].
Let $F$ be the last element of $N$. Remove $F$ from $N$ and include it to $M$.\[begwhile\]
Let $C$ be the Cartan matrix of $F$. Compute the three simple reflections given by $C$.
For each simple reflection $s$, do:\[endwhile\]
- Compute $G:=\{s(v)\mid v\in F\}$. If an element of $G$ has positive and negative coefficients, then return $\{\}$. Otherwise mutliply the negative roots of $G$ by $-1$.
- If $G\notin M$, then append $G$ to $N$.
Return $M$.
We list all $55$ root systems in Appendix \[ap:rs\]. It is also interesting to summarize some of the invariants, which is done in Table 1. Let ${\mathcal O}=\{R^a \mid a \in A\}$ denote the set of different root systems. By identifying objects with the same root system one obtains a quotient Cartan scheme of the simply connected Cartan scheme of the classification. In the fifth column we give the automorphism group of one (equivalently, any) object of this quotient. The last column gives the multiplicities of planes; for example $3^7$ means that there are $7$ different planes containing precisely $3$ positive roots.
Nr. $|R_+^a|$ $|{\mathcal O}|$ $|A|$ $\operatorname{Hom}(a)$ planes
------ ----------- ------------------ ------- --------------------------- --------------------------------------------------------
$1$ $6$ $1$ $24$ $A_3$ $2^{3}, 3^{4}, $
$2$ $7$ $4$ $32$ $A_1\times A_1\times A_1$ $2^{3}, 3^{6}, $
$3$ $8$ $5$ $40$ $B_2$ $2^{4}, 3^{6}, 4^{1}, $
$4$ $9$ $1$ $48$ $B_3$ $2^{6}, 3^{4}, 4^{3}, $
$5$ $9$ $1$ $48$ $B_3$ $2^{6}, 3^{4}, 4^{3}, $
$6$ $10$ $5$ $60$ $A_1\times A_2$ $2^{6}, 3^{7}, 4^{3}, $
$7$ $10$ $10$ $60$ $A_2$ $2^{6}, 3^{7}, 4^{3}, $
$8$ $11$ $9$ $72$ $A_1\times A_1\times A_1$ $2^{7}, 3^{8}, 4^{4}, $
$9$ $12$ $21$ $84$ $A_1\times A_1$ $2^{8}, 3^{10}, 4^{3}, 5^{1}, $
$10$ $12$ $14$ $84$ $A_2$ $2^{9}, 3^{7}, 4^{6}, $
$11$ $13$ $4$ $96$ $G_2\times A_1$ $2^{9}, 3^{12}, 4^{3}, 6^{1}, $
$12$ $13$ $12$ $96$ $A_1\times A_1\times A_1$ $2^{10}, 3^{10}, 4^{3}, 5^{2}, $
$13$ $13$ $2$ $96$ $B_3$ $2^{12}, 3^{4}, 4^{9}, $
$14$ $13$ $2$ $96$ $B_3$ $2^{12}, 3^{4}, 4^{9}, $
$15$ $14$ $56$ $112$ $A_1$ $2^{11}, 3^{12}, 4^{4}, 5^{2}, $
$16$ $15$ $16$ $128$ $A_1\times A_1\times A_1$ $2^{13}, 3^{12}, 4^{6}, 5^{2}, $
$17$ $16$ $36$ $144$ $A_1\times A_1$ $2^{14}, 3^{15}, 4^{6}, 5^{1}, 6^{1}, $
$18$ $16$ $24$ $144$ $A_2$ $2^{15}, 3^{13}, 4^{6}, 5^{3}, $
$19$ $17$ $10$ $160$ $B_2\times A_1$ $2^{16}, 3^{16}, 4^{7}, 6^{2}, $
$20$ $17$ $10$ $160$ $B_2\times A_1$ $2^{16}, 3^{16}, 4^{7}, 6^{2}, $
$21$ $17$ $10$ $160$ $B_2\times A_1$ $2^{18}, 3^{12}, 4^{7}, 5^{4}, $
$22$ $18$ $30$ $180$ $A_2$ $2^{18}, 3^{18}, 4^{6}, 5^{3}, 6^{1}, $
$23$ $18$ $90$ $180$ $A_1$ $2^{19}, 3^{16}, 4^{6}, 5^{5}, $
$24$ $19$ $25$ $200$ $A_1\times A_1\times A_1$ $2^{20}, 3^{20}, 4^{6}, 5^{4}, 6^{1}, $
$25$ $19$ $8$ $192$ $G_2\times A_1$ $2^{21}, 3^{18}, 4^{6}, 6^{4}, $
$26$ $19$ $50$ $200$ $A_1\times A_1$ $2^{20}, 3^{20}, 4^{6}, 5^{4}, 6^{1}, $
$27$ $19$ $25$ $200$ $A_1\times A_1\times A_1$ $2^{20}, 3^{20}, 4^{6}, 5^{4}, 6^{1}, $
$28$ $19$ $8$ $192$ $G_2\times A_1$ $2^{24}, 3^{12}, 4^{6}, 5^{6}, 6^{1}, $
$29$ $20$ $27$ $216$ $B_2$ $2^{20}, 3^{26}, 4^{4}, 5^{4}, 8^{1}, $
$30$ $20$ $110$ $220$ $A_1$ $2^{21}, 3^{24}, 4^{6}, 5^{4}, 7^{1}, $
$31$ $20$ $110$ $220$ $A_1$ $2^{23}, 3^{20}, 4^{7}, 5^{5}, 6^{1}, $
$32$ $21$ $15$ $240$ $B_2\times A_1$ $2^{22}, 3^{28}, 4^{6}, 5^{4}, 8^{1}, $
$33$ $21$ $30$ $240$ $A_1\times A_1\times A_1$ $2^{26}, 3^{20}, 4^{9}, 5^{4}, 6^{2}, $
$34$ $21$ $5$ $240$ $B_3$ $2^{24}, 3^{24}, 4^{9}, 6^{4}, $
$35$ $22$ $44$ $264$ $A_2$ $2^{27}, 3^{25}, 4^{9}, 5^{3}, 6^{3}, $
$36$ $25$ $42$ $336$ $A_1\times A_1\times A_1$ $2^{33}, 3^{34}, 4^{12}, 5^{2}, 6^{3}, 8^{1}, $
$37$ $25$ $14$ $336$ $G_2\times A_1$ $2^{36}, 3^{30}, 4^{9}, 5^{6}, 6^{4}, $
$38$ $25$ $28$ $336$ $A_1\times A_2$ $2^{36}, 3^{30}, 4^{9}, 5^{6}, 6^{4}, $
$39$ $25$ $7$ $336$ $B_3$ $2^{36}, 3^{28}, 4^{15}, 6^{6}, $
$40$ $26$ $182$ $364$ $A_1$ $2^{35}, 3^{39}, 4^{10}, 5^{4}, 6^{3}, 8^{1}, $
$41$ $26$ $182$ $364$ $A_1$ $2^{37}, 3^{36}, 4^{9}, 5^{6}, 6^{3}, 7^{1}, $
$42$ $27$ $49$ $392$ $A_1\times A_1\times A_1$ $2^{38}, 3^{42}, 4^{9}, 5^{6}, 6^{3}, 8^{1}, $
$43$ $27$ $98$ $392$ $A_1\times A_1$ $2^{39}, 3^{40}, 4^{10}, 5^{6}, 6^{2}, 7^{2}, $
$44$ $27$ $98$ $392$ $A_1\times A_1$ $2^{39}, 3^{40}, 4^{10}, 5^{6}, 6^{2}, 7^{2}, $
$45$ $28$ $420$ $420$ $1$ $2^{41}, 3^{44}, 4^{11}, 5^{6}, 6^{2}, 7^{1}, 8^{1}, $
$46$ $28$ $210$ $420$ $A_1$ $2^{42}, 3^{42}, 4^{12}, 5^{6}, 6^{1}, 7^{3}, $
$47$ $28$ $70$ $420$ $A_2$ $2^{42}, 3^{42}, 4^{12}, 5^{6}, 6^{1}, 7^{3}, $
$48$ $29$ $56$ $448$ $A_1\times A_1\times A_1$ $2^{44}, 3^{46}, 4^{13}, 5^{6}, 6^{2}, 8^{2}, $
$49$ $29$ $112$ $448$ $A_1\times A_1$ $2^{45}, 3^{44}, 4^{14}, 5^{6}, 6^{1}, 7^{2}, 8^{1}, $
$50$ $29$ $112$ $448$ $A_1\times A_1$ $2^{45}, 3^{44}, 4^{14}, 5^{6}, 6^{1}, 7^{2}, 8^{1}, $
$51$ $30$ $238$ $476$ $A_1$ $2^{49}, 3^{44}, 4^{17}, 5^{6}, 6^{1}, 7^{1}, 8^{2}, $
$52$ $31$ $21$ $504$ $G_2\times A_1$ $2^{54}, 3^{42}, 4^{21}, 5^{6}, 6^{1}, 8^{3}, $
$53$ $31$ $21$ $504$ $G_2\times A_1$ $2^{54}, 3^{42}, 4^{21}, 5^{6}, 6^{1}, 8^{3}, $
$54$ $34$ $102$ $612$ $A_2$ $2^{60}, 3^{63}, 4^{18}, 5^{6}, 6^{4}, 8^{3}, $
$55$ $37$ $15$ $720$ $B_3$ $2^{72}, 3^{72}, 4^{24}, 6^{10}, 8^{3}, $
[Table 1: Invariants of irreducible root systems of rank three]{}
At first sight, one is tempted to look for a formula for the number of objects in the universal covering depending on the number of roots. There is an obvious one: consider the coefficients of $4/((1-x)^2(1-x^4))$. However, there are exceptions, for example nr. 29 with $20$ positive roots and $216$ objects (instead of $220$).
Rank 3 Nichols algebras of diagonal type with finite irreducible arithmetic root system are classified in [@a-Heck05b Table 2]. In Table 2 we identify the Weyl groupoids of these Nichols algebras.
----------------------------- ---- ---- ---- ---- ---- ---- ---- ---- ----
row in [@a-Heck05b Table 2] 1 2 3 4 5 6 7 8 9
Weyl groupoid 1 5 4 1 5 3 11 1 2
row in [@a-Heck05b Table 2] 10 11 12 13 14 15 16 17 18
Weyl groupoid 2 2 5 13 5 6 7 8 14
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Irreducible root systems of rank three {#ap:rs}
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We give the roots in a multiplicative notation to save space: The word $1^x2^y3^z$ corresponds to $x\alpha_3+y\alpha_2+z\alpha_1$.
Notice that we have chosen a “canonical” object for each groupoid. Write $\pi(R^a_+)$ for the set $R^a_+$ where the coordinates are permuted via $\pi\in S_3$. Then the set listed below is the minimum of $\{\pi(R^a_+)\mid a\in A,\:\: \pi\in S_3\}$ with respect to the lexicographical ordering on the sorted sequences of roots.
Nr. $1$ with $6$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $123$\
Nr. $2$ with $7$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $123$\
Nr. $3$ with $8$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{2}23$\
Nr. $4$ with $9$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{2}23$, $1^{2}23^{2}$\
Nr. $5$ with $9$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{2}23$, $1^{2}2^{2}3$\
Nr. $6$ with $10$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$\
Nr. $7$ with $10$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $123$, $1^{2}23$, $1^{2}2^{2}3$\
Nr. $8$ with $11$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$, $1^{3}2^{2}3$\
Nr. $9$ with $12$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $10$ with $12$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$\
Nr. $11$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $12$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{4}23$, $1^{4}2^{2}3$\
Nr. $13$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $14$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $13^{2}$, $1^{2}23$, $123^{2}$, $1^{2}23^{2}$, $1^{3}23^{2}$, $1^{3}2^{2}3^{2}$\
Nr. $15$ with $14$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $16$ with $15$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$\
Nr. $17$ with $16$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$\
Nr. $18$ with $16$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $19$ with $17$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{4}23$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$\
Nr. $20$ with $17$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{2}3^{2}$\
Nr. $21$ with $17$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{3}3$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$\
Nr. $22$ with $18$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3$\
Nr. $23$ with $18$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $24$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{3}3^{2}$\
Nr. $25$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{6}2^{3}3^{2}$\
Nr. $26$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $12^{2}$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $27$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $28$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3$, $1^{6}2^{4}3$\
Nr. $29$ with $20$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$\
Nr. $30$ with $20$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{3}3^{2}$\
Nr. $31$ with $20$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3^{2}$\
Nr. $32$ with $21$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{3}3^{2}$\
Nr. $33$ with $21$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3$, $1^{6}2^{3}3^{2}$\
Nr. $34$ with $21$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{3}3$, $1^{5}2^{2}3^{2}$, $1^{6}2^{3}3$, $1^{6}2^{3}3^{2}$, $1^{7}2^{3}3^{2}$\
Nr. $35$ with $22$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{5}2^{2}3^{2}$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$\
Nr. $36$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{8}2^{3}3^{2}$\
Nr. $37$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $38$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $12^{2}$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{3}2^{2}3^{2}$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{4}2^{3}3^{2}$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$, $1^{7}2^{4}3^{2}$\
Nr. $39$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{5}2^{2}3^{2}$, $1^{6}2^{3}3$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$, $1^{7}2^{3}3^{2}$, $1^{7}2^{4}3^{2}$\
Nr. $40$ with $26$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$\
Nr. $41$ with $26$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $42$ with $27$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $43$ with $27$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $44$ with $27$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $45$ with $28$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $46$ with $28$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$\
Nr. $47$ with $28$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{11}2^{4}3^{2}$\
Nr. $48$ with $29$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $49$ with $29$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$\
Nr. $50$ with $29$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{11}2^{4}3^{2}$\
Nr. $51$ with $30$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$\
Nr. $52$ with $31$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{5}2$, $1^{4}23$, $1^{6}2$, $1^{5}23$, $1^{4}2^{2}3$, $1^{6}23$, $1^{5}2^{2}3$, $1^{7}23$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{8}2^{2}3$, $1^{9}2^{2}3$, $1^{10}2^{2}3$, $1^{9}2^{3}3$, $1^{10}2^{3}3$, $1^{11}2^{3}3$, $1^{10}2^{3}3^{2}$, $1^{11}2^{3}3^{2}$, $1^{12}2^{3}3^{2}$\
Nr. $53$ with $31$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$, $1^{11}2^{4}3^{2}$\
Nr. $54$ with $34$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{3}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{4}3$, $1^{8}2^{3}3^{2}$, $1^{9}2^{4}3$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$, $1^{11}2^{4}3^{2}$, $1^{11}2^{5}3^{2}$, $1^{12}2^{5}3^{2}$\
Nr. $55$ with $37$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{3}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{9}2^{3}3$, $1^{8}2^{4}3$, $1^{8}2^{3}3^{2}$, $1^{9}2^{4}3$, $1^{9}2^{3}3^{2}$, $1^{10}2^{4}3$, $1^{9}2^{4}3^{2}$, $1^{11}2^{4}3^{2}$, $1^{11}2^{5}3^{2}$, $1^{12}2^{5}3^{2}$, $1^{13}2^{5}3^{2}$
[^1]: In this introduction by a Weyl groupoid we will mean the Weyl groupoid of a connected Cartan scheme, and we assume that the real roots associated to the Weyl groupoid form an irreducible root system in the sense of [@a-CH09a].
| {
"pile_set_name": "ArXiv"
} |
7 P.3d 49 (2000)
Donald L. SEGNITZ, Appellant (Defendant),
v.
The STATE of Wyoming, Appellee (Plaintiff).
Donald L. Segnitz, Appellant (Defendant),
v.
The State of Wyoming, Appellee (Plaintiff).
Nos. 99-223, 99-254.
Supreme Court of Wyoming.
June 2, 2000.
*50 Representing Appellant: Donald L. Segnitz, Pro Se.
Representing Appellee: Gay Woodhouse, Attorney General; Paul S. Rehurek, Deputy Attorney General; and D. Michael Pauling, Senior Assistant Attorney General.
Before LEHMAN, C.J., and THOMAS, MACY, GOLDEN, and HILL, JJ.
MACY, Justice.
Appellant Donald L. Segnitz appeals from the denials of two motions he filed in two separate courts to correct his illegal sentences. The cases were consolidated for purposes of appeal.
We affirm in part and reverse in part.
ISSUES
In Case No. 99-223, Segnitz presents the following issues for our review:
1. Did the District Court [err] by denying Appellant's Motion to Correct an Illegal Sentence, which was filed because while orally sentenced to concurrent sentences, the Written Judgement and Sentence, and Mitimus failed to stipulate that sentence was concurrent[?]
2. Did the District Court [err] by denying Appellant's Motion to Correct ... an ILLEGAL Sentence, which was filed because the Court did not award credit for time served in it[]s Judgement and Sentence, nor Mitimus[?] Nor had it been *51 addressed orally by the Court at sentencing.
In Case No. 99-254, Segnitz presents the following issues for our review:
A. Did the District Court sentence the Appellant to an illegal term by not abiding by W.R.Cr.P. 32(c)2(C), (E), and (F)?
B. Did the District Court by denying the Motion to Correct an Illegal Sentence and then changing the original sentence abuse it[]s d[i]scretion?
C. If the change in sentence was proper then should the Appellant [be] afforded due process by the District Court?
FACTS
In November of 1997, Segnitz was sentenced in Sweetwater County to serve a term in the Wyoming State Penitentiary of not less than one year nor more than three years, with credit for the time he served in presentence confinement, for the offense of felony larceny. He was released on parole to Community Alternatives of Casper on June 25, 1998. On July 30, 1998, Segnitz departed from Community Alternatives of Casper without authorization, stealing a car to facilitate his exit. He drove to Wheatland where he abandoned this car and stole another, which he drove to Indiana.
Both the Platte County and Natrona County authorities issued arrest warrants for the crimes committed in their respective counties. The Board of Parole issued an order of arrest because Segnitz had violated the terms of his parole for the Sweetwater County felony larceny conviction. Segnitz was arrested in Indiana on August 1, 1998, and later charged with felony larceny in both Platte County and Natrona County. He pleaded guilty to the charges. Segnitz was sentenced on September 10, 1998, in Platte County to a term of not less than two years nor more than four years in the Wyoming State Penitentiary. The order was silent with regard to whether the sentence was to be served concurrently with or consecutively to any other sentences. On March 5, 1999, Segnitz was orally sentenced in Natrona County to the stipulated prison term of three to four years. The stipulation provided for the sentence to be served concurrently with the sentences imposed in Sweetwater County and Platte County. The written Judgment and Sentence failed to mention that the sentence was to be served concurrently with the other sentences, but, three months later, the district court entered an order nunc pro tunc to that effect.
Segnitz arrived at the Wyoming State Penitentiary on or shortly after March 5, 1999, the date he was sentenced in Natrona County. On April 12, 1999, the Board of Parole revoked his parole for the Sweetwater County offense, crediting him "with all of the time during which he was released."
Segnitz filed motions in the district courts of Platte County and Natrona County to correct illegal sentences. In his Platte County motion, Segnitz asserted that the Judgment and Sentence failed to specify how the sentence was to be served with regard to his other sentences. He also complained that the Judgment and Sentence failed to state the number of days awarded as presentence incarceration credit. In response, the district court issued an order wherein it announced that it intended for the sentence to be served consecutively to the others and that Segnitz was not entitled to presentence incarceration credit. In his Natrona County motion, Segnitz claimed that the Judgment and Sentence failed to reflect the district court's oral pronouncement that made the sentence run concurrently with the others and failed to award any presentence incarceration credit. Although the district court initially denied Segnitz's motion, it later entered the order nunc pro tunc referenced above which ordered the sentence for the Natrona County crime to be served concurrently with the other sentences.
Segnitz appeals to the Wyoming Supreme Court.
DISCUSSION
A. Presentence Incarceration Credit
Segnitz contends that both district courts erred when they refused to award credit for the time he spent confined before he was sentenced. The state counters that Segnitz was on parole and in the legal custody *52 of the Board of Parole during the entire time he was confined on these two charges and that the Board of Parole awarded him credit against his Sweetwater County sentence for all the time he spent on parole when his parole was eventually revoked.
The decision to grant or deny a motion to correct an illegal sentence is usually left to the sound discretion of the district court. Hamill v. State, 948 P.2d 1356, 1358 (Wyo.1997). The district court's decision is given considerable deference unless a rational basis does not exist for it. Id. A criminal defendant is entitled to receive credit against his sentence for the time he was incarcerated prior to sentencing, provided that such confinement was because of his inability and failure to post bond on the offense for which he was awaiting disposition. Smith v. State, 988 P.2d 39, 40 (Wyo.1999). A sentence which does not include credit for presentence incarceration is illegal and constitutes an abuse of discretion. Id. A defendant is not, however, entitled to credit for the time he spent in custody when that confinement would have continued despite his ability to post bond. Id.
The Board of Parole revoked Segnitz's parole for the Sweetwater County conviction after he had been sentenced in the Platte County and Natrona County cases. Had the Board of Parole revoked Segnitz's parole before he was sentenced in the Platte County and Natrona County cases, there would be no argument about the fact that those district courts refused to award presentence incarceration credit. We, however, are not concerned with this order of events and agree with the state's observation that Segnitz should not be allowed to apply the credit to the new sentences "simply because his parole was fortuitously revoked" after, and not before, his convictions for the new crimes. When the Board of Parole awarded Segnitz full credit against his Sweetwater County sentence for the time he spent on parole, it cured any problems that existed as a result of the failures by the district courts in Platte County and Natrona County to do so.
B. Concurrent Sentences
Segnitz contends that the district court erred when it ordered his Platte County sentence to run consecutively to the other sentences. The state concedes that Segnitz is correct in this assertion.
The original order was silent with regard to how the Platte County sentence was intended to run with the other sentences. Eleven months later, the district court clarified the Judgment and Sentence by ordering the sentence to run consecutively to the others. In the meantime, the district court of Natrona County ordered its sentence to run concurrently with the other sentences.
When the district court of Platte County entered its order, Segnitz had not yet been prosecuted in Natrona County nor had his parole been revoked. If a defendant is subject to prosecution in more than one court, the decision regarding how the sentences will run with respect to one another should be made by the last judge to impose a sentence. 24 C.J.S. Criminal Law § 1524 (1989). The underlying rationale for this theory is that a judge cannot require a sentence to be served consecutively to a sentence that has not yet been imposed. Id. We agree with the state that this is the best practice and conclude that the district court of Platte County abused its discretion when it ordered its sentence to run consecutively to the others. The district court of Natrona County was the last court to impose a sentence, and it ordered its sentence to run concurrently with the others. That portion of the order for the Platte County offense which directed the sentence to run consecutively to the others is illegal and is hereby stricken.
Affirmed in part and reversed in part.
| {
"pile_set_name": "FreeLaw"
} |
Minnesota economic development officials on Monday released 122 pages of documents laying out the economic pitch made to lure an Amazon headquarters to the Twin Cities.
The proposal, made public for the first time, outlines a relatively modest package of $3 million to $4 million in existing state subsidies that were already in statute.
It also included descriptions and some potential property tax breaks, like tax increment financing, for potential locations in about 20 Minnesota communities from North Branch to Elko-New Market.
Minnesota's Amazon bid: Read the details
In 2017, the online retail giant invited cities and states to bid on landing its second headquarters, a proposed $5 billion project outside of its hometown of Seattle that held the promise of thousands of new jobs.
It triggered an incentives war among mayors and governors across the country.
The St. Paul-based regional economic development group Greater MSP and state economic development staff submitted a proposal that ultimately failed.
Although it fell short, Greater MSP initially opposed public disclosure of the offer and fought a lawsuit brought by media and others who wanted to see any incentives Minnesota might offer.
In January, A Ramsey County District Judge ruled that Minnesota's Amazon proposal was not subject to the Minnesota Government Data Practices Act and therefore wasn't public information.
Amazon, however, recently told Greater MSP that it will not oppose disclosure of the Twin Cities bid package, Greater MSP CEO Peter Frosch said late last week.
Amazon eventually split its second headquarters decision between Long Island City, N.Y., and Crystal City, Va. It later retreated from the New York site amid local opposition and moved some of its plans to Nashville, Tenn.
Matt Ehling, executive director with Public Record Media, the nonprofit government transparency group that's pushed for disclosure of subsidies offered to Amazon, said the public has a right to know the financial incentives that governments are offering businesses so they can evaluate them.
"That is a very substantive debate that has to happen," he said prior to the release, noting the pushback to Amazon in New York. "You can't have that debate if you don't know what the terms of the offers are. So that's why we've been so bent on making sure that the public will know those terms going forward." | {
"pile_set_name": "OpenWebText2"
} |
The relationship of impulsivity, sensation seeking, coping, and substance use in youth gamblers.
This study examines the relationship of impulsivity, sensation seeking, coping, and substance use to disordered gambling in a sample of 1,339 youth (637 males and 702 females), 17-21 years old. Results indicate that males with serious gambling problems were more likely than their peers to abuse substances and to use avoidant stress-coping strategies, such as seeking emotional outlets, distracting themselves with other activities, and using humor. In contrast, female disordered gamblers were less likely to engage in active coping and planning strategies. Overall, substance use, coping through distraction, and impulsivity proved the most predictive of disordered gambling for males, and intensity seeking and impulsivity proved most predictive for females. Implications for prevention, intervention, and education are discussed. | {
"pile_set_name": "PubMed Abstracts"
} |
Q:
Retrieve List of picklist values in a Set
I got the following variables(Custom Labels referring to picklist values), and a get method to retrieve List of picklist values of a field.
