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Modelling the Propagation of a Weak Fast-Mode MHD Shock Wave near a 2D Magnetic Null Point Using Nonlinear Geometrical AcousticsMay 24 2012We present the results of analytical modelling of fast-mode magnetohydrodynamic wave propagation near a 2D magnetic null point. We consider both a linear wave and a weak shock and analyse their behaviour in cold and warm plasmas. We apply the nonlinear ... More

Coronal loop transverse oscillations excited by different driver frequenciesMay 14 2019We analyse transverse oscillations of a coronal loop excited by continuous monoperiodic motions of the loop footpoint at different frequencies in the presence of gravity. Using the MPI-AMRVAC code, we perform three-dimensional numerical magnetohydrodynamic ... More

Dimesoatoms production in high energy collisionsSep 19 2016The production of two meson electromagnetic bound states and free meson pairs $\pi^+\pi^-$, $K^+K^-$, $\pi^+ K^{\mp}$ in relativistic collisions has been considered. It was shown that making use of the exact Coulomb wave function for dimesoatom (DMA) ... More

Cathodoluminescence of CdZnSSe crystals synthesized in 19th century bead glassJan 30 2019The letter presents an experimental study of band edge cathodoluminescence spectra of CdZnSSe crystals that nucleated and grew in glass melt during red glass manufacturing. The crystallites exhibit bright band edge cathodoluminescence both at room temperature ... More

Experimentation With Fuzzy Interest Forwarding in Named Data NetworkingFeb 08 2018Feb 14 2018In the current Named Data Networking implementation, forwarding a data request requires finding an exact match between the prefix of the name carried in the request and a forwarding table entry. However, consumers may not always know the exact naming, ... More

Cathodoluminescence of CdZnSSe crystals synthesized in 19th century bead glassJan 30 2019Apr 25 2019The article presents an experimental investigation of band-edge cathodoluminescence of CdZnSSe crystals that nucleated and grew in silicate glass melt during its production. We have studied Zn-rich red glass made for manufacture of seed beads in the 19th ... More

Controllability of 2D Euler and Navier-Stokes Equations by Forcing 4 ModesJul 18 2005We study controllability issues for the 2D Euler and Navier-Stokes (NS) systems under periodic boundary conditions. These systems describe motion of homogeneous ideal or viscous incompressible fluid on a two-dimensional torus $\mathbb{T}^2$. We assume ... More

Fermion masses and quantum numbers from extra dimensionsJun 28 2001We study the localization of fermions on a brane embedded in a space-time with $AdS_n \times M^k$ geometry. Quantum numbers of localized fermions are associated with their rotation momenta around the brane. Fermions with different quantum numbers have ... More

Weak Convergence of Obliquely Reflected DiffusionsSep 06 2015Aug 20 2016Burdzy and Chen (1998) proved results on weak convergence of multidimensional normally reflected Brownian motions. We generalize their work by considering obliquely reflected diffusion processes. We require weak convergence of domains, which is stronger ... More

Proalgebraic crossed modules of quasirational presentationsJul 11 2015Sep 24 2016We introduce the concept of quasirational relation modules for discrete and pro-$p$ presentations of discrete and pro-$p$ groups and show that aspherical presentations and their subpresentations are quasirational. In the pro-$p$-case quasirationality ... More

Building the Signature of Set Theory Using the MathSem ProgramMar 31 2016Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we consider a deductive ... More

A Simple Recurrence Within the $3$-adics and Mixed-Radix $\textbf{2}$-adics of the 3x+1 Accelerated First-Inverse MapJun 25 2015Feb 18 2016This article analyzes the $3x+1$ Accelerated First-Inverse map: we will consider the functional powers of the function $\mathcal{B}: Z_3 \to Z_3$ defined as $$ \mathcal{B}\left(3q+r\right) = \begin{cases} 3q, & r = 0\\ \notag 4q+1, & r = 1\\ \notag 2q+1, ... More

Cohomology theories for highly structured ring spectraNov 18 2002This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological Andr\'e-Quillen cohomology and of topological derivations are described. We give sample calculations of ... More

Exploring mutexes, the Oracle RDBMS retrial spinlocksDec 29 2012Spinlocks are widely used in database engines for processes synchronization. KGX mutexes is new retrial spinlocks appeared in contemporary Oracle versions for submicrosecond synchronization. The mutex contention is frequently observed in highly concurrent ... More

