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Entanglement Entropy in 2D Non-abelian Pure Gauge TheoryMar 20 2014We compute the Entanglement Entropy (EE) of a bipartition in 2D pure non-abelian $U(N)$ gauge theory. We obtain a general expression for EE on an arbitrary Riemann surface. We find that due to area-preserving diffeomorphism symmetry EE does not depend ... 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

Measuring Electromagnetic and Gravitational Responses of Photonic Landau LevelsFeb 13 2018The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it changes its ... More

Supersymmetric waves in Bose-Fermi mixturesApr 29 2015Dec 23 2015Interacting Bose-Fermi mixtures possess a fermionic (super)symmetry when bosons and fermions in the mixture have equal masses, and when the interaction strengths are appropriately tuned. This symmetry is spontaneously broken in the ground state of the ... More

Density-curvature response and gravitational anomalyMar 23 2014We study constraints imposed by the Galilean invariance on linear electromagnetic and elastic responses of two-dimensional gapped systems in background magnetic field. Exact relations between response functions following from the Ward identities are derived. ... More

Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic fieldJan 15 2014We compute electromagnetic, gravitational and mixed linear response functions of two- dimensional free fermions in external quantizing magnetic field at an integer filling factor. The results are presented in the form of the effective action and as an ... More

Thermal Hall Effect and Geometry with TorsionJul 10 2014We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes the classic Luttinger's ... More

Exact Electromagnetic Response of Landau Level ElectronsOct 11 2016We present a simple method that allows to calculate the electromagnetic response of non-interacting electrons in strong magnetic field to arbitrary order in the gradients of external electric and magnetic fields. We illustrate the method on both non-relativistic ... More

Singularities and asymptotic behavior of the Tolman-Bondi modelJun 04 1997The Bondi formula for calculation of the invariant mass in the Tolman- Bondi (TB) model is interprated as a transformation rule on the set of co-moving coordinates. The general procedure by which the three arbitrary functions of the TB model are determined ... More

Soliton solutions of Calogero model in harmonic potentialMar 31 2011A classical Calogero model in an external harmonic potential is known to be integrable for any number of particles. We consider here reductions which play a role of "soliton" solutions of the model. We obtain these solutions both for the model with finite ... More

Boundary effective action for quantum Hall statesJun 23 2015Jul 20 2015We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the low-energy effective ... More

Asymptotic Bethe Ansatz from String Sigma Model on S^3 x RMay 02 2006Aug 05 2006We derive the asymptotic Bethe ansatz (AFS equations) for the string on S^3 x R sector of AdS_5 x S^5 from the integrable nonhomogeneous dynamical spin chain for the string sigma model proposed in GKSV. It is clear from the derivation that AFS equations ... More

Double Scaling and Finite Size Corrections in sl(2) Spin ChainOct 24 2005Feb 01 2007We find explicit expressions for two first finite size corrections to the distribution of Bethe roots, the asymptotics of energy and high conserved charges in the sl(2) quantum Heisenberg spin chain of length J in the thermodynamical limit J->\infty for ... More

Synthetic Landau levels for photonsNov 23 2015Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties[1-7]. Making photons experience a Lorentz force imbues them with handedness, providing unique opportunities ... More

Universal dynamics of a soliton after an interaction quenchAug 15 2014Mar 09 2016We propose a new type of experimentally feasible quantum quench protocol in which a quantum system is prepared in a coherent, localized excited state of a Hamiltonian. During the evolution of this solitonic excitation, the microscopic interaction is suddenly ... More

Framing Anomaly in the Effective Theory of Fractional Quantum Hall EffectOct 24 2014Mar 25 2015We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain correct gravitational linear response functions. ... More

Two-fluid matter-quintessence FLRW models: energy transfer and the equation of state of the universeSep 23 2002Recent observations support the view that the universe is described by a FLRW model with $\Omega_m^0 \approx 0.3$, $\Omega_{\Lambda}^0 \approx 0.7$, and $w \leq -1/3$ at the present epoch. There are several theoretical suggestions for the cosmological ... More

Finite Volume Spectrum of 2D Field Theories from Hirota DynamicsDec 30 2008Dec 05 2009We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic ... More

The Objectives of the Radioscience Experiment in Luna-Resource and Luna-Glob Space ProjectsDec 15 2015Two radio-science instruments have included into the Luna-Glob and Luna-Resource projects in the frame of Russian Luna exploration program: the lander's radio beacon and the orbiter's receiver. Three types of experiments are planned: orbital doppler measurements, ... More

New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin ChainsOct 25 2016Nov 21 2016We conjecture a new way to construct eigenstates of integrable XXX quantum spin chains with SU(N) symmetry. The states are built by repeatedly acting on the vacuum with a single operator Bgood(u) evaluated at the Bethe roots. Our proposal serves as a ... More

Exact AdS/CFT spectrum: Konishi dimension at any couplingJun 23 2009Feb 21 2010We compute the full dimension of Konishi operator in planar N=4 SYM theory it for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically ... 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

Non-Levi closed conjugacy classes of SO_q(N)Dec 11 2011Jul 14 2013We construct explicit quantization of semisimple conjugacy classes of the complex orthogonal group SO(N) with non-Levi isotropy subgroups through an operator realization on highest weight modules of the quantum group U_q(so(N)).