I need to retrieve those List of picklist values in a Set. How can I do this ?
public String dailyValue {
get { return System.Label.Daily.toLowerCase().trim(); }
private set;
}
public String weeklyValue {
get { return System.Label.Weekly.toLowerCase().trim(); }
private set;
}
public String monthlyValue {
get { return System.Label.Monthly.toLowerCase().trim(); }
private set;
}
public String quarterlyValue {
get { return System.Label.Quarterly.toLowerCase().trim(); }
private set;
}
public String biannuallyValue {
get { return System.Label.Bi_Annually.toLowerCase().trim(); }
private set;
}
public String annuallyValue {
get { return System.Label.Annually.toLowerCase().trim(); }
private set;
}
//values from the frequency picklist
public List<SelectOption> getMonitoringFrequency(){
List<SelectOption> frequencyTypes = new List<SelectOption>();
Schema.DescribeFieldResult fieldResult = Metric__c.Monitoring_Frequency__c.getDescribe();
List<Schema.PicklistEntry> ple = fieldResult.getPicklistValues();
for( Schema.PicklistEntry f : ple){
frequencyTypes.add(new SelectOption(
f.getValue().toLowerCase(),f.getLabel().toLowerCase()
));
}
return frequencyTypes;
}
A:
Depending on whether you want the label or the value in your set, create a set:
set<String> picklistValues = new set<String>();
set<String> picklistLabels = new set<String>():
and then in your for-loop, add the value or label, as appropriate:
for( Schema.PicklistEntry f : ple){
frequencyTypes.add(new
SelectOption(f.getValue().toLowerCase(),f.getLabel().toLowerCase()));
picklistValues.add(f.getValue());
picklistLabels.add(f.getLabel());
}
| {
"pile_set_name": "StackExchange"
} |
Fish poisoning may be why Polynesians left paradise
Washington, May 19 (ANI): Scientists have come up with a theory that attributes the historic migrations of the Polynesians from the Cook islands to New Zealand, Easter Island and Hawaii in the 11th to 15th centuries, to fish poisoning.
The theory has been proposed by Teina Rongo, a Cook Island Maori from Rarotonga and a Ph.D. student at the Florida Institute of Technology, and his faculty advisers Professors Robert van Woesik and Mark Bush.
Based on archeological evidence, paleoclimatic data and modern reports of ciguatera poisoning, they theorize that ciguatera outbreaks were linked to climate and that the consequent outbreaks prompted historical migrations of Polynesians.
Ciguatera poisoning is a food-borne disease that can come from eating large, carnivorous reef fish, and causes vomiting, headaches, and a burning sensation upon contact with cold surfaces.
It is known that the historic populations of Cook Islanders was heavily reliant on fish as a source of protein, and the scientists suggest that once their fish resources became inedible, voyaging became a necessity.
Modern Cook Islanders, though surrounded by an ocean teeming with fish, don’t eat fish as a regular part of their diet but instead eat processed, imported foods.
In the late 1990s, lower-income families who could not afford processed foods emigrated to New Zealand and Australia.
The researchers suggest that past migrations had similar roots.
The heightened voyaging from A.D. 1000 to 1450 in eastern Polynesia was likely prompted by ciguatera fish poisoning.
There were few options but to leave once the staple diet of an island nation became poisonous.
According to van Woesik, “Our approach brings us a step closer to solving the mysteries of ciguatera and the storied Polynesian native migrations. We hope it will lead to better forecasting and planning for ciguatera outbreaks.” (ANI) | {
"pile_set_name": "Pile-CC"
} |
Biotechnological production of human milk oligosaccharides.
Human milk contains a large variety of oligosaccharides (HMOs) that have the potential to modulate the gut flora, affect different gastrointestinal functions, and influence inflammatory processes. This review introduces the recent advances in the microbial and coupled enzymatic methods to produce HMOs with grouping them into trisaccharides (sialyllactose and fucosyllactose) and complex oligosaccharides (lacto-N-biose derivatives). The high purity and low cost of HMOs should make their use possible in new fields such as the food or pharmaceutical industries. | {
"pile_set_name": "PubMed Abstracts"
} |
1. Introduction {#sec1-polymers-08-00159}
===============
Phenol-formaldehyde (PF) is a high-performance resin that is synthesized by the copolymerization of phenol with formaldehyde. It is widely applied for industrial uses, including adhesives, impregnating resins, and plastics. The excellent properties of PF resin include high mechanical, thermal, and weather stability \[[@B1-polymers-08-00159]\]. However, the lower curing rate and required higher curing temperature compared to other thermosetting adhesives limit the application of PF resins for use in impregnating resins or adhesives \[[@B2-polymers-08-00159],[@B3-polymers-08-00159]\]. Many attempts have been made to accelerate the curing rate or lower the curing temperature, including testing of various catalysts or additives to alter the reaction kinetics, such as carboxylic acid esters \[[@B4-polymers-08-00159],[@B5-polymers-08-00159]\], anhydrides \[[@B6-polymers-08-00159]\], amides \[[@B7-polymers-08-00159]\], carbonate \[[@B8-polymers-08-00159]\], and metallic ions \[[@B9-polymers-08-00159]\]. Additionally, the effects of the condensation condition on the PF resin structure and properties have been well studied by conventional analytical techniques. For example, various mechanisms of PF resin hardening accelerated by catalysts or additives have been reported \[[@B10-polymers-08-00159]\]. Some additives, such as sodium carbonate, act solely to accelerate the curing reaction, but other additives, such as propylene carbonate, both accelerate the reaction and also increase the average functionality of the PF reaction system to allow a tighter final network \[[@B10-polymers-08-00159]\]. The properties of basic catalysts, such as the valence and ionic radius of hydrated cations, affected the mechanisms and kinetics of PF resin condensation and, thus, the composition of the final products \[[@B9-polymers-08-00159]\]. Some studies also reported that an alkaline catalyst promoted the formation of dimethylene ethers in the polymerization reaction, and that *ortho* to *ortho* (*o*,*o*′) ethers were more stable \[[@B11-polymers-08-00159]\]. However, there has been no comprehensive study about the action of catalysts to increase or decrease the ratio of *ortho*/*para* reaction position or analysis of the corresponding physicochemical properties of the accelerated PF resins.
The aromatic ring of phenol has *ortho* and *para* positions capable of reaction with formaldehyde under certain conditions, but the *para* position has higher reactivity than the *ortho* position. The presence of two *ortho* positions and one *para* position in an aromatic ring generally could lead to a PF resin containing mostly *ortho* hydroxymethyl groups \[[@B2-polymers-08-00159]\]. However, in the process of PF resin synthesis, some catalysts could make more formaldehyde or methylol toward phenol *ortho* positions to increase the ratio of *ortho*/*para* substituted positions \[[@B12-polymers-08-00159]\], leading to more reactive functional groups or more unreacted *para* positions at the curing stage, which may shorten the curing time and increase the cross-linking degree of cured PF resin.
Since metal ions can accelerate the curing of PF resins, we tested the ability of barium hydroxide (Ba(OH)~2~), sodium carbonate (Na~2~CO~3~), lithium hydroxide (LiOH), and zinc acetate ((CH~3~COO)~2~Zn) to decrease curing temperature and accelerate the curing rate of PF resins. To elucidate the chemical structure of the cure-accelerated PF resins, we performed quantitative liquid ^13^C NMR to analyze the structural features. Finally, possible synthesis mechanism of metal-mediated polymerization of PF resins was proposed based on the chemical structure analysis and thermogravimetric (DTG) curve.
2. Materials and Methods {#sec2-polymers-08-00159}
========================
2.1. Materials {#sec2dot1-polymers-08-00159}
--------------
Phenol, formaldehyde (37%), Ba(OH)~2~, Na~2~CO~3~, LiOH, and (CH~3~COO)~2~Zn were obtained from Zhong'an Chemical Industries, Beijing, China and were used directly without further purification, and all other chemicals were AR grade and obtained from Beijing Chemical Industries, Beijing, China.
2.2. Preparation of PF Resins {#sec2dot2-polymers-08-00159}
-----------------------------
The catalyst-accelerated PF resin was synthesized by batch polymerization with phenol and formaldehyde at a molar ratio of 1:2.2, and the additive amount of catalyst was 6% based on the total mass of PF resin. In the first step, phenol was mixed in a flask with one third of the formaldehyde and one third of the catalyst. The mixture was quickly heated to 70 °C, and then the heater was turned off. The temperature of the mixture increased to 90 °C due to the heat produced by polymerization reaction and remained at 93--95 °C for 1 h. In the second step, the remaining formaldehyde and two thirds of the catalyst were added to the flask and the mixture was heated to 90 °C and kept at that temperature for 0.5 h. Finally, the mixture was cooled to 40 °C to yield PF resin. PF resins with different catalysts were synthesized with the same procedure.
2.3. Preparation of Plywood {#sec2dot3-polymers-08-00159}
---------------------------
Three-layer plywood (400 mm × 400 mm × 4.8 mm) was prepared with a single poplar veneer in the middle and two poplar veneers on the top and bottom simulating actual industrial parameters. The middle poplar veneer was coated with 125--150 g/m^2^ resin on each side. Four pieces of three-layer plywood for each catalyst-accelerated resin (including control) were hot-pressed under 1.2 MPa at 100, 110, 120, and 130 °C, respectively. The hot-press time was 7 min, including the first one minute and the last one minute to load and unload the pressure, respectively.
2.4. Characterization of PF Resins {#sec2dot4-polymers-08-00159}
----------------------------------
The solid (non-volatile) content of resol resin was determined in accordance with ASTM standard D4426-01. The viscosity of resin was measured using a Brookfield DV-II viscometer (AMETEK-BROOKFIELD Corporation, Middleboro, MA, USA) using 61\# rotor with spinning rate of 100 rpm. Gel time was defined as the time period from the immersion of the test tube into the oil bath (135 °C) to the beginning of the resin gelation (resin forming a string when a glass rod was lifted from the resin).
2.5. Characterization of the Plywood {#sec2dot5-polymers-08-00159}
------------------------------------
The shear strength was measured as per ASTM D906-98.
2.6. FT-IR Analysis of PF Resins {#sec2dot6-polymers-08-00159}
--------------------------------
The resins were placed in 0.01 MPa vacuum at 60 °C for 4 h to dry to non-volatility. FT-IR spectra of vacuum-dried PF resins were performed in a Nicolet IS10 instrument (Thermo Fisher Scientific Corporation, Waltham, MA, USA). Each spectrum was recorded with 32 scans in a frequency range of 600--4000 cm^−1^ at a spectral resolution of 4 cm^−1^.
2.7. Contact Angle Measurement {#sec2dot7-polymers-08-00159}
------------------------------
The contact angle measurements of the PF resins were performed on the tangential surfaces of wood samples with an optical contact angle apparatus (OCA 20 DataPhysics Instruments GmnH, Filderstadt, Germany). Sessile droplets (3 μL, measured with a microsyringe) of liquid resin were placed on the wood surface. The right and left angles of the drops on the surface were collected at intervals of 0.1 s for a total duration of 60 s, and the average angle was calculated.
2.8. Quantitative Liquid ^13^C NMR Measurement {#sec2dot8-polymers-08-00159}
----------------------------------------------
All of the resins were characterized by quantitative ^13^C NMR spectroscopy with a VARIAN INOUR-300 (JEOL Corporation, Tokyo, Japan) spectrometer with a frequency of 75.51 MHz using the inverse-gated decoupling method. All of the spectra were recorded at room temperature with a delay time of 8 s, a 13 h acquisition time and a 15.4 μs pulse width (90°). About 8000 scans were accumulated to obtain spectra for each spectrum. The chemical shifts of each spectrum were accurate to 0.1 ppm and all the resin samples were directly used for ^13^C NMR measurement.
2.9. Thermogravimetric Analysis (TG) of Resins {#sec2dot9-polymers-08-00159}
----------------------------------------------
Samples were dried at 120 °C for 2 h to evaporate the moisture and then TG was performed in a nitrogen atmosphere within a temperature range from room temperature to 700 °C, with a heating rate of 10 °C/min.
3. Results and Discussion {#sec3-polymers-08-00159}
=========================
3.1. Performance of the Catalyst-Accelerated PF Resin {#sec3dot1-polymers-08-00159}
-----------------------------------------------------
[Table 1](#polymers-08-00159-t001){ref-type="table"} shows the solid content, viscosity, and gel time of the PF resins. We found that the solid contents were similar for all resins, but the viscosity varied greatly for different catalysts. The viscosity of the Na~2~CO~3~-accelerated resin was 153.00 mPa·s, higher than the viscosity of the other catalyst-accelerated PF resins, especially the control resin with a low viscosity of 25.70 mPa·s. Similarly, the gel-time for the catalyst-accelerated resins varied from 11.83 min for the Na~2~CO~3~-accelerated resin to 20.46 min for the control resin. These results indicated that these catalysts were able to accelerate the synthesis reaction to different extents. The ability of the catalysts to accelerate the reactions could be ranked as Na~2~CO~3~ \> (CH~3~COO)~2~Zn \> Ba(OH)~2~ \> LiOH. Under the same reaction conditions, the catalyst Na~2~CO~3~ can dramatically accelerate the synthesis reaction process, increase the viscosity, and decrease the gel time of PF resin.
3.2. Contact Angle of the PF Resins {#sec3dot2-polymers-08-00159}
-----------------------------------
The wettability of PF resin on solid surface is usually evaluated by contact angle \[[@B13-polymers-08-00159]\], which was tested on smoothed wood surface in this study. Due to liquid penetration and spreading on the wood surface, the contact angle changed as a function of time, as shown in [Figure 1](#polymers-08-00159-f001){ref-type="fig"}. The process of adhesive wetting includes three steps \[[@B14-polymers-08-00159]\]: (1) formation of a contact angle at the solid and adhesive interface; (2) spreading of the adhesive over a solid surface; and (3) adhesive penetration into the porous solid substrate, as shown in [Figure 2](#polymers-08-00159-f002){ref-type="fig"}.
As shown in [Figure 1](#polymers-08-00159-f001){ref-type="fig"}, at the initial stage of the wetting process, the contact angle of the resins decreased quickly. As time elapsed, the contact angle decreased more slowly and finally attained relative equilibrium. It was observed that the Na~2~CO~3~-accelerated PF resin showed the largest equilibrium contact angle, and the resins could be ranked as Na~2~CO~3~ \> Ba(OH)~2~ \> LiOH \> (CH~3~COO)~2~Zn \> Control. The results suggested that the Na~2~CO~3~-accelerated PF resin had the largest surface tension, which may be due to its larger viscosity. [Figure 1](#polymers-08-00159-f001){ref-type="fig"} also shows that the (CH~3~COO)~2~Zn-accelerated resin had the fastest rate of contact angle change, which meant that (CH~3~COO)~2~Zn-accelerated resin could spread and penetrate more quickly into the porous structure of wood. Both viscosity and the chemical constitution of PF resin could alter the contact angle change rate. Usually, samples with lower viscosity exhibit a faster contact angle change rate. However, from the data in [Table 1](#polymers-08-00159-t001){ref-type="table"}, (CH~3~COO)~2~Zn-accelerated resin showed higher viscosity than that of the control sample, but had a faster contact angle change rate. Thus, the chemical constitution of (CH~3~COO)~2~Zn-accelerated PF resin may be the main factor altering its contact angle change rate. The hydroxymethyl of PF resin is the main chemical group that can easily connect with the hydroxyl of wood cellulose; thus, our data suggests that (CH~3~COO)~2~Zn-accelerated PF resin may contain more hydroxymethyl.
3.3. FT-IR Spectroscopy {#sec3dot3-polymers-08-00159}
-----------------------
To investigate the structural changes in the PF resins accelerated by different catalysts, FT-IR spectra ([Figure 3](#polymers-08-00159-f003){ref-type="fig"}) were obtained after vacuum-drying the samples. The spectra assignments of the PF resins are shown in [Table 2](#polymers-08-00159-t002){ref-type="table"} \[[@B15-polymers-08-00159],[@B16-polymers-08-00159],[@B17-polymers-08-00159]\].
There were no significant differences between the spectra of the catalyst-accelerated resins and the control sample, which indicated structural similarity. Bands at 1020 cm^−1^ were ascribed to C--O stretching vibration of aliphatic C--OH, aliphatic C--O, and methylol C--OH. Bands at 1600 cm^−1^ were assigned to the elongation of aromatic --C=C--, which were consistent in each reaction system and unaffected by catalyst reaction. Thus, bands at 1600 cm^−1^ could be used as an internal standard for analysis. The ratio of absorption value of 1020 cm^−1^ (variable)/1600 cm^−1^ (constant) was calculated to indicate the degree of hydroxymethyl for phenol in each catalyst accelerated-reaction system, as shown in [Table 3](#polymers-08-00159-t003){ref-type="table"}. The control of PF resins had a relatively larger ratio of 1020 cm^−1^/1600 cm^−1^, which may be explained by the fact that the methylol of catalyst-accelerated PF resin tends to undergo further condensation reactions to form methylene (--CH~2~--). Thus, the control sample had relatively more unreacted methylol. This explanation was confirmed by the fact that the control sample showed the lowest viscosity due to its relatively minimum condensation degree.
3.4. Chemical Structure Analysis {#sec3dot4-polymers-08-00159}
--------------------------------
In order to identify the effect of different catalysts on the functional groups, quantitative ^13^C NMR was used to study the difference of chemical shifts between the control and catalyst-accelerated PF resins. The ^13^C NMR spectra are shown in [Figure 4](#polymers-08-00159-f004){ref-type="fig"}, and their corresponding assignments of groups' signals are shown in [Figure 5](#polymers-08-00159-f005){ref-type="fig"} \[[@B12-polymers-08-00159],[@B18-polymers-08-00159],[@B19-polymers-08-00159],[@B20-polymers-08-00159]\].
The chemical shift of 150.0--158.0 ppm was assigned to phenoxy carbons (C1--OH), which was used as an integral standard and analytical standpoint. 156.2--156.8 ppm and 153.4--156.1 ppm were assigned to *para* alkylated groups and *ortho* alkylated groups, respectively. Usually, phenolic *ortho* and *para* carbons' chemical shifts vary with the sodium hydroxide contents of the resin due to the ionization of phenoxy group and the kind of substituted groups. Substitution with methylol groups in the *para* and *ortho* carbon positions was shown at 129.0--130.4 ppm and 127.0--128.1 ppm. Unsubstituted *para* and *ortho* carbons, the main reactive sites for the methylolation reaction, occurred at 119.2--120.4 ppm and 115.0--116.6 ppm, respectively. The unsubstituted *para* and *ortho* carbon peaks were only present in the control and Ba(OH)~2~-accelerated PF resins, which indicated that Na~2~CO~3~, LiOH, and (CH~3~COO)~2~Zn facilitate the reaction of formaldehyde with phenolic *ortho* and *para* position more than what occurs in the control and Ba(OH)~2~ samples. A sharp peak of methanol was evident around 50 ppm for all resins. Industrial formaldehyde usually contains a small amount of methanol which can also be formed during resin synthesis from the Canizzaro reaction of formaldehyde. The signal peak of methylol is sharper than the methylene peak due to its higher group mobility and less variation in the environment within the polymer structure. Thus, the two peaks at 63.3--65.5 ppm and 61.1--61.5 ppm were assigned to *para* methylol and *ortho* methylol. Theoretically, condensation between two methylols can occur to form methylene ether bridges. However, the data in [Figure 4](#polymers-08-00159-f004){ref-type="fig"} shows no peak between 69 and 74 ppm, indicating that methylene ether bridges were not formed between phenolic units during the synthesis of PF resin. The methylene bridges were easily observed in the range of 34--41 ppm. In a different chemical environment, different methylene linkages showed a different chemical shift, 39.7--41.0 ppm and 34.3--35.7 ppm were assigned to *para*--*para* and *ortho*--*para* methylene bridges, respectively. In order to remove the interference of carbon in CH~3~COO^−^ for ^13^C NMR analysis, the Zn(NO~3~)~2~-accelerated resin was also tested by ^13^C NMR analysis and used as a control for the ^13^C NMR analysis of (CH~3~COO)~2~Zn-accelerated resin.
Further analysis of quantitative ^13^C NMR is needed to elucidate the details of the cure-acceleration effect of different catalysts on the structure and compositions of PF resin. In this study, the ratios of integral values of the substituted position *ortho* (127.0--128.1 ppm)/*para* (129.0--130.4 ppm), *ortho* methylol (61.1--61.5 ppm)/*para* methylol (63.3--65.5 ppm), and methylene bridges *ortho-para* (34.3--35.7 ppm)/*para--para* (39.7--41.0 ppm) were calculated, as shown in [Table 4](#polymers-08-00159-t004){ref-type="table"}. PF resins supplemented with Na~2~CO~3~, LiOH, and especially (CH~3~COO)~2~Zn, possessed higher ratios of *ortho*/*para*-substituted positions than did the control or the PF resin with Ba(OH)~2~. In case of the *ortho*/*para* ratio of methylol, the values of Na~2~CO~3~-accelerated and (CH~3~COO)~2~Zn-accelerated PF resins were not calculated (NC), because their ^13^C NMR spectra showed no signal for *para* methylol. Either Na~2~CO~3~ and (CH~3~COO)~2~Zn promoted the complete *para* methylol condensation reaction or drive formaldehyde toward the phenol *ortho* position exclusively. The ratio of *ortho* methylol/*para* methylol for the Zn(NO~3~)~2~-accelerated resin was much higher than other samples, excluding the Na~2~CO~3~-accelerated and (CH~3~COO)~2~Zn-accelerated PF resins. Usually, *para* methylol groups react more easily with other *para* positions to form *para--para* linkages. However, the data in [Table 5](#polymers-08-00159-t005){ref-type="table"} indicates that *ortho-para* linkages were equal to *para--para* linkages in the Na~2~CO~3~-accelerated, Zn(NO~3~)~2~-accelerated, and (CH~3~COO)~2~Zn-accelerated PF resins, suggesting that Na~2~CO~3~, Zn(NO~3~)~2~, and (CH~3~COO)~2~Zn were able to promote the condensation reaction to form *ortho-para* linkages. These results could be further proved by [Table 1](#polymers-08-00159-t001){ref-type="table"} that Na~2~CO~3~ and Zn(NO~3~)~2~-accelerated PF resins had higher viscosity, indicating that the significant promotion of phenol *ortho* position reactivity made Na~2~CO~3~ and Zn(NO~3~)~2~-accelerated PF resins have a tighter final network.
In conclusion, all the catalysts tested showed accelerating effect to promote phenol *ortho* reactivity. However, (CH~3~COO)~2~Zn and Na~2~CO~3~ were able to significantly promote the reaction activity of phenol *ortho* position and the condensation reaction of *ortho* methylol or directed formaldehyde exclusively toward the phenol *ortho* position.
3.5. Plywood Performance {#sec3dot5-polymers-08-00159}
------------------------
[Figure 6](#polymers-08-00159-f006){ref-type="fig"} shows the bonding strength of the plywood prepared with these different PF resins. Each kind of plywood was prepared at four hot-pressing temperatures, namely 100, 110, 120, and 130 °C. Higher hot-pressed temperatures allowed the resin to cure more completely and, thus, increase the bonding strength. Under the same hot-pressing temperature, the plywood prepared with catalyst-accelerated PF resins exhibited higher bonding strength than the control sample, especially the one with Na~2~CO~3~-accelerated PF resin. The data in [Figure 6](#polymers-08-00159-f006){ref-type="fig"} shows that the plywood prepared with Na~2~CO~3~-accelerated resin at 110 °C yielded almost the same bonding strength of plywood with Ba(OH)~2~-accelerated resin at 120 °C, which is higher than that of the control sample pressed at 120 °C. The reason may be that the Na~2~CO~3~-accelerated PF resin had the highest viscosity among PF resins from [Table 1](#polymers-08-00159-t001){ref-type="table"}, or that Na~2~CO~3~ significantly improved PF resin performance by promoting the reaction activity of phenol *ortho* position.
3.6. Thermal Behavior of the Cured PF Resins {#sec3dot6-polymers-08-00159}
--------------------------------------------
To characterize the thermal stability of the catalyst-accelerated PF resins, TG analysis was performed next, as shown in [Figure 7](#polymers-08-00159-f007){ref-type="fig"}. The temperatures at which the maximum degradation speed took place (*T*~max~) for the different thermal events of cured catalyst-accelerated PF resins are shown in [Table 5](#polymers-08-00159-t005){ref-type="table"}.
It was previously known that phenolic resin degrades in three steps: post-curing, thermal reforming, and ring stripping \[[@B21-polymers-08-00159],[@B22-polymers-08-00159]\]. The mass loss (about 5%) of the first thermal event at the lower temperature range (\<155 °C) contributed to the evaporation of free water. In the second stage, with a temperature range from 230 to 300 °C, mass loss was due to the evaporation of water formed by the condensation reaction of methylol groups. The mass loss in the third event (from 350 to 440 °C) was due to the loss of water formed by the condensation reaction of methylol and phenolic hydrogen, as well as between two hydroxyl functional groups, which could cause further structure change of the cured products to a more tightly cross-linked network. In the fourth event (\>450 °C), the mass loss was due to the loss of carbon monoxide and methane formed by degradation of the methylene linkage. As the temperature further increased, the remaining mass was from 65% to 68% at 700 °C, and that of Ba(OH)~2~, Na~2~CO~3~, and (CH~3~COO)~2~Zn-accelerated PF resins was higher than other samples, indicating that a tighter network and higher thermal stability was possessed by their molecular structure.
[Figure 7](#polymers-08-00159-f007){ref-type="fig"} shows TG (a) and DTG (b) curves of the catalyst-accelerated PF resins. All of the PF resins showed similar thermal stability in the first three stages of thermal events. However, in the final event, the DTG curve of the (CH~3~COO)~2~Zn-accelerated resin showed lower degradation speed than the other PF resins, and had double peaks of degradation speed. According to Pizzi and Mohamed *et al.* \[[@B23-polymers-08-00159],[@B24-polymers-08-00159],[@B25-polymers-08-00159]\], when a benzene ring was blended with a zinc ion, a complex compound between the phenolic nuclei and the zinc ion could be formed by a metal-ligand mode, which can accelerate the initial reaction of formaldehyde toward the phenolic nuclei by forming a carbocation of strong positive charge. As shown in [Scheme 1](#polymers-08-00159-sch001){ref-type="scheme"}, the mobility of the polymer chain was restricted by ion-polymer and ion-interaction, resulting in a higher thermal stability of PF resin than the control sample. Thus, the first of double peaks at 493 °C may indicate the breakage of the metal-ligand bonding mode, and the second peak of the double peaks at 518 °C may indicate the degradation of the methylene linkage.
4. Conclusions {#sec4-polymers-08-00159}
==============
The poly-condensations of PF resins with different catalysts suggested different abilities to accelerate the reaction. In general, the accelerating efficiency of the catalysts was Na~2~CO~3~ \> (CH~3~COO)~2~Zn \> Ba(OH)~2~ \> LiOH.
