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Multidimensional SDE with anticipating initial process and reflection | In this paper, the strong solutions $ (X, L)$ of multidimensional stochastic
differential equations with reflecting boundary and possible anticipating
initial random variables is established. The key is to obtain some substitution
formula for Stratonovich integrals via a uniform convergence of the
corresponding Riemann sums and to prove continuity of functionals of $ (X, L)$.
|
Constructing a quadrilateral inside another one | Connect each vertex of a convex quadrilateral Q to the midpoint of the next
(proceeding counterclockwise) side. The four connecting lines create an
interior quadrilateral I. We study the ratio area(I)/area(Q). We also determine
what happens to area(I)/area(Q) when the four midpoints are replaced by points
which divide the sides in the ratio of rho to (1-rho) proceeding clockwise.
Here rho is any fixed number satisfying 0 < rho < 1.
|
Complex quotients by nonclosed groups and their stratifications | We define the notion of complex stratification by quasifolds and show that
such spaces occur as complex quotients by certain nonclosed subgroups of tori
associated to convex polytopes. The spaces thus obtained provide a natural
generalization to the nonrational case of the notion of toric variety
associated with a rational convex polytope.
|
A Cohen-Macaulay algebra has only finitely many semidualizing modules | We prove the result stated in the title, which answers the equicharacteristic
case of a question of Vasconcelos.
|
Twin Paradox and Causality | After pointing out the historical avatar at the origin of a would be twin or
clock paradox, we argue that, at least on a local scale, the (re-qualified)
paradox is but a necessary consequence of the sole principle of causality.
|
Remarks to Glazek's results on n-ary groups | It is a survey of the results obtained by K. Glazek's and his co-workers. We
restrict our attention to the problems of axiomatizations of n-ary groups,
classes of n-ary groups, properties of skew elements and homomorphisms induced
by skew elements, constructions of covering groups, classifications and
representations of n-ary groups. Some new results are added too.
|
Modelling Thickness-Dependence of Ferroelectric Thin Film Properties | We present a segregrated strain model that describes the thickness-dependent
dielectric properties of ferroelectric films. Using a phenomenological Landau
approach, we present results for two specific materials, making comparison with
experiment and with first-principles calculations whenever possible. We also
suggest a "smoking gun" benchtop probe to test our elastic scenario.
|
Parabolic surfaces in hyperbolic space with constant curvature | We study parabolic linear Weingarten surfaces in hyperbolic space
$\rlopezh^3$. In particular, we classify two family of parabolic surfaces:
surfaces with constant Gaussian curvature and surfaces that satisfy the
relation $a\kappa_1+b\kappa_2=c$, where $\kappa_i$ are the principal
curvatures, and $a,b$ and $c$ are constant.
|
The Orientation of the Reconnection X-line | We propose a criterion for identifying the orientation of the X-line when two
regions of plasma with arbitrary densities, temperatures, and magnetic fields
undergo reconnection. The X-line points in the direction that maximizes the
(suitably-defined) Alfv\'en speed characterizing the reconnection outflow. For
many situations a good approximation is that the X-line bisects the angle
formed by the magnetic fields.
|
A remark on helical waveguides | Motivated by a proposal to create an optical helix-shaped waveguides for cold
atoms and molecules, we discuss local perturbations which can create bound
states in such a setting. This is known about a local slowdown of the twist; we
show that a similar effect can result from a local tube protrusion or a change
of the helix radius in correlation with its pitch angle.
|
Moriond QCD 2007 - Theory Summary | Developments reported at the 2007 Moriond Workshop on QCD and Hadronic
Interactions are reviewed and placed in a theoretical context.
|
Results for a turbulent system with unbounded viscosities: weak
formulations, existence of solutions, boundedness, smoothness' | We consider a circulation system arising in turbulence modelling in fluid
dynamics with unbounded eddy viscosities. Various notions of weak solutions are
considered and compared. We establish existence and regularity results. In
particular we study the boundedness of weak solutions. We also establish an
existence result for a classical solution
|
Holonomy representations which are a diagonal direct sum of two faithful
representations | We study holonomy representations admitting a pair of supplementary faithful
sub-representations. In particular the cases where the sub-representations are
isomorphic respectively dual to each other are treated. In each case we have a
closer look at the classification in small dimension.