Non-Levi closed conjugacy classes of SP_q(2n)Oct 12 2011Jun 22 2012We construct explicit quantization of closed conjugacy classes of the complex symplectic group SP(2n) with non-Levi isotropy subgroups through an operator realization on highest weight modules over the quantum group U_q(sp(2n)).

Quotients of conic bundlesDec 24 2013Apr 21 2015Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over projective line by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any quotient is ... More

On the Thermal History of Calculable Gauge MediationJul 23 2009Oct 27 2009Many messenger models with realistic gaugino masses are based on meta-stable vacua. In this work we study the thermal history of some of these models. Analyzing R-symmetric models, we point out that while some of the known messenger models clearly prefer ... 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

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

Weil-Petersson Volumes of the Moduli Spaces of CY ManifoldsAug 04 2004Mar 25 2007In this paper it is proved that the volumes of the moduli spaces of polarized CY manifolds with respect to the Weil-Petersson metrics are finite and they are rational numbers.

Reply to Comment on "Spectra of strong magnetohydrodynamic turbulence from high-resolution simulations"Oct 03 2014In a Comment by Perez et al (2014) it is claimed that recently published simulations of Beresnyak (2014) are grossly underresolved, compared to theirs, and that Beresnyak (2014) failed to estimate numerical error. Both claims are contrary to the fact. ... More

The Flow Around a Cosmic String, Part I: Hydrodynamic SolutionJan 15 2015Cosmic strings are linear topological defects which are hypothesized to be produced during inflation. Most searches for strings have been relying on the string's lensing of background galaxies or CMB. In this paper I obtained the solution for the supersonic ... More

Wave Mechanics: Behavior of a Distributed Electron Charge in an AtomApr 04 2013In Part one of this Paper a hypothesis is forwarded of the electron charge in an atom existing in a distributed form. To check it by methods of electrodynamics and mechanics (without invoking the formalism of quantum mechanics and the concepts of the ... 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

On the mechanism of prompt emission of gamma-ray burstsNov 05 2003We propose a model in which prompt gamma emission of gamma-ray bursts is the synchrotron radiation of electron-positron plasma in the ordered magnetic field in the direct vicinity of horizon of a young black hole formed in the core collapse of a massive ... More

Brane collisions in anti-de Sitter spaceSep 11 2001From the requirement of continuous matching of bulk metric around the point of brane collision we derive a conservation law for collisions of p-branes in (p+2)-dimensional space-time. This conservation law relates energy densities on the branes before ... More

Kolmogorov Complexity and the Garden of Eden TheoremDec 09 2012Suppose $\tau$ is a cellular automaton over an amenable group and a finite alphabet. Celebrated Garden of Eden theorem states, that pre-injectivity of $\tau$ is equivalent to non-existence of Garden of Eden configuration. In this paper we will prove, ... More

Degenerate Sklyanin AlgebrasMar 08 2009New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for $sl(2,\mathbb{C})$. These solutions are shown to be related ... More

Polynomials associated with fixed points on the instanton moduli spaceApr 21 2014Using the Okounkov-Maulik stable map, we identify the equivariant cohomology of instanton moduli spaces with the space of polynomials on an infinite number of variables. We define the generalized Jack polynomials as the polynomials representing the classes ... More

How typical are pathological foliations in partially hyperbolic dynamics: an exampleJul 21 2009Jun 24 2010We show that for a large space of volume preserving partially hyperbolic diffeomorphisms of the 3-torus with non-compact central leaves the central foliation generically is non-absolutely continuous.

Penalty Method for Obliquely Reflected DiffusionsSep 06 2015Sep 20 2016Consider a multidimensional obliquely reflected diffusion in a smooth domain. We approximate it by solutions of SDEs without reflection using the penalty method. We emulate the "hard barrier" of reflection by a "soft barrier" of a properly chosen drift ... More

Saturation model in the non-Glauber approachJul 15 2007Jul 31 2007In this paper a new saturation model is presented. This model is based on the theoretical solution for the generating functional, and it is quite different and not more complicated than the Glauber-like approach used before. The model describes the structure ... More

Optimal sequential multiple hypothesis testsNov 08 2008This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized. ... 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

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

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 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

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.

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

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

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.