The addition of Na~2~CO~3~ had a remarkable influence on the performance of PF resin. The viscosity of Na~2~CO~3~-accelerated PF resin increased to around 153 mPa·s quickly, five-fold greater than the viscosity of the control resin. Moreover, the gel time of PF resin decreased significantly and the bonding strength of plywood increased by the addition of Na~2~CO~3~. The quantitative ^13^C NMR analysis showed that the (CH~3~COO)~2~Zn and Na~2~CO~3~ catalysts could significantly promote the reaction activity of the phenol *ortho* position, and favor the condensation reaction of *ortho* methylol or direct formaldehyde toward the phenol *ortho* position exclusively. Compared with Na~2~CO~3~, the catalyst (CH~3~COO)~2~Zn showed a slightly weaker accelerating effect, but the contact angle analysis found that the (CH~3~COO)~2~Zn-accelerated resin showed a faster contact angle change rate, which represents a better wettability on the wood surface. Furthermore, the different peaks in the DTG curve and higher weight residue of TG data indicated that (CH~3~COO)~2~Zn has a different accelerating mechanism to improve the thermal stability of PF resin. That mechanism may include metal-ligand bonding between the benzene ring and zinc ion formed by ion-polymer and ion-interaction.
In conclusion, catalysts such as Na~2~CO~3~ and (CH~3~COO)~2~Zn showed significant accelerating effects to promote the curing of PF resin at lower temperatures and to improve PF resin performance. Thus, good catalyst-accelerated PF resins have promised to overcome the shortcoming of high curing temperature and to broaden their application.
This work was supported by the Chinese National Science and Technology Support Program (2015BAD14B03), the Special Fund for Forestry Research in the Public Interest (Project 201504502), and China Postdoctoral Science Foundation Funded Project (2015M570039).
Zhao Yi contributed to synthesis, test, data analysis, and wrote manuscript. Jizhi Zhang, Jianzhang Li and Wei Zhang suggested and supervised the work and revised the manuscript. Shifeng Zhang, and Qiang Gao provided constructive suggestions about this work.
The authors declare no conflict of interest.
Figures, Scheme and Tables
==========================
{#polymers-08-00159-f001}
{#polymers-08-00159-f002}
{#polymers-08-00159-f003}
{#polymers-08-00159-f004}
{#polymers-08-00159-f005}
{#polymers-08-00159-f006}
{#polymers-08-00159-f007}
{#polymers-08-00159-sch001}
polymers-08-00159-t001_Table 1
######
PF resin characteristics.
Catalyst type Performance
----------------- ------------- -------- -------
Control 43 25.70 20.46
Ba(OH)~2~ 46 73.70 15.57
Na~2~CO~3~ 44 153.00 11.83
LiOH 46 58.30 15.88
(CH~3~COO)~2~Zn 44 81.00 13.98
polymers-08-00159-t002_Table 2
######
Assignments of FT-IR spectra of the PF resin.
Wavenumbers (cm^−1^) Assignment
---------------------- ----------------------------------------------------------------------------------
3,367 --OH stretching vibration
2,900 C--H stretching vibration of methylene
1,600, 1440 The elongation of aromatic --C=C--
1,270 C--O stretching vibration of phenolic C--OH and phenolic C--O
1,020 C--O stretching vibration of aliphatic C--OH, aliphatic C--O, and methylol C--OH
970 C--H stretching vibration of vinyl
polymers-08-00159-t003_Table 3
######
The ratio of absorption value of 1020 cm^−1^ (variable)/1600 cm^−1^ (constant) of the PF resins with different catalysts.
Wavenumbers (cm^−1^) Absorption
---------------------- ------------ ------- ------- ------- -------
1,020 43.46 32.63 33.79 45.43 29.85
1,600 29.75 28.14 29.94 38.54 24.81
Ratio (1,020/1,600) 1.46 1.16 1.13 1.17 1.20
polymers-08-00159-t004_Table 4
######
Liquid ^13^C NMR analysis results of PF resin formed with different catalysts.
PF resin *ortho*/*para* (Substituted position) *ortho*/*para* (Methylol) *ortho-para*/*para--para* (Methylene bridges)
--------------------------------- --------------------------------------- --------------------------------- -----------------------------------------------
   
Control   
Ba(OH)~2~
Na~2~CO~3~
LiOH
(CH~3~COO)~2~Zn
Zn(NO~3~)~2~
polymers-08-00159-t005_Table 5
######
Thermal properties of the cured PF resins.
Catalyst type *T~max~* of Thermal event (°C) Weight residue (%) at 700 °C
----------------- -------------------------------- ------------------------------ ----- ----- ----- ------
Control 155 260 394 507 -- 65.5
Ba(OH)~2~ 156 262 390 503 -- 68.0
Na~2~CO~3~ 153 300 386 512 -- 65.5
LiOH 158 283 381 497 -- 68.0
(CH~3~COO)~2~Zn 155 273 381 493 518 68.0
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P21S Carnauba Paste Wax is a non-chalky wax, leaving no powder residue or ugly white stains on rubber or plastic. This unique carnauba-beeswax blend goes on and comes off with incredible ease and delivers a great long lasting shine. You will enhance ...
Product Description LG 5231EL1003B Dryer Lint Filter Assembly with Felt Rim Seal. This part number replaces part number 5231EL1003E. For use with the following LG Electronics models: 5231EL1003B, DLE2512W, DLE2514W, DLE2515S, DLE2516W, DLE3733S, DLE3...
Permatex Dielectric Tune-Up Grease protects electrical connections and wiring from salt, dirt and corrosion. Required for modern high energy ignition systems, dialectric grease extends the life of bulb sockets and prevents voltage leaks around any el...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ... | {
"pile_set_name": "Pile-CC"
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The United States and Japan will step up their defence cooperation to deal with the threat from nuclear-armed North Korea as tensions in East Asia remain high, officials from the two allies said on Thursday.
Mr Wright started a relationship with Elizabeth after divorcing three earlier wives.
Olivia is the youngest of Mr Wright's four children but she had a difficult relationship with her father, who was frequently absent and gave little support for her single mother before his death in 2012.
She had not met older siblings Leonie Baldock, Alexandra Burt and Myles Wright prior to his death.
Olivia challenged her father's will because her $3 million trust fund had onerous conditions and could not be accessed until she was the age of 30.
Related Articles
She sought an immediate $12 million share of her father's estate, estimated at more than $1 billion, but in February the WA Supreme Court instead awarded her $25 million, the largest such payout in Australian legal history.
Olivia told the Seven Network's Sunday Night program there had been many personal hurdles during her long legal battle.
While she is ready to contest the appeal, she said she's unsure if she would go through the initial legal battle again. | {
"pile_set_name": "Pile-CC"
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Loagan Bunut National Park
The Loagan Bunut National Park () is a national park located in Miri Division, Sarawak, Malaysia, on the Borneo island. The park was named after the Loagan Bunut lake nearby, which is connected to Sungai Bunut (sungai is Malay for river), Sungai Baram and Sungai Tinjar. This park occupies a space of and is well known for its rich biodiversity and unique aquatic ecosystem.
The national park was gazetted on January 1, 1990 and it was opened to public on August 29, 1991.
See also
List of national parks of Malaysia
References
Category:National parks of Malaysia
Category:Protected areas of Sarawak
Category:Miri, Malaysia
Category:1990 establishments in Malaysia | {
"pile_set_name": "Wikipedia (en)"
} |
RALEIGH
Complete with everything from excellent school systems and a thriving local economy to miles of parkland and bountiful culinary & cultural attractions, the greater Raleigh metropolitan area truly has it all. See for yourself why so many families and businesses chose to move here, grow here, and stay here. | {
"pile_set_name": "Pile-CC"
} |
A Delicious Way to Support the Princeton Schools This Weekend at Eno Terra
Noriko and Erik Svenson and their children with Eno Terra server Giovanni Maselli last weekend..
Eno Terra is donating four days of lunch proceeds to the PowerUp! PRS Technology Campaign to benefit the Princeton Regional Schools.
This Saturday and Sunday if you eat lunch at Eno Terra, you will be supporting fundraising efforts to improve technology in the public schools.
The Terra Momo Restaurant Group, owner of Eno Terra, is donating the net proceeds from lunch sale both last weekend and this weekend to the Princeton Education Foundation.
Since 1995, the Princeton Education Foundation has encouraged private philanthropy to enhance public education. Since its inception, PEF has contributed over $1 million to the Princeton Public Schools for capital improvements, educational programs and teacher support.
“The donated funds from Eno Terra will go directly to PowerUp! PRS, our campaign to provide much needed technology upgrades to every school in the district,” said PEF Executive Director Adrienne Rubin. “We are very grateful to Eno Terra for this promotion as well as for their ongoing support of our schools.”
Eno Terra, located on Route 27 in Kingston, recently opened for lunch on the weekends. You can make a reservation for lunch for this Saturday, March 24, or this Sunday, March 25 by calling (609) 497-1777.
Raoul Momo, co-owner Terra Momo Restaurant Group, said that it is crucial that schools find new ways of raising money to ensure a high standard of education for all students in Princeton.
“With all the challenges at the state level with school finances, it is important to look to develop local partnerships with businesses like Eno Terra,” he said. “In the end, our children are our most important investment.” | {
"pile_set_name": "Pile-CC"
} |
Yves Niaré
Yves Niaré (20 July 1977 – 5 December 2012) was a shot putter from France.
Career
Niaré was born in Saint-Maurice, Val-de-Marne. He father was Malian shot putter Namakoro Niaré. His main honor was the silver medal at the 2009 European Indoor Championships with a throw of 20.42 metres. He also finished eleventh at the 1996 World Junior Championships, and fourth at the 2009 Mediterranean Games.
Niaré competed at the 2001 World Championships, the 2006 European Championships, the 2007 World Championships, the 2008 Olympic Games and the 2009 World Championships without reaching the final.
His personal best throw in the shot put was 20.72 metres, a French national record, achieved in May 2008 in Versailles. He also had 63.44 metres in the discus throw, achieved in May 2007 in Chelles.
He is the brother of French High Jumper Gaëlle Niaré.
Death
Niaré was killed on the morning of 5 December 2012 in an automobile accident. A statement regarding his death was issued by the French Athletics Federation. He was 35.
Competition record
References
External links
Category:1977 births
Category:2012 deaths
Category:Sportspeople from Val-de-Marne
Category:French male shot putters
Category:French male discus throwers
Category:Athletes (track and field) at the 2008 Summer Olympics
Category:Olympic athletes of France
Category:Road incident deaths in France
Category:French people of Malian descent | {
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} |
// DO NOT EDIT.
//
// Generated by the Swift generator plugin for the protocol buffer compiler.
// Source: google/protobuf/unittest_proto3_arena.proto
//
// For information on using the generated types, please see the documenation:
// https://github.com/apple/swift-protobuf/
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// 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.
import Foundation
import SwiftProtobuf
// If the compiler emits an error on this type, it is because this file
// was generated by a version of the `protoc` Swift plug-in that is
// incompatible with the version of SwiftProtobuf to which you are linking.
// Please ensure that your are building against the same version of the API
// that was used to generate this file.
fileprivate struct _GeneratedWithProtocGenSwiftVersion: SwiftProtobuf.ProtobufAPIVersionCheck {
struct _2: SwiftProtobuf.ProtobufAPIVersion_2 {}
typealias Version = _2
}
enum Proto3ArenaUnittest_ForeignEnum: SwiftProtobuf.Enum {
typealias RawValue = Int
case foreignZero // = 0
case foreignFoo // = 4
case foreignBar // = 5
case foreignBaz // = 6
case UNRECOGNIZED(Int)
init() {
self = .foreignZero
}
init?(rawValue: Int) {
switch rawValue {
case 0: self = .foreignZero
case 4: self = .foreignFoo
case 5: self = .foreignBar
case 6: self = .foreignBaz
default: self = .UNRECOGNIZED(rawValue)
}
}
var rawValue: Int {
switch self {
case .foreignZero: return 0
case .foreignFoo: return 4
case .foreignBar: return 5
case .foreignBaz: return 6
case .UNRECOGNIZED(let i): return i
}
}
}
#if swift(>=4.2)
extension Proto3ArenaUnittest_ForeignEnum: CaseIterable {
// The compiler won't synthesize support with the UNRECOGNIZED case.
static var allCases: [Proto3ArenaUnittest_ForeignEnum] = [
.foreignZero,
.foreignFoo,
.foreignBar,
.foreignBaz,
]
}
#endif // swift(>=4.2)
/// This proto includes every type of field in both singular and repeated
/// forms.
struct Proto3ArenaUnittest_TestAllTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
/// Singular
var optionalInt32: Int32 {
get {return _storage._optionalInt32}
set {_uniqueStorage()._optionalInt32 = newValue}
}
var optionalInt64: Int64 {
get {return _storage._optionalInt64}
set {_uniqueStorage()._optionalInt64 = newValue}
}
var optionalUint32: UInt32 {
get {return _storage._optionalUint32}
set {_uniqueStorage()._optionalUint32 = newValue}
}
var optionalUint64: UInt64 {
get {return _storage._optionalUint64}
set {_uniqueStorage()._optionalUint64 = newValue}
}
var optionalSint32: Int32 {
get {return _storage._optionalSint32}
set {_uniqueStorage()._optionalSint32 = newValue}
}
var optionalSint64: Int64 {
get {return _storage._optionalSint64}
set {_uniqueStorage()._optionalSint64 = newValue}
}
var optionalFixed32: UInt32 {
get {return _storage._optionalFixed32}
set {_uniqueStorage()._optionalFixed32 = newValue}
}
var optionalFixed64: UInt64 {
get {return _storage._optionalFixed64}
set {_uniqueStorage()._optionalFixed64 = newValue}
}
var optionalSfixed32: Int32 {
get {return _storage._optionalSfixed32}
set {_uniqueStorage()._optionalSfixed32 = newValue}
}
var optionalSfixed64: Int64 {
get {return _storage._optionalSfixed64}
set {_uniqueStorage()._optionalSfixed64 = newValue}
}
var optionalFloat: Float {
get {return _storage._optionalFloat}
set {_uniqueStorage()._optionalFloat = newValue}
}
var optionalDouble: Double {
get {return _storage._optionalDouble}
set {_uniqueStorage()._optionalDouble = newValue}
}
var optionalBool: Bool {
get {return _storage._optionalBool}
set {_uniqueStorage()._optionalBool = newValue}
}
var optionalString: String {
get {return _storage._optionalString}
set {_uniqueStorage()._optionalString = newValue}
}
var optionalBytes: Data {
get {return _storage._optionalBytes}
set {_uniqueStorage()._optionalBytes = newValue}
}
var optionalNestedMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage {
get {return _storage._optionalNestedMessage ?? Proto3ArenaUnittest_TestAllTypes.NestedMessage()}
set {_uniqueStorage()._optionalNestedMessage = newValue}
}
/// Returns true if `optionalNestedMessage` has been explicitly set.
var hasOptionalNestedMessage: Bool {return _storage._optionalNestedMessage != nil}
/// Clears the value of `optionalNestedMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalNestedMessage() {_uniqueStorage()._optionalNestedMessage = nil}
var optionalForeignMessage: Proto3ArenaUnittest_ForeignMessage {
get {return _storage._optionalForeignMessage ?? Proto3ArenaUnittest_ForeignMessage()}
set {_uniqueStorage()._optionalForeignMessage = newValue}
}
/// Returns true if `optionalForeignMessage` has been explicitly set.
var hasOptionalForeignMessage: Bool {return _storage._optionalForeignMessage != nil}
/// Clears the value of `optionalForeignMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalForeignMessage() {_uniqueStorage()._optionalForeignMessage = nil}
var optionalImportMessage: ProtobufUnittestImport_ImportMessage {
get {return _storage._optionalImportMessage ?? ProtobufUnittestImport_ImportMessage()}
set {_uniqueStorage()._optionalImportMessage = newValue}
}
/// Returns true if `optionalImportMessage` has been explicitly set.
var hasOptionalImportMessage: Bool {return _storage._optionalImportMessage != nil}
/// Clears the value of `optionalImportMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalImportMessage() {_uniqueStorage()._optionalImportMessage = nil}
var optionalNestedEnum: Proto3ArenaUnittest_TestAllTypes.NestedEnum {
get {return _storage._optionalNestedEnum}
set {_uniqueStorage()._optionalNestedEnum = newValue}
}
var optionalForeignEnum: Proto3ArenaUnittest_ForeignEnum {
get {return _storage._optionalForeignEnum}
set {_uniqueStorage()._optionalForeignEnum = newValue}
}
var optionalStringPiece: String {
get {return _storage._optionalStringPiece}
set {_uniqueStorage()._optionalStringPiece = newValue}
}
var optionalCord: String {
get {return _storage._optionalCord}
set {_uniqueStorage()._optionalCord = newValue}
}
/// Defined in unittest_import_public.proto
var optionalPublicImportMessage: ProtobufUnittestImport_PublicImportMessage {
get {return _storage._optionalPublicImportMessage ?? ProtobufUnittestImport_PublicImportMessage()}
set {_uniqueStorage()._optionalPublicImportMessage = newValue}
}
/// Returns true if `optionalPublicImportMessage` has been explicitly set.
var hasOptionalPublicImportMessage: Bool {return _storage._optionalPublicImportMessage != nil}
/// Clears the value of `optionalPublicImportMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalPublicImportMessage() {_uniqueStorage()._optionalPublicImportMessage = nil}
var optionalLazyMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage {
get {return _storage._optionalLazyMessage ?? Proto3ArenaUnittest_TestAllTypes.NestedMessage()}
set {_uniqueStorage()._optionalLazyMessage = newValue}
}
/// Returns true if `optionalLazyMessage` has been explicitly set.
var hasOptionalLazyMessage: Bool {return _storage._optionalLazyMessage != nil}
/// Clears the value of `optionalLazyMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalLazyMessage() {_uniqueStorage()._optionalLazyMessage = nil}
var optionalLazyImportMessage: ProtobufUnittestImport_ImportMessage {
get {return _storage._optionalLazyImportMessage ?? ProtobufUnittestImport_ImportMessage()}
set {_uniqueStorage()._optionalLazyImportMessage = newValue}
}
/// Returns true if `optionalLazyImportMessage` has been explicitly set.
var hasOptionalLazyImportMessage: Bool {return _storage._optionalLazyImportMessage != nil}
/// Clears the value of `optionalLazyImportMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalLazyImportMessage() {_uniqueStorage()._optionalLazyImportMessage = nil}
/// Repeated
var repeatedInt32: [Int32] {
get {return _storage._repeatedInt32}
set {_uniqueStorage()._repeatedInt32 = newValue}
}
var repeatedInt64: [Int64] {
get {return _storage._repeatedInt64}
set {_uniqueStorage()._repeatedInt64 = newValue}
}
var repeatedUint32: [UInt32] {
get {return _storage._repeatedUint32}
set {_uniqueStorage()._repeatedUint32 = newValue}
}
var repeatedUint64: [UInt64] {
get {return _storage._repeatedUint64}
set {_uniqueStorage()._repeatedUint64 = newValue}
}
var repeatedSint32: [Int32] {
get {return _storage._repeatedSint32}
set {_uniqueStorage()._repeatedSint32 = newValue}
}
var repeatedSint64: [Int64] {
get {return _storage._repeatedSint64}
set {_uniqueStorage()._repeatedSint64 = newValue}
}
var repeatedFixed32: [UInt32] {
get {return _storage._repeatedFixed32}
set {_uniqueStorage()._repeatedFixed32 = newValue}
}
var repeatedFixed64: [UInt64] {
get {return _storage._repeatedFixed64}
set {_uniqueStorage()._repeatedFixed64 = newValue}
}
var repeatedSfixed32: [Int32] {
get {return _storage._repeatedSfixed32}
set {_uniqueStorage()._repeatedSfixed32 = newValue}
}
var repeatedSfixed64: [Int64] {
get {return _storage._repeatedSfixed64}
set {_uniqueStorage()._repeatedSfixed64 = newValue}
}
var repeatedFloat: [Float] {
get {return _storage._repeatedFloat}
set {_uniqueStorage()._repeatedFloat = newValue}
}
var repeatedDouble: [Double] {
get {return _storage._repeatedDouble}
set {_uniqueStorage()._repeatedDouble = newValue}
}
var repeatedBool: [Bool] {
get {return _storage._repeatedBool}
set {_uniqueStorage()._repeatedBool = newValue}
}
var repeatedString: [String] {
get {return _storage._repeatedString}
set {_uniqueStorage()._repeatedString = newValue}
}
var repeatedBytes: [Data] {
get {return _storage._repeatedBytes}
set {_uniqueStorage()._repeatedBytes = newValue}
}
var repeatedNestedMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] {
get {return _storage._repeatedNestedMessage}
set {_uniqueStorage()._repeatedNestedMessage = newValue}
}
var repeatedForeignMessage: [Proto3ArenaUnittest_ForeignMessage] {
get {return _storage._repeatedForeignMessage}
set {_uniqueStorage()._repeatedForeignMessage = newValue}
}
var repeatedImportMessage: [ProtobufUnittestImport_ImportMessage] {
get {return _storage._repeatedImportMessage}
set {_uniqueStorage()._repeatedImportMessage = newValue}
}
var repeatedNestedEnum: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] {
get {return _storage._repeatedNestedEnum}
set {_uniqueStorage()._repeatedNestedEnum = newValue}
}
var repeatedForeignEnum: [Proto3ArenaUnittest_ForeignEnum] {
get {return _storage._repeatedForeignEnum}
set {_uniqueStorage()._repeatedForeignEnum = newValue}
}
var repeatedStringPiece: [String] {
get {return _storage._repeatedStringPiece}
set {_uniqueStorage()._repeatedStringPiece = newValue}
}
var repeatedCord: [String] {
get {return _storage._repeatedCord}
set {_uniqueStorage()._repeatedCord = newValue}
}
var repeatedLazyMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] {
get {return _storage._repeatedLazyMessage}
set {_uniqueStorage()._repeatedLazyMessage = newValue}
}
var oneofField: OneOf_OneofField? {
get {return _storage._oneofField}
set {_uniqueStorage()._oneofField = newValue}
}
var oneofUint32: UInt32 {
get {
if case .oneofUint32(let v)? = _storage._oneofField {return v}
return 0
}
set {_uniqueStorage()._oneofField = .oneofUint32(newValue)}
}
var oneofNestedMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage {
get {
if case .oneofNestedMessage(let v)? = _storage._oneofField {return v}
return Proto3ArenaUnittest_TestAllTypes.NestedMessage()
}
set {_uniqueStorage()._oneofField = .oneofNestedMessage(newValue)}
}
var oneofString: String {
get {
if case .oneofString(let v)? = _storage._oneofField {return v}
return String()
}
set {_uniqueStorage()._oneofField = .oneofString(newValue)}
}
var oneofBytes: Data {
get {
if case .oneofBytes(let v)? = _storage._oneofField {return v}
return SwiftProtobuf.Internal.emptyData
}
set {_uniqueStorage()._oneofField = .oneofBytes(newValue)}
}
var unknownFields = SwiftProtobuf.UnknownStorage()
enum OneOf_OneofField: Equatable {
case oneofUint32(UInt32)
case oneofNestedMessage(Proto3ArenaUnittest_TestAllTypes.NestedMessage)
case oneofString(String)
case oneofBytes(Data)
#if !swift(>=4.1)
static func ==(lhs: Proto3ArenaUnittest_TestAllTypes.OneOf_OneofField, rhs: Proto3ArenaUnittest_TestAllTypes.OneOf_OneofField) -> Bool {
switch (lhs, rhs) {
case (.oneofUint32(let l), .oneofUint32(let r)): return l == r
case (.oneofNestedMessage(let l), .oneofNestedMessage(let r)): return l == r
case (.oneofString(let l), .oneofString(let r)): return l == r
case (.oneofBytes(let l), .oneofBytes(let r)): return l == r
default: return false
}
}
#endif
}
enum NestedEnum: SwiftProtobuf.Enum {
typealias RawValue = Int
case zero // = 0
case foo // = 1
case bar // = 2
case baz // = 3
/// Intentionally negative.
case neg // = -1
case UNRECOGNIZED(Int)
init() {
self = .zero
}
init?(rawValue: Int) {
switch rawValue {
case -1: self = .neg
case 0: self = .zero
case 1: self = .foo
case 2: self = .bar
case 3: self = .baz
default: self = .UNRECOGNIZED(rawValue)
}
}
var rawValue: Int {
switch self {
case .neg: return -1
case .zero: return 0
case .foo: return 1
case .bar: return 2
case .baz: return 3
case .UNRECOGNIZED(let i): return i
}
}
}
struct NestedMessage {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
/// The field name "b" fails to compile in proto1 because it conflicts with
/// a local variable named "b" in one of the generated methods. Doh.