|
The Complexity of Simple Stochastic Games | In this paper we survey the computational time complexity of assorted simple
stochastic game problems, and we give an overview of the best known algorithms
associated with each problem.
|
Pseudocontinuation and cyclicity for random power series | We prove that a random function in the Hardy space $H^2$ is a non-cyclic
vector for the backward shift operator almost surely. The question of existence
of a local pseudocontinuation for a random analytic function is also studied.
|
Time-dependent Density Functional calculation of e-H scattering | Phase shifts for single-channel elastic electron-atom scattering are derived
from time-dependent density functional theory. The H$^-$ ion is placed in a
spherical box, its discrete spectrum found, and phase shifts deduced.
Exact-exchange yields an excellent approximation to the ground-state Kohn-Sham
potential, while the adiabatic local density approximation yields good singlet
and triplet phase shifts.
|
Raman spectra of L-leucine crystals | Single crystal samples of L-leucine, C6H13NO2, a fundamental aliphatic amino
acid of the human body, have been studied by Raman spectroscopy at temperatures
from 300 to 430 K over the spectral range from 50 to 3100 cm-1. A tentative
assignment of all bands is given. For high temperatures, several modifications
on the Raman spectra were observed at about 353 K, giving evidence that the
L-leucine crystal undergoes a structural phase transition.
|
The equivariant analytic index for proper groupoid actions | The paper constructs the analytic index for an elliptic pseudodifferential
family of $L^{m}_{\rho,\de}$-operators invariant under the proper action of a
continuous family groupoid on a $G$-compact, $C^{\infty,0}$ $G$-space.
|
On-Shell Methods in Perturbative QCD | We review on-shell methods for computing multi-parton scattering amplitudes
in perturbative QCD, utilizing their unitarity and factorization properties. We
focus on aspects which are useful for the construction of one-loop amplitudes
needed for phenomenological studies at the Large Hadron Collider.
|
The Fourier algebra for locally compact groupoids | We introduce and investigate using Hilbert modules the properties of the {\em
Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a
duality theorem for such groupoids in terms of multiplicative module maps. This
includes as a special case the classical duality theorem for locally compact
groups proved by P. Eymard.
|
Approximating reals by sums of rationals | We consider the question of approximating any real number $\alpha$ by sums of
$n$ rational numbers $\frac{a_1}{q_1} + \frac{a_2}{q_2} + ... +
\frac{a_n}{q_n}$ with denominators $1 \leq q_1, q_2, ..., q_n \leq N$. This
leads to an inquiry on approximating a real number by rational numbers with a
prescribed number of prime factors in the denominator.
|
Light projectile scattering off the Color Glass Condensate | We systematically compute the Gaussian average of Wilson lines inherent in
the Color Glass Condensate, which provides useful formulae for evaluation of
the scattering amplitude in the collision of a light projectile and a heavy
target.
|
Fermions in Self-dual Vortex Background on a String-like Defect | By using the self-dual vortex background on extra two-dimensional Riemann
surfaces in 5+1 dimensions, the localization mechanism of bulk fermions on a
string-like defect with the exponentially decreasing warp-factor is obtained.
We give the conditions under which localized spin 1/2 and 3/2 fermions can be
obtained.
|
Motzkin numbers of higher rank: Generating function and explicit
expression | The generating function and an explicit expression is derived for the
(colored) Motzkin numbers of higher rank introduced recently. Considering the
special case of rank one yields the corresponding results for the conventional
colored Motzkin numbers for which in addition a recursion relation is given.
|
Comments on six papers published by S.P. Anjali Devi and R. Kandasamy | Comments on six papers published by S.P. Anjali Devi and R. Kandasamy in Heat
and Mass Transfer, ZAMM, Mechanics Research Communications, International
Communications in Heat and Mass Transfer, Communications in Numerical Methods
in Engineering, Journal of Computational and Applied Mechanics
In conclusion all the above papers are of very low quality, written without
care and are partly or completely wrong.
