total 5706took 0.18s

Torsion in thin regions of Khovanov homologyMar 13 2019In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are known to only contain $\mathbb{Z}_2$ torsion. In this paper, we ... More

Rapid acceleration of electrons in the magnetosphere by fast-mode MHD wavesMar 29 2000During major megnetic storms, enhanced flux of relativistic electrons in the inner magnetosphere have been observed to correleated with ULF waves. The enhancements can take place over a period of several hours. In order to account for such a rapid generation ... More

String-- and Brane--Localized Causal Fields in a Strongly Nonlocal ModelDec 18 2005Dec 13 2006We study a weakly local, but nonlocal model in spacetime dimension $d \geq 2$ and prove that it is maximally nonlocal in a certain specific quantitative sense. Nevertheless, depending on the number of dimensions $d$, it has string--localized or brane--localized ... More

An Algebraic Characterization of Vacuum States in Minkowski Space. III. Reflection MapsSep 09 2003Oct 21 2003Employing the algebraic framework of local quantum physics, vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables and corresponding ... More

A Performance and Stability Analysis of Low-inertia Power Grids with Stochastic System InertiaMar 02 2019Traditional synchronous generators with rotational inertia are being replaced by low-inertia renewable energy resources (RESs) in many power grids and operational scenarios. Due to emerging market mechanisms, inherent variability of RESs, and existing ... More

Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field TheoriesMay 15 2010Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations of C*-dynamical ... More

Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-timesJul 06 2002We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker space-times. We show that the worldline of an observer in such space-times determines a unique orbit in the local conformal group SO(4,1) of the space-time ... More

An Algebraic Characterization of Vacuum States in Minkowski Space. II. Continuity AspectsSep 01 1999Nov 19 1999An algebraic characterization of vacuum states in Minkowski space is given which relies on recently proposed conditions of geometric modular action and modular stability for algebras of observables associated with wedge-shaped regions. In contrast to ... More

Self-assembly of, and optimal encoding inside, thin rectangles at temperature-1 in 3DAug 10 2018In this paper, we study the self-assembly of rectangles in a non-cooperative, 3D version of Winfree's abstract Tile Assembly Model. We prove four main results -- the first two negative and the last two positive. First, we use Catalan numbers and a restricted ... More

Fractional electrical dimensionality in the spin solid phase of artificial honeycomb latticeFeb 18 2018Two-dimensional artificial magnetic honeycomb lattice is at the forefront of research on unconventional magnetic materials. Among the many emergent magnetic phases that are predicted to arise as a function of temperature, the low temperature spin solid ... More

The Observational Effects and Signatures of Tidally Distorted Solid ExoplanetsOct 08 2014Our work examines the detectability of tidally distorted solid exoplanets in synchronous rotation. Previous work has shown that tidally distorted shapes of close-in gas giants can give rise to radius underestimates and subsequently density overestimates ... More

Parsing Images of Overlapping Organisms with Deep Singling-Out NetworksDec 19 2016This work is motivated by the mostly unsolved task of parsing biological images with multiple overlapping articulated model organisms (such as worms or larvae). We present a general approach that separates the two main challenges associated with such ... More

Exact and approximate analytical solutions of Weiss equation of ferromagnetism and their experimental relevanceFeb 14 2017The recent progress in the theory of generalized Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical purposes. Precise approximate analytical solutions are ... More

Instance Segmentation by Deep ColoringJul 26 2018We propose a new and, arguably, a very simple reduction of instance segmentation to semantic segmentation. This reduction allows to train feed-forward non-recurrent deep instance segmentation systems in an end-to-end fashion using architectures that have ... More

Perfectly matched layers for the stationary Schrodinger equation in a periodic structureJun 12 2008We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show ... More

Corrections to the book ``Vertex algebras for beginners'', second edition, by Victor KacJan 18 1999These are corrections to the second edition of the book ``Vertex algebras for beginners'', University Lecture Series, 10, American Mathematical Society, Providence, RI, 1998.

