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Radiation in equilibrium with plasma and plasma effects on cosmic microwave backgroundMar 13 2019The spectrum of the radiation of a body in equilibrium is given by Planck's law. In plasma, however, waves below the plasma frequency cannot propagate, consequently, the equilibrium radiation inside plasma is necessary different from the Planck spectrum. ... More

Example of shock wave in unstaible medium: The focusing nonlinear Schrodinger equationApr 21 1994Dissipationless shock waves in modulational unstable one-dimensional medium are investigated on the simplest example of integrable focusing nonlinear Schr\''odinger (NS) equation. Our approach is based on the construction of special exact solution of ... More

Forecasting using incomplete modelsMay 12 2017Nov 29 2018We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of incomplete models, i.e. ... More

BeatBox - HPC Simulation Environment for Biophysically and Anatomically Realistic Cardiac ElectrophysiologyMay 19 2016Feb 12 2017The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy ... More

Around Hilbert-Arnold ProblemNov 06 2001This lectures notes consists of four lectures. The first lecture discusses questions around Hilbert-Arnold Problem which is naturally arises from Quantitative Hilbert 16-th problem. In the second lecture we outline author's solution of a weak form of ... More

Ideal DatabasesDec 30 2015From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath theorem from Database Dependency theory. Next, we leverage Algebra/Geometry dictionary ... More

Algorithm for multivariate data standardization up to third momentApr 18 2012An algorithm for transforming multivariate data to a form with normalized first, second and third moments is presented.

Kondo resonance in the case of strong Coulomb screeningNov 05 1995The effect of Coulomb screening on the magnetic impurity behavior is analysed. Two types of the behavior corresponding to either integer or fractional occupation numbers of the low lying magnetic level are described. The features in the dependence of ... More

Pentagramma Mirificum and elliptic functionsJun 18 2011We give an exposition of fragments from Gauss [G] where he discovered, with the help of some work of Jacobi, a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in ... More

Local structure of moduli spacesAug 05 1997Aug 06 1997We describe the algebra of a universal formal deformation as the zeroth cohomology of the dg Lie algebra corresponding to this deformation problem. A report at Arbeitstagung 1997 on the joint work with V.Hinich.

A remark on virtual orientations for complete intersectionsAug 03 1997The aim of this note is to give a simple definition of genus zero virtual orientation classes (or fundamental classes) for projective complete intersections or, more generally, for complete intersections in convex varieties, and to prove a push forward ... More

Boundary relations and boundary conditions for general (not necessarily definite) canonical systems with possibly unequal deficiency indicesSep 10 2011Sep 13 2011We investigate in the paper general (not necessarily definite) canonical systems of differential equation in the framework of extension theory of symmetric linear relations. For this aim we first introduce the new notion of a boundary relation $\G:\gH^2\to\HH$ ... More

Borel Reductions and Cub GamesJul 09 2012It is shown that the power set of $\k$ ordered by the subset relation modulo various versions of the non-stationary deal can be embedded into the partial order of Borel equivalence relations on $2^\k$ under Borel reducibility. Here $\k$ is uncountable ... More

The Grammar Hammer of 2012Dec 17 2012This document is a case study in aggressive self-archiving. It collects all initiatives undertaken by its author in 2012, including unpublished ones, explains their relevance and relation with one another. Discussed topics include guided convergence of ... More

Symmetric operators with real defect subspaces of the maximal dimension. Applications to differential operatorsDec 17 2010Let $\gH$ be a Hilbert space and let $A$ be a simple symmetric operator in $\gH$ with equal deficiency indices $d:=n_\pm(A)<\infty$. We show that if, for all $\l$ in an open interval $I\subset\bR$, the dimension of defect subspaces $\gN_\l(A)(=\Ker (A^*-\l))$ ... More

Investigation of heavy ions diffusion under the influence of current-driven mechanism and compositional waves in plasmaMay 25 2016We consider diffusion caused by a combined influence of the Hall effect and electric currents, and argue that such diffusion forms chemical inhomogeneities in plasma. The considered mechanism can be responsible for the formation of element spots in laboratory ... More

Diffusion in plasma: the Hall effect, compositional waves, and chemical spotsSep 12 2016We consider diffusion caused by a combined influence of the electric current and the Hall effect, and argue that such diffusion can form inhomogeneities of the chemical composition in plasma. The considered mechanism can be responsible for a formation ... More