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

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

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

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

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

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

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

Semantic clustering of Russian web search results: possibilities and problemsSep 04 2014Oct 26 2014The paper deals with word sense induction from lexical co-occurrence graphs. We construct such graphs on large Russian corpora and then apply this data to cluster Mail.ru Search results according to meanings of the query. We compare different methods ... 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

CDF Searches for New Physics with PhotonsOct 10 2007We present results of searches for new physics in final states with photons at CDF in approximately 1 fb-1 of ppbar collisions at 1.96 TeV. We give an overview of the data-driven photon background estimation techniques used for the analyses. We report ... More

High-Order Splitting Methods for Forward PDEs and PIDEsMar 07 2014This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations are consistent. ... More

Statistical Investigation of Increments of Currency Rates LogarithmsJul 20 2011May 08 2013We consider the currency rates dynamics for 12 currencies, including dollar and euro, with respect to Russian rouble. We prove that the Samuelson model (geometric Brownian motion) is not suitable for this dynamics. We also prove that another model (with ... More

Construction of a Sturm-Liouville vessel using Gelfand-Levitan theory. On solution of the Korteweg-de Vries equation in the first quadrantDec 07 2012Using Gelfand-Levitan theory on a half line, we construct a vessel for the class of potentials, whose spectral functions satisfy a certain regularity assumption. When the singular part of the spectral measure is absent, we construct a canonical model ... More

Three-dimensional Spontaneous Magnetic ReconnectionJan 30 2013Oct 27 2016Magnetic reconnection is best known from observations of the Sun where it causes solar flares. Observations estimate the reconnection rate a small, but non-negligible fraction of the Alfv\'en speed, so-called fast reconnection. Until recently, the prevailing ... More

Basic Properties of MHD Turbulence in the Inertial RangeNov 22 2011Apr 04 2012We revisit the issue of spectral slope of MHD turbulence in the inertial range and argue that numerics favor Goldreich-Sridhar -5/3 slope rather than -3/2 slope. We also did precision measurements of anisotropy of MHD turbulence and determined the anisotropy ... More

Ray Singer Analytic Torsion of Calabi Yau manifolds IApr 07 2000Apr 19 2000In this paper we generalized the variational formulas for the determinants of the Laplacians on functions of CY metrics to forms of type (0,q) on CY manifolds. We also computed the Ray Singer Analytic torsion on CY manifolds we proved that it is bounded ... More

Local SUSY-breaking minima in N_f=N_c SQCD?Oct 04 2007We study non-supersymmetric minima in N_f=N_c SQCD conjectured by Intriligator, Seiberg and Shih (ISS). We show that the existence of such minima depends on the signs of three non-calculable parameters and that no evidence can be inferred by deforming ... More

Clifford algebra and the projective model of Hyperbolic spacesFeb 27 2016I apply the algebraic framework developed in [1] to study geometry of hyperbolic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in [2].

Localization of Kaluza-Klein gauge fields on a braneFeb 28 2001In phenomenological models with extra dimensions there is a natural symmetry group associated to a brane universe, -- the group of rotations of normal bundle of the brane. We consider Kaluza-Klein gauge fields corresponding to this group and show that ... More

On transverse hyperplanes to self-similar Jordan arcsSep 02 2013We consider self-similar Jordan arcs $\gamma$ in $R^d$, different from a line segment and show that they cannot be projected to a line bijectively. Moreover, we show that the set of points $x\in\gamma$, for which there is a hyperplane, intersecting $\gamma$ ... More

Separation of Potentials in the Two-Body ProblemSep 28 2012In contrast to the well-known solution of the two-body problem through the use of the concept of reduced mass, a solution is proposed involving separation of potentials. It is shown that each of the two point bodies moves in its own stationary potential ... More

Tail Asymptotic of Sum and Product of Random Variables with Applications in the Theory of Extremes of Conditionally Gaussian ProcessesJul 20 2011May 08 2013We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome but purely technical computations and requires the use of the Laplace ... More

Integral Property of Laplace OperatorJun 13 2014Relations have been derived which establish connection between a scalar or a vector functions and the integral of Laplace operator of these functions (the integral property of Laplace operator). The integral property of Laplace operator was employed to ... More

Orthogonal basis for the Shapovalov form on $A_n$Jun 16 2012Aug 31 2014Let $U$ be either classical or quantized universal enveloping algebra of $\s\l(n+1)$ extended over the field of fractions of the Cartan subalgebra. We suggest a PBW basis in $U$ over the extended Cartan subalgebra diagonalizing the contravariant Shapovalov ... More

R-matrix and inverse Shapovalov formDec 10 2014Feb 17 2016We construct the inverse Shapovalov form of a simple complex quantum group from its universal R-matrix based on a generalized Nagel-Moshinsky approach to lowering operators. We establish a connection between this algorithm and the ABRR equation for dynamical ... More

Remarks on differentiability in the initial data for stochastic reflecting flowDec 20 2012Stochastic flows generated by reflected SDEs in a half-plane with an additive diffusion term are considered. A derivative in the initial data is represented a.s. as an infinite product of matrices. We use this representation and construct an example of ... More

Homotopy of profinite groupsMay 19 2012Sep 28 2015We study simplicial profinite groups with a view towards applications in profinite combinatorial group theory. This approach provides a natural framework to the concept of pro-$\mathfrak{C}$-presentation of a pro-$\mathfrak{C}$-group $G$ as a 1-truncation ... More