Quantum ChromodynamicsMay 08 2012The classical Lagrangian of chromodynamics, its quantization in the perturbation theory framework, and renormalization form the subject of these lectures. Symmetries of the theory are discussed. The dependence of the coupling constant $\alpha_s$ on the ... More

Special relativity (in Russian)Aug 03 2011May 30 2015A modern elementary introduction to special relativity for advanced school children or first-year university students, in Russian. I try to demonstrate that relativity does not contradict common sense; on the contrary, it follows from common sense logically. ... More

Explicit Rates of Exponential Convergence for Reflected Jump-Diffusions on the Half-LineSep 06 2015May 12 2016Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary distribution, as time goes ... More

Classical R-matrices for generalized so(p,q) topsJan 19 2004An integrable deformation of the known integrable model of two interacting p-dimensional and q-dimensional spherical tops is considered. After reduction this system gives rise to the generalized Lagrange and the Kowalevski tops. The corresponding Lax ... More

The Maupertuis principle and canonical transformations of the extended phase spaceJan 01 2001We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals of motion, ... More

Canonical transformations of the time for the Toda lattice and the Holt systemOct 29 1999For the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are invariant under change of the time. On the other hand, mapping of the time ... More

On integrable deformations of the spherical topSep 07 1999The motion on the sphere $S^2$ with the potential $V= (x_1x_2x_3)^{-2/3}$ is considered. The Lax representation and the linearisation procedure for this two-dimensional integrable system are discussed.

Effect of Activity and Inter-Cluster Correlations on Information-Theoretic Properties of Neural NetworksNov 06 2014On the basis of solutions of the master equation for networks with a small number of neurons it is shown that the conditional entropy and integrated information of neural networks depend on their average activity and inter-cluster correlations.

The Analogue of Dedekind Eta Functions for Calabi-Yau Manifilolds II. (Algebraic, Analytic Discriminants and the Analogue of Baily-Borel Compactification of the Moduli Space of CY Manifolds.)May 07 2008In this paper we construct the analogue of Dedekind eta-function on the moduli space of polarized CY manifolds. We prove that the L-two norm of eta is the regularized determinants of the Laplacians of the CY metric on (0,1) forms. We construct the analogue ... More

Determinants of the Calabi-Yau Metrics on K3 Surfaces, Discriminants, Theta Lifts and Counting Problems in the A and B ModelsDec 06 2006Dec 09 2006The Dedekind eta functions plays important role in different branches of Mathematics and Theoretical Physics. One way to construct Dedekind Eta function to use the explicit formula (Kroncker limit formula) for the regularized determinants of the Laplacian ... More

Witten's Geometric Quantization of the Moduli of CY ThreefoldsApr 07 2000Mar 06 2007In this paper we will use our results about the local deformation theory of Calabi-Yau manifolds to define a Higgs field on the tangent bundle of the moduli space of CY threefolds. Combining this Higgs field with the Levi-Chevitta connection of the Weil-Petersson ... More

Comment on Perez et al [PRX 2, 041005 (2012), arXiv:1209.2011]Jan 30 2013Recently Perez et al [arXiv:1209.2011] wrote on the spectral slope of MHD turbulence claiming that it is consistent with -3/2. This work contains a number of errors, factual inaccuracies and puzzling methods in the interpretation of numerics. We argue ... More

On the parallel spectrum in MHD TurbulenceJul 09 2014Feb 03 2015Anisotropy of MHD turbulence has been studied extensively for many years, most prominently by measurements in the solar wind and high resolution simulations. The spectrum parallel to the local magnetic field was observed to be steeper than perpendicular ... More

A Candidate for Solvable Large N Lattice Gauge Theory in D>2Oct 11 1999I propose a class of D\geq{2} lattice SU(N) gauge theories dual to certain vector models endowed with the local [U(N)]^{D} conjugation-invariance and Z_{N} gauge symmetry. In the latter models, both the partitition function and Wilson loop observables ... More

Nonabelian Duality and Solvable Large N Lattice SystemsNov 01 1999We introduce the basics of the nonabelian duality transformation of SU(N) or U(N) vector-field models defined on a lattice. The dual degrees of freedom are certain species of the integer-valued fields complemented by the symmetric groups' \otimes_{n} ... More

Lectures on Soft-Collinear Effective TheoryNov 27 2016Dec 04 2016Introductory lectures on SCET mainly following the first chapters of arXiv:1410.1892