The meaning of concurrent programsOct 07 2008The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on event sequences ... More

Hori--Vafa mirror models for complete intersections in weighted projective spaces and weak Landau--Ginzburg modelsMar 26 2010Jul 12 2011We prove that Hori--Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials.

Astrophysical Data and Conformal Unified TheoryOct 31 2002Astrophysical data reformulated in the units of the relative Paris meter and running Planck mass are used for restoration of a conformal version of the unified theory where the absolute Planck mass belongs to ordinary initial data (like the absolute Ptolemaeus ... More

Non stationary nucleation: the model with averaged velocityFeb 01 2013A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. The key characteristic which arises in frames of this theory is the mean ... More

Late periods of the condensation processNov 15 2010The full evolution during the late periods of the condensation process is described in the analytical form. The process is split into several periods and for every period the simple approximate solution is given.

Different approaches to describe depletion regions in first order phase transition kineticsJul 31 2002The theory of nucleation with depletion zones is discussed. The approach of stochastic effects of solitary droplet is analyzed. The negative features of a solution with fixed boundary are outlined. A new solution with effective fixed boundary is proposed. ... More

Non stationary nucleation: the model with minimal environmentJan 06 2013A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. As the result the free energy has to be recalculated which brings a new ... More

Variations of parameters in nucleation process under different external conditionsAug 21 2008The nucleation process under different external conditions is considered. It is shown that the duration of this process can be connected with the microscopic corrections to the free energy of the critical embryo. Connection between variations in the value ... More

Some properties of evolution equation for homogeneous nucleation period under the smooth behavior of initial conditionsMar 10 2005The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated ... More

Multicomponent nonisothermal nucleation. 1. Kinetic equationSep 03 1999The first part of the theory for the multicomponent nonisothermal nucleation is presented. On the base of analysis of the elementary acts of interation between an embryo and environment the kinetic equation is derived. This equation will be solved later ... More

Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebrasAug 16 2000We give a detailed calculation of the Hochschild and cyclic homology of the algebra $\CIc(G)$ of locally constant, compactly supported functions on a reductive p-adic group G. We use these calculations to extend to arbitrary elements the definition the ... More

Super-connections and non-commutative geometryJun 14 1996Aug 21 1996We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in the spectrum. ... More

An index theorem for families invariant with respect to a bundle of Lie groupsJun 28 1999Aug 16 2000We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle $\GR$ of Lie groups. If the fibers of $\GR \to B$ are simply-connected solvable, we then compute the Chern character of the ... More

Two-point free energy distribution function in (1+1) directed polymersApr 24 2013May 07 2013In this brief technical communication it is demonstrated how using Bethe ansatz technique the explicit expression for the two-point free energy distribution function in (1+1) directed polymers can be derived in rather simple way. Obtained result is equivalent ... More

Two-time free energy distribution function in (1+1) directed polymersApr 02 2013Aug 09 2013The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the $N$-particle quantum ... More

Context-free manifold calculus and the Fulton-MacPherson OperadApr 02 2012The paper gives an explicit description of the Weiss embedding tower in terms of spaces of maps of truncated modules over the framed Fulton-MacPherson operad.

On H.Weyl and H.Minkowski PolynomialsFeb 06 2007Feb 14 2007We introduce certain polynomials, so-called H.Weyl and H.Minkowski polynomials, which have a geometric origin. The location of roots of these polynomials is studied.

Burns' equivariant Tamagawa invariant T Omega^{loc}(N/\Q,1) for some quaternion fieldsMar 01 2002We verify one of Burn's equivariant Tamagawa number conjectures for some families of quaternion fields.

