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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

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

Ratio of productions of pi+pi-atoms to free pi+pi- pairs with account of the strong interaction in final statesOct 05 1998The ratio of productions of pi+pi- atoms to free pi+pi- pairs is calculated with account of the strong interaction in final states. It is shown that this ratio is expressed via a squared ratio of the well-known Coulomb wave functions and thus can be calculated ... 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

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

Towards Blockchain-based Multi-Agent Robotic Systems: Analysis, Classification and ApplicationsJul 17 2019Decentralization, immutability and transparency make of Blockchain one of the most innovative technology of recent years. This paper presents an overview of solutions based on Blockchain technology for multi-agent robotic systems, and provide an analysis ... 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

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

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

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

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

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

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

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

Degree versions of theorems on intersecting families via stabilityOct 01 2018May 20 2019The matching number of a family of subsets of an $n$-element set is the maximum number of pairwise disjoint sets. The families with matching number $1$ are called intersecting. The famous Erd\H os-Ko-Rado theorem determines the size of the largest intersecting ... 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

Elliptic stable envelope for Hilbert scheme of points in the planeApr 23 2018Jul 21 2019We find an explicit formula for the elliptic stable envelope in the case of the Hilbert scheme of points on a complex plane. The formula has a structure of a sum over trees in Young diagrams. In the limit we obtain the formulas for the stable envelope ... More

Delta -- new logic programming language and Delta-methodology for p-computable programs on Turing Complete LanguagesJul 12 2019In paper describes the new logic programming language Delta, which have a many good properties. Delta-programs is p-computable, verifiable and can translation on other languages. Also we describe the Delta-methodology for constructing p-computable programs ... More

A Workflow-Forecast Approach To The Task Scheduling Problem In Distributed Computing SystemsOct 06 2013The aim of this paper is to provide a description of deep-learning-based scheduling approach for academic-purpose high-performance computing systems. The share of academic-purpose distributed computing systems (DCS) reaches 17.4 percents amongst TOP500 ... More

Partisan Lean of States: Electoral College and Popular VoteMay 11 2019Jul 02 2019We compare federal election results for each state versus the USA in 1992, 1994, until 2018, to model partisan lean of each state and its dependence on the nationwide popular vote. For each state, we model both its current partisan lean and its rate of ... 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.

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

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

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

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

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

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.

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

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

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

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

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

The nonlocal Darboux transformation of the 2D stationary Schrödinger equation and its relation to the Moutard transformationMar 23 2013Mar 16 2014The nonlocal Darboux transformation of the two - dimensional stationary Schr\"odinger equation is considered and its relation to the Moutard transformation is established. It is shown that a special case of the nonlocal Darboux transformation provides ... 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

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

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

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

Elliptic stable envelope for Hilbert scheme of points in the planeApr 23 2018Apr 30 2018We find an explicit formula for the elliptic stable envelope in the case of the Hilbert scheme of points on a complex plane. The formula has a structure of a sum over trees in Young diagrams. In the limit we obtain the formulas for the stable envelope ... 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

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

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

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.

Limit mixed Hodge structures of hyperkähler manifoldsJul 11 2018Jun 11 2019This 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

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

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

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)).

Generalisation of the explicit expression for the Deprit generator to Hamiltonians nonlinearly dependent on small parameterDec 15 2016This work explores a structure of the Deprit perturbation series and its connection to a Kato resolvent expansion. It extends the formalism previously developed for the Hamiltonians linearly dependent on perturbation parameter to a nonlinear case. We ... 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

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

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

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