/// This file needs to compile in proto1 to test backwards-compatibility.
var bb: Int32 = 0
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
init() {}
fileprivate var _storage = _StorageClass.defaultInstance
}
#if swift(>=4.2)
extension Proto3ArenaUnittest_TestAllTypes.NestedEnum: CaseIterable {
// The compiler won't synthesize support with the UNRECOGNIZED case.
static var allCases: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] = [
.zero,
.foo,
.bar,
.baz,
.neg,
]
}
#endif // swift(>=4.2)
struct Proto3ArenaUnittest_TestPackedTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var packedInt32: [Int32] = []
var packedInt64: [Int64] = []
var packedUint32: [UInt32] = []
var packedUint64: [UInt64] = []
var packedSint32: [Int32] = []
var packedSint64: [Int64] = []
var packedFixed32: [UInt32] = []
var packedFixed64: [UInt64] = []
var packedSfixed32: [Int32] = []
var packedSfixed64: [Int64] = []
var packedFloat: [Float] = []
var packedDouble: [Double] = []
var packedBool: [Bool] = []
var packedEnum: [Proto3ArenaUnittest_ForeignEnum] = []
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
/// Explicitly set packed to false
struct Proto3ArenaUnittest_TestUnpackedTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var repeatedInt32: [Int32] = []
var repeatedInt64: [Int64] = []
var repeatedUint32: [UInt32] = []
var repeatedUint64: [UInt64] = []
var repeatedSint32: [Int32] = []
var repeatedSint64: [Int64] = []
var repeatedFixed32: [UInt32] = []
var repeatedFixed64: [UInt64] = []
var repeatedSfixed32: [Int32] = []
var repeatedSfixed64: [Int64] = []
var repeatedFloat: [Float] = []
var repeatedDouble: [Double] = []
var repeatedBool: [Bool] = []
var repeatedNestedEnum: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] = []
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
/// This proto includes a recusively nested message.
struct Proto3ArenaUnittest_NestedTestAllTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var child: Proto3ArenaUnittest_NestedTestAllTypes {
get {return _storage._child ?? Proto3ArenaUnittest_NestedTestAllTypes()}
set {_uniqueStorage()._child = newValue}
}
/// Returns true if `child` has been explicitly set.
var hasChild: Bool {return _storage._child != nil}
/// Clears the value of `child`. Subsequent reads from it will return its default value.
mutating func clearChild() {_uniqueStorage()._child = nil}
var payload: Proto3ArenaUnittest_TestAllTypes {
get {return _storage._payload ?? Proto3ArenaUnittest_TestAllTypes()}
set {_uniqueStorage()._payload = newValue}
}
/// Returns true if `payload` has been explicitly set.
var hasPayload: Bool {return _storage._payload != nil}
/// Clears the value of `payload`. Subsequent reads from it will return its default value.
mutating func clearPayload() {_uniqueStorage()._payload = nil}
var repeatedChild: [Proto3ArenaUnittest_NestedTestAllTypes] {
get {return _storage._repeatedChild}
set {_uniqueStorage()._repeatedChild = newValue}
}
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
fileprivate var _storage = _StorageClass.defaultInstance
}
/// Define these after TestAllTypes to make sure the compiler can handle
/// that.
struct Proto3ArenaUnittest_ForeignMessage {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var c: Int32 = 0
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
/// TestEmptyMessage is used to test behavior of unknown fields.
struct Proto3ArenaUnittest_TestEmptyMessage {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
// MARK: - Code below here is support for the SwiftProtobuf runtime.
fileprivate let _protobuf_package = "proto3_arena_unittest"
extension Proto3ArenaUnittest_ForeignEnum: SwiftProtobuf._ProtoNameProviding {
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
0: .same(proto: "FOREIGN_ZERO"),
4: .same(proto: "FOREIGN_FOO"),
5: .same(proto: "FOREIGN_BAR"),
6: .same(proto: "FOREIGN_BAZ"),
]
}
extension Proto3ArenaUnittest_TestAllTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestAllTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .standard(proto: "optional_int32"),
2: .standard(proto: "optional_int64"),
3: .standard(proto: "optional_uint32"),
4: .standard(proto: "optional_uint64"),
5: .standard(proto: "optional_sint32"),
6: .standard(proto: "optional_sint64"),
7: .standard(proto: "optional_fixed32"),
8: .standard(proto: "optional_fixed64"),
9: .standard(proto: "optional_sfixed32"),
10: .standard(proto: "optional_sfixed64"),
11: .standard(proto: "optional_float"),
12: .standard(proto: "optional_double"),
13: .standard(proto: "optional_bool"),
14: .standard(proto: "optional_string"),
15: .standard(proto: "optional_bytes"),
18: .standard(proto: "optional_nested_message"),
19: .standard(proto: "optional_foreign_message"),
20: .standard(proto: "optional_import_message"),
21: .standard(proto: "optional_nested_enum"),
22: .standard(proto: "optional_foreign_enum"),
24: .standard(proto: "optional_string_piece"),
25: .standard(proto: "optional_cord"),
26: .standard(proto: "optional_public_import_message"),
27: .standard(proto: "optional_lazy_message"),
115: .standard(proto: "optional_lazy_import_message"),
31: .standard(proto: "repeated_int32"),
32: .standard(proto: "repeated_int64"),
33: .standard(proto: "repeated_uint32"),
34: .standard(proto: "repeated_uint64"),
35: .standard(proto: "repeated_sint32"),
36: .standard(proto: "repeated_sint64"),
37: .standard(proto: "repeated_fixed32"),
38: .standard(proto: "repeated_fixed64"),
39: .standard(proto: "repeated_sfixed32"),
40: .standard(proto: "repeated_sfixed64"),
41: .standard(proto: "repeated_float"),
42: .standard(proto: "repeated_double"),
43: .standard(proto: "repeated_bool"),
44: .standard(proto: "repeated_string"),
45: .standard(proto: "repeated_bytes"),
48: .standard(proto: "repeated_nested_message"),
49: .standard(proto: "repeated_foreign_message"),
50: .standard(proto: "repeated_import_message"),
51: .standard(proto: "repeated_nested_enum"),
52: .standard(proto: "repeated_foreign_enum"),
54: .standard(proto: "repeated_string_piece"),
55: .standard(proto: "repeated_cord"),
57: .standard(proto: "repeated_lazy_message"),
111: .standard(proto: "oneof_uint32"),
112: .standard(proto: "oneof_nested_message"),
113: .standard(proto: "oneof_string"),
114: .standard(proto: "oneof_bytes"),
]
fileprivate class _StorageClass {
var _optionalInt32: Int32 = 0
var _optionalInt64: Int64 = 0
var _optionalUint32: UInt32 = 0
var _optionalUint64: UInt64 = 0
var _optionalSint32: Int32 = 0
var _optionalSint64: Int64 = 0
var _optionalFixed32: UInt32 = 0
var _optionalFixed64: UInt64 = 0
var _optionalSfixed32: Int32 = 0
var _optionalSfixed64: Int64 = 0
var _optionalFloat: Float = 0
var _optionalDouble: Double = 0
var _optionalBool: Bool = false
var _optionalString: String = String()
var _optionalBytes: Data = SwiftProtobuf.Internal.emptyData
var _optionalNestedMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage? = nil
var _optionalForeignMessage: Proto3ArenaUnittest_ForeignMessage? = nil
var _optionalImportMessage: ProtobufUnittestImport_ImportMessage? = nil
var _optionalNestedEnum: Proto3ArenaUnittest_TestAllTypes.NestedEnum = .zero
var _optionalForeignEnum: Proto3ArenaUnittest_ForeignEnum = .foreignZero
var _optionalStringPiece: String = String()
var _optionalCord: String = String()
var _optionalPublicImportMessage: ProtobufUnittestImport_PublicImportMessage? = nil
var _optionalLazyMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage? = nil
var _optionalLazyImportMessage: ProtobufUnittestImport_ImportMessage? = nil
var _repeatedInt32: [Int32] = []
var _repeatedInt64: [Int64] = []
var _repeatedUint32: [UInt32] = []
var _repeatedUint64: [UInt64] = []
var _repeatedSint32: [Int32] = []
var _repeatedSint64: [Int64] = []
var _repeatedFixed32: [UInt32] = []
var _repeatedFixed64: [UInt64] = []
var _repeatedSfixed32: [Int32] = []
var _repeatedSfixed64: [Int64] = []
var _repeatedFloat: [Float] = []
var _repeatedDouble: [Double] = []
var _repeatedBool: [Bool] = []
var _repeatedString: [String] = []
var _repeatedBytes: [Data] = []
var _repeatedNestedMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] = []
var _repeatedForeignMessage: [Proto3ArenaUnittest_ForeignMessage] = []
var _repeatedImportMessage: [ProtobufUnittestImport_ImportMessage] = []
var _repeatedNestedEnum: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] = []
var _repeatedForeignEnum: [Proto3ArenaUnittest_ForeignEnum] = []
var _repeatedStringPiece: [String] = []
var _repeatedCord: [String] = []
var _repeatedLazyMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] = []
var _oneofField: Proto3ArenaUnittest_TestAllTypes.OneOf_OneofField?
static let defaultInstance = _StorageClass()
private init() {}
init(copying source: _StorageClass) {
_optionalInt32 = source._optionalInt32
_optionalInt64 = source._optionalInt64
_optionalUint32 = source._optionalUint32
_optionalUint64 = source._optionalUint64
_optionalSint32 = source._optionalSint32
_optionalSint64 = source._optionalSint64
_optionalFixed32 = source._optionalFixed32
_optionalFixed64 = source._optionalFixed64
_optionalSfixed32 = source._optionalSfixed32
_optionalSfixed64 = source._optionalSfixed64
_optionalFloat = source._optionalFloat
_optionalDouble = source._optionalDouble
_optionalBool = source._optionalBool
_optionalString = source._optionalString
_optionalBytes = source._optionalBytes
_optionalNestedMessage = source._optionalNestedMessage
_optionalForeignMessage = source._optionalForeignMessage
_optionalImportMessage = source._optionalImportMessage
_optionalNestedEnum = source._optionalNestedEnum
_optionalForeignEnum = source._optionalForeignEnum
_optionalStringPiece = source._optionalStringPiece
_optionalCord = source._optionalCord
_optionalPublicImportMessage = source._optionalPublicImportMessage
_optionalLazyMessage = source._optionalLazyMessage
_optionalLazyImportMessage = source._optionalLazyImportMessage
_repeatedInt32 = source._repeatedInt32
_repeatedInt64 = source._repeatedInt64
_repeatedUint32 = source._repeatedUint32
_repeatedUint64 = source._repeatedUint64
_repeatedSint32 = source._repeatedSint32
_repeatedSint64 = source._repeatedSint64
_repeatedFixed32 = source._repeatedFixed32
_repeatedFixed64 = source._repeatedFixed64
_repeatedSfixed32 = source._repeatedSfixed32
_repeatedSfixed64 = source._repeatedSfixed64
_repeatedFloat = source._repeatedFloat
_repeatedDouble = source._repeatedDouble
_repeatedBool = source._repeatedBool
_repeatedString = source._repeatedString
_repeatedBytes = source._repeatedBytes
_repeatedNestedMessage = source._repeatedNestedMessage
_repeatedForeignMessage = source._repeatedForeignMessage
_repeatedImportMessage = source._repeatedImportMessage
_repeatedNestedEnum = source._repeatedNestedEnum
_repeatedForeignEnum = source._repeatedForeignEnum
_repeatedStringPiece = source._repeatedStringPiece
_repeatedCord = source._repeatedCord
_repeatedLazyMessage = source._repeatedLazyMessage
_oneofField = source._oneofField
}
}
fileprivate mutating func _uniqueStorage() -> _StorageClass {
if !isKnownUniquelyReferenced(&_storage) {
_storage = _StorageClass(copying: _storage)
}
return _storage
}
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
_ = _uniqueStorage()
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularInt32Field(value: &_storage._optionalInt32)
case 2: try decoder.decodeSingularInt64Field(value: &_storage._optionalInt64)
case 3: try decoder.decodeSingularUInt32Field(value: &_storage._optionalUint32)
case 4: try decoder.decodeSingularUInt64Field(value: &_storage._optionalUint64)
case 5: try decoder.decodeSingularSInt32Field(value: &_storage._optionalSint32)
case 6: try decoder.decodeSingularSInt64Field(value: &_storage._optionalSint64)
case 7: try decoder.decodeSingularFixed32Field(value: &_storage._optionalFixed32)
case 8: try decoder.decodeSingularFixed64Field(value: &_storage._optionalFixed64)
case 9: try decoder.decodeSingularSFixed32Field(value: &_storage._optionalSfixed32)
case 10: try decoder.decodeSingularSFixed64Field(value: &_storage._optionalSfixed64)
case 11: try decoder.decodeSingularFloatField(value: &_storage._optionalFloat)
case 12: try decoder.decodeSingularDoubleField(value: &_storage._optionalDouble)
case 13: try decoder.decodeSingularBoolField(value: &_storage._optionalBool)
case 14: try decoder.decodeSingularStringField(value: &_storage._optionalString)
case 15: try decoder.decodeSingularBytesField(value: &_storage._optionalBytes)
case 18: try decoder.decodeSingularMessageField(value: &_storage._optionalNestedMessage)
case 19: try decoder.decodeSingularMessageField(value: &_storage._optionalForeignMessage)
case 20: try decoder.decodeSingularMessageField(value: &_storage._optionalImportMessage)
case 21: try decoder.decodeSingularEnumField(value: &_storage._optionalNestedEnum)
case 22: try decoder.decodeSingularEnumField(value: &_storage._optionalForeignEnum)
case 24: try decoder.decodeSingularStringField(value: &_storage._optionalStringPiece)
case 25: try decoder.decodeSingularStringField(value: &_storage._optionalCord)
case 26: try decoder.decodeSingularMessageField(value: &_storage._optionalPublicImportMessage)
case 27: try decoder.decodeSingularMessageField(value: &_storage._optionalLazyMessage)
case 31: try decoder.decodeRepeatedInt32Field(value: &_storage._repeatedInt32)
case 32: try decoder.decodeRepeatedInt64Field(value: &_storage._repeatedInt64)
case 33: try decoder.decodeRepeatedUInt32Field(value: &_storage._repeatedUint32)
case 34: try decoder.decodeRepeatedUInt64Field(value: &_storage._repeatedUint64)
case 35: try decoder.decodeRepeatedSInt32Field(value: &_storage._repeatedSint32)
case 36: try decoder.decodeRepeatedSInt64Field(value: &_storage._repeatedSint64)
case 37: try decoder.decodeRepeatedFixed32Field(value: &_storage._repeatedFixed32)
case 38: try decoder.decodeRepeatedFixed64Field(value: &_storage._repeatedFixed64)
case 39: try decoder.decodeRepeatedSFixed32Field(value: &_storage._repeatedSfixed32)
case 40: try decoder.decodeRepeatedSFixed64Field(value: &_storage._repeatedSfixed64)
case 41: try decoder.decodeRepeatedFloatField(value: &_storage._repeatedFloat)
case 42: try decoder.decodeRepeatedDoubleField(value: &_storage._repeatedDouble)
case 43: try decoder.decodeRepeatedBoolField(value: &_storage._repeatedBool)
case 44: try decoder.decodeRepeatedStringField(value: &_storage._repeatedString)
case 45: try decoder.decodeRepeatedBytesField(value: &_storage._repeatedBytes)
case 48: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedNestedMessage)
case 49: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedForeignMessage)
case 50: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedImportMessage)
case 51: try decoder.decodeRepeatedEnumField(value: &_storage._repeatedNestedEnum)
case 52: try decoder.decodeRepeatedEnumField(value: &_storage._repeatedForeignEnum)
case 54: try decoder.decodeRepeatedStringField(value: &_storage._repeatedStringPiece)
case 55: try decoder.decodeRepeatedStringField(value: &_storage._repeatedCord)
case 57: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedLazyMessage)
case 111:
if _storage._oneofField != nil {try decoder.handleConflictingOneOf()}
var v: UInt32?
try decoder.decodeSingularUInt32Field(value: &v)
if let v = v {_storage._oneofField = .oneofUint32(v)}
case 112:
var v: Proto3ArenaUnittest_TestAllTypes.NestedMessage?
if let current = _storage._oneofField {
try decoder.handleConflictingOneOf()
if case .oneofNestedMessage(let m) = current {v = m}
}
try decoder.decodeSingularMessageField(value: &v)
if let v = v {_storage._oneofField = .oneofNestedMessage(v)}
case 113:
if _storage._oneofField != nil {try decoder.handleConflictingOneOf()}
var v: String?
try decoder.decodeSingularStringField(value: &v)
if let v = v {_storage._oneofField = .oneofString(v)}
case 114:
if _storage._oneofField != nil {try decoder.handleConflictingOneOf()}
var v: Data?
try decoder.decodeSingularBytesField(value: &v)
if let v = v {_storage._oneofField = .oneofBytes(v)}
case 115: try decoder.decodeSingularMessageField(value: &_storage._optionalLazyImportMessage)
default: break
}
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
if _storage._optionalInt32 != 0 {
try visitor.visitSingularInt32Field(value: _storage._optionalInt32, fieldNumber: 1)
}
if _storage._optionalInt64 != 0 {
try visitor.visitSingularInt64Field(value: _storage._optionalInt64, fieldNumber: 2)
}
if _storage._optionalUint32 != 0 {
try visitor.visitSingularUInt32Field(value: _storage._optionalUint32, fieldNumber: 3)
}
if _storage._optionalUint64 != 0 {
try visitor.visitSingularUInt64Field(value: _storage._optionalUint64, fieldNumber: 4)
}
if _storage._optionalSint32 != 0 {
try visitor.visitSingularSInt32Field(value: _storage._optionalSint32, fieldNumber: 5)
}
if _storage._optionalSint64 != 0 {
try visitor.visitSingularSInt64Field(value: _storage._optionalSint64, fieldNumber: 6)
}
if _storage._optionalFixed32 != 0 {
try visitor.visitSingularFixed32Field(value: _storage._optionalFixed32, fieldNumber: 7)
}
if _storage._optionalFixed64 != 0 {
try visitor.visitSingularFixed64Field(value: _storage._optionalFixed64, fieldNumber: 8)
}
if _storage._optionalSfixed32 != 0 {
try visitor.visitSingularSFixed32Field(value: _storage._optionalSfixed32, fieldNumber: 9)
}
if _storage._optionalSfixed64 != 0 {
try visitor.visitSingularSFixed64Field(value: _storage._optionalSfixed64, fieldNumber: 10)
}
if _storage._optionalFloat != 0 {
try visitor.visitSingularFloatField(value: _storage._optionalFloat, fieldNumber: 11)
}
if _storage._optionalDouble != 0 {
try visitor.visitSingularDoubleField(value: _storage._optionalDouble, fieldNumber: 12)
}
if _storage._optionalBool != false {
try visitor.visitSingularBoolField(value: _storage._optionalBool, fieldNumber: 13)
}
if !_storage._optionalString.isEmpty {
try visitor.visitSingularStringField(value: _storage._optionalString, fieldNumber: 14)
}
if !_storage._optionalBytes.isEmpty {
try visitor.visitSingularBytesField(value: _storage._optionalBytes, fieldNumber: 15)
}
if let v = _storage._optionalNestedMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 18)
}
if let v = _storage._optionalForeignMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 19)
}
if let v = _storage._optionalImportMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 20)
}
if _storage._optionalNestedEnum != .zero {
try visitor.visitSingularEnumField(value: _storage._optionalNestedEnum, fieldNumber: 21)
}
if _storage._optionalForeignEnum != .foreignZero {
try visitor.visitSingularEnumField(value: _storage._optionalForeignEnum, fieldNumber: 22)
}
if !_storage._optionalStringPiece.isEmpty {
try visitor.visitSingularStringField(value: _storage._optionalStringPiece, fieldNumber: 24)
}
if !_storage._optionalCord.isEmpty {
try visitor.visitSingularStringField(value: _storage._optionalCord, fieldNumber: 25)
}
if let v = _storage._optionalPublicImportMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 26)
}
if let v = _storage._optionalLazyMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 27)
}
if !_storage._repeatedInt32.isEmpty {
try visitor.visitPackedInt32Field(value: _storage._repeatedInt32, fieldNumber: 31)
}
if !_storage._repeatedInt64.isEmpty {
try visitor.visitPackedInt64Field(value: _storage._repeatedInt64, fieldNumber: 32)
}
if !_storage._repeatedUint32.isEmpty {
try visitor.visitPackedUInt32Field(value: _storage._repeatedUint32, fieldNumber: 33)
}
if !_storage._repeatedUint64.isEmpty {
try visitor.visitPackedUInt64Field(value: _storage._repeatedUint64, fieldNumber: 34)
}
if !_storage._repeatedSint32.isEmpty {
try visitor.visitPackedSInt32Field(value: _storage._repeatedSint32, fieldNumber: 35)
}
if !_storage._repeatedSint64.isEmpty {
try visitor.visitPackedSInt64Field(value: _storage._repeatedSint64, fieldNumber: 36)
}
if !_storage._repeatedFixed32.isEmpty {
try visitor.visitPackedFixed32Field(value: _storage._repeatedFixed32, fieldNumber: 37)
}
if !_storage._repeatedFixed64.isEmpty {
try visitor.visitPackedFixed64Field(value: _storage._repeatedFixed64, fieldNumber: 38)
}
if !_storage._repeatedSfixed32.isEmpty {
try visitor.visitPackedSFixed32Field(value: _storage._repeatedSfixed32, fieldNumber: 39)
}
if !_storage._repeatedSfixed64.isEmpty {
try visitor.visitPackedSFixed64Field(value: _storage._repeatedSfixed64, fieldNumber: 40)
}
if !_storage._repeatedFloat.isEmpty {
try visitor.visitPackedFloatField(value: _storage._repeatedFloat, fieldNumber: 41)
}
if !_storage._repeatedDouble.isEmpty {
try visitor.visitPackedDoubleField(value: _storage._repeatedDouble, fieldNumber: 42)
}
if !_storage._repeatedBool.isEmpty {
try visitor.visitPackedBoolField(value: _storage._repeatedBool, fieldNumber: 43)
}
if !_storage._repeatedString.isEmpty {
try visitor.visitRepeatedStringField(value: _storage._repeatedString, fieldNumber: 44)
}
if !_storage._repeatedBytes.isEmpty {
try visitor.visitRepeatedBytesField(value: _storage._repeatedBytes, fieldNumber: 45)
}
if !_storage._repeatedNestedMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedNestedMessage, fieldNumber: 48)
}
if !_storage._repeatedForeignMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedForeignMessage, fieldNumber: 49)
}
if !_storage._repeatedImportMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedImportMessage, fieldNumber: 50)
}
if !_storage._repeatedNestedEnum.isEmpty {
try visitor.visitPackedEnumField(value: _storage._repeatedNestedEnum, fieldNumber: 51)
}
if !_storage._repeatedForeignEnum.isEmpty {
try visitor.visitPackedEnumField(value: _storage._repeatedForeignEnum, fieldNumber: 52)
}
if !_storage._repeatedStringPiece.isEmpty {
try visitor.visitRepeatedStringField(value: _storage._repeatedStringPiece, fieldNumber: 54)
}
if !_storage._repeatedCord.isEmpty {
try visitor.visitRepeatedStringField(value: _storage._repeatedCord, fieldNumber: 55)
}
if !_storage._repeatedLazyMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedLazyMessage, fieldNumber: 57)
}
switch _storage._oneofField {
case .oneofUint32(let v)?:
try visitor.visitSingularUInt32Field(value: v, fieldNumber: 111)
case .oneofNestedMessage(let v)?:
try visitor.visitSingularMessageField(value: v, fieldNumber: 112)
case .oneofString(let v)?:
try visitor.visitSingularStringField(value: v, fieldNumber: 113)
case .oneofBytes(let v)?:
try visitor.visitSingularBytesField(value: v, fieldNumber: 114)
case nil: break
}
if let v = _storage._optionalLazyImportMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 115)
}
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestAllTypes, rhs: Proto3ArenaUnittest_TestAllTypes) -> Bool {
if lhs._storage !== rhs._storage {
let storagesAreEqual: Bool = withExtendedLifetime((lhs._storage, rhs._storage)) { (_args: (_StorageClass, _StorageClass)) in
let _storage = _args.0
let rhs_storage = _args.1
if _storage._optionalInt32 != rhs_storage._optionalInt32 {return false}
if _storage._optionalInt64 != rhs_storage._optionalInt64 {return false}
if _storage._optionalUint32 != rhs_storage._optionalUint32 {return false}
if _storage._optionalUint64 != rhs_storage._optionalUint64 {return false}
if _storage._optionalSint32 != rhs_storage._optionalSint32 {return false}
if _storage._optionalSint64 != rhs_storage._optionalSint64 {return false}
if _storage._optionalFixed32 != rhs_storage._optionalFixed32 {return false}
if _storage._optionalFixed64 != rhs_storage._optionalFixed64 {return false}
if _storage._optionalSfixed32 != rhs_storage._optionalSfixed32 {return false}
if _storage._optionalSfixed64 != rhs_storage._optionalSfixed64 {return false}
if _storage._optionalFloat != rhs_storage._optionalFloat {return false}
if _storage._optionalDouble != rhs_storage._optionalDouble {return false}
if _storage._optionalBool != rhs_storage._optionalBool {return false}
if _storage._optionalString != rhs_storage._optionalString {return false}
if _storage._optionalBytes != rhs_storage._optionalBytes {return false}
if _storage._optionalNestedMessage != rhs_storage._optionalNestedMessage {return false}
if _storage._optionalForeignMessage != rhs_storage._optionalForeignMessage {return false}
if _storage._optionalImportMessage != rhs_storage._optionalImportMessage {return false}
if _storage._optionalNestedEnum != rhs_storage._optionalNestedEnum {return false}
if _storage._optionalForeignEnum != rhs_storage._optionalForeignEnum {return false}
if _storage._optionalStringPiece != rhs_storage._optionalStringPiece {return false}
if _storage._optionalCord != rhs_storage._optionalCord {return false}
if _storage._optionalPublicImportMessage != rhs_storage._optionalPublicImportMessage {return false}
if _storage._optionalLazyMessage != rhs_storage._optionalLazyMessage {return false}
if _storage._optionalLazyImportMessage != rhs_storage._optionalLazyImportMessage {return false}
if _storage._repeatedInt32 != rhs_storage._repeatedInt32 {return false}
if _storage._repeatedInt64 != rhs_storage._repeatedInt64 {return false}
if _storage._repeatedUint32 != rhs_storage._repeatedUint32 {return false}
if _storage._repeatedUint64 != rhs_storage._repeatedUint64 {return false}
if _storage._repeatedSint32 != rhs_storage._repeatedSint32 {return false}
if _storage._repeatedSint64 != rhs_storage._repeatedSint64 {return false}
if _storage._repeatedFixed32 != rhs_storage._repeatedFixed32 {return false}
if _storage._repeatedFixed64 != rhs_storage._repeatedFixed64 {return false}
if _storage._repeatedSfixed32 != rhs_storage._repeatedSfixed32 {return false}
if _storage._repeatedSfixed64 != rhs_storage._repeatedSfixed64 {return false}
if _storage._repeatedFloat != rhs_storage._repeatedFloat {return false}
if _storage._repeatedDouble != rhs_storage._repeatedDouble {return false}
if _storage._repeatedBool != rhs_storage._repeatedBool {return false}
if _storage._repeatedString != rhs_storage._repeatedString {return false}
if _storage._repeatedBytes != rhs_storage._repeatedBytes {return false}
if _storage._repeatedNestedMessage != rhs_storage._repeatedNestedMessage {return false}