Time reversal in photoacoustic tomography and levitation in a cavityMay 24 2014A class of photoacoustic acquisition geometries in n-space is considered such that the spherical mean transform admits an exact filtered back projection reconstruction formula. The reconstruction is interpreted as a time reversion mirror that reproduces ... More

Stellar scintillation in short exposure regime and atmospheric coherence time evaluationMar 31 2011Accurately measuring the atmospheric coherence time is still an important problem despite a variety of applicable methods. The Multi-aperture scintillation sensor (MASS) designed for the vertical profiling of optical turbulence, also provides a measurements ... More

Non-perturbative microscopic theory of superconducting fluctuations near a quantum critical pointOct 10 2007We consider an inhomogeneous anisotropic gap superconductor in the vicinity of the quantum critical point, where the transition temperature is suppressed to zero by disorder. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action for ... More

Linear Datalog and Bounded Path Duality of Relational StructuresApr 07 2005Jun 28 2005In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems, all these concepts ... More

Generalized Majority-Minority Operations are TractableSep 19 2006Sep 27 2006Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where all constraint ... More

Calabi-Yau algebrasDec 06 2006Jan 09 2007We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution. In dimension ... More

A remark on a theorem of M. HaimanJul 04 2005We deduce a special case of a theorem of M. Haiman concerning alternating polynomials in 2n variables from our results about almost commuting variety, obtained earlier in a joint work with W.-L. Gan.

Lectures on Noncommutative GeometryJun 29 2005These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild cohomology, Serre ... More

Isospectral commuting variety, the Harish-Chandra D-module, and principal nilpotent pairsAug 26 2011Sep 07 2011Let g be a complex reductive Lie algebra with Cartan algebra h. Hotta and Kashiwara defined a holonomic D-module M, on g x h, called Harish-Chandra module. We relate gr(M), an associated graded module with respect to a canonical Hodge filtration on M, ... More

Perverse sheaves on a Loop group and Langlands' dualityNov 13 1995Nov 20 2000An intrinsic construction of the tensor category of finite dimensional representations of the Langlands dual group of G in terms of a tensor category of perverse sheaves on the loop group, LG, is given. The construction is applied to the study of the ... More

Quarkonium suppression as a probe of a saturated gluon plasma ?Jun 21 2001A dense parton system is expected to be formed in the early stage of relativistic heavy-ion collisions at RHIC energies and above. The probability of a quark gluon plasma production and the resulting strength of its signatures depends strongly on the ... More

A nonclassical symbolic theory of working memory, mental computations, and mental setJan 08 2009The paper tackles four basic questions associated with human brain as a learning system. How can the brain learn to (1) mentally simulate different external memory aids, (2) perform, in principle, any mental computations using imaginary memory aids, (3) ... More

A rational construction of Lie algebras of type E_7Sep 27 2013Jul 03 2015We give an explicit construction of Lie algebras of type $E_7$ out of a Lie algebra of type $D_6$ with some restrictions. Up to odd degree extensions, every Lie algebra of type $E_7$ arises this way. For Lie algebras that admit a $56$-dimensional representation ... More

Scaling Exponents of Strong Turbulence in the Eddy Viscosity ApproximationJul 20 1996A dynamic equation for velocity structure functions $S_{n}(r) = <(u(x)-u(x'))^{n}>$ in strong turbulence is derived in the one-loop (eddy viscosity) approximation. This homogemeous differential equation yields scaling exponents $\xi_{n}$ in the relations ... More

On a puzzle posed by the Kurien-Sreenivasan boundary layer experimentJun 24 2002The Kolmogorov inertial range ratio of the mixed- to- longitudinal third-order structure functions of isotropic and homogeneous turbulence is $\frac{S_{1,2}}{S_{3,0}}=1/3$. Recent measurements by Kurien and Sreenivasan (Phys. Rev. E {\bf 64}, 056302 (2001)), ... More

Two-time free energy distribution function in the KPZ problemJul 22 2015The explicit expression for the two time free energy distribution function in one-dimensional random directed polymers is derived in terms of the Bethe ansatz replica technique. It is show that such type of the distribution function can be represented ... More

100 years of Weyl's lawAug 13 2016We discuss the asymptotics of the eigenvalue counting function for partial differential operators and related expressions paying the most attention to the sharp asymptotics. We consider Weyl asymptotics, asymptotics with Weyl principal parts and correction ... More