Compositional waves and variations in the atmospheric abundances of magnetic starsFeb 01 2016The stars of the middle main sequence often have relatively quiescent outer layers and spot-like chemical structures may develope in their atmospheres. Recent observations show that abundance peculiarities can change as stars evolve on the main sequence ... More

Element spots in Ap- and HgMn-stars from current-driven diffusionJan 25 2016The stars of the middle main sequence often have spot-like chemical structures at their surfaces. We consider the diffusion process caused by electric currents that can lead to the formation of such chemical spots. Diffusion is considered using the partial ... More

On the first continuous $L^2$-cohomology of free group factorsDec 19 2013Jan 06 2014We prove that the first continuous $L^2$-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of free difference quotients and shows that one can not distinguish free group factors by means ... More

On the Equivalence Problem of Generalized Abel ODEs under the Action of the Linear Transformations PseudogroupNov 20 2014Nov 28 2015In the present paper we establish the necessary and sufficient conditions for two generalized Abel differential equations to be locally equivalent under the action of the pseudogroup of linear transformations of the form $\{x\mapsto f(x),~ y\mapsto g(x)\cdot ... More

Bars and spheroids in gravimetry problemApr 23 2016The direct gravimetry problem is solved by dividing each deposit body into a set of vertical adjoining bars, whereas in the inverse problem, each deposit body is modelled by a homogeneous ellipsoid of revolution (spheroid). Well-known formulae for the ... More

Phase transitions in the time synchronization modelJan 17 2012We continue the study of the time synchronization model from arXiv:1201.2141 . There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any ... More

The probabilistic approach to limited packings in graphsNov 07 2013We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for any vertex $v\in V(G)$, $\left|N[v] \cap X\right| \le k$, where N[v] is the closed neighbourhood of v. The k-limited ... More

Two-Dimensional Toda-Heisenberg LatticeFeb 04 2013Jun 12 2013We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which ... More

Wegner Estimate for Indefinite Anderson Potentials: Some Recent Results and ApplicationsOct 17 2005We review recent and give some new results on the spectral properties of Schroedinger operators with a random potential of alloy type. Our point of interest is the so called Wegner estimate in the case where the single site potentials change sign. The ... More

A rigidity result for normalized subfactorsMar 12 2019We show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is normalized by the ... More

An extension of the Artin-Mazur theoremSep 01 1999Let M be a compact manifold. We call a mapping f in C^r(M,M) an Artin-Mazur mapping if the number of isolated periodic points of f^n grows at most exponentially in n. Artin and Mazur posed the following problem: What can be said about the set of Artin-Mazur ... More

Microlocal approach to Lusztig's symmetriesJan 23 2014Mar 14 2014We reformulate the De Concini -- Toledano Laredo conjecture about the monodromy of the Casimir connection in terms of a relation between the Lusztig's symmetries of quantum group modules and the monodromy in the vanishing cycles of factorizable sheaves. ... More

Chiral De Rham complex over locally complete intersectionsJun 02 2014We define a version of a derived chiral De Rham complex over a locally complete intersection, thereby "chiralizing" a result by Illusie and Bhatt. A similar construction attaches to a graded ring a dg vertex algebra, which we prove to be Morita equivalent ... More

Factorizable D-modulesNov 18 1996A braided tensor category $FM_{\kappa}$ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category $FS_q$ of factorizable sheaves from q-alg/9604001. This category is equivalent to the category of finite dimensional ... More

Galactic Rotation Curve and Spiral Density Wave Parameters from 73 MasersOct 27 2013Based on kinematic data on masers with known trigonometric parallaxes and measurements of the velocities of HI clouds at tangential points in the inner Galaxy, we have refined the parameters of the Allen-Santillan model Galactic potential and constructed ... More

Stars Outside the Hipparcos List Closely Encountering the Solar SystemSep 24 2010Based on currently available kinematic data, we have searched for stars outside the Hipparcos list that either closely encountered in the past or will encounter in the future the Solar system within several parsecs. For the first time, we have identified ... More

Perverse sheaves and graphs on surfacesJan 08 2016We give an explicit combinatorial description of the category Perv(S,N) of perverse sheaves on an oriented surface S (with boundary) with singularities at a given finite set N. The description is given in terms of any spanning graph K in S with the set ... More

Spinor Fields on the Surface of Revolution and their Integrable Deformations via the mKdV-HierarchyJun 21 1999Spinor fields on surfaces of revolution conformally immersed into 3-dimensional space are considered in the framework of the spinor representations of surfaces. It is shown that a linear problem (a 2-dimensional Dirac equation) related with a modified ... More

Periodic orbits in outer billiardsAug 21 2006Sep 28 2006It is shown that the set of 4-period orbits in outer billiard with piecewise smooth convex boundary has an empty interior, provided that no four corners of the boundary form a parallelogram.