if _storage._repeatedForeignMessage != rhs_storage._repeatedForeignMessage {return false}
if _storage._repeatedImportMessage != rhs_storage._repeatedImportMessage {return false}
if _storage._repeatedNestedEnum != rhs_storage._repeatedNestedEnum {return false}
if _storage._repeatedForeignEnum != rhs_storage._repeatedForeignEnum {return false}
if _storage._repeatedStringPiece != rhs_storage._repeatedStringPiece {return false}
if _storage._repeatedCord != rhs_storage._repeatedCord {return false}
if _storage._repeatedLazyMessage != rhs_storage._repeatedLazyMessage {return false}
if _storage._oneofField != rhs_storage._oneofField {return false}
return true
}
if !storagesAreEqual {return false}
}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestAllTypes.NestedEnum: SwiftProtobuf._ProtoNameProviding {
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
-1: .same(proto: "NEG"),
0: .same(proto: "ZERO"),
1: .same(proto: "FOO"),
2: .same(proto: "BAR"),
3: .same(proto: "BAZ"),
]
}
extension Proto3ArenaUnittest_TestAllTypes.NestedMessage: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = Proto3ArenaUnittest_TestAllTypes.protoMessageName + ".NestedMessage"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .same(proto: "bb"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularInt32Field(value: &self.bb)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if self.bb != 0 {
try visitor.visitSingularInt32Field(value: self.bb, fieldNumber: 1)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestAllTypes.NestedMessage, rhs: Proto3ArenaUnittest_TestAllTypes.NestedMessage) -> Bool {
if lhs.bb != rhs.bb {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestPackedTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestPackedTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
90: .standard(proto: "packed_int32"),
91: .standard(proto: "packed_int64"),
92: .standard(proto: "packed_uint32"),
93: .standard(proto: "packed_uint64"),
94: .standard(proto: "packed_sint32"),
95: .standard(proto: "packed_sint64"),
96: .standard(proto: "packed_fixed32"),
97: .standard(proto: "packed_fixed64"),
98: .standard(proto: "packed_sfixed32"),
99: .standard(proto: "packed_sfixed64"),
100: .standard(proto: "packed_float"),
101: .standard(proto: "packed_double"),
102: .standard(proto: "packed_bool"),
103: .standard(proto: "packed_enum"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 90: try decoder.decodeRepeatedInt32Field(value: &self.packedInt32)
case 91: try decoder.decodeRepeatedInt64Field(value: &self.packedInt64)
case 92: try decoder.decodeRepeatedUInt32Field(value: &self.packedUint32)
case 93: try decoder.decodeRepeatedUInt64Field(value: &self.packedUint64)
case 94: try decoder.decodeRepeatedSInt32Field(value: &self.packedSint32)
case 95: try decoder.decodeRepeatedSInt64Field(value: &self.packedSint64)
case 96: try decoder.decodeRepeatedFixed32Field(value: &self.packedFixed32)
case 97: try decoder.decodeRepeatedFixed64Field(value: &self.packedFixed64)
case 98: try decoder.decodeRepeatedSFixed32Field(value: &self.packedSfixed32)
case 99: try decoder.decodeRepeatedSFixed64Field(value: &self.packedSfixed64)
case 100: try decoder.decodeRepeatedFloatField(value: &self.packedFloat)
case 101: try decoder.decodeRepeatedDoubleField(value: &self.packedDouble)
case 102: try decoder.decodeRepeatedBoolField(value: &self.packedBool)
case 103: try decoder.decodeRepeatedEnumField(value: &self.packedEnum)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if !self.packedInt32.isEmpty {
try visitor.visitPackedInt32Field(value: self.packedInt32, fieldNumber: 90)
}
if !self.packedInt64.isEmpty {
try visitor.visitPackedInt64Field(value: self.packedInt64, fieldNumber: 91)
}
if !self.packedUint32.isEmpty {
try visitor.visitPackedUInt32Field(value: self.packedUint32, fieldNumber: 92)
}
if !self.packedUint64.isEmpty {
try visitor.visitPackedUInt64Field(value: self.packedUint64, fieldNumber: 93)
}
if !self.packedSint32.isEmpty {
try visitor.visitPackedSInt32Field(value: self.packedSint32, fieldNumber: 94)
}
if !self.packedSint64.isEmpty {
try visitor.visitPackedSInt64Field(value: self.packedSint64, fieldNumber: 95)
}
if !self.packedFixed32.isEmpty {
try visitor.visitPackedFixed32Field(value: self.packedFixed32, fieldNumber: 96)
}
if !self.packedFixed64.isEmpty {
try visitor.visitPackedFixed64Field(value: self.packedFixed64, fieldNumber: 97)
}
if !self.packedSfixed32.isEmpty {
try visitor.visitPackedSFixed32Field(value: self.packedSfixed32, fieldNumber: 98)
}
if !self.packedSfixed64.isEmpty {
try visitor.visitPackedSFixed64Field(value: self.packedSfixed64, fieldNumber: 99)
}
if !self.packedFloat.isEmpty {
try visitor.visitPackedFloatField(value: self.packedFloat, fieldNumber: 100)
}
if !self.packedDouble.isEmpty {
try visitor.visitPackedDoubleField(value: self.packedDouble, fieldNumber: 101)
}
if !self.packedBool.isEmpty {
try visitor.visitPackedBoolField(value: self.packedBool, fieldNumber: 102)
}
if !self.packedEnum.isEmpty {
try visitor.visitPackedEnumField(value: self.packedEnum, fieldNumber: 103)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestPackedTypes, rhs: Proto3ArenaUnittest_TestPackedTypes) -> Bool {
if lhs.packedInt32 != rhs.packedInt32 {return false}
if lhs.packedInt64 != rhs.packedInt64 {return false}
if lhs.packedUint32 != rhs.packedUint32 {return false}
if lhs.packedUint64 != rhs.packedUint64 {return false}
if lhs.packedSint32 != rhs.packedSint32 {return false}
if lhs.packedSint64 != rhs.packedSint64 {return false}
if lhs.packedFixed32 != rhs.packedFixed32 {return false}
if lhs.packedFixed64 != rhs.packedFixed64 {return false}
if lhs.packedSfixed32 != rhs.packedSfixed32 {return false}
if lhs.packedSfixed64 != rhs.packedSfixed64 {return false}
if lhs.packedFloat != rhs.packedFloat {return false}
if lhs.packedDouble != rhs.packedDouble {return false}
if lhs.packedBool != rhs.packedBool {return false}
if lhs.packedEnum != rhs.packedEnum {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestUnpackedTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestUnpackedTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .standard(proto: "repeated_int32"),
2: .standard(proto: "repeated_int64"),
3: .standard(proto: "repeated_uint32"),
4: .standard(proto: "repeated_uint64"),
5: .standard(proto: "repeated_sint32"),
6: .standard(proto: "repeated_sint64"),
7: .standard(proto: "repeated_fixed32"),
8: .standard(proto: "repeated_fixed64"),
9: .standard(proto: "repeated_sfixed32"),
10: .standard(proto: "repeated_sfixed64"),
11: .standard(proto: "repeated_float"),
12: .standard(proto: "repeated_double"),
13: .standard(proto: "repeated_bool"),
14: .standard(proto: "repeated_nested_enum"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeRepeatedInt32Field(value: &self.repeatedInt32)
case 2: try decoder.decodeRepeatedInt64Field(value: &self.repeatedInt64)
case 3: try decoder.decodeRepeatedUInt32Field(value: &self.repeatedUint32)
case 4: try decoder.decodeRepeatedUInt64Field(value: &self.repeatedUint64)
case 5: try decoder.decodeRepeatedSInt32Field(value: &self.repeatedSint32)
case 6: try decoder.decodeRepeatedSInt64Field(value: &self.repeatedSint64)
case 7: try decoder.decodeRepeatedFixed32Field(value: &self.repeatedFixed32)
case 8: try decoder.decodeRepeatedFixed64Field(value: &self.repeatedFixed64)
case 9: try decoder.decodeRepeatedSFixed32Field(value: &self.repeatedSfixed32)
case 10: try decoder.decodeRepeatedSFixed64Field(value: &self.repeatedSfixed64)
case 11: try decoder.decodeRepeatedFloatField(value: &self.repeatedFloat)
case 12: try decoder.decodeRepeatedDoubleField(value: &self.repeatedDouble)
case 13: try decoder.decodeRepeatedBoolField(value: &self.repeatedBool)
case 14: try decoder.decodeRepeatedEnumField(value: &self.repeatedNestedEnum)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if !self.repeatedInt32.isEmpty {
try visitor.visitRepeatedInt32Field(value: self.repeatedInt32, fieldNumber: 1)
}
if !self.repeatedInt64.isEmpty {
try visitor.visitRepeatedInt64Field(value: self.repeatedInt64, fieldNumber: 2)
}
if !self.repeatedUint32.isEmpty {
try visitor.visitRepeatedUInt32Field(value: self.repeatedUint32, fieldNumber: 3)
}
if !self.repeatedUint64.isEmpty {
try visitor.visitRepeatedUInt64Field(value: self.repeatedUint64, fieldNumber: 4)
}
if !self.repeatedSint32.isEmpty {
try visitor.visitRepeatedSInt32Field(value: self.repeatedSint32, fieldNumber: 5)
}
if !self.repeatedSint64.isEmpty {
try visitor.visitRepeatedSInt64Field(value: self.repeatedSint64, fieldNumber: 6)
}
if !self.repeatedFixed32.isEmpty {
try visitor.visitRepeatedFixed32Field(value: self.repeatedFixed32, fieldNumber: 7)
}
if !self.repeatedFixed64.isEmpty {
try visitor.visitRepeatedFixed64Field(value: self.repeatedFixed64, fieldNumber: 8)
}
if !self.repeatedSfixed32.isEmpty {
try visitor.visitRepeatedSFixed32Field(value: self.repeatedSfixed32, fieldNumber: 9)
}
if !self.repeatedSfixed64.isEmpty {
try visitor.visitRepeatedSFixed64Field(value: self.repeatedSfixed64, fieldNumber: 10)
}
if !self.repeatedFloat.isEmpty {
try visitor.visitRepeatedFloatField(value: self.repeatedFloat, fieldNumber: 11)
}
if !self.repeatedDouble.isEmpty {
try visitor.visitRepeatedDoubleField(value: self.repeatedDouble, fieldNumber: 12)
}
if !self.repeatedBool.isEmpty {
try visitor.visitRepeatedBoolField(value: self.repeatedBool, fieldNumber: 13)
}
if !self.repeatedNestedEnum.isEmpty {
try visitor.visitRepeatedEnumField(value: self.repeatedNestedEnum, fieldNumber: 14)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestUnpackedTypes, rhs: Proto3ArenaUnittest_TestUnpackedTypes) -> Bool {
if lhs.repeatedInt32 != rhs.repeatedInt32 {return false}
if lhs.repeatedInt64 != rhs.repeatedInt64 {return false}
if lhs.repeatedUint32 != rhs.repeatedUint32 {return false}
if lhs.repeatedUint64 != rhs.repeatedUint64 {return false}
if lhs.repeatedSint32 != rhs.repeatedSint32 {return false}
if lhs.repeatedSint64 != rhs.repeatedSint64 {return false}
if lhs.repeatedFixed32 != rhs.repeatedFixed32 {return false}
if lhs.repeatedFixed64 != rhs.repeatedFixed64 {return false}
if lhs.repeatedSfixed32 != rhs.repeatedSfixed32 {return false}
if lhs.repeatedSfixed64 != rhs.repeatedSfixed64 {return false}
if lhs.repeatedFloat != rhs.repeatedFloat {return false}
if lhs.repeatedDouble != rhs.repeatedDouble {return false}
if lhs.repeatedBool != rhs.repeatedBool {return false}
if lhs.repeatedNestedEnum != rhs.repeatedNestedEnum {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_NestedTestAllTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".NestedTestAllTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .same(proto: "child"),
2: .same(proto: "payload"),
3: .standard(proto: "repeated_child"),
]
fileprivate class _StorageClass {
var _child: Proto3ArenaUnittest_NestedTestAllTypes? = nil
var _payload: Proto3ArenaUnittest_TestAllTypes? = nil
var _repeatedChild: [Proto3ArenaUnittest_NestedTestAllTypes] = []
static let defaultInstance = _StorageClass()
private init() {}
init(copying source: _StorageClass) {
_child = source._child
_payload = source._payload
_repeatedChild = source._repeatedChild
}
}
fileprivate mutating func _uniqueStorage() -> _StorageClass {
if !isKnownUniquelyReferenced(&_storage) {
_storage = _StorageClass(copying: _storage)
}
return _storage
}
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
_ = _uniqueStorage()
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularMessageField(value: &_storage._child)
case 2: try decoder.decodeSingularMessageField(value: &_storage._payload)
case 3: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedChild)
default: break
}
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
if let v = _storage._child {
try visitor.visitSingularMessageField(value: v, fieldNumber: 1)
}
if let v = _storage._payload {
try visitor.visitSingularMessageField(value: v, fieldNumber: 2)
}
if !_storage._repeatedChild.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedChild, fieldNumber: 3)
}
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_NestedTestAllTypes, rhs: Proto3ArenaUnittest_NestedTestAllTypes) -> Bool {
if lhs._storage !== rhs._storage {
let storagesAreEqual: Bool = withExtendedLifetime((lhs._storage, rhs._storage)) { (_args: (_StorageClass, _StorageClass)) in
let _storage = _args.0
let rhs_storage = _args.1
if _storage._child != rhs_storage._child {return false}
if _storage._payload != rhs_storage._payload {return false}
if _storage._repeatedChild != rhs_storage._repeatedChild {return false}
return true
}
if !storagesAreEqual {return false}
}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_ForeignMessage: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".ForeignMessage"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .same(proto: "c"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularInt32Field(value: &self.c)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if self.c != 0 {
try visitor.visitSingularInt32Field(value: self.c, fieldNumber: 1)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_ForeignMessage, rhs: Proto3ArenaUnittest_ForeignMessage) -> Bool {
if lhs.c != rhs.c {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestEmptyMessage: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestEmptyMessage"
static let _protobuf_nameMap = SwiftProtobuf._NameMap()
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let _ = try decoder.nextFieldNumber() {
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestEmptyMessage, rhs: Proto3ArenaUnittest_TestEmptyMessage) -> Bool {
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
| {
"pile_set_name": "Github"
} |
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As an officially licensed and endorsed product, you get the full spectrum of courses, teams, and drivers you'd expect from watching Formula One on TV or following it in the trade press. | {
"pile_set_name": "Pile-CC"
} |
Isla Damas
Isla Damas, or Damas Island, is a small (6 km²) island in Costa Rica in the vicinity of Quepos. It is particularly noted for its estuaries lined with mangroves. Fauna on the island include white-faced monkeys, sloths, green iguanas, crocodiles, spectacled caimans, boas, crab-eating raccoons and silky anteaters, as well as crabs and numerous bird species, such as: heron, pelicans. Boat and kayak tours through the island's estuaries are popular excursions with tourists staying in Quepos, Manuel Antonio National Park, or Jacó.
Gallery
Damas | {
"pile_set_name": "Wikipedia (en)"
} |
Raigam Tele'es Best Teledrama Art Director Award
The Raigam Tele'es Best Teledrama Art Director Award is a Raigam Tele'es awared presented annually in Sri Lanka by the Kingdom of Raigam companies for the best Sri Lankan art director of the year in television.
The award was first given in 2005.
Award list in each year
References
Category:Performing arts awards
Category:Raigam Tele'es | {
"pile_set_name": "Wikipedia (en)"
} |
Detection and ecology of leptospirosis in Iowa wildlife.
To gain additional information on the extent of leptospirosis in wildlife following a human outbreak in Iowa, wild mammals and lower forms of life were collected. Isolation, darkfield microscopic, serologic and pathologic procedures were used to identify past or present evidence of leptospiral infection. Leptospires were isolated from 7 of 75 (9%) mammals. Serotype grippotyphosa was isolated from three raccoons (procyon lotor) and one Western Harvest Mouse (Reithrodontomys megalotis). Serotype ballum was isolated from three opossums (Didelphis marsupialis). Leptospires, unidentified to date, were isolated from frog (Rana pipiens) kidneys. Other positive serologic and pathologic tests gave evidence of infection or previous infection. Utilization of Darkfield microscopic and silver staining techniques did not detect all cases of leptospiral infection. Macroscopic and microscopic serologic methods failed to identify evidence of leptospirosis in all mammals from which leptospires were isolated. Pathologic lesions could only be considered presumptive evidence for leptospirosis. These findings indicate that detection of leptospirosis in wildlife cannot be limited to a single diagnostic test. A combination of diagnostic procedures and clinical evaluation is necessary. Although serotype pomona was implicated as the predominant infecting leptospire in the human cases and domestic animals and was isolated from water at a swimming site, only serotypes grippotyphosa, ballum and ICF (frog isolate) were isolated from wild mammals and lower forms of life in the same vicinity. | {
"pile_set_name": "PubMed Abstracts"
} |
As your personal Realtor, I will focus on your complete satisfaction. I am fully committed to meeting your real estate needs. Whether it''s finding the right home, or helping you get the most out of selling your home, I am happy to help. I will listen to your needs and will work hard to meet them. I believe communication is key in meeting your goals and building our relationship.
Please use my Website, www.StacySchwenk.com to find a wide range of information, including Local Services, finding a lender, finding a home, or learning how to prepare your home for sale. If I can be of service, please feel free to contact me at StacySchwenk@remax.net, or call 269-503-0204. Visit me on Facebook https://www.facebook.com/StacySchwenkREMAX/ and Like my Page!Giving Back:In addition to many local donations, I donate to Children's Miracle Network each time I sell a home. This money stays in Michigan to help local children's hospitals.
My Success Depends on the Satisfaction of My Clients and Customers. My satisfied clients are my best resource for new business. In this very competitive business of real estate, service makes the difference. If you are considering a real estate professional, please give me the opportunity to earn your business as well. I am confident you will be very happy! I am a college graduate, and have my Bachelor''s Degree in Business Administration. I grew up in the Leonidas/Colon area.Professional Designations: | {
"pile_set_name": "Pile-CC"
} |
Ca2+- and voltage-dependent K+ conductance in dispersed parathyroid cells.
The membrane ionic conductances of dispersed parathyroid cells kept in primary culture were studied using the "whole-cell" and "inside-out excised patch" variants of the patch-clamp technique. The major component of the total current was a voltage-dependent outward K+ current without an appreciable inward current. The amplitude of the K+ current was markedly reduced when free internal Ca2+ was buffered by addition of 10 mM EGTA. Recordings of single-channel current in excised membrane patches revealed the presence of K+ channels with large unitary conductance (200 pS in symmetrical 130 mM K+ solutions) which were also activated by depolarization when internal Ca2+ concentration was about 10(-5)-10(-6) M. At any membrane voltage these channels were closed most of the time at internal Ca2+ concentrations lower than 10(-10) M. These results demonstrate the existence of a Ca2+- and voltage-dependent K+ permeability in parathyroid cells which may participate in the unusual membrane potential changes induced by alterations of external Ca2+ and, possibly, in the regulation of parathormone secretion. | {
"pile_set_name": "PubMed Abstracts"
} |
Philip Evans (headmaster)
Dr Ian Philip Evans OBE FRSC (born 1948) is a British educationalist and a former Headmaster of Bedford School.
Biography
Born on 2 May 1948 and educated in North Wales at Ruabon Boys Grammar school, Dr Philip Evans read Natural Sciences at Churchill College, Cambridge and obtained a doctorate in inorganic chemistry from Imperial College London, working in the laboratory of Professor Sir Geoffrey Wilkinson. He taught chemistry at St Paul's School, London and, in 1991, he was appointed as Headmaster of Bedford School, a position which he held until the summer of 2008. He was also appointed as a government advisor on education, from which post he retired in 1999, and was subsequently awarded an OBE for his work. He is currently an appointed member of the council of the Royal Society of Chemistry.
Publications
I. P. Evans, A. Spencer, & G. Wilkinson "Dichlorotetrakis(dimethyl sulfoxide)ruthenium(II) and its use as a source material for new ruthenium(II) complexes" Jrnl. Chem. Soc. Dalton Trans. (1973) 204-209
References
[[Category:Welsh schoolteachers]
Category:Alumni of Churchill College, Cambridge
Category:Living people
Category:1948 births
Category:Alumni of Imperial College London
Category:Headmasters of Bedford School
Category:Officers of the Order of the British Empire
Category:Fellows of the Royal Society of Chemistry | {
"pile_set_name": "Wikipedia (en)"
} |
Description du produit
Comes with a download code. Epic 2016 album from the French metal juggernauts ... their first in 4 years, and first since relocating to New York! Includes "Stranded".
Critique
Sixième brûlot du groupe de death metal progressif français le plus épique, Magma marque d’entrée son universalité en s’éloignant des clichés collés à la peau d’un genre souvent réduit à un déluge de décibels manquant de créativité. « The Shooting Star », à la rythmique plombée parfaitement assumée par le batteur virtuose Mario Duplantier, ouvre ainsi avec fracas les hostilités, dévoilant du même coup le chant posé et hautement hypnotique de son frère Joe.
Plus ouvert que ses prédécesseurs, Magma pourrait bien être, à l’instar du Black Album de Metallica, le disque qui permettra à Gojira d’accroître une base de fans déjà impressionnante et de dépasser son genre de prédilection. Une remise en question appelée par la peine vécue par les deux frères Duplantier, qui ont connu la douleur de perdre leur mère au moment même où démarrait l’enregistrement de ce nouvel opus.
L’humeur de ce dernier s’en trouverait radicalement changée, servant littéralement de catharsis. Le simple « Silveria », toujours animé par la fibre écologiste chère au groupe, réserve des parties de guitare incroyables tandis que le chant possédé et la batterie martiale de « The Cell » seront loin de déplaire aux amateurs de la première heure. Car s’il marque une rupture avec l’œuvre pré-existante de Gojira, Magma sait aussi assurer les fondamentaux, promettant de nouveaux glorieux moments de headbanging, comme sur « Pray » ou encore le furieux et libérateur « Only Pain ».
L’ouverture se matérialise surtout sur des morceaux tels que « Stranded » ou même « Magma », qu’il ne serait pas impossible de diffuser en radio. Avec Magma, Gojira fait assurément un immense pas en avant, prenant et assumant les risques, comme celui de faire reculer d’un cran le chant guttural de Joe Duplantier au profit de l’aspect mélodique d’un chant plus clair. Un pari réussi haut la main et qui place le groupe à un endroit stratégique de l’échiquier metal.
Olivier Roubin - Copyright 2017 Music Story | {
"pile_set_name": "OpenWebText2"
} |
/(-6)*2*9/132
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224/28*(-1)/4
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5/(-15)*-2*3/(-6)
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9/((-882)/35)*(-8)/10
2/7
Evaluate (1/((-4)/(-12)))/((-1)/(-1)).
3
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Evaluate ((-1)/10*2)/(52/390).
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What is (-9*(-8)/144)/((-5)/(-6))?
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What is (-11)/(((-84)/(-14))/6)?
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(1/(-39))/(((-1659)/(-126))/79)
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(-216)/(-90)*(-15)/(-4)
9
What is ((-14)/(-5))/((-3)/(135/(-18)))?
7
Calculate 126/84*4/(-6)*-7.
7
Calculate (-35)/(-14)*18/(-15).
-3
What is (2/10)/(((-72)/(-10))/9)?
1/4
Evaluate (24/(-40))/(((-9)/(-6))/1).
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What is the value of (-45)/(-18)*((-72)/(-15))/3?
4
Evaluate ((-8)/16)/(6/84).
-7
What is (-9)/((-27)/6)*(-21)/6?
-7
20/30*(-6)/8*2
-1
(-30)/(-12)*(-52)/195
-2/3
What is -5*((-12)/(-3))/(-20)?
1
(((-12)/(-9))/((-2)/(-9)))/3
2
What is (-30)/(-5)*(-16)/48?
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Evaluate ((99/11)/(-54))/(1/(-8)).
4/3
(-1)/(4/(40/5))
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Evaluate ((-65)/(-130))/(-1*(-10)/(-4)).
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8*-1*5/8
-5
What is the value of (8/(-12))/((-238)/51)?
1/7
((-132)/154)/(3/9*3)
-6/7
Calculate (4/40)/(-4*(-6)/(-60)).
-1/4
What is (-63)/(-105)*(-30)/(-2)?
9
Evaluate 4/5*6/(-12).
-2/5
6/14*(-2)/24*-4
1/7
Evaluate ((-20)/18)/(9/((-81)/6)).
5/3
What is 6/(-4)*(-24)/18?
2
What is ((-84)/90)/(-14)*-3?
-1/5
What is the value of (-1)/((-1)/(-24)*-3*-2)?
-4
What is 0/(((-210)/(-10))/7)?
0
(-141)/(-470)*15/(-12)
-3/8
((-1)/(-36)*6)/(-1)
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What is the value of (-16)/24*7/35?
-2/15
What is ((-12)/(-8))/((-5)/(-50)*3)?
5
((-4)/10)/(5/(-5)*2)
1/5
Calculate (152/(-57))/((-5)/((-60)/8)).
-4
What is the value of ((-66)/693)/(6/7)?
-1/9
Calculate -1*-5*15/(-25).
-3
Calculate (182/(-26))/(7/(-2)).
2
((-6)/(-30))/((-1)/5)
-1
(-8)/2*5/(300/(-6))
2/5
Evaluate ((-1)/((-18)/9)*-2)/(-1).
1
20/(-40)*(-8)/78*-3
-2/13
4/(-30)*45/9
-2/3
(-18)/(-12)*42/(-9)
-7
Evaluate ((-8)/28)/(2*(-1)/8).
8/7
Evaluate -2*(-3)/(-4)*(-20)/(-15).
-2
Evaluate (1*16/(-4))/((-9)/18).
8
((-12)/(-72))/((-3)/9)
-1/2
(-5)/70*-2*2
2/7
Calculate 1*(48/(-160))/(3/(-2)).
1/5
What is (((-3)/(-2))/(63/168))/10?
2/5
Evaluate ((-1)/(-2))/((-3)/12).
-2
Calculate (4/(-12))/((3/36)/1).
-4
Evaluate 4/(-8)*-5*(-6)/30.
-1/2
(-6)/18*0/(-6)
0
((6/(-3))/(2/(-4)))/2
2
Evaluate (-1)/2*8/(-2).
2
Evaluate 4/(-8)*-6*3/9.
1
Evaluate ((-27)/72)/(1*4/16).
-3/2
-1*(-12)/(-3)*-1
4
Calculate ((4/(-2))/2)/((-33)/165).
5
Evaluate 10/((-240)/3)*2.
-1/4
Calculate ((-72)/60)/((-2)/10).
6
Calculate 9/54*-7*-6.
7
What is 12/8*(-8)/30?
-2/5
Calculate (-8)/(-12)*279/434.