|
Symmetric Crystals for $\gl_\infty$ | In the preceding paper, we formulated a conjecture on the relations between
certain classes of irreducible representations of affine Hecke algebras of type
B and symmetric crystals for $\gl_\infty$. In the present paper, we prove the
existence of the symmetric crystal and the global basis for $\gl_\infty$.
|
An analogue of Gutzmer's formula for Hermite expansions | We prove an analogue of Gutzmer's formula for Hermite expansions. As a
consequence we obtain a new proof of a characterisation of the image of $
L^2(\R^n) $ under the Hermite semigroup. We also obtain some new orthogonality
relations for complexified Hermite functions.
|
Simplified Chain Inflation | We propose a simplified chain inflation model and calculate the primordial
power spectra of the scalar and tensor fluctuations. The spectral index and the
tensor-scalar ratio are respectively 0.972 and 0.089 which are consistent with
present cosmological observations.
|
The 2d Gross-Neveu Model at Finite Temperature and Density with Finite
Corrections | We use the linear $\delta$ expansion, or optimized perturbation theory, to
evaluate the effective potential for the two dimensional Gross-Neveu model at
finite temperature and density obtaining analytical equations for the critical
temperature, chemical potential and fermionic mass which include finite $N$
corrections. Our results seem to improve over the traditional large-N
predictions.
|
Kahane-Khinchin type Averages | We prove a Kahane-Khinchin type result with a few random vectors, which are
distributed independently with respect to an arbitrary log-concave probability
measure on $\R^n$. This is an application of small ball estimate and Chernoff's
method, that has been recently used in the context of Asymptotic Geometric
Analysis in [1], [2].
|
Primitive flag-transitive generalized hexagons and octagons | Suppose that an automorphism group $G$ acts flag-transitively on a finite
generalized hexagon or octagon $\cS$, and suppose that the action on both the
point and line set is primitive. We show that $G$ is an almost simple group of
Lie type, that is, the socle of $G$ is a simple Chevalley group.
|
On the Complement of the Projective Hull in C^n | We prove that if $K$ is a compact subset of an affine variety O = P^n - D
(where D is a projective hypersuface), and if K is a compact subset of a closed
analytic subvariety V \subset O, then the projective hull K^ of K has the
property that K^ \cap O is contained in V. If V is smooth and 1-dimensional,
then K^ \cap O is also closed in O. The result has applications to graphs in
C^2 of functions in the disk algebra.
|
Dynamical Complexity, Intermittent Turbulence, Coarse-Grained
Dissipation, Criticality and Multifractal Processes | The ideas of dynamical complexity induced intermittent turbulence by sporadic
localized interactions of coherent structures are discussed. In particular, we
address the phenomenon of magnetic reconfiguration due to coarse-grained
dissipation as well as the interwoven connection between criticality and
multifractal processes. Specific examples are provided.
|
Double covering of the Painlev\'e I equation and its singular analysis | In this note, we will do analysis of accessible singular points for a
polynomial Hamiltonian system obtained by taking a double covering of the
Painlev\'e I equation. We will show that this system passes the Painlev\'e
$\alpha$-test for all accessible singular points $P_i \ (i=1,2,3)$. We note its
holomorphy condition of the first Painlev\'e system.
|
On some Hamiltonian structures of coupled Painlev\'e II systems in
dimension four | We find and study a two-parameter family of coupled Painlev\'e II systems in
dimension four with affine Weyl group symmetry of several types. Moreover, we
find a three-parameter family of polynomial Hamiltonian systems in two
variables $t,s$. Setting $s=0$, we can obtain an autonomous version of the
coupled Painlev\'e II systems. We also show its symmetry and holomorphy
conditions.
|
Studies on the Garnier system in two variables | We study some Hamiltonian structures of the Garnier system in two variables
from the viewpoints of its symmetry and holomorphy properties. We also give a
generalization of {\it Okamoto transformation \it}of the sixth Painlev\'e
system.
|
Coupled Painlev\'e III system with affine Weyl group symmetry of type
$D_6^{(1)}$ | We find and study a six-parameter family of coupled Painlev\'e III systems in
dimension six with affine Weyl group symmetry of type $D_6^{(1)}$. We also find
and study its degenerate systems with affine Weyl group symmetry of types
$B_5^{(1)}$ and $D_5^{(2)}$.