A key to the projective model of homogeneous metric spacesDec 28 2014A metric introduced on a projective space yields a homogeneous metric space known as a Cayley-Klein geometry. This construction is applicable not only to Euclidean and non-Euclidean spaces but also to kinematic spaces (space-times). A convenient algebraic ... More

Clifford algebra and the projective model of homogeneous metric spaces: FoundationsJul 08 2013This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to physicists ... More

Optimal sequential procedures with Bayes decision rulesNov 30 2008Jul 02 2009In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed ... More

Semantic programming: method $Δ_0^p$-enrichments and polynomial computable fixed pointsMar 19 2019Computer programs fast entered in our live and the questions associated with the execution of these programs have become the most relevant in our days. Programs should work efficiently, i.e. work as quickly as possible and spend as little resources as ... More

Modeling Magnetic Field Amplification in Nonlinear Diffusive Shock AccelerationApr 23 2009This research was motivated by the recent observations indicating very strong magnetic fields at some supernova remnant shocks, which suggests in-situ generation of magnetic turbulence. The dissertation presents a numerical model of collisionless shocks ... More

Towards classification of Fracton phases: the multipole algebraDec 12 2018We present an effective field theory approach to the Fracton phases. The approach is based the notion of a multipole algebra. It is an extension of space(-time) symmetries of a charge-conserving matter that includes global symmetries responsible for the ... More

Geometric Defects in Quantum Hall StatesApr 13 2016We describe a geometric (or gravitational) analogue of the Laughlin quasiholes in the fractional quantum Hall states. Analogously to the quasiholes these defects can be constructed by an insertion of an appropriate vertex operator into the conformal block ... More

Semantic programming: method of $Δ_0^p$-enrichments and polynomial analogue of the Gandy fixed point theoremMar 19 2019May 09 2019Computer programs fast entered in our life and the questions associated with the execution of these programs have become the most relevant in our days. Programs should work efficiently, i.e. work as quickly as possible and spend as little resources as ... More

The exactly solvable two-dimensional stationary Schrödinger operators obtaining by the nonlocal Darboux transformationNov 24 2012The Fokker-Planck equation associated with the two - dimensional stationary Schr\"odinger equation has the conservation low form that yields a pair of potential equations. The special form of Darboux transformation of the potential equations system is ... More

Computational geometry in Heisenberg group Heis^3Apr 10 2002Among eight possible geometric structures on three-dimensional manifolds less studied from the differential geometric point of view are those modelled on the Heisenberg group $Heis^3$. We consider the Heisenberg left-invariant metric and use some results ... More

Stochastic flows with reflectionOct 25 2008Some topological properties of stochastic flow $\varphi_t(x)$ generated by stochastic differential equation in a ${\mathbb R}^d_+$ with normal reflection at the boundary are investigated. Sobolev differentiability in initial condition is received. The ... More

Rationality of capped descendent vertex in $K$-theoryDec 04 2016In this paper we analyze the fundamental solution of the \textit{quantum difference equation} (qde) for the moduli space of instantons on two-dimensional projective space. The qde is a $K$-theoretic generalization of the quantum differential equation ... More

On the André motive of generalized Kummer type varietiesApr 25 2019We study Andr\'e motives of projective hyperk\"ahler manifolds that are deformation equivalent to the generalized Kummer varieties. We prove that the motives of such manifolds are abelian, i.e. they are contained in the subcategory generated by the motives ... More

Spectral Geometry of Riemannian SubmanifoldsJul 21 2005In this thesis we study the geometry of the fixed point set $\Sigma$ of a smooth mapping $\Phi: M\to M$ on a smooth compact Riemannian manifold $M$ without boundary by computing the asymptotic expansion of the deformed heat trace $\Trace \Phi\exp(t\Delta)$ ... More

Solution of the KdV equation using evolutionary vesselsOct 16 2011Nov 09 2011In this work we present a new method for solving of the Korteweg-de Vries (KdV) equation q'_t = - \dfrac{3}{2} q q'_x + \dfrac{1}{4} q"'_{xxx}. The proposed method is a particular case of the theory of evolutionary vessels, developed in this work. Inverse ... More

Infinite Systems of Competing Brownian ParticlesMar 17 2014Sep 04 2016Consider a system of infinitely many Brownian particles on the real line. At any moment, these particles can be ranked from the bottom upward. Each particle moves as a Brownian motion with drift and diffusion coefficients depending on its current rank. ... More

