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Fate of the $η'$ in the Quark Gluon PlasmaMar 13 2019In this paper we study the $\eta'$ mass in $N_f=2+1+1$ lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results favour a small dip ... More

Correlations of Abelian monopoles in quark-gluon plasmaAug 27 2012In this paper the properties of thermal Abelian monopoles in the deconfinement phase of the SU(2) gluodynamics are considered. In particular, to study the properties of the Abelian monopole component of QGP we calculate three-point correlation functions ... More

Study of shear viscosity of SU (2)-gluodynamics within lattice simulationJul 22 2015This paper is devoted to the study of two-point correlation function of the energy-momentum tensor T_{12}T_{12} for SU(2)-gluodynamics within lattice simulation of QCD. Using multilevel algorithm we carried out the measurement of the correlation function ... More

Lattice field theory simulations of Dirac semimetalsApr 24 2017Jun 13 2017In this paper the observed Dirac semimetals Na$_3$Bi and Cd$_3$As$_2$ are studied within lattice simulation. We formulate lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice ... More

Ultrahigh refractive index sensitivity of TE-polarized electromagnetic waves in graphene at the interface between two dielectric mediaMay 30 2013The behavior of the TE and TM electromagnetic waves in graphene at the interface between two semi-infinite dielectric media is studied. The dramatic influence on the TE waves propagation even at very small changes in the optical contrast between the two ... More

Lattice study of QCD at finite chiral density: topology and confinementFeb 25 2019In this paper we study the properties of QCD at nonzero chiral density $\rho_5$, which is introduced through chiral chemical potential $\mu_5$. The study is performed within lattice simulation of QCD with dynamical rooted staggered fermions. We first ... More

On the Wiener complexity and the Wiener index of fullerene graphsMay 05 2019Fullerenes are molecules in the form of cage-like polyhedra, consisting solely of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex $v$ of a graph is the sum of distances from $v$ to all the other ... More

Statistical Significance of the Netflix ChallengeJul 24 2012Inspired by the legacy of the Netflix contest, we provide an overview of what has been learned---from our own efforts, and those of others---concerning the problems of collaborative filtering and recommender systems. The data set consists of about 100 ... More

On properties of a flow generated by an SDE with discontinuous driftJul 05 2012Dec 20 2012We consider a stochastic flow on $\mathds{R}$ generated by an SDE with its drift being a function of bounded variation. We show that the flow is differentiable with respect to the initial conditions. Asymptotic properties of the flow are studied.

On the strong uniqueness of a solution to singular stochastic differential equationsDec 12 2011We prove the existence and uniqueness of a strong solution for an SDE on a semi-axis with singularities at the point 0. The result obtained yields, for example, the strong uniqueness of non-negative solutions to SDEs governing Bessel processes.

On Brownian motion on the plane with membranes on rays with a common endpointFeb 02 2009We consider a Brownian motion on the plane with semipermeable membranes on n rays that have a common endpoint in the origin. We obtain the necessary and sufficient conditions for the process to reach the origin and we show that the probability of hitting ... More

Lattice Quantum Monte Carlo Study of Chiral Magnetic Effect in Dirac SemimetalsJul 31 2017Dec 08 2017In this paper Chiral Magnetic Effect (CME) in Dirac semimetals is studied by means of lattice Monte Carlo simulation. We measure conductivity of Dirac semimetals as a function of external magnetic field in parallel $\sigma_{\parallel}$ and perpendicular ... More

Monte-Carlo study of Dirac semimetals phase diagramAug 25 2016In this paper the phase diagram of Dirac semimetals is studied within lattice Monte-Carlo simulation. In particular, we concentrate on the dynamical chiral symmetry breaking which results in semimetal/insulator transition. Using numerical simulation we ... More