|
Characters of highest weight modules over affine Lie algebras are
meromorphic functions | We show that the characters of all highest weight modules over an affine Lie
algebra with the highest weight away from the critical hyperplane are
meromorphic functions in the positive half of Cartan subalgebra, their
singularities being at most simple poles at zeros of real roots. We obtain some
information about these singularities.
|
Explicit Green functions for spin-orbit Hamiltonians | We derive explicit expressions for Green functions and some related
characteristics of the Rashba and Dresselhaus Hamiltonians with a uniform
magnetic field.
|
Helicity-type integral invariants for Hamiltonian systems | In this note, we consider generalizations of the asymptotic Hopf invariant,
or helicity, for Hamiltonian systems with one-and-a-half degrees of freedom and
symplectic diffeomorphisms of a two-disk to itself.
|
Convex comparison of service disciplines in real time queues | We present a comparison of the service disciplines in real-time queueing
systems (the customers have a deadline before which they should enter the
service booth). We state that giving priority to customers having an early
deadline minimizes the average stationary lateness. We show this result by
comparing adequate random vectors with the Schur-Convex majorization ordering.
|
Quantum p-adic spaces and quantum p-adic groups | We discuss examples of non-commutative spaces over non-archimedean fields.
Those include non-commutative and quantum affinoid algebras, quantized K3
surfaces and quantized locally analytic p-adic groups.
|
Schwartz functions on Nash manifolds | In this paper we extend the notions of Schwartz functions, tempered functions
and generalized Schwartz functions to Nash (i.e. smooth semi-algebraic)
manifolds. We reprove for this case classically known properties of Schwartz
functions on $R^n$ and build some additional tools which are important in
representation theory.
|
Discrete and Continuum Quantum Gravity | I review discrete and continuum approaches to quantized gravity based on the
covariant Feynman path integral approach.
|
A 2-generated 2-related group with no non-trivial finite factors | We construct a 2-generated 2-related group without non-trivial finite
factors. That answers a question of J. Button.
|
Green's function of a finite chain and the discrete Fourier transform | A new expression for the Green's function of a finite one-dimensional lattice
with nearest neighbor interaction is derived via discrete Fourier transform.
Solution of the Heisenberg spin chain with periodic and open boundary
conditions is considered as an example. Comparison to Bethe ansatz clarifies
the relation between the two approaches.
|
Some group theory problems | This is a survey of some problems in geometric group theory which I find
interesting. The problems are from different areas of group theory. Each
section is devoted to problems in one area. It contains an introduction where I
give some necessary definitions and motivations, problems and some discussions
of them. For each problem, I try to mention the author. If the author is not
given, the problem, to the best of my knowledge, was formulated by me first.
|
On weakly convex star-shaped polyhedra | Weakly convex polyhedra which are star-shaped with respect to one of their
vertices are infinitesimally rigid. This is a partial answer to the question
whether every decomposable weakly convex polyhedron is infinitesimally rigid.
The proof uses a recent result of Izmestiev on the geometry of convex caps.
|
Uniqueness thresholds on trees versus graphs | Counter to the general notion that the regular tree is the worst case for
decay of correlation between sets and nodes, we produce an example of a
multi-spin interacting system which has uniqueness on the $d$-regular tree but
does not have uniqueness on some infinite $d$-regular graphs.
|
Excedance numbers for permutations in complex reflection groups | Recently, Bagno, Garber and Mansour studied a kind of excedance number on the
complex reflection groups and computed its multidistribution with the number of
fixed points on the set of involutions in these groups. In this note, we
consider the similar problems in more general cases and make a correction of
one result obtained by them.
|
Some smooth Finsler deformations of hyperbolic surfaces | Given a closed hyperbolic Riemannian surface, the aim of the present paper is
to describe an explicit construction of smooth deformations of the hyperbolic
metric into Finsler metrics that are not Riemannian and whose properties are
such that the classical Riemannian results about entropy rigidity, marked
length spectrum rigidity and boundary rigidity all fail to extend to the
Finsler category.