Minimax theorem for the spectral radius of the product of non-negative matricesMar 17 2016Sep 29 2016We prove the minimax equality for the spectral radius $\rho(AB)$ of the product of matrices $A\in\mathcal{A}$ and $B\in\mathcal{B}$, where $\mathcal{A}$ and $\mathcal{B}$ are compact sets of non-negative matrices of dimensions $N\times M$ and $M\times ... More

Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Viéte--Euler identity to Anderson localizationApr 28 2016It is shown that in a large class of disordered systems with non-degenerate disorder, in presence of non-local interactions, the Integrated Density of States (IDS) is at least H\"older continuous in one dimension and universally infinitely differentiable ... More

Bricklayer: An Authentic Introduction to the Functional Programming Language SMLDec 16 2014Functional programming languages are seen by many as instrumental to effectively utilizing the computational power of multi-core platforms. As a result, there is growing interest to introduce functional programming and functional thinking as early as ... More

Toric Landau-Ginzburg modelsSep 24 2018This is a review of the theory of toric Landau-Ginzburg models - the effective approach to mirror symmetry for Fano varieties. We mainly focus on the cases of dimensions 2 and 3, as well as on the case of complete intersections in weighted projective ... More

An efficient algorithm to decide periodicity of b-recognisable sets using LSDF conventionAug 21 2017Dec 19 2018Let b be an integer strictly greater than 1. Each set of nonnegative integers is represented in base b by a language over {0,1,...,b-1}. The set is said to be b-recognisable if it is represented by a regular language. It is known that ultimately periodic ... More

Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?Jul 26 2017Nov 25 2017We choose some special unit vectors $\boldsymbol{n}_1,\dots,\boldsymbol{n}_5$ in $\mathbb{R}^3$ and denote by $\mathscr{L}\subset\mathbb{R}^5$ the set of all points $(L_1,\dots,L_5)\in\mathbb{R}^5$ with the following property: there exists a compact convex ... More

The Dehn Function of Richard Thompson's Group F is QuadraticNov 26 2002We prove that the Dehn function (that is, the smallest isoperimetric function) of the Richard Thompson's group F is quadratic.

On a theorem of V. Bernik in the metrical theory of Diophantine approximationFeb 13 2008This paper goes back to a famous problem of Mahler in metrical Diophantine approximation. The problem has been settled by Sprindzuk and subsequently improved by Alan Baker and Vasili Bernik. In particular, Bernik's result establishes a convergence Khintchine ... More

Converting of algebraic Diophantine equations to a diagonal form with the help of an integer non-orthogonal transformation, maintaining the asymptotic behavior of the number of its integer solutionsAug 04 2017The author showed that any homogeneous algebraic Diophantine equation of the second order can be converted to a diagonal form using an integer non-orthogonal transformation maintaining asymptotic behavior of the number of its integer solutions. In this ... More

Estimations of the number of solutions of algebraic Diophantine equations with natural coefficients using the circle method of Hardy-LittlewoodDec 22 2015This article discusses the question - how to estimate the number of solutions of algebraic Diophantine equations with natural coefficients using Circular method developed by Hardy and Littlewood. This paper considers the estimate of the number of solutions ... More

Conformal equivalent metrics in a plane domain are uniquely determined from travel timesNov 11 2005An integral stability estimate is proved for refraction coefficients of two conformal metrics in a plane domain in terms of its travel times. No assumption on absence of conjugate points of geodesics is made.