Lattice simulation of $QC_2D$ with $N_f=2$ at non-zero baryon densityNov 16 2015The lattice simulations of $QC_2D$ with two flavors of staggered fermions and non-zero quark chemical potential $\mu_q$ have been performed. Dependencies of the Polyakov loop, chiral condensate and baryon number density on $\mu_q$ were studied. We found ... More

Electromagnetic superconductivity of vacuum induced by strong magnetic field: numerical evidence in lattice gauge theoryApr 19 2011Jan 03 2013Using numerical simulations of quenched SU(2) gauge theory we demonstrate that an external magnetic field leads to spontaneous generation of quark condensates with quantum numbers of electrically charged rho mesons if the strength of the magnetic field ... More

Optimization of the parameters in the RHIC single crystal heavy ion collimationNov 29 2001In the framework of the project to design and test a collimation system prototype using bent channeling crystal for cleaning of the RHIC heavy ion beam halo, we have studied the optimal length and bending angle of a silicon (110) single crystal proposed ... More

Lattice study of static quark-antiquark interactions in dense quark matterAug 20 2018Feb 09 2019In this paper we study the interactions among a static quark-antiquark pair in the presence of dense two-color quark matter with lattice simulation. To this end we compute Polyakov line correlation functions and determine the renormalized color averaged, ... More

Poisson homology of r-matrix type orbits I: example of computationDec 25 1998Oct 01 1999In this paper we consider the Poisson algebraic structure associated with a classical $r$-matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the $r$-matrix type Poisson orbits. ... More

Fate of the $η'$ in the Quark Gluon PlasmaMar 13 2019Mar 25 2019In this paper we study the $\eta'$ in $N_f=2+1+1$ lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results favour a small dip in ... More

Flow polynomials as Feynman amplitudes and their $α$-representationSep 05 2016Let $G$ be a connected graph; denote by $\tau(G)$ the set of its spanning trees. Let $\mathbb F_q$ be a finite field, $s(\alpha,G)=\sum_{T\in\tau(G)} \prod_{e \in E(T)} \alpha_e$, where ${\alpha_e\in \mathbb F_q}$. Kontsevich conjectured in 1997 that ... More

Baryons in a soft-wall AdS-Schwarzschild approach at low temperatureMay 06 2019Recently we derived a soft-wall AdS-Schwarzschild approach at small temperatures for the description of hadrons with integer spin and adjustable number of constituents (mesons, tetraquarks, dibaryons, etc.). In the present paper we extend our formalism ... More

Mesons in a soft-wall AdS-Schwarzschild approach at low temperatureFeb 04 2019Apr 01 2019We derive a holographic soft-wall approach in five dimensional AdS-Schwarzschild space for the description of mesons at finite temperature. In this first application we consider the small temperature limit and derive analytical expression for the mass ... More

Sobolev functions on infinite-dimensional domainsSep 21 2013We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from ... More

Observation of light dragging in rubidium vapor cellDec 23 2003We report on the experimental demonstration of light dragging effect due to atomic motion in a rubidium vapor cell. We found that the minimum group velocity is achieved for light red-shifted from the center of the atomic resonance, and that the value ... More

Virtually free finite-normal-subgroup-free groups are strongly verbally closedDec 09 2017Jun 22 2018Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup.

On The Zariski Topology Of Automorphism Groups Of Affine Spaces And AlgebrasJul 09 2012Dec 13 2016We study the Zariski topology of the ind-groups of polynomial and free associative algebras $\Aut(K[x_1,...,x_n])$ (which is equivalent to the automorphism group of the affine space $\Aut(K^n))$) and $\Aut(K< x_1,..., x_n>$ via $\Ind$-schemes, toric varieties, ... More

Independence of the B-KK Isomorphism of Infinite PrimeDec 21 2015Feb 27 2019We investigate a certain class of $\Ind$-scheme morphisms corresponding to homomorphisms between the automorphism group of the $n$-th complex Weyl algebra and the group of Poisson structure-preserving automorphisms of the commutative complex polynomial ... More