|
Higher genus Gromov-Witten invariants of the Grassmannian, and the
Pfaffian Calabi-Yau threefolds | We solve Bershadsky-Cecotti-Ooguri-Vafa (BCOV) holomorphic anomaly equation
to determine the higher genus Gromov-Witten invariants ($g \leq 5$) of the
derived equivalent Calabi-Yau threefolds, which are of the appropriate
codimensions in the Grassmannian Gr(2,7) and the Pfaffian Pf(7).
|
Controlling statistical properties of stored light | Statistical properties of outgoing light pulses are studies after they have
been stored in a medium of atoms in the tripod configuration. A generalized
Hong-Ou-Mandel interference, storing of squeezed states and homodyne signal
analysis are discussed in the context of their dependence on the parameters of
the control fields used for light storage and release.
|
Quantum Parrondo's game with random strategies | We present a quantum implementation of Parrondo's game with randomly switched
strategies using 1) a quantum walk as a source of ``randomness'' and 2) a
completely positive (CP) map as a randomized evolution. The game exhibits the
same paradox as in the classical setting where a combination of two losing
strategies might result in a winning strategy. We show that the CP-map scheme
leads to significantly lower net gain than the quantum walk scheme.
|
A link polynomial via a vertex-edge-face state model | We construct a 2-variable link polynomial, called $W_L$, for classical links
by considering simultaneously the Kauffman state models for the Alexander and
for the Jones polynomials. We conjecture that this polynomial is the product of
two 1-variable polynomials, one of which is the Alexander polynomial.
We refine $W_L$ to an ordered set of 3-variable polynomials for those links
in 3-space which contain a Hopf link as a sublink.
|
An Exact Bosonization Rule for c=1 Noncritical String Theory | We construct a string field theory for c=1 noncritical strings using the loop
variables as the string field. We show how one can express the nonrelativistic
free fermions which describes the theory, in terms of these string fields.
|
On maximal entanglement between two pairs in four-qubit pure states | We show that the state with the highest known average two-particle von
Neumann entanglement entropy proposed by Sudbery and one of the authors gives a
local maximum of this entropy. We also show that this is not the case for an
alternative highly entangled state proposed by Brown et al.
|
Group-theoretic Description of Riemannian Spaces | It is shown that a locally geometrical structure of arbitrarily curved
Riemannian space is defined by a deformed group of its diffeomorphisms
|
Direct simulation for a homogenous gas | A probabilistic analysis of the direct simulation of a homogeneous gas is
given. A hierarchy of equations similar to the BBGKY hierarchy for the reduced
probability densities is derived. By invoking the molecular chaos assumption,
an equation similar to the Boltzmann equation for the single particle
probability density and the corresponding H-theorem is derived.
|
The Vogel-Fulcher-Tamman law in the elastic theory of glass transition | We propose that the origin of the Vogel-Fulcher-Tammann law is the increase
of the range of elastic interaction between local relaxation events in a
liquid. In this picture, we discuss the origin of cooperativity of relaxation,
the absence of divergence of relaxation time at a finite temperature and the
crossover to a more Arrhenius behaviour at low temperature.
|
On the alpha-Amenability of Hypergroups | Let $UC(K)$ denote the Banach space of all bounded uniformly continuous
functions on a hypergroup $K$. The main results of this article concern on the
$\alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It
is also shown that a Sturm-Liouville hypergroup with a positive index is
$\alpha$-amenable if and only if $\alpha=1$.
|
Canonical Deformed Groups of Diffeomorphisms and Finite Parallel
Transports in Riemannian Spaces | We show that finite parallel transports of vectors in Riemannian spaces,
determined by the multiplication law in the deformed groups of diffeomorphisms,
and sequences of infinitesimal parallel transports of vectors along geodesics
are equivalent.
|
On the geometric quantization of twisted Poisson manifolds | We study the geometric quantization process for twisted Poisson manifolds.