Two-Sided Infinite Systems of Competing Brownian ParticlesSep 06 2015Jun 15 2017Two-sided infinite systems of Brownian particles with rank-dependent dynamics, indexed by all integers, exhibit different properties from their one-sided infinite counterparts, indexed by positive integers, and from finite systems. Consider the gap process, ... More

Value range of solutions to the chordal Loewner equation with restriction on the driving functionMay 08 2019May 14 2019We consider a value range $\{g(i,T)\}$ of solutions to the chordal Loewner equation with the restriction $|\lambda(t)| \le c$ on the driving function. We use reachable set methods and the Pontryagin maximum principle.

Controllability of the cubic Schroedinger equation via a low-dimensional source termMay 09 2011Nov 15 2011We study controllability of $d$-dimensional defocusing cubic Schroedinger equation under periodic boundary conditions. The control is applied additively, via a source term, which is a linear combination of few complex exponentials (modes) with time-variant ... More

Controlling Multiparticle System on a Line. ISep 13 2008We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among those: studying ... More

Solution of the KdV equation on the line with analytic initial potentialMar 21 2013We present a theory of Sturm-Liouville non-symmetric vessels, realizing an inverse scattering theory for the Sturm-Liouville operator with analytic potentials on the line. This construction is equivalent to the construction of a matrix spectral measure ... More

Solution of the Sturm-Liouville and the Korteweg-de-Vries equations with periodic and quasi-periodic parameters using theory of vesselsMay 23 2012Dec 08 2012We prove the existence of solutions to the Sturm-Liouville (SL) equation -y"(x)+q(x)y(x) = s^2 y(x) with periodic and quasi-periodic potential q(x) using theory of SL vessels, implementing a Backlund transformation of SL equation. In this paper quasi-periodic ... More

Quantum sphere S^4 as a non-Levi conjugacy classOct 12 2011Oct 25 2011We construct a U_h(sp(4))-equivariant quantization of the four-dimensional complex sphere S^4 regarded as a conjugacy class, Sp(4)/Sp(2)x Sp(2), of a simple complex group with non-Levi isotropy subgroup, through an operator realization of the quantum ... More

Surgery for partially hyperbolic dynamical systems I. Blow-ups of invariant submanifoldsSep 19 2016We suggest a method to construct new examples of partially hyperbolic diffeomorphisms. We begin with a partially hyperbolic diffeomorphism $f\colon M\to M$ which leaves invariant a submanifold $N\subset M$. We assume that $N$ is an Anosov submanifold ... More

On dynamical smash productAug 30 2007In the theory of dynamical Yang-Baxter equation, with any Hopf algebra $H$ and a certain $H$-module and $H$-comodule algebra $L$ (base algebra) one associates a monoidal category. Given an algebra $A$ in that category, one can construct an associative ... More

Exploring Oracle RDBMS latches using Solaris DTraceNov 02 2011Rise of hundreds cores technologies bring again to the first plan the problem of interprocess synchronization in database engines. Spinlocks are widely used in contemporary DBMS to synchronize processes at microsecond timescale. Latches are Oracle RDBMS ... More

Effective weak Lagrangians in the Standard Model and B decaysNov 04 2013Weak processes (e.g., B decays) with characteristic energies <<M_W can be described by an effective theory which does not contain W, Z and other heavy particles (Higgs, t). Its Lagrangian contains four-fermion interaction operators. Essentially it is ... More

Decoupling in QED and QCDDec 20 2012Feb 06 2013Decoupling of a heavy flavour in QCD is discussed in a pedagogical way. First we consider a simpler case: decoupling of muons in QED. All calculations are done up to 2 loops.

Quantum computer for dummies (in Russian)Aug 17 2011An introduction (in Russian) to quantum computers, quantum cryptography, and quantum teleportation for students who have no previous knowledge of these subjects, but know quantum mechanics. Several simple examples are considered in detail using the quantum ... More

Lectures on QED and QCDAug 23 2005The lectures are a practical introduction to perturbative calculations in QED and QCD. I discuss methods of calculation of one- and two-loop diagrams in dimensional regularization, MSbar and on-shell renormalization schemes, decoupling of heavy-particle ... More

New solvable stochastic volatility models for pricing volatility derivativesMay 16 2012Jun 30 2012Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter $\gamma$ takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 ... More

Splitting and Matrix Exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumpsMay 23 2014May 27 2014This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order ... More