Harmonic Twistor Formalism and Transgression on Hyperkähler manifoldsDec 26 2000In this paper we continue our study of the fourth order transgression on hyper\"ahler manifolds introduced in the previous paper. We give a local construction for the fourth-order transgression of the Chern character form of an arbitrary vector bundle ... More

Curving Yang-Mills-Higgs Gauge TheoriesOct 26 2015Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like ... More

Geometry on Lie algebroids I: compatible geometric structures on the baseMar 14 2016The object of our study is a Lie algebroid $A$ or a Cartan-Lie algebroid $(A,\nabla)$ (a Lie algebroid with a compatible connection) over a base manifold $M$ equipped with appropriately compatible geometrical structures. The main focus is on a Riemannian ... More

The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge TheoriesDec 20 2018Dec 21 2018We show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a Leibniz algebra (with one of its induced quotient Lie algebras embedded into a rigid symmetry Lie algebra that provides ... More

Gauge PDE and AKSZ-type Sigma ModelsMar 07 2019Apr 22 2019A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV-BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular attention to globally ... More

Weak Antiferromagnetic Order in Anisotropic Quantum PyrochloresOct 07 2008We study the ground state properties of an anisotropic, quasi-2D version of the quantum (S=1/2) pyrochlore antiferromagnet. In the presence of Dzyaloshinsky-Moriya interactions, in addition to the Heisenberg exchanges, it is shown that two types of ordered ... More

Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometriesApr 11 2019Consider an anchored bundle $(E,\rho)$, i.e. a vector bundle $E\to M$ equipped with a bundle map $\rho \colon E \to TM$ covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle ... More

Towards Generic Deobfuscation of Windows API CallsFeb 13 2018A common way to get insight into a malicious program's functionality is to look at which API functions it calls. To complicate the reverse engineering of their programs, malware authors deploy API obfuscation techniques, hiding them from analysts' eyes ... More

Local BRST cohomology for AKSZ field theories: a global approach IOct 01 2013Nov 22 2013We study the Lagrangian antifield BRST formalism, formulated in terms of exterior horizontal forms on the infinite order jet space of graded fields for topological field theories associated to $Q$-bundles. In the case of a trivial Q-bundle with a flat ... More

Gauge PDE and AKSZ-type Sigma ModelsMar 07 2019A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV-BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular attention to globally ... More

Analysis of a certain polycyclic-group-based cryptosystemApr 20 2015We investigate security properties of the Anshel-Anshel-Goldfeld commutator key-establishment protocol used with certain polycyclic groups. We show that despite low success of the length based attack the protocol can be broken by a deterministic polynomial-time ... More

Gauging without Initial SymmetryMar 31 2014Apr 10 2014The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional Lie(G)-valued ... More

Lie algebroids, gauge theories, and compatible geometrical structuresMar 14 2016Apr 12 2019The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular ... More

Finite-temperature correlations in a quantum spin chain near saturationJul 17 2017Oct 02 2017Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the $S=1/2$ Heisenberg spin chain compound K$_2$CuSO$_4$Cl$_2$ at several temperatures ... More

Lifting of Polynomial Symplectomorphisms and Deformation QuantizationJul 20 2017Feb 05 2018We study the problem of lifting of polynomial symplectomorphisms in characteristic zero to automorphisms of the Weyl algebra by means of approximation by tame automorphisms. We utilize -- and reprove -- D. Anick's fundamental result on approximation of ... More

Non-reciprocal geometric phase in nonlinear frequency conversionApr 12 2017We describe analytically and numerically the geometric phase arising from nonlinear frequency conversion and show that such a phase can be made non-reciprocal by momentum-dependent photonic transition. Such non-reciprocity is immune to the shortcomings ... More

Wave packet dynamics and valley filter in strained grapheneMay 05 2011The time evolution of a wavepacket in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudo-magnetic field, on the wave packet trajectories and zitterbewegung ... More