First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for
twisted Poisson manifolds and we use it in order to characterize their
prequantization bundles and to establish their prequantization condition. Next,
we introduce a polarization and we discuss the quantization problem. In each
step, several examples are presented.
|
Fluctuation theorems and orbital magnetism in nonequilibrium state | We study Langevin dynamics of a driven charged particle in the presence as
well as in the absence of magnetic field. We discuss the validity of various
work fluctuation theorems using different model potentials and external drives.
We also show that one can generate an orbital magnetic moment in a
nonequilibrium state which is absent in equilibrium.
|
Spontaneous Lorentz Violation, Gravity, and Nambu-Goldstone Modes | A brief summary is presented of recent work examining the fate of the
Nambu-Goldstone modes in gravitational theories with spontaneous Lorentz
violation.
|
Four-Quark Condensates in Nucleon QCD Sum Rules | The in-medium behavior of the nucleon spectral density including
self-energies is revisited within the framework of QCD sum rules. Special
emphasis is given to the density dependence of four-quark condensates. A
complete catalog of four-quark condensates is presented and relations among
them are derived. Generic differences of such four-quark condensates occurring
in QCD sum rules for light baryons and light vector mesons are discussed.
|
On the Conditions to Extend Ricci Flow | Along a Ricci flow solution on a closed manifold, we show that if Ricci
curvature is uniformly bounded from below, then a scalar curvature integral
bound is enough to extend flow. Moreover, this integral bound condition is
optimal in some sense.
|
Order preserving transformations of the Hilbert grassmannian: complex
case | Let $H$ be a separable complex Hilbert space. Denote by ${\mathcal
G}_{\infty}(H)$ the Grassmannian consisting of closed linear subspaces with
infinite dimension and codimension. This Grassmannian is partially ordered by
the inclusion relation. We show that every continuous order preserving
bijective transformation of ${\mathcal G}_{\infty}(H)$ is induced by an
invertible bounded semi-linear operator.
|
Optical Multicolor Photometry of Spectrophotometric Standard Stars | Photoelectric data on the Johnson-Kron-Cousins UBVRI broadband photometric
system are provided for a set of stars which have been used as
spectrophotometric standard stars at the Hubble Space Telescope.
|
Algebraic Bethe ansatz for the elliptic quantum group
$E_{\tau,\eta}(A_2^{(2)})$ | We implement the Bethe anstaz method for the elliptic quantum group
$E_{\tau,\eta}(A_2^{(2)})$. The Bethe creation operators are constructed as
polynomials of the Lax matrix elements expressed through a recurrence relation.
We also give the eigenvalues of the family of commuting transfer matrices
defined in the tensor product of fundamental representations.
|
Involutory quasi-Hopf algebras | We introduce and investigate the basic properties of an involutory (dual)
quasi-Hopf algebra. We also study the representations of an involutory
quasi-Hopf algebra and prove that an involutory dual quasi-Hopf algebra with
non-zero integral is cosemisimple.
|
Spectral Analysis of GRBs Measured by RHESSI | The Ge spectrometer of the RHESSI satellite is sensitive to Gamma Ray Bursts
(GRBs) from about 40 keV up to 17 MeV, thus ideally complementing the Swift/BAT
instrument whose sensitivity decreases above 150 keV. We present preliminary
results of spectral fits of RHESSI GRB data. After describing our method, the
RHESSI results are discussed and compared with Swift and Konus.
|
Exact N=4 correlators of AdS(3)/CFT(2) | We extend to chiral N=4 operators the holographic agreement recently found
between correlators of the symmetric orbifold of M^4 at large N and type IIB
strings propagating in AdS(3) x S^3 x M^4, where M^4=T^4 or K3. We also present
expressions for some bulk correlators not yet computed in the boundary.
|
Representation Of Level Paths Of An Analytic Function | We find an arc-parameterization of the contour on which an given analytic
function has constant modulus. This contour is seen to satisfy a differential
equation which we explicitly give.
|
Some integer sequences based on derangements | Sequences whose terms are equal to the number of functions with specified
properties are considered. Properties are based on the notion of derangements
in a more general sense. Several sequences which generalize the standard notion
of derangements are thus obtained. These sequences generate a number of integer
sequences from the well-known Sloane's encyclopedia.