3/7
((-11)/(165/(-10)))/((-4)/24)
-4
Calculate ((-24)/16)/(-3*4/(-24)).
-3
1/(-6)*(-15)/20*10
5/4
What is the value of (10*10/200)/((-2)/3)?
-3/4
Calculate 36/(-3)*(-5)/15.
4
What is 6/(-5)*(-200)/120?
2
What is (48/66)/((-20)/110)?
-4
What is the value of (49/28)/(((-9)/12)/(-3))?
7
What is 0/(-3*(-24)/18)?
0
Calculate (-29)/(-29)*0/(1/1).
0
What is the value of 20/(-12)*(-2)/(15*2)?
1/9
What is the value of 5/((-70)/(-6))*1?
3/7
What is the value of 15/(-12)*2*-2?
5
Calculate ((-8)/(-48))/((-1)/((-18)/4)).
3/4
Calculate -2*7/14*(-5)/1.
5
(-1*4)/(70/(-15)*3)
2/7
What is the value of (-14)/(-24)*(-111)/(-518)?
1/8
Calculate (2/20*-2)/(9/(-27)).
3/5
What is the value of ((-10)/8)/1*324/(-81)?
5
What is the value of ((-2)/(-4))/((-7)/56)?
-4
18/162*(-6)/(-1)
2/3
Evaluate 70/7*(-2)/(-24).
5/6
1/(-6)*120/(-110)
2/11
Calculate ((119/14)/(-17))/(1/2).
-1
What is the value of ((576/(-84))/12)/((-4)/(-2))?
-2/7
48/36*((-21)/(-2))/(-7)
-2
What is -2*4/(-48)*3*6?
3
Evaluate (-6*1/2)/(-3).
1
Calculate (2/(-22))/(178/(-712)).
4/11
Calculate (-3)/((-4)/(8/2)).
3
4/(-1)*111/148
-3
What is (1*-1)/(((-25)/(-5))/(-5))?
1
Evaluate (-6)/(12/16*4/2).
-4
Evaluate (-30)/(-2)*(-132)/330.
-6
What is (0*(-3)/(-9))/(2*-1)?
0
Evaluate (-1375)/110*4/(-10).
5
What is 1/(-50)*-5*4/1?
2/5
What is the value of 55/(-11)*4/10?
-2
Calculate (0/(28/7))/1.
0
Evaluate (3/3*-1)/(-2).
1/2
What is ((-18)/(-3)*-1)/(6/(-4))?
4
What is the value of (0/1)/(-4*5/(-20))?
0
What is the value of (-3)/2*20/45*-3?
2
What is 2/((48/20)/(-6))?
-5
4*3/(-6)*6/4
-3
Calculate ((-2)/(-42)*3)/(-1).
-1/7
(-2)/8*2*-10
5
What is the value of (((-2)/3)/(-1))/(2/12)?
4
Evaluate 32/(-48)*2/34*-3.
2/17
Calculate (-1)/(-2)*(-20)/5.
-2
Calculate (1/3)/((-28)/(-24)).
2/7
Evaluate (-90)/60*(-8)/(-18).
-2/3
Calculate ((-60)/(-8))/((-63)/84).
-10
Calculate (((-4)/2)/(-6))/((-20)/(-24)).
2/5
((-1)/5*-1)/((-117)/(-65))
1/9
What is the value of ((-9)/((-135)/(-24)))/((-6)/15)?
4
What is the value of ((-25)/(-225))/(2/18*-3)?
-1/3
What is 8/20*10/6?
2/3
Calculate 2/(-8)*12*1.
-3
5/(-3)*(-5)/5
5/3
What is ((-390)/(-520))/(9/(-2))?
-1/6
2/((-6)/3*7)
-1/7
Calculate 3*4/4*(-1)/1.
-3
(27/((-135)/2))/((-9)/(-5))
-2/9
What is the value of ((-16)/52)/4*(-6)/3?
2/13
What is the value of ((-192)/(-120))/(2/5)?
4
Evaluate (-7)/2*(-20)/(-35).
-2
Evaluate 44/33*(-9)/(-15).
4/5
What is the value of 45/(-39)*12/(-30)?
6/13
Calculate 0/6*2/4.
0
Calculate ((-84)/98)/((-2)/(-21)*-3).
3
What is the value of (6/(-3*1))/((-300)/30)?
1/5
What is 2/4*((-100)/(-1))/(-10)?
-5
Calculate (-4)/(-2)*6/12.
1
(-36)/2*(-20)/(400/10)
9
Calculate (6/(-108))/((-3)/12).
2/9
Calculate -21*(80/(-15))/16.
7
Evaluate 6*4/(-540)*3.
-2/15
2*(10/(-44))/(-5)
1/11
((-4)/10)/(1*(-4)/(-20))
-2
(24/(-21))/(3/(-21))
8
Evaluate ((4/25)/(-2))/(222/370).
-2/15
Calculate (-2)/8*(-3)/6*-2.
-1/4
Calculate ((-1)/4)/(-6*14/112).
1/3
What is (-3*(-12)/(-162))/(-2)?
1/9
(17/((-34)/(-24)))/(-2)
-6
What is the value of (-3)/((26/65)/(16/60))?
-2
What is the value of ((-20)/(-25))/((-3)/15)?
-4
What is the value of 12/240*16/(-6)?
-2/15
Evaluate (9/12)/(4/32).
6
Calculate (1/1*-2)/(13/(-26)).
4
Calculate (-10)/(-8)*(-20)/45*-9.
5
Evaluate (0/(-1))/(26/26).
0
Evaluate ((-4)/(-5))/(-16*(-12)/(-480)).
-2
Calculate 2*3*10/(-15).
-4
Calculate (5/((-30)/27))/((-135)/180).
6
4/16*-3*(-3)/18
1/8
Calculate (12/14)/((-69)/(-322)).
4
Calculate 3/(12*(-10)/(-40)).
1
Calculate (2/(-5))/(7/7).
-2/5
Evaluate ((-1)/(-12))/(38/(-114)).
-1/4
What is 9*((-6)/(-75))/((-18)/(-15))?
3/5
-1*1*(-44)/(-44)
-1
What is the value of 8/4*5/240*-4?
-1/6
What is the value of ((-1)/9)/(1/6)?
-2/3
What is 1/(12/16)*6/(-52)?
-2/13
Evaluate 1*-1*(-26)/78.
1/3
Evaluate (-16)/(-10)*(-385)/(-308).
2
Evaluate (6/2)/(-6)*0/(-7).
0
Evaluate (8/42*3)/((-2)/(-2)).
4/7
Evaluate ((-3)/(-4)*-4)/((-9)/15).
5
Evaluate -5*-3*3/27*-3.
-5
(1*2)/(((-90)/5)/(-6))
2/3
What is 2/(63/(35/5))*-9?
-2
Calculate ((-3)/(-5))/((2/2)/5).
3
What is the value of (18/(-2))/(189/(-42))?
2
4/14*-3*(-35)/(- | {
"pile_set_name": "DM Mathematics"
} |
You are here:
Yes I'm a newb to the Turnkey Linux thing, as well as EC2. All I'm trying to do is open up a different port to run a virtual host. I've added port 85 to the EC2 security group, and added an accept rule to the Linux Firewall for port 85 coming from any address. I've also created a virtual host that responds to any inbound address on port 85. However, the connection is getting refused.
Since multiple things could be going wrong, it's best to try and diagnose the issue by progressing incrementally. By default the firewall is disabled so unless you enabled it, that shouldn't be an issue which leaves the web server and the EC2 security groups.
Test the EC2 security groups first. Use netcat to listen on port 85 and then make sure you can connect to it remotely. If that doesn't work (and you don't have a firewall up) you know it's the EC2 group. | {
"pile_set_name": "Pile-CC"
} |
Marginal improvement in Assam situation
Last updated on: November 21, 2003 13:13 IST
An uneasy calm prevails in Assam with no major incident of violence reported overnight while curfew in worst-hit Tinsukia town was relaxed for two hours from 11.30 a.m. to enable people to buy essential commodities.
Official sources in Guwahati said the fear of reprisal continues to stalk some residents of Tinsukia, Dibrugarh, Dhubri, Bongaigaon and Nalbari towns. In Nalbari, curfew was suspended for 10 hours from 6 am.
The curfew in Tinsukia and Dibrugarh districts has hit train services. The districts have a sizeable Bihari population but many opted to leave the state and made a beeline for railway stations.
Dibrugarh district Deputy Commissioner N Verma told PTI that the dusk-to-dawn curfew was clamped from 5 pm to 5 am in the oil town of Duliajan, the fertiliser town of Namrup, Tengakhat, Tingkhong and Moran to prevent any fresh outbreak of violence.
Prohibitory orders under Section 144 of the Criminal Procedure Code continued to remain in force in Bihari-dominated areas in Dibrugarh district. | {
"pile_set_name": "Pile-CC"
} |
Q:
How do I move JQuery draggable element without mouse
Is there a different way of JQuery draggable element moving?
Think yourself as a spammer.
A:
it should not be such a big deal, only calling the correct sequence of: .mousedown(), .mousemove() and .mouseup()
as the official documentation says (http://api.jquery.com/mousedown/):
Bind an event handler to the "mousedown" JavaScript event, or trigger that event on an element.
the same is true for the other two jquery function descriptions
| {
"pile_set_name": "StackExchange"
} |
Introduction {#Sec1}
============
Headache is the commonest neurological disorder in the community with variable intensity, ranging from a trivial nuisance to a severe, disabling, acute or chronic disorder, and may impose a substantial burden on sufferers and on society \[[@CR1], [@CR2]\]. It is one of the commonest reasons for visiting the neurology clinics worldwide \[[@CR3]--[@CR5]\], exerting significant burden on its sufferers and impairing daily function especially when accompanied by other symptoms, hence adversely affecting quality of life \[[@CR6]\]. According to the World Health Organisation (WHO), 1.7 -- 4% of the adult population of the world have headaches on 15 or more days every month \[[@CR7]\] and a lifetime prevalence of more than 90% has been attributed to headache disorders in most populations of the world \[[@CR8]\].
It is known that Africans have a higher threshold for pain and may not present to the clinic just for an 'ordinary headache' \[[@CR9]\]. Local experiences show that patients suffering from other chronic neurological disorders present very late to doctors and sometimes never do so \[[@CR9]\]. Chronic headaches produce individual and societal burdens, the former referring to its effect on family, social and recreational activities and the latter referring to effects on healthcare cost (direct costs) and work and function (indirect costs), including absenteeism and reduced effectiveness \[[@CR10]\].
There is limited data for headache prevalence in Africa. In 2004, the 1-year prevalence of headache from a door-to-door survey of rural south Tanzania was 23.1% (18.8% males and 26.4% females) \[[@CR11]\]. Getahu and colleagues in Ethiopia found a 1-year prevalence rate of 73.2% \[[@CR12]\]. A 1992 study from Ibadan, South West Nigeria, found the crude life-time prevalence for at least one episode of headache to be 51% \[[@CR13]\].
In Nigeria, there is a paucity of data on the national prevalence and burden of chronic headaches \[[@CR14]\] despite the fact that it is the commonest presenting neurological disorder in the authors' environment \[[@CR1], [@CR3]\], and therefore the possibility that a big headache problem exists in Nigeria. There are also no known studies of the prevalence and characterization of headache among Nigerian healthcare workers or healthcare workers in South East Nigeria hence the relevance of this study.
Aim of the study {#Sec2}
----------------
The aim of this preliminary study was to determine the frequency and pattern of headaches among a population of healthcare workers in a tertiary health institution located in South East Nigeria.
Methods {#Sec3}
=======
This was an epidemiological sampling-based study (Figure [1](#Fig1){ref-type="fig"}) using a semi-structured questionnaire. The questionnaire was pre-tested in another health facility at Nsukka (a local government area similar to the study area) for content validity. English language was used to reduce cross- cultural misinterpretations and wrong understanding of terms.Figure 1**Flow chart of research activities.**
The questionnaire was self- administered to all various cadres of health workers in medical unit of University of Nigeria Teaching Hospital, a tertiary health institution located in Enugu, South- East Nigeria, over a 3- month period from September -- November 2013, selected by simple random method out of the various units in the hospital e.g. surgical, medical, laboratory, physiotherapy, nutrition, administrative, laundry, transport, security, and medical record. Within these are various cadres of hospital staff: physicians, nurses, pharmacists and cleaners. Out of a total of 141 only 133 gave consent and hence were studied, giving a response rate of 94.3%. To ascertain the overall prevalence of headache, subjects were asked if they have ever had a headache within the previous six months and to note any association. They were to rate the severity of headache based on a scale of mild, moderate and severe. The impact of these severe headaches on the daily activity and the number of days they occur in a month were recorded. The character of the pain, location, duration, and the total numbers of times in the 6 months preceding the date of administering the questionnaire were also noted.
Statistical Package for Social Sciences version 16 was used in statistical analysis. Comparison of multiplex groups was carried out with One Way ANOVA test. On the other hand comparison of two distinct groups was carried out with student t test. Chi-square test (and/or Fisher's exact test) was used in analysis of categorical variables. The results were revealed as mean ± SD. P value \<0.05 was interpreted as statistically meaningful. Ethical approval was obtained from the hospital ethics committee.
Results {#Sec4}
=======
Of the 2,450 hospital employees (450 medical doctors, 630 nurses, 50 pharmacists, and 1320 laboratory and administrative staff), 141 were selected using simple random method from the employment register and eventually only 133 health workers (71 males and 62 females) gave informed consent and were studied (response rate 94.3%). More of the respondents were males (53.4%) and most were within the 25 - 34 years age group (46.6%). Most of the workers had worked for only ≤5 years (72.9%). Table [1](#Tab1){ref-type="table"} illustrates.Table 1**Demographic distribution and work experience of health workers**VariableFrequencyPercent***Sex***Male7153.4Female6246.6Total133100.0***Age Group***15 -- 24139.825 -- 346246.635 -- 443627.145 -- 541511.355 -- 6464.565 and above10.7Total133100.0***Number of years worked***1 -- 59772.96 -- 101813.511 -- 1575.316 -- 2043.021 -- 2553.826 -- 3021.5Total133100.0
The prevalence of headache in the past 6 months was 88.0% (among males the prevalence was 87.3% while in females it was 88.7%). There was no significant difference observed between the sexes (p = 0.806). In both sexes, primary headaches were more prevalent (71.0% in males and 76.4% in females). There was also no significant difference in the prevalence of the primary headaches among the sexes (p = 0.509). See Table [2](#Tab2){ref-type="table"}.Table 2**Prevalence of headache among the health workers**General prevalence of headache in the past 6 monthsVariablesFrequencyPercentHeadache present11788.0Headache absent1612.0**Sex prevalence of headache**Male (%)Female (%)Headache present62 (87.3)55 (88.7)Headache absent9 (12.7)7 (11.3)Total71 (100.0)62 (100.0)χ^2^ = 0.060; P value = 0.806Type of headachePrimary44 (71.0)42 (76.4)\*Secondary18 (29.0)13 (23.6)Total62 (100.0)55 (100.0)χ^2^ = 0.436; P value = 0.509\*Secondary headache is headache with a definitive and identifiable cause found for it i.e. those with pre-existing conditions that may cause the headache e.g. hypertension, cervical spondylosis, refractive error, sleep apnoea, malaria and other febrile conditions \[[@CR15]\].
Most respondents reported ≤5 episodes of headache in the last 6 months (74.4%) and these were typically of short-lasting durations, \<60 minutes (44.4%). There was no observed periodicity to the headaches in 57.3% of cases (see Table [3](#Tab3){ref-type="table"}). Most of the headaches were not located in any particular part of the head or side-locked (71.7%); were described as mildly severe in 59.8% of cases while 88.0% of respondents did not suffer any sleep disruption. The headaches were often not significantly disabling (73.4%) and in 93.2% of respondents did not lead to absenteeism or affect productivity at work (Table [4](#Tab4){ref-type="table"}).Table 3**Characterization of the headaches**Variable/CharacteristicsFrequency (N =117)Percent***Number of episodes in past 6 months***1 -- 58774.46 -- 102521.411 -- 1532.616 -- 2021.6**Usual duration of headaches**Seconds1916.2Minutes5244.4Hours3630.9Days108.5***Usual time of day of the headache***Morning1815.4Afternoon1512.8Night1311.1Continuous43.4No particular time6757.3***Is the headache becoming stronger, last longer or occur more frequent?***Yes2218.8No9581.2**What is the commonest nature of the headache?**Throbbing/exploding4336.8Sharp43.4Tightness54.3Dull65.1Aching2420.5Pressure in head3227.3Grinding32.6Table 4**Usual location and severity of the headache*Usual Location of headache***FrequencyPercentLeft side32.6Forehead97.7Around the head/ill-defined119.4Right side21.7Both Temples21.7Top of the head10.9Neck21.7Back of head32.6No particular side8471.7***Severity of headache***Mild7059.8Moderate4538.5severe21.7***Is the headache strong enough to wake you from sleep?***Yes1412.0No10388.0***Effect of headache on daily activities***No significant disability1613.7Mild disability8673.4Moderate32.6Severe disability1210.3***Headache --related work absenteeism or reduced productivity?***Yes86.8No10993.2
Stress (35.0%) and head trauma/illness/infection (18.8%) were the commonest predisposing conditions to the headache (Table [5](#Tab5){ref-type="table"}). Refractive errors were present in 16.2% of respondents with headaches. In 25.6% there were headache prodromes and these included irritability (10.3%) and fatigue (5.1%). During the headaches, associated symptoms occurred in 30.8% of respondents and these included nasal congestion, redness of eyes, sinusitis or allergies (26.5%) as depicted in Table [6](#Tab6){ref-type="table"}. In most cases, there was no known family history of migraines or other chronic headaches (Figure [2](#Fig2){ref-type="fig"}).Table 5**Predisposing conditions to the headache**Factors preceding the headacheFrequency (N =117)PercentAccident, illness or infection2218.8Odours54.3Fatigue3429.1School21.7Hunger1714.5Noise43.4Stress4135.0Exercise10.9Family problem21.7Menstrual flow21.7Lack of sleep86.8Hot weather21.7None4941.9**Existing chronic medical conditions that may cause headache**Hypertension108.5Cervical spondylosis32.6Refractive errors1916.2Diabetes mellitus21.7Sleep apnoea10.9None9782.9Note that some respondents filled more than one option.Table 6**Headache prodromes and other features associated with the headaches**Frequency (N =117)Percent***Presence of warning signs before headache***Yes3025.6No8774.4***Warning signs***Pallor10.9Mood swing65.1Irritability1210.3Dizziness32.6Tired/sleepy65.1Rings around the eyes10.9Hyperactivity10.9Eye problems21.7None10488.9Other symptoms associated with the headaches***Presence of other symptoms during the headaches***Yes3630.8No8169.2Nasal congestion, redness of eyes, sinusitis or allergies associated with the headache3126.5Nausea.21.7Stomach pain97.7Vomiting10.9Confusion32.6Numbness in arms and legs65.1Diarrhoea10.9Dropping of the eyes10.9Fever1210.3Note that some respondents filled more than one option.Figure 2**Family member with history of headaches, migraines, sick headaches, motion sickness or had trouble taking birth control pills because of headaches.**
Management of headache was varied among respondents. In most cases (47.9%) no intervention was required. However in other instances, investigations (11.1%) and eye checks (7.7%) were done. The over-the counter- available analgesic, paracetamol, (83.8%) was the commonest treatment received (Table [7](#Tab7){ref-type="table"}).Table 7**Management received for the last headache episode**Management actionsFrequency (N =117)Percent*Headache was managed by --*Health worker1916.2Self4235.9No treatment received5647.9*A. Investigations done*Laboratory1311.1Eye check97.7*B. Treatment received*Anti-malaria76.0Ergotamine10.9Food10.9Ibuprofen54.3Other NSAIDs\*21.7Paracetamol9883.8Tramadol (narcotic analgesic)10.9Eye glasses were prescribed1613.7Relaxation10.9*Other actions that relieve the headaches*Cold compress1311.1Eating2017.1Massage32.6Moving around32.6Relaxation4740.2Sleep3126.5Vomiting10.9Others10.9\*NSAIDs = non-steroidal anti-inflammatory agents.Note that some respondents filled more than one option.
The health workers' ages did not significantly affect both the presence and treatment of headache (p = 0.483 and 0.293 respectively) but significantly affected the type of headache (p = 0.005) i.e. whether it was primary or secondary headache (Table [8](#Tab8){ref-type="table"}). Years of working in the hospital did not significantly affect the prevalence of headache (P = 0.123), type of headache (P = 0.423) or treatment of the headaches (P = 0.535) as shown in Table [9](#Tab9){ref-type="table"}. There was no correlation between the number of headache episodes and the number of years worked in the hospital \[Pearson Correlation (r) = - 0.066\] or age of the health worker \[r = 0.001\].Table 8**Age group and management of headache**Age group in yearsVariables15 -2425 - 3435 - 4445 - 5455 - 64≤ 65***Presence of headache***Yes12(92.3)53(85.5)34(94.4)13(86.7)4(66.7)1(100.0)No1(7.7)9(14.5)2(5.6)2(23.3)2(33.3)0(0.0)Total13 (100.0)62(100.0)36(100.0)15(100.0)6(100.0)1(100.0)Likelihood-ratio χ^2^ = 4.480; P value = 0.483***Type of headache***Primary7(58.3)45(84.9)27(79.4)6(46.2)1(33.3)0(0.0)Secondary5(41.7)8(15.1)7(20.6)7(53.8)3(66.7)1(100.0)Total12(100.0)53(100.0)34(100.0)13(100.0)4(100.0)1(100.0)Likelihood-ratio χ^2^ = 16.995; P value = 0.005 (significant)***Treatment of headache***Other health worker10(83.3)33(62.3)18(52.9)10(76.9)3(66.7)1(100.0)Self2(16.7)20(37.7)16(47.1)3(23.1)1(33.3)0(0.0)Total12(100.0)53(100.0)34(100.0)13(100.0)4(100.0)1(100.0)Likelihood-ratio χ^2^ = 6.135; P value = 0.293Table 9**Number of years worked in the hospital and management of headache**Number of years worked in the hospitalVariables1 - 1011 - 2021 - 30***Presence of headache***Yes101(87.8)11(100.0)5(71.4)No14(12.2)0(0.0)2(28.6)Total115(100.0)11(100.0)7(100.0)Likelihood-ratio χ^2^ = 4.199; P value =0.123***Type of headache***Primary75(65.2)8(72.7)3(42.9)Secondary40(34.8)3(27.3)4(57.1)Total115(100.0)11(100.0)7(100.0)Likelihood-ratio χ^2^ = 1.719; P value = 0.423***Treatment of headache***Other health worker78(67.8)7(63.6)6(85.7)Self37(32.2)4(36.4)1(14.3)Total115(100.0)11(100.0)7(100.0)Likelihood-ratio χ^2^ = 1.250; P value = 0.535
Discussion {#Sec5}
==========
Headache is the commonest presenting neurological disorder in most communities and clinical settings worldwide \[[@CR2], [@CR12]\]. Studies from Nigeria, including Enugu, also support this \[[@CR1], [@CR3], [@CR13]\]. The prevalence of headache in health care workers has been variously reported from Western countries \[[@CR16], [@CR17]\] but there is a paucity of similar data from Nigeria and Africa. There was an inability to assess headaches as distinctly experienced in the various cadres of hospital workers and it was also not possible in this study to ascertain distinct headache entities and their roles. Other limitations of this study were its small sample size, the possibility of recall bias arising from patients' answers to occurrences of headaches in the past 6 months, and use of a 3-point pain scale instead of the 10-point Visual Analogue Scale (VAS) which has greater scale refinement and discrimination power. VAS has been noted to be a valid instrument for measurement of pain intensity in patients with headaches \[[@CR18]\].
A prevalence of 88.0% was obtained for headaches amongst the hospital workers, with slightly higher rates in females than males. Though the study periods vary, the figure compares favourably with the rate of 84.4% obtained amongst from health workers in the United States \[[@CR16]\] but is significantly higher than the 54.7% and 27.1% prevalence rates obtained from Italian and Turkish health workers respectively \[[@CR16], [@CR19]\]. A survey of headache in Ethiopian textile workers found a prevalence of 73% \[[@CR12]\]. The headache prevalence of 88% for hospital workers in this study compares favourably with the 88.3% prevalence found in a study of medical students in the same locality \[[@CR20]\]. The prevalence is also higher than the community prevalence rates of 51% and 23.1% seen in Ibadan, South West Nigeria and rural south Tanzania respectively \[[@CR11], [@CR13]\]. It is possible that the different figures may reflect a combination of environmental challenges, durations of study and varied survey instruments used.
It is well noted that females tend to have higher rates for headache prevalence across cultures and continents \[[@CR1], [@CR3], [@CR12], [@CR16], [@CR17], [@CR19]\] and while this seemed to be the case in our study, the difference was not statistically significant. Reasons adduced for the higher female prevalence include the influence of oestrogens and progesterone on headaches after menarche and the greater propensity for females to seek medical attention for headaches \[[@CR21]\].
Most of our subjects had probable primary headaches although no further attempts were made in this study to distinguish between the various different types (which include the trigeminal associated cephalalgias (TACs), migraine and tension- type headaches). Headaches were of short duration (\<60 minutes) and were not side --locked in most instances unlike the longer duration (\>6 hours) migraine headaches noted in the Turkish study \[[@CR19]\]. Migraine headache prevalence rate is uniformly low across much of Africa but was found to be significantly high in a cohort of textile mill workers in Ethiopia \[[@CR12], [@CR22]\].
Stress, probably related to challenges in the work environment, played the greatest role (35.0%) in this study and this reflected in the calming role attributed to relaxation techniques utilized by the health workers (40.2%) to manage their headaches. Besides life and work stress, personality traits such as aggression, anger and type A behaviour are factors that may aggravate stress and are frequently found in headache patients but were not sought for in this study \[[@CR22]--[@CR24]\].
There was no significant association or correlation found between the prevalence of headaches and years of working experience in this study. Non-pharmacological treatment was suitable for almost half of respondents (47.9%) while the over-the --counter medicine, paracetamol, was the most utilised drug treatment. This finding is essentially similar to that of health workers with headaches in the Unites States but contrasts with the use of NSAIDs in a Turkey study \[[@CR17], [@CR19]\]. Despite working in a health facility, self-medication was commonly practised (35.9%) but this was even more significant among Turkish health workers (54.6%) \[[@CR19]\].