Efficient Solution of Backward Jump-Diffusion PIDEs with Splitting and Matrix ExponentialsApr 10 2013Apr 12 2014We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on financial processes ... More

Pricing options with VG model using FFTMar 16 2005Jan 15 2010We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, Carr-Madan's FFT method could blow up for certain values of the model parameters ... More

The Maupertuis principle and integrable systemsSep 25 2000We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals of motion, ... More

Duality between integrable Stackel systemsNov 27 1998For the Stackel family of the integrable systems a non-canonical transformation of the time variable is considered. This transformation may be associated to the ambiguity of the Abel map on the corresponding hyperelliptic curve. For some Stackel's systems ... More

Canonical transformations of the extended phase space, Toda lattices and Stackel family of integrable systemsSep 10 1999We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to transformations ... More

Dynamical boundary conditions for integrable latticesJan 09 1998Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.

Universal Nonlinear Small-Scale DynamoSep 21 2011We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds numbers (Re). We argue that it is universal in a sense that magnetic energy grows at a rate which is a constant fraction C_E of the total turbulent dissipation rate. On the basis ... More

The Spectral Slope and Kolmogorov Constant of MHD turbulenceNov 10 2010The spectral slope of strong MHD turbulence has recently been a matter of controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3 slope of turbulence, shallower slopes were often reported by numerical studies. We argue that earlier ... More

Quotients of cubic surfacesJun 16 2015Let $\Bbbk$ be any field of characteristic zero, $X$ be a cubic surface in $\mathbb{P}^3_{\Bbbk}$ and $G$ be a group acting on $X$. We show that if $X(\Bbbk) \ne \varnothing$ and $G$ is not trivial and not a group of order $3$ acting in a special way ... More

Brane world cosmological constant in the models with large extra dimensionsJan 16 2001We consider ``brane universe'' with nonzero tension in the models with large extra dimensions. We find exact solutions of higher-dimensional Einstein equations with single flat Minkowsky brane of arbitrary large tension (or brane cosmological constant) ... More

Two-Sided Infinite Systems of Competing Brownian ParticlesSep 06 2015Oct 14 2016Two-sided infinite systems of Brownian particles with rank-dependent dynamics, indexed by all integers, exhibit qualitatively different properties from their one-sided infinite counterparts, indexed by positive integers, and from finite systems. Consider ... More

Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial CyclesOct 01 2007Nov 19 2007We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification of three-geometries) ... More

Sequential multiple hypothesis testing in presence of control variablesDec 15 2008Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ at this stage can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the problem ... More

Optimal sequential testing of two simple hypotheses in presence of control variablesDec 07 2008Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the classical problem ... More

The Dirac equation as one fourth-order equation for one function -- a general, manifestly covariant formFeb 09 2015Oct 21 2017Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac spinor function. ... More

One real function instead of the Dirac spinor functionAug 28 2010Aug 19 2011Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of the fourth order for the ... More

Efficient Heating of Thin Cylindrical Targets by Broad Electromagnetic Beams IMay 18 2004In many high-profile applications, such as nuclear fusion and pumping of active media of short-wavelength lasers, it is necessary to achieve high specific input of power of an electromagnetic beam in a target. Diffraction sets the lower limit to the transverse ... More

On dilaton-assisted generation of the Fermi scale from the Planck scaleMar 27 2019In scale-invariant theories of gravity the Planck mass $M_P$, which appears due to spontaneous symmetry breaking, can be the only scale at the classical level. It was argued that the second scale can be generated by a quantum non-perturbative gravitational ... More

Multilayered Model of SpeechJan 08 2018Human speech is the most important part of General Artificial Intelligence and subject of much research. The hypothesis proposed in this article provides explanation of difficulties that modern science tackles in the field of human brain simulation. The ... More

Some resolvent set properties of band operators with matrix elementsDec 23 2014For operators generated by a certain class of infinite band matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order finite difference equations. This enables us ... More

Smooth conjugacy of Anosov diffeomorphisms on higher dimensional toriApr 24 2008Sep 27 2008Let $L$ be a hyperbolic automorphism of $\mathbb T^d$, $d\ge3$. We study the smooth conjugacy problem in a small $C^1$-neighborhood $\mathcal U$ of $L$. The main result establishes $C^{1+\nu}$ regularity of the conjugacy between two Anosov systems with ... More

Notes on Chern-Simons Theory in the Temporal GaugeOct 27 2009We analyze the perturbative series expansion of vacuum expectation values (vevs) for Wilson loop operators in Chern-Simons (CS) gauge theory in the temporal gauge $A_{0}=0$. Following J. Labastida and E. P\'erez we introduce the notion of the kernels ... More

On a Class of Diverse Market ModelsJan 25 2013Oct 29 2013A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which means that its ... More

Two-dimensional dynamical systems admitting the normal shiftNov 18 2000Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.