On a filtered multiplicative basis of group algebrasSep 01 2000Let $K$ be a field of characteristic $p$ and $G$ a nonabelian metacyclic finite $p$-group. We give an explicit list of all metacyclic $p$-groups $G$, such that the group algebra $KG$ over a field of characteristic $p$ has a filtered multiplicative $K$-basis. ... More

Modular Shimura varieties and forgetful mapsMar 13 2003Apr 25 2008We consider several maps that occur naturally between modular Shimura varieties, Hilbert-Blumenthal varieties and the moduli spaces of polarized abelian varieties when forgetting certain endomorphism structures. We prove that, up to birational equivalences, ... More

Probabilistic approach to the distribution of primes and to the proof of Legendre and Elliott-Halberstam conjecturesJan 28 2015Mar 01 2015Probabilistic models for the distribution of primes in the natural numbers are constructed in the article. The author found and proved the probabilistic estimates of the deviation $R(x)=|\pi(x)- Li(x)|$. The author has analyzed the probabilistic models ... More

Predicate Logic with DefinitionsJun 07 1999Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition is a definition ... More

What is 1-term relation for higher homology of long knotsOct 31 2005Vassiliev's spectral sequence for long knots is discussed. Briefly speaking we study what happens if the strata of non-immersions are ignored. Various algebraic structures on the spectral sequence are introduced. General theorems about these structures ... More

A generalized Weierstrass representation of Lorentzian surfaces in $\mathbb{R}^{2,2}$ and applicationsNov 24 2015Feb 29 2016We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space $\mathbb{R}^{2,2}$ using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in {\bf the} Anti-de Sitter space ... More

Recovery of time dependent volatility coefficient by linearizationJul 17 2013We study the problem of reconstruction of special special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization technique and we conclude ... More

Projective varieties with bad reduction at 3 onlyMar 15 2010Oct 18 2012Suppose F=W(k)[1/p] where W(k) is the ring of Witt vectors with coefficients in algebraically closed field k of characteristic p>2. We construct integral theory of p-adic semi-stable representations of the absolute Galois group of F with Hodge-Tate weights ... More

Floyd maps to the boundaries of relatively hyperbolic groupsJan 25 2010Apr 26 2012A continuous equivariant map from the Floyd boundary of a relatively hyperbolic group (RHG for short) to its Bowditch boundary is constructed. Such a map is unique unless the group is two-ended. In order to optimize the proof and the usage of the map ... More

Aguilar-Balslev-Combes theorem for the Laplacian on a manifold with an axial analytic asymptotically cylindrical endMar 12 2010Feb 09 2011We develop the complex scaling for a manifold with an asymptotically cylindrical end under an assumption on the analyticity of the metric with respect to the axial coordinate of the end. We allow for arbitrarily slow convergence of the metric to its limit ... More

The set of flexible nondegenerate polyhedra of a prescribed combinatorial structure is not always algebraicAug 17 2015We construct some example of a closed nondegenerate nonflexible polyhedron $P$ in Euclidean 3-space that is the limit of a sequence of nondegenerate flexible polyhedra each of which is combinatorially equivalent to $P$. This implies that the set of flexible ... More

Continuous deformations of polyhedra that do not alter the dihedral anglesDec 19 2012Jan 03 2013We prove that, both in the hyperbolic and spherical 3-spaces, there exist nonconvex compact boundary-free polyhedral surfaces without selfintersections which admit nontrivial continuous deformations preserving all dihedral angles and study properties ... More

Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: Part IMar 02 2017Jun 29 2018The non-elementary integrals $\text{Si}_{\beta,\alpha}=\int [\sin{(\lambda x^\beta)}/(\lambda x^\alpha)] dx,\beta\ge1,\alpha\le\beta+1$ and $\text{Ci}_{\beta,\alpha}=\int [\cos{(\lambda x^\beta)}/(\lambda x^\alpha)] dx, \beta\ge1, \alpha\le2\beta+1$, ... More

Evaluation of the non-elementary integral $\int e^{λx^α} dx, α\ge2$, and other related integralsFeb 25 2017Jul 01 2018A formula for the non-elementary integral $\int e^{\lambda x^\alpha} dx$ where $\alpha$ is real and greater or equal two, is obtained in terms of the confluent hypergeometric function $_1F_1$. This result is verified by directly evaluating the area under ... More