On the Lipschitz continuity of the integrated density of states for sign-indefinite potentialsAug 06 2004Mar 23 2006The present paper is devoted to the study of spectral properties of random Schroedinger operators. Using a finite section method for Toeplitz matrices, we prove a Wegner estimate for some alloy type models where the single site potential is allowed to ... More

Manifestly-covariant chiral PT calculation of nucleon Compton scatteringMar 28 2008Dec 16 2008We compute the Compton scattering off the nucleons in the framework of manifestly covariant baryon chiral perturbation theory (B$\chi$PT). The results for observables differ substantially from the corresponding calculations in heavy-baryon chiral perturbation ... More

The structure and the number of $P_7$-free bipartite graphsJul 29 2016We show that the number of labelled $P_7$-free bipartite graphs with $n$ vertices grows as $n^{\Theta(n)}$. This resolves an open problem posed by Allen [P. Allen, Forbidden induced bipartite graphs. J. Graph Theory 60 (2009), no. 3, 219--241.], and completes ... More

Clique-width of unit interval graphsSep 12 2007The clique-width is known to be unbounded in the class of unit interval graphs. In this paper, we show that this is a minimal hereditary class of unbounded clique-width, i.e., in every hereditary subclass of unit interval graphs the clique-width is bounded ... More

On invariant random positive definite functionsApr 27 2018We give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an invariant random subgroup and a character. We use von Neumann algebras to show that all invariant random positive definite ... More

Hopf decomposition and horospheric limit setsJul 07 2008By looking at the relationship between the recurrence properties of a countable group action with a quasi-invariant measure and the structure of its ergodic components we establish a simple general description of the Hopf decomposition of the action into ... More

About Algebraic Foundations of Majorana-Oppenheimer Quantum Electrodynamics and de Broglie-Jordan Neutrino Theory of LightSep 22 2001Dec 18 2001An algebraic description of basic physical fields (neutrino field, electron-positron field and electromagnetic field) is studied. It is sown that the electromagnetic field can be described within a quotient representation of the proper orthochronous Lorentz ... More

A locally integrable non-separable analytic geodesic flowMar 03 2018Aug 20 2018We explicitely construct an example of an analytic metric on $T^2$ which is non-separable but it is locally integrable on an energy surface. The construction is based on a KAM-like approach and a careful control on what happens on the energy surface.

Measure continuous derivations on von Neumann algebras and applications to L^2-cohomologyOct 27 2011Jul 25 2013We prove that norm continuous derivations from a von Neumann algebra into the algebra of operators affiliated with its tensor square are automatically continuous for both the strong operator topology and the measure topology. Furthermore, we prove that ... More

Boundary effect in competition processesJan 30 2018Sep 03 2018This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a pair of independent ... More

Origin of a sensitive dependence of calculated $ββ$-decay amplitudes on the particle-particle residual interactionFeb 14 2011Jul 12 2011In the present work the sensitivity of the QRPA calculation results to a realistic residual interaction is analyzed in the framework of the approach of Refs. \cite{Rum98,Rodin05}. Both Gamow-Teller (GT) and Fermi (F) \bb-decay amplitudes $M^{2\nu}$, along ... More

Dynamical vs. Auxiliary Fields in Gravitational Waves around a Black HoleMar 30 2007Nov 05 2007The auxiliary/dynamic decoupling method of hep-th/0609001 applies to perturbations of any co-homogeneity 1 background (such as a spherically symmetric space-time or a homogeneous cosmology). Here it is applied to compute the perturbations around a Schwarzschild ... More

Quantum Pump for Fractional ChargeDec 19 2007May 06 2008We propose a theoretical scenario for pumping of fractionally charged quasi-particle in the context of $\nu=1/3$ fractional quantum Hall liquid. We consider quasi-particle pumping across an anti-dot level tuned close to the resonance. Fractional charge ... More

Well-Covered Graphs Without Cycles of Lengths 4, 5 and 6Oct 25 2012A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, ... More