Directional visible light scattering by silicon nanoparticlesDec 13 2012Directional light scattering by spherical silicon nanoparticles in the visible spectral range is experimentally demonstrated for the first time. These unique scattering properties arise due to simultaneous excitation and mutual interference of magnetic ... More

Experimental Study For The Feasibility Of A Crystalline UndulatorAug 07 2002We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic micro-scratches (trenches) by means of a diamond blade. The X-ray tests of the crystal deformation due to given ... 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

Noncommutative Bialynicki-Birula TheoremAug 14 2018Dec 12 2018In this short note we prove that every maximal torus action on the free algebra is conjugate to a linear action. This statement is the free algebra analogue of a classical theorem of A. Bia{\l}ynicki-Birula.

On the Power-law Scaling of Turbulence Cospectra Part 1: Stably Stratified Atmospheric Boundary LayerNov 21 2018Turbulent fluxes in the atmospheric surface layer are key input for the prediction of weather, hydrology, and carbon dioxide concentration. In numerical modelling of turbulent fluxes, a -7/3 power-law scaling in turbulence cospectra is usually assumed ... More

High-contrast Kerr Frequency CombsDec 02 2016Dec 23 2016Kerr frequency combs with depressed harmonic at the optical pump frequency are theoretically explained and experimentally demonstrated. This result is achieved in a MgF$_2$ photonic belt resonator having reduced density of modes in its spectrum and configured ... More

Seeing the unseen: observation of an anapole with dielectric nanoparticlesNov 30 2014Nonradiating current configurations attract attention of physicists for many years as possible models of stable atoms in the field theories. One intriguing example of such a nonradiating source is known as anapole (which means without poles in Greek), ... More

Temperature dependence of shear viscosity of $SU(3)$--gluodynamics within lattice simulationJan 09 2017Jan 12 2017In this paper we study the shear viscosity temperature dependence of $SU(3)$--gluodynamics within lattice simulation. To do so, we measure the correlation functions of energy-momentum tensor in the range of temperatures $T/T_c\in [0.9, 1.5]$. To extract ... 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

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

Contravariant form on tensor product of highest weight modulesSep 25 2017May 07 2018We give a criterion for complete reducibility of tensor product $V\otimes Z$ of two irreducible highest weight modules over a classical or quantum reductive group in terms of a contravariant form on $V\otimes Z$. We endow the tensor product of modules ... 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

On a Generalization of Bernoulli and Euler NumbersJul 20 2011May 08 2013We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and identical distribution ... 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

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

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

Electrodynamic spherical harmonicMar 28 2008Electrodynamic spherical harmonic is a second rank tensor in three-dimensional space. It allows to separate the radial and angle variables in vector solutions of Maxwell's equations. Using the orthonormalization for electrodynamic spherical harmonic, ... 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

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

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

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

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

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

Ideals on the Quantum Plane's jet spaceMar 20 2016The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime ideals. We will prove some results (theorems 1-4) about the prime spectrum ... More

Modal logic of some products of neighborhood framesMay 26 2014We consider modal logics of products of neighborhood frames and prove that for any pair $L$ and $L'$ of logics from set $\{S4, D4, D, T\}$ modal logic of products of $L$-neighborhood frames and $L'$-neighborhood frames is the fusion of $L$ and $L'$.