|
Open quantum dynamics via environmental monitoring | A general method is discussed to obtain Markovian master equations which
describe the interaction with the environment in a microscopic and
non-perturbative fashion. It is based on combining time-dependent scattering
theory with the concept of continuous quantum measurements. The applications to
the case of a Brownian point particle and to the case of a complex molecule,
both in the presence of a gaseous environment, are outlined.
|
On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics | In Bohmian mechanics the distribution $|\psi|^2$ is regarded as the
equilibrium distribution. We consider its uniqueness, finding that it is the
unique equivariant distribution that is also a local functional of the wave
function $\psi$.
|
Pure Virtual Braids Homotopic to the Identity Braid | Two virtual link diagrams are homotopic if one may be transformed into the
other by a sequence of virtual Reidemeister moves, classical Reidemeister
moves, and self crossing changes. We recall the pure virtual braid group. We
then describe the set of pure virtual braids that are homotopic to the identity
braid.
|
Triacontagonal coordinates for the E(8) root system | This note gives an explicit formula for the elements of the E(8) root system.
The formula is triacontagonally symmetric in that one may clearly see an action
by the cyclic group with 30 elements. The existence of such a formula is due to
the fact that the Coxeter number of E(8) is 30.
|
Extensions of operator algebras I | We transcribe a portion of the theory of extensions of C*-algebras to general
operator algebras. We also include several new general facts about
approximately unital ideals in operator algebras and the C*-algebras which they
generate.
|
Ordered involutive operator spaces | This is a companion to recent papers of the authors; here we construct the
`noncommutative
Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of
Hilbert space operators. The morphisms in the universal property of the
boundary preserve order.
As an application, we consider `maximal' and `minimal' unitizations of such
ordered operator spaces.
|
Elliptic hypergeometric functions | This is a brief overview of the status of the theory of elliptic
hypergeometric functions to the end of 2012 written as a complementary chapter
to the Russian edition of the book by G.E. Andrews, R. Askey, and R. Roy,
Special Functions, Encycl. of Math. Appl. 71, Cambridge Univ. Press, 1999.
|
Communication through plasma sheaths | We wish to transmit messages to and from a hypersonic vehicle around which a
plasma sheath has formed. For long distance transmission, the signal carrying
these messages must be necessarily low frequency, typically 2 GHz, to which the
plasma sheath is opaque. The idea is to use the plasma properties to make the
plasma sheath appear transparent.
|
Studying the scalar bound states of the $K\bar K$ system in the
Bethe-Salpeter formalism | We study the possible bound states of the $K\bar K$ system in the
Bethe-Salpeter formalism in the ladder and instantaneous approximations. We
find that the bound states exist. However, these bound states have very small
decay widths. Therefore, besides the possible $K\bar K$ component, there may be
some other structures in the observed $f_0(980)$ and $a_0(980)$ .
|
Proof of the Flohr-Grabow-Koehn conjectures for characters of
logarithmic conformal field theory | In a recent paper Flohr, Grabow and Koehn conjectured that the characters of
the logarithmic conformal field theory c_{k,1}, of central charge
c=1-6(k-1)^2/k, admit fermionic representations labelled by the Lie algebra
D_k. In this note we provide a simple analytic proof of this conjecture.
|
Two-parameter Poisson-Dirichlet measures and reversible exchangeable
fragmentation-coalescence processes | We show that for $0<\alpha<1$ and $\theta>-\alpha$, the Poisson-Dirichlet
distribution with parameter $(\alpha, \theta)$ is the unique reversible
distribution of a rather natural fragmentation-coalescence process. This
completes earlier results in the literature for certain split and merge
transformations and the parameter $\alpha =0$.
|
The existence of superinvolutions | Superinvolutions on graded associative algebras constitute a source of Lie
and Jordan superalgebras. Graded versions of the classical Albert and
Albert-Riehm Theorems on the existence of superinvolutions are proven.