Automorphisms of pointless surfacesJul 17 2018For a geometrically rational surface X over a perfect field of characteristic different from 2 that contains all roots of 1, we show that either X is birational to a product of a projective line and a conic, or the group of birational automorphisms of ... More

On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivativeJun 04 2012Feb 25 2013In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the pseudogroup of contact transformations. These conditions ... More

On the error control at numerical solution of reaction-difusion equationsNov 06 2017We suggest guaranteed, robust a posteriori error bounds for approximate solutions of the reaction-diffusion equations, modeled by the equation $-\Delta u+\sigma u= f$ in $\Omega$ with any $\sigma={\mathrm{const}}\ge 0$. We also term our bounds consistent ... More

Gaussian fluctuations for products of random matricesDec 16 2018Jan 28 2019We study global fluctuations for singular values of $M$-fold products of several right-unitarily invariant $N \times N$ random matrix ensembles. As $N \to \infty$, we show the fluctuations of their height functions converge to an explicit Gaussian field, ... More

A Schauder and Riesz Basis Criterion for Non-Self-Adjoint Schrödinger Operators with Periodic and Antiperiodic Boundary ConditionsApr 26 2011Jun 04 2011Under the assumption that $V \in L^2([0,\pi]; dx)$, we derive necessary and sufficient conditions for (non-self-adjoint) Schr\"odinger operators $-d^2/dx^2+V$ in $L^2([0,\pi]; dx)$ with periodic and antiperiodic boundary conditions to possess a Riesz ... More

On conjugacy of convex billiardsMar 06 2012Given a strictly convex domain $\Omega$ in $\R^2$, there is a natural way to define a billiard map in it: a rectilinear path hitting the boundary reflects so that the angle of reflection is equal to the angle of incidence. In this paper we answer a relatively ... More

Magnetic and spin evolution of isolated neutron stars with the crustal magnetic fieldJan 12 1998We consider the magnetic and spin evolution of isolated neutron stars assuming that the magnetic field is initially confined to the crust. The evolution of the crustal field is determined by the conductive properties of the crust which, in its turn, depend ... More

Recovering Grammar Relationships for the Java Language SpecificationAug 25 2010Grammar convergence is a method that helps discovering relationships between different grammars of the same language or different language versions. The key element of the method is the operational, transformation-based representation of those relationships. ... More

Dynamics of the dominant Hamiltonian, with applications to Arnold diffusionOct 07 2014Jan 23 2015It is well known that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associated averaged system, called slow system. Each resonance is defined by a ... More

The singularly continuous spectrum and non-closed invariant subspacesMar 05 2004Jul 28 2004Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\mathfrak{H}_0$ is of codimension 1, we study the variation ... More

Critical Independent Sets of a GraphJul 28 2014Let $G$ be a simple graph with vertex set $V\left( G\right) $. A set $S\subseteq V\left( G\right) $ is independent if no two vertices from $S$ are adjacent, and by $\mathrm{Ind}(G)$ we mean the family of all independent sets of $G$. The number $d\left( ... More

Failures of the Silver Dichotomy in the Generalised Baire SpaceAug 19 2014We prove results that falsify Silver's dichotomy for Borel equivalence relations on the generalised Baire space under the assumption V=L.

Sofic boundaries of groups and coarse geometry of sofic approximationsAug 07 2016Mar 02 2018Sofic groups generalise both residually finite and amenable groups, and the concept is central to many important results and conjectures in measured group theory. We introduce a topological notion of a sofic boundary attached to a given sofic approximation ... More

Very well-covered graphs with log-concave independence polynomialsNov 10 2004If for any $k$ the $k$-th coefficient of a polynomial $I(G;x)$ is equal to the number of stable sets of cardinality $k$ in the graph $G$, then it is called the independence polynomial of $G$ (Gutman and Harary, 1983). Alavi, Malde, Schwenk and Erdos (1987) ... More

Very well-covered graphs and the unimodality conjectureJun 30 2004If for any $k$ the $k$-th coefficient of a polynomial I(G;x) is equal to the number of stable sets of cardinality $k$ in the graph $G$, then it is called the independence polynomial of $G$ (Gutman and Harary, 1983). Let $a$ be the size of a maximum stable ... More

Recognizing generating subgraphs revisitedNov 11 2018A graph $G$ is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function $w$ is defined on its vertices. Then $G$ is $w$-well-covered if all maximal independent sets are of the same weight. For every graph ... More