The low rate of medical consultation for headache in hospital workers is of interest. In this study centre, headache ranks low among the disorders seen at both the Pain Clinic and Neurology Clinic accounting for only 2.7% of all neurological cases seen in the latter and 9^th^ of the top 10 disorders encountered \[[@CR3]\]. Some reasons adduced for the low rate of presentations to clinics for headaches as well as low rates of success in headache treatment amongst Africans include underdiagnoses or misdiagnoses due to lack of adequate knowledge by healthcare professionals, headache sufferers being ignorant of effective prophylaxis and treatment, perception of headaches as a trivial problem, and great tolerance to pain \[[@CR25]--[@CR29]\]. Other reasons include poor healthcare facilities \[[@CR30]\], low economic power \[[@CR25]\], gender/child discrimination \[[@CR28]\], and unavailability of effective medication \[[@CR28], [@CR29]\]. The authors are of the opinion that African patients' preference for/reliance on non-drug options (complementary and alternative medicine, CAM) \[[@CR25], [@CR28], [@CR30]\] for pain relief may also be contributory.
Of important economic interest is the rarity of absenteeism from work or loss of productive time as reported in this study. These factors are important because many headache sufferers are at the peak of their work-productive life \[[@CR26]\]. Employers may lose an average of 12 days per year because of an employee headache syndrome \[[@CR27]\]. The authors relate reason for the rarity of work absenteeism and loss of productive time to the majority of headaches being of a mild nature with low disabling rates. A similar negligible rate of absenteeism was the outcome among Italian health workers with headache \[[@CR16]\].
Conclusion {#Sec6}
==========
This preliminary study has revealed headaches to be common in this community of healthcare workers. However, the seemingly low effect of headache on health workers productivity in this study, despite its high prevalence rate and contrary to views \[[@CR28]\] from other African studies, is of notable relief in a developing economy like Nigeria where health indicators are unimpressive and medical services still face huge challenges. In addition, presentation to Pain or Neurology clinic for headache disorders by respondents in this study has been shown to be low, demonstrating the need for increased and continuous health awareness on headache disorders as well as enhanced occupational health services in Nigerian hospitals. By the findings of this work, the authors encourage more robust studies on headache disorders among healthcare workers in African countries with a view to informing better practice decisions and reducing the global headache burden.
**Competing interest**
The authors declare that they have no competing interests.
**Authors' contributions**
TO and IO conceptualised the study; TO, IO, EA, BE, OE and EO designed the questionnaire and collected data; TO, EA and IO analysed the data; all authors participated in drafting the manuscript; all authors read and approved the final manuscript.
The authors are grateful to Dr. Ada Shirley for her co-operation with data collection.
**Declaration**
This study was not supported by a grant.
| {
"pile_set_name": "PubMed Central"
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Jalalabad, Ardabil
Jalalabad (, also Romanized as Jalālābād) is a village in Shal Rural District, Shahrud District, Khalkhal County, Ardabil Province, Iran. At the 2006 census, its population was 82, in 14 families.
References
Category:Towns and villages in Khalkhal County | {
"pile_set_name": "Wikipedia (en)"
} |
Phospholipid spherules (liposomes) as a model for biological membranes.
This review describes the properties of artificial spherules composed of phospholipids and various long-chain anions or cations. The lipids, which are in the liquid-crystal state, trap aqueous solutes such as cations, anions, glucose, or glycine in aqueous compartments between a series of lipid bilayers. The diffusion of these solutes from the spherules can be studied in the same way that diffusion across biological membranes is studied. The spherules exhibit many of the properties of natural membrane-bounded structures: they are capable of ion-discrimination, osmotic swelling, and response to a variety of physiologic and pharmacologic agents. These agents (steroids, drugs, toxins, antibiotics) accelerate or retard diffusion of ions or molecules from the spherules in a way that qualitatively mimics their action on erythrocytes, lysosomes, or mitochondria. Thus the spherules constitute a valuable model system with which to study the properties of biological membranes that may be dependent on their lipid components. | {
"pile_set_name": "PubMed Abstracts"
} |
Low-maintenance management: using a simple classification to rate employees' productivity and support requirements.
Employees vary in their productivity and their need for guidance, support, and other inputs that may be called "maintenance." This article provides a guide to classifying your team members by a gross ratio of perceived managerial inputs to productivity outputs. It also gives some approaches to understanding your own reactions and dealing with the needs of each group. | {
"pile_set_name": "PubMed Abstracts"
} |
Menu
The Freedom of Choice
In every moment we have a choice. The freedom to choose our actions that create our day, month and year all adding up to the life we are creating for ourself. Even if you think are not choosing, you are. No decision is a decision. The choices we make either support our goals and the life we truly want to live or they are taking us further away. Our choices cause us to feel great pleasure in our life or they are creating pain and suffering. Without focusing on the past too much, reflect back on the last couple of days, the last week or even the last month. What choices have you made that led you to where you are or allowed you to stay stagnant with no growth at all? What do you want to accomplish? How do you want to feel? If you’re not sure what choices you have made, then just look at your actions.
If you want to lose weight and you choose to not work out or eat fast food, than the choices you are making do not support your goal. Every time you look in the mirror and see no progress you create pain and suffering for yourself. If you want a new job, but you don’t update your résumé, network or apply for jobs, than your choices are not supporting your goal and everyday when you go to work at a job you don’t want to be at, you create pain and suffering for yourself. If you are unhappily in a relationship and you choose to complain to everyone around you, rather than communicating to your partner to see how they feel, make an effort to improve your relationship by working on you or decide to end the relationship, than you create pain and suffering for yourself and your partner. How about anytime you need to drive somewhere you have never been and are unfamiliar with. If your goal is to arrive at your destination, you can choose to put the address into the navigation on your phone, print out directions, use a map, or you could just get in the car and drive, hoping that you get there. Which choice will allow you to arrive at your destination? Which choice do you think will give you more pleasure than pain?
You can take this formula and apply it to any part of your life. The formula to feeling pleasure is not complicated, but it’s also very easy to feel pain and suffering. So you have a choice, what do you want to feel, pleasure or pain? Choice is a decision to take action or not.Tony Robbins said, “A real decision is measured by the fact that you’ve taken a new action. If there is no action, you haven’t truly decided.” So whatever your goals are, whatever life you want to create for yourself, the first thing you have to do is choose to take actions that will support your goal so you can ultimately feel more pleasure and less pain. | {
"pile_set_name": "Pile-CC"
} |
Portasystemic shunt fraction quantification using transrectal administration of iodine-123 iodoamphetamine in dogs with chronic bile duct ligation and after propranolol administration.
Following transrectal administration, 123I iodoamphetamine (IMP) has been shown in both animal and patient studies to be capable of detecting the presence of portasystemic shunting (PSS). However, the ability of this method to actually quantitate PSS in the presence of cirrhosis and propranolol has not been demonstrated. We studied nine dogs with hitologically proven cirrhosis induced by chronic bile duct ligation. After intravenous injection of propranolol, PSS were measured with both the IMP method and the standard of portal vein infusion of 99mTc macroaggregated albumin (MAA) given through a mesenteric vein catheter. Based on linear regression, a close relationship was seen, given by the equation: MAA = IMP 0.9 + 0.035, with correlation coefficient of 0.99. Thus, in dogs with cirrhosis secondary to chronic bile duct ligation and after propranolol administration, PSS can be quantitated with the transrectal IMP method. | {
"pile_set_name": "PubMed Abstracts"
} |
The programme is part of a cooperative effort between the state's Addiction Treatment and Abuse Fund (ATAF) and the Long Live Egypt fund to upgrade Hepatitis C treatment in Egypt, in the frame of the country's national plan to eliminate the disease.
Wali said the new programme will begin by testing 400 recovered addicts and treating those who test positive for the disease. According to ATAF, Egypt registered a 2.4 percent drug addiction rate, and 10 percent abuse rate in the general population for 2016. The fund said it treated 75,000 drug addicts in 2015. According to the World Health Organisation (WHO), more than 150 million people suffer from Hepatitis C worldwide.
Egypt has one of the highest prevalence rates of the virus in the world, according to WHO.
According to 2015 statistics, some 15 million Egyptians -- out of a population of 91 million -- carried the disease, or around 22 percent of the population.
In 2016, The Health Ministry achieved a 96 percent cure rate of the disease nationwide, through intensive efforts over the past two years using a variety of treatments.
The ministry has vowed to completely eliminate the disease in Egypt by 2021.
The WHO has praised Egypt's efforts to combat the virus, including government subsidies for new treatments.
"Egypt has a become an example to follow all over the world, not only for giving hope [that we can combat] the disease, but also for its concerted efforts in a national action plan that includes protection through raising the societal awareness of the paths of infection and means of treatment, providing medicine for patients, follow-up and continued evaluation of the action plan," the organisation's Director-General Margaret Chan said in a statement last year.
Short link:
| {
"pile_set_name": "OpenWebText2"
} |
Aug 23, 2016 at 10:38 // News
Nina Lyon Author
The UAE and Kimberley Process is to use Blockchain technology to fight “blood diamonds” trading on the world market.
Blockchain technology is already used for luxury goods, real estate, art authenticity and ownership registration. Now, Ahmed bin Sulayem, chairman of the international Kimberley Process (KP) organization in the UAE, has proposed its use in the global trade of precious stones.
He stated:
"We have introduced the possibility of using Blockchain technology to create a seamless and continued global process for the KP certification scheme."
The Kimberley Process is an international organization that was founded by the United Nations to prevent the flow of conflict diamonds, as they are used to finance criminal activities and wars against legitimate governments all over the world.
Fighting Blood Diamonds
While a lot of people used to shame cryptocurrencies and Bitcoin for being used for illegal activities, to date, cash and blood diamonds are the most likely to be used for those purposes. The size of the global diamond industry in 2015 was estimated at about $75 to $80 billion, however, about 5% to 10% of the world’s diamonds are traded illegally.
“Blockchain tech is exceptionally good in law for tracking limited or restricted goods in trade. For example, we have a carbon coin we just announced with SAP that can tracing ability in climate finance to combat financial crime. Lots of other cool application along that vein,” commented Christine Duhaime, a lawyer and Certified Financial Crime and Anti-Money Laundering Specialist.
Now the implementation of Blockchain technology in the business of precious stones could establish a tamper-proof record of the provenance of diamonds and help the Kimberley Process.
Blockchain Technology in Precious Stones and Metals Industry
Everledger is a startup that is already doing diamonds certification and authentication using Blockchain technology against fraud.
“We take the 40 metadata points that make up the diamond. The laboratory houses inspect the stone, they effectively digitize each of those diamonds… All of the angles and the cuts and the pavilions and all of the crown. And we take all of that, as well as the serial number, as well as the four Cs, and we put all that into the blockchain,” said Leanne Kemp, CEO of Everledger to TechCrunch about the technology of certification.
“Many people would argue that using blockchain for precious metals and stones is important as it will help to prevent the movement of conflict stones or blood diamonds as they are often called,” commented Jan Skoyles, co-founder and CEO of gold trading platform The Real Asset Co to CoinIdol.com.
She noted that it is also of interest to insurance companies. However, there is a difference in diamonds and gold authentification. Jan Skoyles continued:
“The difference with precious metals and precious stones is a block of gold from the ground can look very similar to another block of gold from the ground. And if you refine them then it is impossible to tell which one came from which mine. The difference with diamonds is that each one is unique, so you can effectively record their fingerprints on the blockchain. With gold it is not so easy. There are many uses for blockchain in the gold market, but in regard to provenance from mine through to retail or investment then I am not sure how this could be managed given the ease at which you can refine the metal and reform it.”
Kimberley Process Blockchain initiative
According to the report, Ahmed bin Sulayem has already had a meeting with the Global Blockchain Council of Dubai for the pilot project.
This Kimberley Process initiative to use Blockchain might also become one of the UAE’s projects with FinTech and Blockchain technology as the key elements, and another sign of the UAE’s plans to become the global center for creating and exploring the future. | {
"pile_set_name": "OpenWebText2"
} |
Effects of intestinal bacteria on the development of colonic neoplasm II. Changes in the immunological environment.
To study the effects of intestinal bacteria on the development of colonic neoplasm, we have established gnotobiotic mice with a single species of intestinal bacteria. In the previous study, the incidence of colonic adenoma induced with 1,2-dimethylhydrazine (DMH) in the gnotobiotic mice with Lactobacillus acidophilus, gnotobiotic mice with Escherichia coli and germ-free mice were 30, 50 and 74%, respectively. In this study, 7-week-old mice in each group were sacrificed without the administration of DMH to examine the constituents of immuno-competent cells in various mouse organs using flow cytometry. In the gnotobiotic mice, CD3 intermediate interleukin (IL)-2Rbeta positive cells were observed predominantly in the liver. In the gnotobiotic mice with L. acidophilus, Mac-1 positive Gr-1 positive cells were observed predominantly in the colonic lamina propria. The activation of extrathymic T cells in the liver and granulocytes in the colonic mucosa may be related to anti-neoplastic effects of L. acidophilus in this experimental model. | {
"pile_set_name": "PubMed Abstracts"
} |
Roosevelt High School (Roosevelt, New York)
Roosevelt High School is a four-year public high school located in Roosevelt as part of the Roosevelt School District, serving students in grades 9 through 12. It is located in the hamlet of Roosevelt in the Town of Hempstead, Nassau County, New York, U.S. After years of failing test scores, Roosevelt High School is the first high school in New York to be taken over by the state.
As of the 2014-15 school year, the school had an enrollment of 964 students and 56.6 classroom teachers (on an FTE basis), for a student–teacher ratio of 17.0:1. There were 247 students (25.6% of enrollment) eligible for free lunch and 46 (4.8% of students) eligible for reduced-cost lunch.
Academics
Roosevelt High School has a grading and promotion policy. In order for a student to be admitted to the ninth grade, a student must pass 3 of the 4 major subject areas each year:
English
Mathematics
Science
Social Studies
The student can fail no more than the equivalent of 1 credit in
minor subjects each year (i.e. Technology 1/2 credit, Home Career 1/2 credit, etc.)
To be promoted from grade 9 to 10, a student must earn 4 units of credit.
These units must include: 1 in English and 1 in Social Studies. To be promoted from grade 10 to grade 11, a student must have earned 9 units of credit. These units must include: 2 units in English, 2 units in Social Studies, 1 unit in Mathematics, 1 unit in Science.
A student must receive a minimum grade of 70 in order to advance.
Demographics
The student body in the 2007-2008 school year consisted of:
2 American Indian or Alaska Native students or 0% of the student body
615 Black or African American students or 77% of the student body
181 Hispanic or Latino students or 23% of the student body
1 Asian or Native Hawaiian/Other Pacific Islander students or 0% of the student body
0 White students or 0% of the student body
0 Multiracial students or 0% of the student body
Notable alumni
Notable Roosevelt Junior-Senior High School alumni include:
Chuck D, political activist and member of the hip hop group Public Enemy.
Eddie Murphy, comedian and actor.
Julius Erving, otherwise known as "Dr. J", member of the Basketball Hall of Fame who played for the Philadelphia 76ers until his retirement.
Howard Stern, radio personality.
Gabriel Casseus, Actor (New Jersey Drive, Fallen, Their Eyes Were Watching God), Writer & Producer (Takers).
Melvyn M. Sobel, James V. Petrungaro and David D. Weinberg, Members of the Long Island Rock & Roll Band known as The Ravens, popular from 1965-1969.
References
External links
Great Schools Web site information on Roosevelt High School
Category:Public high schools in New York (state)
Category:Schools in Nassau County, New York
Category:Educational institutions established in 1956 | {
"pile_set_name": "Wikipedia (en)"
} |
---
abstract: 'Let $(R,{\mathfrak{m}})$ be a complete Noetherian local ring and let $M$ be a finite $R$–module of positive Krull dimension $n$. It is shown that any subset $T$ of ${\mbox{Assh}\,}_R(M)$ can be expressed as the set of attached primes of the top local cohomology module ${\mbox{H}\, }^n_{\mathfrak{a}}(M)$ for some ideal ${\mathfrak{a}}$ of $R$. Moreover if ${\mathfrak{a}}$ is an ideal of $R$ such that the set of attached primes of ${\mbox{H}\, }^n_{\mathfrak{a}}(M)$ is a non–empty proper subset of ${\mbox{Assh}\,}_R(M)$, then ${\mbox{H}\, }^n_{\mathfrak{a}}(M)\cong{\mbox{H}\, }^n_{\mathfrak{b}}(M)$ for some ideal ${\mathfrak{b}}$ of $R$ with ${\mbox{dim}\,}_R (R/{\mathfrak{b}})=1$.'
address:
- |
Mohammad T. Dibaei\
Faculty of Mathematical Sciences, Teacher Training University, Tehran, Iran, and Institute for Theoretical Physics and Mathematics (IPM), Tehran, Iran.
- |
Raheleh Jafari\
Faculty of Mathematical Sciences, Teacher Training University, Tehran, Iran
author:
- 'Mohammad T. Dibaei'
- Raheleh Jafari
title: |
Top local cohomology modules\
with specified attached primes
---
Introduction
============
Throughout $(R,{\mathfrak{m}})$ is a commutative Noetherian local ring with maximal ideal ${\mathfrak{m}}$, $M$ is a non-zero finite (i.e. finitely generated) $R$–module with positive Krull dimension $n:={\mbox{dim}\,}_R(M)$ and ${\mathfrak{a}}$ denotes an ideal of $R$. Recall that for an $R$–module $N$, a prime ideal ${\mathfrak{p}}$ of $R$ is said to be an [*attached prime*]{} of $N$, if ${\mathfrak{p}}={\mbox{Ann}\,}_R(N/K)$ for some submodule $K$ of $N$ (see [@MS]). The set of attached primes of $N$ is denoted by ${\mbox{Att}\,}_R(N)$. If $N$ is an Artinian $R$–module so that $N$ admits a reduced secondary representation $N=N_1+\cdots+N_r$ such that $N_i$ is ${\mathfrak{p}}_i$–secondary, $i=1,\ldots,r$, then ${\mbox{Att}\,}_R(N)=\{{\mathfrak{p}}_1,\ldots,{\mathfrak{p}}_r\}$ is a finite set.
Denote by ${\mbox{H}\, }^n_{\mathfrak{a}}(M)$ the $n$th right derived functor of $$\Gamma_{\mathfrak{a}}(M)=\{x\in M|\, {\mathfrak{a}}^rx=0 \ \mbox{for some positive
integer} \ r \}$$ applied to $M$. It is well-known that ${\mbox{H}\, }^n_{\mathfrak{a}}(M)$ is an Artinian module. Macdonald and Sharp, in [@MS], studied ${\mbox{H}\, }^n_{\mathfrak{m}}(M)$ and showed that ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{m}}(M))= {\mbox{Assh}\,}_R(M)$ where ${\mbox{Assh}\,}_R(M):=\{{\mathfrak{p}}\in
{\mbox{Ass}\,}_R(M)|\, {\mbox{dim}\,}_R(R/{\mathfrak{p}})=n\}$. It is shown in [@DY1 Theorem A], that for any arbitrary ideal ${\mathfrak{a}}$ of $R$, ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))=\{{\mathfrak{p}}\in{\mbox{Ass}\,}_R(M)|\, {\mbox{H}\, }^n_{\mathfrak{a}}(R/{\mathfrak{p}})\neq 0\}$ which is a subset of ${\mbox{Assh}\,}_R(M)$. In [@DY2], the structure of ${\mbox{H}\, }^n_{\mathfrak{a}}(M)$ is studied by the first author and Yassemi and they showed that, in case $R$ is complete, for any pair of ideals ${\mathfrak{a}}$ and ${\mathfrak{b}}$ of $R$, if ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))={\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{b}}(M))$, then ${\mbox{H}\, }^n_{\mathfrak{a}}(M) \cong {\mbox{H}\, }^n_{\mathfrak{b}}(M)$. They also raised the following question in [@DY3 Question 2.9] which is the main object of this paper.
[**Question.**]{} For any subset $T$ of ${\mbox{Assh}\,}_R(M)$, is there an ideal ${\mathfrak{a}}$ of $R$ such that ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M)) = T$?
This paper provides a positive answer for this question in the case $R$ is complete.
Main Result
===========
In this section we assume that $R$ is complete with respect to the ${\mathfrak{m}}$–adic topology. As mentioned above, ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{m}}(M)) =
{\mbox{Assh}\,}_R(M)$ and ${\mbox{Att}\,}_R({\mbox{H}\, }^n_R(M)) = \emptyset$ is the empty set. Also ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M)) \subseteq {\mbox{Assh}\,}_R(M)$ for all ideals ${\mathfrak{a}}$ of $R$. Our aim is to show that as ${\mathfrak{a}}$ varies over ideals of $R$, the set ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))$ takes all possible subsets of ${\mbox{Assh}\,}_R(M)$ (see Theorem 2.8). In the following results we always assume that $T$ is a non–empty proper subset of ${\mbox{Assh}\,}_R(M)$
In our first result we find a characterization for a subset of ${\mbox{Assh}\,}_R (M)$ to be the set of attached primes of the top local cohomology of $M$ with respect to an ideal ${\mathfrak{a}}$.
Assume that $n:={\mbox{dim}\,}_R(M)\geq 1$ and that $T$ is a proper non-empty subset of ${\mbox{Assh}\,}_R(M)$. Set ${\mbox{Assh}\,}_R(M)\setminus
T=\{{\mathfrak{q}}_1,\ldots,{\mathfrak{q}}_r\}$. The following statements are equivalent.
1. There exists an ideal ${\mathfrak{a}}$ of $R$ such that ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))=T$.
2. For each $i,\,1\leq i\leq r$, there exists $Q_i\in {\mbox{Supp}\,}_R(M)$ with ${\mbox{dim}\,}_R(R/Q_i)=1$ such that $$\underset{{\mathfrak{p}}\in T}{\bigcap}{\mathfrak{p}}\nsubseteq Q_i \quad \mbox{and}
\quad {\mathfrak{q}}_i\subseteq Q_i.$$
With $Q_i,\, 1\leq i\leq r$, as above, ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))=T$ where ${\mathfrak{a}}=\bigcap\limits_{i=1}^rQ_i$.
$(i)\Rightarrow (ii)$. By [@DY1 Theorem A], ${\mbox{H}\, }^n_{\mathfrak{a}}(R/{\mathfrak{p}})\neq 0$ for all ${\mathfrak{p}}\in T$, that is ${\mathfrak{a}}+{\mathfrak{p}}$ is ${\mathfrak{m}}$–primary for all ${\mathfrak{p}}\in T$ (by [Lichtenbaum-Hartshorne Theorem]{}). On the other hand, for $1\leq i\leq r, {\mathfrak{q}}_i\notin T$ which is equivalent to say that ${\mathfrak{a}}+{\mathfrak{q}}_i$ is not an ${\mathfrak{m}}$–primary ideal. Hence there exists a prime ideal $Q_i\in {\mbox{Supp}\,}_R(M)$ such that ${\mbox{dim}\,}_R(R/Q_i)=1$ and ${\mathfrak{a}}+{\mathfrak{q}}_i\subseteq Q_i$. It follows that $\underset{{\mathfrak{p}}\in
T}{\bigcap}{\mathfrak{p}}\nsubseteq Q_i$.\
$(ii)\Rightarrow (i)$. Set ${\mathfrak{a}}:=\bigcap\limits_{i=1}^rQ_i$. For each $i, 1\leq i\leq r$, ${\mathfrak{a}}+{\mathfrak{q}}_i\subseteq Q_i$ implies that ${\mathfrak{a}}+{\mathfrak{q}}_i$ is not ${\mathfrak{m}}$–primary and so ${\mbox{H}\, }^n_{\mathfrak{a}}(R/{\mathfrak{q}}_i)= 0$. Thus ${\mbox{Att}\,}_R{\mbox{H}\, }_{\mathfrak{a}}^n(M)\subseteq T$. Assume ${\mathfrak{p}}\in T$ and $Q\in
{\mbox{Supp}\,}(M)$ such that ${\mathfrak{a}}+{\mathfrak{p}}\subseteq Q$. Then $Q_i\subseteq Q$ for some $i, 1\leq i\leq r$. Since ${\mathfrak{p}}\nsubseteq Q_i$, we have $Q_i\neq
Q$, so $Q={\mathfrak{m}}$. Hence ${\mathfrak{a}}+ {\mathfrak{p}}$ is ${\mathfrak{m}}$–primary ideal. Now, by [Lichtenbaum-Hartshorne Theorem]{}, and by [@DY1 Theorem A], it follows that ${\mathfrak{p}}\in{\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))$.
If ${\mbox{H}\, }^n_{\mathfrak{a}}(M)\not=o$ then there is an ideal ${\mathfrak{b}}$ of $R$ such that ${\mbox{dim}\,}_R(R/{\mathfrak{b}})\leq 1$ and ${\mbox{H}\, }^n_{\mathfrak{a}}(M)\cong{\mbox{H}\, }^n_{\mathfrak{b}}(M)$.
If ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))= {\mbox{Assh}\,}_R(M)$, then ${\mbox{H}\, }^n_{\mathfrak{a}}(M)=
{\mbox{H}\, }^n_{\mathfrak{m}}(M)$. Otherwise $n\geq 1$ and ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))$ is a proper subset of ${\mbox{Assh}\,}_R(M)$. Set ${\mbox{Assh}\,}_R(M)\setminus
{\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M)):=\{{\mathfrak{q}}_1, \cdots, {\mathfrak{q}}_r\}$. By Proposition 2.1, there are $Q_i\in {\mbox{Supp}\,}_R(M)$ with ${\mbox{dim}\,}_R(R/Q_i)= 1, \ i=1, \cdots,
r$, such that ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))= {\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{b}}(M))$ with ${\mathfrak{b}}= {\bigcap\limits_{i=1}^rQ_i}$. Now, by [@DY2 Theorem 1.6], we have ${\mbox{H}\, }^n_{\mathfrak{a}}(M)\cong {\mbox{H}\, }^n_{\mathfrak{b}}(M)$. As ${\mbox{dim}\,}(R/{\mathfrak{b}})= 1$, the proof is complete.
If ${\mbox{dim}\,}_R(M)=1$ then any subset $T$ of ${\mbox{Assh}\,}_R(M)$ is equal to the set ${\mbox{Att}\,}_R({\mbox{H}\, }^1_{\mathfrak{a}}(M))$ for some ideal ${\mathfrak{a}}$ of $R$.