Explicit Rational Solution of the KZ Equation (example)Sep 07 2007We investigate the Knizhnik-Zamolodchikov linear differential system. The coefficients of this system are rational functions. We have proved that the solution of the KZ system is rational when k is equal to two and n is equal to three (see [5]) . In this ... More

Rational Solution of the KZ equation (example)Dec 06 2006We investigate the Knizhnik-Zamolodchikov linear differential system. The coefficients of this system are rational functions. We prove that the solution of the KZ system is rational when $k$ is equal to two and $n$ is equal to three. While doing so, we ... More

Classification of KdV vessels with constant parameters and two dimensional outer spaceJul 06 2014In this article we classify vessels producing solutions of some completely integrable PDEs, presenting a \textit{unified} approach for them. The classification includes such important examples as Korteweg-de Vries (KdV) and evolutionary Non Linear Schr\" ... More

Regularization of Mickelsson generators for non-exceptional quantum groupsDec 29 2015Let $\mathfrak{g}'\subset \mathfrak{g}$ be the pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces $\mathbb{C}^{N-2}\subset \mathbb{C}^N$ and $U_q(\mathfrak{g}')\subset U_q(\mathfrak{g})$ the ... More

Change of word types to word tokens ratio in the course of translation (based on Russian translations of K. Vonnegut novels)Mar 01 2010The article provides lexical statistical analysis of K. Vonnegut's two novels and their Russian translations. It is found out that there happen some changes between the speed of word types and word tokens ratio change in the source and target texts. The ... More

Using descriptive mark-up to formalize translation quality assessmentSep 18 2008The paper deals with using descriptive mark-up to emphasize translation mistakes. The author postulates the necessity to develop a standard and formal XML-based way of describing translation mistakes. It is considered to be important for achieving impersonal ... More

A new method for solving completely integrable PDEsDec 08 2012The inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV), the family of evolutionary Non Linear Schrodinger (NLS) equations, Kadomtzev-Petviashvili ... More

On free decompositions of verbally closed subgroups of free products of finite groupsMay 05 2016Jul 06 2016For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.

Searches for New Physics in Photon Final StatesApr 17 2006Jul 10 2006The Run I results on the searches for new physics in photon final states were intriguing. The rare 2 electrons + 2 photons + missing transverse energy (MET) candidate event and the measured event rate for the signature lepton + photon + MET, which was ... More

A new model test in high energy physics in frequentist and Bayesian statistical formalismsJul 14 2016A problem of a new physical model test given observed experimental data is a typical one for modern experiments of high energy physics (HEP). A solution of the problem may be provided with two alternative statistical formalisms, namely frequentist and ... More

Taxation as an instrument of stimulation of innovation-active business entitiesDec 07 2014The analysis of the theoretical material revealed the lack of consensus on defini-tion of the tax stimulation of innovation-active business entities within the re-gional taxation. The definition tax stimulation of innovation-active business en-tities ... More

Star-product on complex sphere $\mathbb{S}^{2n}$Aug 28 2016We construct a $U_q(\mathrm{so}(2n+1))$-equivariant local star-product on the complex sphere $\mathbb{S}^{2n}$ as a Non-Levi conjugacy class $SO(2n+1)/SO(2n)$.

Irreducibility of fusion modules over twisted Yangians at generic pointDec 23 2006Jan 28 2007With any skew Young diagram one can associate a one parameter family of "elementary" modules over the Yangian $\Yg(\g\l_N)$. Consider the twisted Yangian $\Yg(\g_N)\subset \Yg(\g\l_N)$ associated with a classical matrix Lie algebra $\g_N\subset\g\l_N$. ... More

On neighborhood product of some Horn axiomatizable logicsSep 11 2016We consider modal logics of products of neighborhood frames. We define n-product of modal logics as the logic of all products of neighborhood frames of corresponding logics and find n-product of any two pretransitive Horn axiomatizable logics. As a corrolary ... More