On Relating Edges in Graphs without Cycles of Length 4Aug 27 2009An edge xy is relating in the graph G if there is an independent set S, containing neither x nor y, such that S_{x} and S_{y} are both maximal independent sets in G. It is an NP-complete problem to decide whether an edge is relating (Brown, Nowakowski, ... More

1-well-covered graphs revisitedOct 13 2016A graph is well-covered if all its maximal independent sets are of the same size (M. D. Plummer, 1970). A well-covered graph (with at least two vertices) is 1-well-covered if the deletion of every vertex leaves a graph which is well-covered as well (J. ... More

Weighted Well-Covered Claw-Free GraphsDec 29 2013A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, ... More

The Intersection of All Maximum Stable Sets of a Tree and its Pendant VerticesAug 01 2000A stable set in a graph G is a set of mutually non-adjacent vertices, alpha(G) is the size of a maximum stable set of G, and core(G) is the intersection of all its maximum stable sets. In this paper we demonstrate that in a tree T, of order n greater ... More

Coupled-channel effective field theory and proton-$^7$Li scatteringSep 13 2011Oct 21 2011We apply the renormalisation group (RG) to analyse scattering by short-range forces in systems with coupled channels. For two S-wave channels, we find three fixed points, corresponding to systems with zero, one or two bound or virtual states at threshold. ... More

Geometry of antimatroidal point setsJun 12 2008The notion of "antimatroid with repetition" was conceived by Bjorner, Lovasz and Shor in 1991 as a multiset extension of the notion of antimatroid. When the underlying set consists of only two elements, such two-dimensional antimatroids correspond to ... More

On Unimodality of Independence Polynomials of some Well-Covered TreesNov 03 2002The number of stable sets of cardinality $k$ in graph $G$ is the $k$-th coefficient of the independence polynomial of $G$ (I. Gutman and F. Harary, 1983). In 1990, Y. O. Hamidoune proved that for any claw-free graph, its independence polynomial is unimodal, ... More

On $α$-Square-Stable GraphsDec 30 1999The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G) + mu(G) equals its order, then G is a Koenig-Egervary graph. We call G an $\alpha ... More

The Roller-Coaster Conjecture RevisitedDec 12 2016A graph is well-covered if all its maximal independent sets are of the same cardinality (Plummer, 1970). If G is a well-covered graph, has at least two vertices, and G-v is well-covered for every vertex v, then G is a 1-well-covered graph (Staples, 1975). ... More

Kinetic Entropy as a Diagnostic in Particle-in-Cell Simulations of Astrophysical, Heliospheric, and Planetary PlasmasFeb 07 2019We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic electromagnetic particle-in-cell (PIC) simulations and investigate some of its uses to interpret plasma physics processes in astrophysical, heliospheric, and planetary ... More

KdV shock-like waves as invariant solutions of KdV equation symmetriesApr 07 1994We consider the following hypothesis: some of KdV equation shock-like waves are invariant with respect to the combination of the Galilean symmetry and KdV equation higher symmetries. Also we demonstrate our approach on the example of Burgers equation. ... More

Dichotic harmony for the musical practiceMay 14 2010Jul 05 2010The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the different groups of ... More

Major and minor. The formula of musical emotionsMay 22 2009Sep 01 2009The new formulas, which determine sign and amplitude of utilitarian emotions, are proposed on the basis of the information theory of emotions. In area of perception of musical chords the force of emotions depends on the relative pitch of sounds of major ... More

The Information Theory of Emotions of Musical ChordsSep 22 2009Sep 10 2011The paper offers a solution to the centuries-old puzzle - why the major chords are perceived as happy and the minor chords as sad - based on the information theory of emotions. A theory and a formula of musical emotions were created. They define the sign ... More

Theory of a Narrow roton Absorption Line in the Spectrum of a Disk-Shaped SHF ResonatorSep 22 2010Feb 27 2011We calculate the probability of the birth of a circular phonon (c-phonon) in He II by a c-photon of the resonator. It is shown that this probability has sharp maxima at frequencies, where the effective group velocity of the c-phonon is equal to zero; ... More

Mach-Zehnder interferometer in the Fractional Quantum Hall regimeDec 23 2006Aug 15 2007We consider tunneling between two edges of Quantum Hall liquids (QHL) of filling factors $\nu_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, through two point contacts forming Mach-Zehnder interferometer. Quasi-particle description of the interferometer ... More

Factorizable sheaves and quantum groupsDec 01 1997Apr 15 1998The category $\cal{C}$ (studied by Andersen-Jantzen-Soergel) of representations of a Lusztig's small quantum group at a root of unity, together with its modular structure, is defined geometrically, using configuration spaces.