Surprisingly, the existence of superinvolutions of the first kind is a rare
phenomenon, as nontrivial central division superalgebras are never endowed with
this kind of superinvolutions.
|
Hartree-Fock Approximation and Entanglement | The relation between the correlation energy and the entanglement is
analytically constructed for the Moshinsky's model of two coupled harmonic
oscillators. It turns out that the two quantities are far to be proportional,
even at very small couplings. A comparison is made also with the 2-point Ising
model.
|
A study of global monopole in Lyra geometry | A class of exact static solution around a global monopole resulting from the
breaking of a global S0(3) symmetry is obtained in the context of Lyra
geometry. Our solution is shown to possess an interesting feature like
wormholes space-time. It has been shown that the global monopole exerts no
gravitational force on surrounding non-relativistic matter.
|
Inverse Geometric Approach to the Simulation of the Circular Growth. The
Case of Multicellular Tumor Spheroids | We demonstrate the power of the genetic algorithms to construct the cellular
automata model simulating the growth of 2-dimensional close-to-circular
clusters revealing the desired properties, such as the growth rate and, at the
same time, the fractal behavior of their contours. The possible application of
the approach in the field of tumor modeling is outlined.
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Algorithm for Evaluation of the Interval Power Function of Unconstrained
Arguments | We describe an algorithm for evaluation of the interval extension of the
power function of variables x and y given by the expression x^y. Our algorithm
reduces the general case to the case of non-negative bases.
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Complex data processing: fast wavelet analysis on the sphere | In the general context of complex data processing, this paper reviews a
recent practical approach to the continuous wavelet formalism on the sphere.
This formalism notably yields a correspondence principle which relates wavelets
on the plane and on the sphere. Two fast algorithms are also presented for the
analysis of signals on the sphere with steerable wavelets.
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Fold cobordisms and stable homotopy groups | We show that the cobordism groups of negative codimensional folds maps
contain direct sums of stable homotopy groups of Thom spaces of vector bundles
like the circle and the infinite dimensional projective space. We give
geometrical invariants which detect these direct summands.
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Uniformly continuous maps between ends of R-trees | There is a well-known correspondence between infinite trees and ultrametric
spaces which can be interpreted as an equivalence of categories and comes from
considering the end space of the tree.
In this equivalence, uniformly continuous maps between the end spaces are
translated to some classes of coarse maps (or even classes of metrically proper
lipschitz maps) between the trees.
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New Form of the T-Duality Due to the Stability of a Compact Dimension | We study behaviors of a compact dimension and the $T$-duality, in the
presence of the wrapped closed bosonic strings. When the closed strings
interact and form another system of strings, the radius of compactification
increases. This modifies the $T$-duality, which we call it as $T$-duality-like.
Some effects of the $T$-duality-like will be studied.
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Severi varieties and self rational maps of K3 surfaces | Self-rational maps of generic algebraic K3 surfaces are conjectured to be
trivial. We relate this conjecture to a conjecture concerning the
irreducibility of the universal Severi varieties parametrizing nodal curves of
given genus and degree lying on some K3 surface. We also establish a number of
numerical constraints satisfied by such non trivial rational maps, that is of
topological degree >1.
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A dual lagrangian for non-Abelian tensor gauge fields | For non-Abelian tensor gauge fields of the lower rank we have found an
alternative expression for the field strength tensors, which transform
homogeneously with respect to the complementary gauge transformations and allow
us to construct the dual Lagrangian.
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Grafting hyperbolic metrics and Eisenstein series | The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non
holomorphic Eisenstein series $E(\zeta;2)$ are combined to provide an explicit
expansion for the hyperbolic metrics for degenerating families of Riemann
surfaces. Applications include an asymptotic expansion for the Weil-Petersson
metric and a local form of symplectic reduction.
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A Critical Phenomenon in Solitonic Ising Chains | We discuss a phase transition of the second order taking place in non-local
1D Ising chains generated by specific infinite soliton solutions of the KdV and
BKP equations.
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Effects of Eye-phase in DNA unzipping | The onset of an "eye-phase" and its role during the DNA unzipping is studied
when a force is applied to the interior of the chain. The directionality of the
hydrogen bond introduced here shows oscillations in force-extension curve
similar to a "saw-tooth" kind of oscillations seen in the protein unfolding
experiments. The effects of intermediates (hairpins) and stacking energies on
the melting profile have also been discussed.
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