With notations as in Proposition 2.1, we take $Q_i={\mathfrak{q}}_i$ for $i=1,\cdots, r$.
By a straightforward argument one may notice that the condition “complete" is superficial, for if $T$ is a non–empty proper subset of ${\mbox{Assh}\,}_R(M)$, then $T={\mbox{Att}\,}_R({\mbox{H}\, }^1_{\mathfrak{a}}(M))$, where ${\mathfrak{a}}=\underset{{\mathfrak{p}}\in{\mbox{Assh}\,}_R(M)\setminus T}{\cap}{\mathfrak{p}}$.
The following is an example to Proposition 2.1.
Set $R=k[[X,Y,Z,W]]$, where $k$ is a field and $X,Y,Z,W$ are independent indeterminates. Then $R$ is a complete Noetherian local ring with maximal ideal ${\mathfrak{m}}=(X,Y,Z,W)$. Consider prime ideals $${\mathfrak{p}}_1=(X,Y) \quad , \quad {\mathfrak{p}}_2=(Z,W)\quad , \quad {\mathfrak{p}}_3=(Y,Z)
\quad , \quad {\mathfrak{p}}_4=(X,W)$$ and set $\displaystyle
M=\frac{R}{{\mathfrak{p}}_1{\mathfrak{p}}_2{\mathfrak{p}}_3{\mathfrak{p}}_4}$ as an $R$–module, so that we have ${\mbox{Assh}\,}_R(M)=\{{\mathfrak{p}}_1,{\mathfrak{p}}_2,{\mathfrak{p}}_3,{\mathfrak{p}}_4\}$ and ${\mbox{dim}\,}_R(M)=2$. We get $\{{\mathfrak{p}}_i\}={\mbox{Att}\,}_R({\mbox{H}\, }^2_{{\mathfrak{a}}_i}(M))$, where ${\mathfrak{a}}_1={\mathfrak{p}}_2,
{\mathfrak{a}}_2={\mathfrak{p}}_1, {\mathfrak{a}}_3={\mathfrak{p}}_4, {\mathfrak{a}}_4={\mathfrak{p}}_3$, and $\{{\mathfrak{p}}_i,{\mathfrak{p}}_j\}={\mbox{Att}\,}_R({\mbox{H}\, }^2_{{\mathfrak{a}}_{ij}}(M))$, where $$\begin{array}{l}
{\mathfrak{a}}_{12}=(Y^2+YZ,Z^2+YZ,X^2+XW,W^2+WX),\\
{\mathfrak{a}}_{34}=(Z^2+ZW,X^2+YX,Y^2+YX,W^2+WZ),\\
{\mathfrak{a}}_{13}=(Z^2+XZ,W^2+WY,X^2+XZ),\\
{\mathfrak{a}}_{14}=(W^2+WY,Z^2+ZY,Y^2+YW),\\
{\mathfrak{a}}_{23}=(X^2+XZ,Y^2+WY,W^2+ZW),\\
{\mathfrak{a}}_{24}=(X^2+XZ,Y^2+WY,Z^2+ZW).\\
\end{array}$$ Finally, we have $\{{\mathfrak{p}}_i,{\mathfrak{p}}_j,{\mathfrak{p}}_k\}={\mbox{Att}\,}_R({\mbox{H}\, }^2_{{\mathfrak{a}}_{ijk}}(M))$, where ${\mathfrak{a}}_{123}=(X,W,Y+Z)$, ${\mathfrak{a}}_{234}=(X,Y,W+Z)$, ${\mathfrak{a}}_{134}=(Z,W,Y+X)$.\
Assume that $n:={\mbox{dim}\,}_R(M)\geq 2$, and that $T$ is a non-empty subset of ${\mbox{Assh}\,}_R(M)$ such that $\underset{{\mathfrak{p}}\in T}{\bigcap} {\mathfrak{p}}\nsubseteq \underset
{{\mathfrak{q}}\in {\mbox{Assh}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})}{\bigcap} {\mathfrak{q}}$, where $T'={\mbox{Assh}\,}_R(M)\setminus T$. Then there exists a prime ideal $Q\in {\mbox{Supp}\,}_R(M)$ with ${\mbox{dim}\,}_R(R/Q)=1$ and ${\mbox{Att}\,}_R({\mbox{H}\, }^n_Q(M))=T.$
Set $s:={\mbox{ht}\,}_M(\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})$. We have $s\leq n-1$, otherwise ${\mbox{Assh}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})= \{{\mathfrak{m}}\}$ which contradicts the condition $\underset{{\mathfrak{p}}\in T}{\bigcap} {\mathfrak{p}}\nsubseteq \underset
{{\mathfrak{q}}\in {\mbox{Assh}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})}{\bigcap} {\mathfrak{q}}$. As $R$ is catenary, we have ${\mbox{dim}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in
T'}{\mathfrak{p}})=n-s$. We first prove, by induction on $j$, $0\leq j\leq
n-s-1$, that there exists a chain of prime ideals $Q_0 \subset Q_1
\subset \cdots \subset Q_j \subset {\mathfrak{m}}$ such that $Q_0\in{\mbox{Assh}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})$, ${\mbox{dim}\,}_R(R/Q_j)=n-s-j$ and $\underset{{\mathfrak{p}}\in T}{\bigcap}{\mathfrak{p}}\nsubseteq Q_j$. There is $Q_0\in{\mbox{Assh}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})$ such that $\underset{{\mathfrak{p}}\in T}{\bigcap}{\mathfrak{p}}\nsubseteq Q_0$. Note that ${\mbox{dim}\,}_R(R/Q_0)={\mbox{dim}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})=n-s$. Now, assume that $0<j\leq n-s-1$ and that we have proved the existence of a chain $Q_0 \subset Q_1 \subset \cdots \subset Q_{j-1}$ of prime ideals such that $Q_0\in{\mbox{Assh}\,}_R(R/\sum\limits_{{\mathfrak{p}}\in T'}{\mathfrak{p}})$, ${\mbox{dim}\,}_R(R/Q_j)=n-s-(j-1)$ and that $\underset{{\mathfrak{p}}\in
T}{\bigcap}{\mathfrak{p}}\nsubseteq Q_{j-1}$. Note that we have $n-s-(j-1)=n-s+1-j\geq 2$. Therefore the set $V$ defined as\
$$\begin{array}{ll}
V= \{{\mathfrak{q}}\in {\mbox{Supp}\,}_R(M) |& Q_{j-1}\subset {\mathfrak{q}}\subset {\mathfrak{q}}'\subseteq
{\mathfrak{m}}, {\mbox{dim}\,}_R(R/{\mathfrak{q}})=n-s-j,\\ &
{\mathfrak{q}}'\in{\mbox{Spec}\,}(R)\, \mbox{and}\, {\mbox{dim}\,}_R(R/{\mathfrak{q}}')=n-s-j-1\}
\end{array}$$\
is non-empty and so, by Ratliff’s weak existence theorem [@M Theorem 31.2], is not finite. As $\underset{{\mathfrak{p}}\in
T}{\bigcap}{\mathfrak{p}}\nsubseteq Q_{j-1}$, we have $Q_{j-1}\subset
Q_{j-1}+\underset{{\mathfrak{p}}\in T}{\bigcap}{\mathfrak{p}}$. If, for ${\mathfrak{q}}\in V$, $\underset{{\mathfrak{p}}\in T}{\bigcap}{\mathfrak{p}}\subseteq {\mathfrak{q}}$, then ${\mathfrak{q}}$ is a minimal prime of $Q_{j-1}+\underset{{\mathfrak{p}}\in T}{\bigcap}{\mathfrak{p}}$. As $V$ is an infinite set, there is $Q_j\in V$ such that $\underset{{\mathfrak{p}}\in
T}{\bigcap}{\mathfrak{p}}\nsubseteq Q_j$. Thus the induction is complete. Now by taking $Q:=Q_{n-s-1}$ and by Proposition 2.1, the claim follows.
Assume that $n:={\mbox{dim}\,}_R(M)\geq 2$ and $T$ is a non-empty subset of ${\mbox{Assh}\,}_R(M)$ with $|T|=|{\mbox{Assh}\,}_R(M)|-1$. Then there is an ideal ${\mathfrak{a}}$ of $R$ such that ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))=T$.
Note that ${\mbox{Assh}\,}_R(M)\setminus T$ is a singleton set $\{{\mathfrak{q}}\}$, say, and so ${\mbox{ht}\,}_M({\mathfrak{q}})=0$ and $\underset{{\mathfrak{p}}\in T}{\bigcap}{\mathfrak{p}}\nsubseteq
{\mathfrak{q}}$. Therefore, by Lemma 2.5, the result follows.
Assume that $n:={\mbox{dim}\,}_R(M)\geq 2$ and ${\mathfrak{a}}_1$ and ${\mathfrak{a}}_2$ are ideals of $R$. Then there exists an ideal ${\mathfrak{b}}$ of $R$ such that ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{b}}(M))={\mbox{Att}\,}_R({\mbox{H}\, }^n_{{\mathfrak{a}}_{1}}(M))\cap{\mbox{Att}\,}_R({\mbox{H}\, }^n_{{\mathfrak{a}}_{2}}(M))$.
Set $T_{1}={\mbox{Att}\,}_R({\mbox{H}\, }^n_{{\mathfrak{a}}_{1}}(M))$ and $T_{2}={\mbox{Att}\,}_R({\mbox{H}\, }^n_{{\mathfrak{a}}_{2}}(M))$. We may assume that $T_1\bigcap
T_2$ is a non–empty proper subset of ${\mbox{Assh}\,}_R(M)$. Assume that ${\mathfrak{q}}\in {\mbox{Assh}\,}_R(M)\setminus (T_1\bigcap T_2)=({\mbox{Assh}\,}_R(M)\setminus
T_1)\bigcup({\mbox{Assh}\,}_R(M)\setminus T_2) $. By Proposition 2.1, there exists $Q\in {\mbox{Supp}\,}_R(M)$ with ${\mbox{dim}\,}_R(R/Q)=1$ such that ${\mathfrak{q}}\subseteq Q$ and $\bigcap_{{\mathfrak{p}}\in T_1\bigcap T_2}{\mathfrak{p}}\nsubseteq
Q$. Now, by Proposition 2.1, again there exists an ideal ${\mathfrak{b}}$ of $R$ such that ${\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{b}}(M))=T_1\bigcap T_2$.
Now we are ready to present our main result.
Assume that $T\subseteq {\mbox{Assh}\,}_R(M)$, then there exists an ideal ${\mathfrak{a}}$ of $R$ such that $T={\mbox{Att}\,}_R({\mbox{H}\, }^n_{\mathfrak{a}}(M))$.
By Corollary 2.3, we may assume that ${\mbox{dim}\,}_R(M)\geq 2$ and that $T$ is a non-empty proper subset of ${\mbox{Assh}\,}_R(M)$. Set $T=\{{\mathfrak{p}}_1,\ldots,{\mathfrak{p}}_t\}$ and ${\mbox{Assh}\,}_R(M)\setminus
T=\{{\mathfrak{p}}_{t+1},\ldots,{\mathfrak{p}}_{t+r}\}$. We use induction on $r$. For $r=1$, Corollary 2.6 proves the first step of induction. Assume that $r>1$ and that the case $r-1$ is proved. Set $T_1=\{{\mathfrak{p}}_1,\ldots,{\mathfrak{p}}_t,{\mathfrak{p}}_{t+1}\}$ and $T_2=\{{\mathfrak{p}}_1,\ldots,{\mathfrak{p}}_t,{\mathfrak{p}}_{t+2}\}$. By induction assumption there exist ideals ${\mathfrak{a}}_1$ and ${\mathfrak{a}}_2$ of $R$ such that $T_1={\mbox{Att}\,}_R({\mbox{H}\, }^n_{{\mathfrak{a}}_1}(M))$ and $T_2={\mbox{Att}\,}_R({\mbox{H}\, }^n_{{\mathfrak{a}}_2}(M))$. Now by the Lemma 2.7 there exists an ideal ${\mathfrak{a}}$ of $R$ such that $T=T_1\bigcap T_2={\mbox{Att}\,}_R({\mbox{H}\, }^n_{{\mathfrak{a}}}(M))$.
(See [@C Corollary 1.7]) With the notations as in Theorem 2.8, the number of non-isomorphic top local cohomology modules of $M$ with respect to all ideals of $R$ is equal to $2^{|{\mbox{Assh}\,}_R (M)|}$.
It follows from Theorem 2.8 and [@DY2 Theorem 1.6].
[**Acknowledgment.**]{}The authors would like to thank the referee for her/his comments.
[10]{}
F. W. Call, *On local cohomology modules*, J. Pure Appl. Algebra **43** (1986), no. 2, 111–117.
M. T. Dibaei and S. Yassemi, *Some regidity results for highest order local cohomology modules*, Algebra Colloq., to appear.
M. T. Dibaei and S. Yassemi, *Top local cohomology modules*, Algebra Colloq., to appear.
M. T. Dibaei and S. Yassemi, *Attached primes of the top local cohomology modules with respect to an ideal*, Arch. Math. (Basel) **84** (2005), no. 4, 292–297.
I. G. Macdonald and R. Y. Sharp, *An elementary proof of the non-vanishing of certain local cohomology modules*, Quart. J. Math. Oxford **23** (1972), 197–204.
H. Matsumura, *Commutative ring theory*, Cambridge Studies in Advanced Mathematics, 8. Cambridge University Press, Cambridge, 1986.
| {
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Q:
Is there any way to break on the next line of code executed in Visual Studio?
I'm trying to track down a bug that occurs when I click a particular element on an aspx page...
In the past I've had to track down the class that handles that particular event and put a break point on the line that I think should be hit. Often it takes me several tries before I finally find the correct class....especially if the class is a user control buried somewhere...
So it's left me wondering if there is any way to get Visual Studio to break at the next line of code executed after I click an element (say a button) on an aspx page. I know there is a way to break on any exception that is thrown so I'm thinking maybe there is something similar that could help me.
If this sort of feature isn't a possibility, perhaps someone could suggest a better way for me to quickly find the class I want to debug...
A:
Have you tried the Debug > Break All ("pause") button? (Ctrl+Break)
It'll usually break somewhere pretty low on the stack, like at Show() for your main form in a WinForms app, but if you then Step Into to get past that, it'll often work pretty well for this sort of thing.
A:
Are you looking for the Step Into (F11) or Step Over (F10) ?
-- Edit
Do you also know about the Call Stack window? It can help you determine your location, and what is happening.
| {
"pile_set_name": "StackExchange"
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Oxford Instruments - Trading Update
Oxford Instruments plc, a leading provider of high technology products and services to industrial companies and scientific research communities, is today issuing a trading update.
Given the current uncertainty from Covid-19 and the impact on trading, Oxford Instruments plc is issuing its pre-close for the financial year 2019/20 earlier than usual.
The severe disruption as a result of Covid-19 has impacted our customers, with a number of product shipments and installations in the final quarter of the financial year being delayed, in addition to an enforced site closure in California. While we are seeing some re-opening of customer sites in China, the situation in Europe and North America is deteriorating. As a result, the Group currently expects adjusted operating profit for the full year of between £47m to £50m.
Looking ahead, we expect current events to adversely impact trading during the first half of the financial year 2020/21, but at this stage there remains considerable uncertainty. The Group has a strong balance sheet and substantial liquidity, with net cash of over £50m. We operate in robust markets with a well-positioned portfolio of products and solutions for attractive end markets. We remain committed to our strategy and would expect trading to recover in line with a reduction in disruption from Covid-19.
Oxford Instruments' results for the year ended 31 March 2020 will be released on 9 June 2020.
Note: Oxford Instruments compiled consensus analyst forecast for adjusted operating profit (year to 31 March 2020) is £53.3m. This excludes analysts that have not updated forecasts following the disposals of OI Healthcare and our share in Scienta Omicron.
Enquiries:
Oxford Instrumentsplc Tel: 01865 393200
Ian Barkshire, Chief Executive
Gavin Hill, Group Finance Director
MHP CommunicationsTel: 020 3128 8100
Rachel Hirst/Alice McLaren
- Ends -
Issued for and on behalf of Oxford Instruments plc
Notes to Editors
About Oxford Instruments plc
Oxford Instruments designs, supplies and supports high-technology tools and systems with a focus on research and industrial applications. Innovation has been the driving force behind Oxford Instruments' growth and success for 60 years, supporting its core purpose to address some of the world's most pressing challenges.
The first technology business to be spun out from Oxford University, Oxford Instruments is now a global company and is listed on the FTSE250 index of the London Stock Exchange (OXIG). Its strategy focuses on being a customer-centric, market-focused Group, understanding the technical and commercial challenges faced by its customers. Key market segments include Semiconductor & Communications, Advanced Materials, Healthcare & Life Science, and Quantum Technology.
Their portfolio includes a range of core technologies in areas such as low temperature and high magnetic field environments; Nuclear Magnetic Resonance; X-ray, electron, laser and optical based metrology; atomic force microscopy; optical imaging; and advanced growth, deposition and etching.
Oxford Instruments is helping enable a greener economy, increased connectivity, improved health and leaps in scientific understanding. Their advanced products and services allow the world's leading industrial companies and scientific research communities to image, analyse and manipulate materials down to the atomic and molecular level, helping to accelerate R&D, increase manufacturing productivity and make ground-breaking discoveries.
This information is provided by RNS, the news service of the London Stock Exchange. RNS is approved by the Financial Conduct Authority to act as a Primary Information Provider in the United Kingdom. Terms and conditions relating to the use and distribution of this information may apply. For further information, please contact [email protected] or visit www.rns.com.
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Q:
Parse php associative array to javascript object
I want to have a javascript array of "country" objects which at this stage will have only two attributes: name, and geonameId.
I get these countries from a database like so:
$sql = "SELECT name, geonameId FROM countryinfo";
$result = $conn->query($sql);
if ($result->num_rows > 0) {
$rows = array ();
while($row = $result->fetch_assoc()) {
$country["geonameId"]);
$rows[$row['geonameId']] = $row['name'];
}
}
$conn->close();
?>
I then have this javascript script which turns the php array into a javascript one:
<script type="text/javascript">
var allCountries = <? echo json_encode($rows); ?>;
console.log(allCountries);
</script>
I just want to turn that array of key/value pairs into an array of objects so I have easier access to new attributes that I may add in the future. At the moment the javascript array logs to the console like this:
Object {0: "Netherlands Antilles", 49518: "Rwanda", 51537: "Somalia", 69543: "Yemen", 99237: "Iraq", 102358: "Saudi Arabia", 130758: "Iran", 146669: "Cyprus", 149590: "Tanzania", 163843: "Syria", 174982: "Armenia", 192950: "Kenya", 203312:...
How do I convert that array of key/value pairs to an array from javascript objects (with refactoring, I will be adding a Country class and the array will contain Country objects).
A:
My relevant code was changed to this to get it to work:
$sql = "SELECT name, geonameId FROM countryinfo";
$result = $conn->query($sql);
$allCountries = [];
if ($result->num_rows > 0) {
$rows = array ();
while($row = $result->fetch_assoc()) {
$country = array(
"name" => $row['name'],
"geonameId" => $row['geonameId']
);
$allCountries[] = $country;
}
}
$conn->close();
?>
<script type="text/javascript">
var allCountries = <?php echo json_encode($allCountries, JSON_PRETTY_PRINT) ?>;
console.log(allCountries)
</script>
| {
"pile_set_name": "StackExchange"
} |
1. Field of the Invention
The present invention relates to an intake device of an internal combustion engine.
2. Description of the Related Art
In order to create a swirl motion in the combustion chamber when the engine is operating under a light load and to obtain a high volumetric efficiency when the engine is operating under a heavy load at a high speed, it is well known, to equip each cylinder in an engine with a pair of intake valves, and to arrange a fuel injection in an intake passage. The intake passage is divided into two branch intake passages at a position downstream of the fuel injector, and these branch intake passages are connected to the combustion chamber via the corresponding intake valves. A control valve which is closed when the engine is operating under a light load is arranged in one of the branch intake passages (See Japanese Unexamined Patent Publication (Kokai) No. 57-70914). In the above arrangement, when the engine is operating under a light load, and since the control valve is closed, air is fed into the combustion chamber from only one of the branch intake passages, thus creating a swirl motion in the combustion chamber. Conversely, when the engine is operating under a heavy load, and since the control valve is open, air is fed to the combustion chamber from both branch intake passages, and a high volumetric efficiency can be obtained. However, since the fuel injector is arranged upstream of the control valve, some of the fuel injected from the fuel injector when the control valve is closed adheres to the control valve. Therefore, since all of the fuel injected from the fuel injector is not instantaneously fed into the combustion chamber, a good accelerating operation cannot be obtained.
Also, since a swirl motion is created in the combustion chamber when the engine is operating under a light load, the burning velocity of the air-fuel mixture in the combustion chamber can be improved. However, in the above arrangement, ignitability is neglected.
Also, well known is an engine in which each cylinder is equipped with a pair of intake valves and a pair of independently arranged intake passages. A control valve which is closed when the engine is operating under a light load is arranged in one of the intake passages. The intake passages are interconnected via a connecting hole at a position downstream of the control valve, and the fuel injector is arranged in the connecting hole (See Japanese Unexamined Patent Publication No. 57-105534). In this engine, when the engine is operating under a heavy load, and since the control valve is open, air is fed to the combustion chamber from both intake passages, and a high volumetric efficiency can be obtained. In addition, since the fuel injector is arranged downstream of the control valve, there is no danger that fuel injected from the fuel injector will adhere to the control valve.
However, in this engine, since the intake passages are interconnected at a position downstream of the control valve, air is fed to the combustion chamber from both intake passages even if the control valve is closed when the engine is operating under a light load. As a result, the velocity of the air flowing into the combustion chamber is inevitably reduced, and, since it is difficult to create a strong swirl motion in the combustion chamber, it is impossible to sufficiently increase the burning velocity of the air-fuel mixture in the combustion chamber. In this engine, also ignitability is neglected. | {
"pile_set_name": "USPTO Backgrounds"
} |
President Trump abruptly announced Tuesday that acting Defense Secretary Patrick Shanahan is withdrawing from consideration to lead the Pentagon and he's naming Secretary of the Army Mark Esper as his replacement.
While speculation has brewed for days about Shanahan's status, the announcement came shortly after the publication of an explosive USA Today report that the FBI has been probing a violent domestic dispute from 2010 between Shanahan and his then-wife as part of his background investigation.
Speaking to reporters outside the White House, the president said, “it's a difficult time for Pat,” adding Shanahan would take “some time off for family matters.”
WHO IS MARK ESPER, TRUMP’S NEW ACTING SECRETARY OF DEFENSE PICK?
“Mark Esper will be outstanding,” the president said of Shanahan’s replacement. “And, we look forward to working with him for a long period of time to come.”
In a resignation letter Tuesday, Shanahan said “it is unfortunate that a painful and deeply personal family situation from long ago is being dredged up and painted in an incomplete and therefore misleading way in the course of this process.” The Pentagon said Shanahan's resignation will take effect at midnight Sunday.
“I believe my continuing in the confirmation process would force my three children to relive a traumatic chapter in our family's life and reopen wounds we have worked years to heal,” Shanahan said. “Ultimately, their safety and well-being is my highest priority.”
He added, “I would welcome the opportunity to be Secretary of Defense, but not at the expense of being a good father.”
After the 2010 incident, Shanahan and then-wife Kimberley both told police the other punched them, according to USA Today. Shanahan denied the allegations. "Though my marriage ended in sorrow and disappointment, I never laid a hand on my then-wife and cooperated fully in a thorough law enforcement investigation that resulted in her being charged with assault against me—charges which I had dropped in the interest of my family,” Shanahan told USA Today.
The Washington Post also published a story Tuesday detailing other domestic violence incidents involving Shanahan's family, including how his son was arrested in 2011 after allegedly beating his mother with a baseball bat. The Post said Shanahan defended his son, saying at the time he acted in self-defense. Shanahan told the paper this week that resurfacing the incident “will ruin my son’s life,” while backing away from his original self-defense claim.
Without referencing the reporting, Trump announced on Twitter earlier Tuesday the acting secretary will not go forward with confirmation in order to focus on his family.
“Acting Secretary of Defense Patrick Shanahan, who has done a wonderful job, has decided not to go forward with his confirmation process so that he can devote more time to his family,” the president tweeted. “I thank Pat for his outstanding service and will be naming Secretary of the Army, Mark Esper, to be the new Acting Secretary of Defense. I know Mark, and have no doubt he will do a fantastic job!”
Esper has served as secretary of the United States Army since 2017. He graduated from the United States Military Academy in 1986 — the same year as Secretary of State Mike Pompeo.
Last month, the White House announced Trump's intention to have Shanahan permanently lead the department, following his time serving as acting secretary. At the time, Shanahan said he was "honored" by Trump's decision.
“If confirmed by the Senate, I will continue the aggressive implementation of our National Defense Strategy," he said. "I remain committed to modernizing the force so our remarkable Soldiers, Sailors, Airmen, and Marines have everything they need to keep our military lethal and our country safe.”
But in recent days, there were signs that Shanahan’s confirmation had stalled, as the Senate Armed Services Committee -- the panel that would have held hearings on the nomination -- still had not received paperwork formally nominating Shanahan to the position. Fox News was told the panel was still waiting for paperwork from the FBI’s background check.
Shanahan worked at Boeing for over 30 years before coming to the Pentagon as then-Defense Secretary Jim Mattis’s deputy at the start of the Trump administration. He has filled the role of acting defense secretary since Mattis' resignation last year.
Fox News' Lucas Tomlinson and Elizabeth Zwirz contributed to this report. | {
"pile_set_name": "OpenWebText2"
} |
Divergent ontogeny of sigma and phencyclidine binding sites in the rat brain.
The postnatal developmental patterns of sigma (sigma) and phencyclidine (PCP) binding sites were compared in the rat brain. The results show diametrically different ontogenic patterns for the sites. While both the affinity and the density of sigma sites remain constant throughout the developmental period tested (postnatal day 1 to 1 year), the density of PCP binding sites increases from the time of birth, reaching the adult level by postnatal day 14. The differences in developmental patterns provide evidence for distinctive properties of cerebral sigma and PCP binding sites. | {
"pile_set_name": "PubMed Abstracts"
} |
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