Kinematic Control of the Inertiality of the System of Tycho-2 and UCAC2 Stellar Proper MotionsAug 26 2006Based on the Ogorodnikov-Milne model, we analyze the proper motions of Tycho-2 and UCAC2 stars. We have established that the model component that describes the rotation of all stars under consideration around the Galactic y axis differs significantly ... More

Coherent States for generalized oscillator with finite-dimensional Hilbert spaceDec 19 2006The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As example we consider ... More

Integrality of Framing and Geometric Origin of 2-functionsFeb 23 2017Mar 06 2017We say that a formal power series $\sum a_n z^n$ with rational coefficients is a 2-function if the numerator of the fraction $a_{n/p}-p^2 a_n$ is divisible by $p^2$ for every prime number $p$. One can prove that 2-functions with rational coefficients ... More

Mean-field theory for symmetry-breaking Fermi surface deformations on a square latticeFeb 09 2005We analyze a mean-field model of electrons with pure forward scattering interactions on a square lattice which exhibits spontaneous Fermi surface symmetry breaking with a d-wave order parameter: the surface expands along the kx-axis and shrinks along ... More

Evaluating Callable and Putable Bonds: An Eigenfunction Expansion ApproachJun 22 2012We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction ... More

Accretion-caused deceleration of a gravitationally powerful compact stellar object moving within a dense Fermi gasJan 13 2016We consider accretion-caused deceleration of a gravitationally-powerful compact stellar object traveling within a cold Fermi-gas medium. We provide analytical and numerical estimates of the effect manifestation.

Enhancing the sensitivity of mesoscopic light reflection statistics in weakly disordered media by interface reflectionsDec 30 2015Reflection statistics have not been well studied for optical random media whose mean refractive indices do not match with the refractive indices of their surrounding media. Here, we theoretically study how this refractive index mismatch between a one ... More

Arithmetic-Progression-Weighted Subsequence SumsFeb 25 2011Jun 28 2011Let $G$ be an abelian group, let $S$ be a sequence of terms $s_1,s_2,...,s_{n}\in G$ not all contained in a coset of a proper subgroup of $G$, and let $W$ be a sequence of $n$ consecutive integers. Let $$W\odot S=\{w_1s_1+...+w_ns_n:\;w_i {a term of} ... More

$π$-kinks in strongly ac driven sine-Gordon systemsSep 20 1998We demonstrate that $\pi$-kinks exist in non-parametrically ac driven sine-Gordon systems if the ac drive is sufficiently fast. It is found that, at a critical value of the drive amplitude, there are two stable and two unstable equilibria in the sine-Gordon ... More

The Birman-Schwinger principle in von Neumann algebras of finite typeOct 09 2006We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the ... More

Matrix random products with singular harmonic measureJul 07 2008Any Zariski dense countable subgroup of $SL(d,R)$ is shown to carry a non-degenerate finitely supported symmetric random walk such that its harmonic measure on the flag space is singular. The main ingredients of the proof are: (1) a new upper estimate ... More

Dynamics of filaments of scroll wavesMar 26 2014This has been written as a chapter for "Engineering Chemical Complexity II", and as such does not have an abstract.

Conditions for propagation and block of excitation in an asymptotic model of atrial tissueNov 07 2005Dec 08 2005Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for asymptotic reduction of the models. ... More

Ergodic properties of boundary actions and Nielsen--Schreier theoryJan 29 2009Aug 26 2011We study the basic ergodic properties (ergodicity and conservativity) of the action of an arbitrary subgroup $H$ of a free group $F$ on the boundary $\partial F$ with respect to the uniform measure. Our approach is geometrical and combinatorial, and it ... More

Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi mapsApr 04 2018We study the peculiarities of the solitary state appearance in the ensemble of nonlocally coupled chaotic maps. We show that nonlocal coupling and features of the partial elements lead to arising of multistability in the system. The existence of solitary ... More

Existence and stability of periodic solutions in a neural field equationDec 27 2017We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption that the activation function is a discontinuous step function and the ... More

Transverse Thermoelectric Response as a Probe for Existence of QuasiparticlesSep 07 2016The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey sigma_{xy} = - sigma_{yx}. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, alpha_{xy}= ... More