On dynamical adjoint functorMar 27 2012We give an explicit formula relating the dynamical adjoint functor and dynamical twist over nonalbelian base to the invariant pairing on parabolic Verma modules. As an illustration, we give explicit $U(sl(n))$- and $U_\hbar(sl(n))$-invariant star product ... More

Reflection equation and twisted YangiansDec 23 2006Jul 14 2007With any involutive anti-algebra and coalgebra automorphism of a quasitriangular bialgebra we associate a reflection equation algebra. A Hopf algebraic treatment of the reflection equation of this type and its universal solution is given. Applications ... More

Summing next-to-next-to-leading logarithms in b->c transitions at zero recoilSep 28 2005Nov 02 2005Perturbative corrections to b->c transitions at zero recoil are considered in the two-step matching scheme. The matching coefficient for the b->c currents from the intermediate effective theory (between the scales m_b and m_c) to the low-energy effective ... More

The functional mechanics: evolution of the moments of distribution function and the Poincare recurrence theoremMay 17 2013This paper consider the functional mechanics as one of modern approaches to a problem of the correspondence between classical mechanics and the statistical physics. Deviations from classical trajectories are calculated and evolution of the moments of ... More

LSV models with stochastic interest rates and correlated jumpsNov 04 2015Dec 14 2015Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be extended by ... More

Nonlinear PDEs risen when solving some optimization problems in finance, and their solutionsOct 16 2015We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and discuss the ... More

To sigmoid-based functional description of the volatility smileJul 01 2014Dec 08 2014We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied volatilities which ... More

Kato perturbation expansion in classical mechanics and an explicit expression for a Deprit generatorJul 12 2013Aug 26 2014This work explores the structure of Poincare-Lindstedt perturbation series in Deprit operator formalism and establishes its connection to Kato resolvent expansion. A discussion of invariant definitions for averaging and integrating perturbation operators ... More

Penalty Method for Obliquely Reflected DiffusionsSep 06 2015Nov 13 2017Consider a multidimensional normally or obliquely reflected diffusion in a smooth domain. We approximate it by solutions of stochastic differential equations without reflection using the penalty method. That is, we approximate the reflection term with ... More

Clifford algebra and the projective model of Minkowski (pseudo-Euclidean) spacesJul 16 2013Jul 18 2013I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The emphasis is ... More

Clifford algebra and the projective model of Elliptic spacesOct 10 2013I apply the algebraic framework developed in arXiv:1101.4542 to study geometry of elliptic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in arXiv:1307.2917. ... More

Large Radius Limit and SYZ Fibrations of Hyper-Kahler ManifoldsAug 22 2003Aug 26 2003In this paper the relations between the existence of Lagrangian fibration of Hyper-K\"{a}hler manifolds and the existence of the Large Radius Limit is established. It is proved that if the the rank of the second homology group of a Hyper-K\"{a}hler manifold ... More

Chiral Topological Elasticity and Fracton OrderDec 18 2017Feb 18 2019We analyze the "higher rank" gauge theories, that capture some of the phenomenology of the Fracton order. It is shown that these theories lose gauge invariance when arbitrarily weak and smooth curvature is introduced. We propose a resolution to this problem ... More

Equivariant vector bundles over quantum projective spacesMay 07 2018We construct equivariant vector bundles over quantum projective spaces making use of parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of projective space as a subalgebra in ... More

Limit mixed Hodge structures of hyperkähler manifoldsJul 11 2018Oct 04 2018This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk\"ahler manifolds. We show that when the monodromy action on $H^2$ has ... More

Self-organization of grid fields under supervision of place cells in the model of neuron with associative plasticityMar 26 2015Jun 30 2015The grid cells (GCs) of the medial entorhinal cortex (MEC) and place cells (PCs) of the hippocampus are key elements of the brain network for the metric representation of space. Currently, any of the existing theoretical models can explain all aspects ... More

Weak Convergence of Obliquely Reflected DiffusionsSep 06 2015Jun 15 2017Burdzy 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

Triple and Simultaneous Collisions of Competing Brownian ParticlesJan 24 2014Jan 29 2015Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. A triple collision occurs if ... More

Evolution of gluon TMDs from small to moderate xOct 23 2015Recently we obtained an evolution equation of gluon TMDs, which addresses a problem of unification of different kinematic regimes. It describes evolution in the whole range of Bjorken $x_B$ and the whole range of transverse momentum $k_\perp$. In this ... More