Max-relaxation iteration procedure for building of Barabanov norms: convergence and examplesFeb 17 2010Mar 02 2010The problem of construction of Barabanov norms for analysis of properties of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In previous papers of the author the method of Barabanov norms was the ... More

A unified approach to three themes in harmonic analysis ($1^{st}$ part)Feb 11 2019In the present paper and its sequel "A unified approach to three themes in harmonic analysis ($2^{nd}$ part)", we address three rich historical themes in harmonic analysis that rely fundamentally on the concept of non-zero curvature. Namely, we focus ... More

Traveller Salesman Property and Richard Thompson's Group $F$Jul 30 2005Recently Akhmedov introduced a property of finitely generated groups called the Traveller Salesman Property (TSP). It was shown by Thurston that TSP implies non-amenability. Akhmedov conjectured that R. Thompson's group $F$ has TSP. The aim of this article ... More

The global rigidity of a framework is not an affine-invariant propertyFeb 25 2019Mar 09 2019It is well-known that the property of a bar-and-joint framework `to be infinitesimally rigid' is invariant under projective transformations of Eucliean $d$-space for every $d\geqslant 2$. It is less known that the property of a bar-and-joint framework ... More

Reply to Paris's Comments on Exactification of Stirling's Approximation for the Logarithm of the Gamma FunctionAug 07 2014In a recent paper [arXiv:1406.1320] Paris has made several comments concerning the author's recent work on the exactification of Stirling's approximation for the logarithm of the gamma function, $\ln \Gamma(z)$. Despite acknowledging that the calculations ... More

Exactification of Stirling's Approximation for the Logarithm of the Gamma FunctionApr 10 2014Exactification is the process of obtaining exact values of a function from its complete asymptotic expansion. Here Stirling's approximation for the logarithm of the gamma function or $\ln \Gamma(z)$ is derived completely whereby it is composed of the ... More

Tensor categories (after P. Deligne)Jan 25 2004These notes give an exposition of Deligne's theorem on the existense of super fiber functor.

Asymptotics of the ground state energy of heavy molecules and related topics. IIOct 04 2012Jan 23 2013We consider asymptotics of the ground state energy of heavy atoms and molecules in the strong external magnetic field and derive it including Schwinger and Dirac corrections (if magnetic field is not too strong). We also consider related topics: an excessive ... More

Asymptotics of the ground state energy of heavy molecules and related topicsOct 03 2012We consider asymptotics of the ground state energy of heavy atoms and molecules and derive it including Schwinger and Dirac corrections. We consider also related topics: an excessive negative charge, ionization energy and excessive negative charge when ... More

A mathematical formalization of data parallel operationsFeb 07 2016We give a mathematical formalization of `generalized data parallel' operations, a concept that covers such common scientific kernels as matrix-vector multiplication, multi-grid coarsening, load distribution, and many more. We show that from a compact ... More

Spectral Asymptotics for Magnetic Schrödinger Operator Stabilizing at InfinityOct 06 2016In this article we consider even and odd-dimensional Schr\"odinger operators with magnetic field stabilizing at infinity (or constant) and electric potential tending to $0$ at infinity. In the even-dimensional case we have sequences of eigenvalues tending ... More

State equations for discrete state systemsAug 04 2016A method for specifying the behavior and architecture of discrete state systems such as digital electronic devices and software. The method draws on state machine theory, automata products, and recursive functions and is ordinary working mathematics, ... More

Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworksJun 19 2000We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient ... More

On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curvesOct 16 2011Dec 31 2015We are proving $L^2(\R)\times L^2(\R)\,\rightarrow\,L^1(\R)$ bounds for the bilinear Hilbert transform $H_{\Gamma}$ along curves $\Gamma=(t,-\gamma(t))$ with $\gamma$ being a smooth "non-flat" curve near zero and infinity.

The Polynomial Carleson OperatorMay 19 2011We prove that the generalized Carleson operator with polynomial phase function is of strong type $(p,p)$ for $1<p<\infty$, thus answering a question asked by E. Stein. A key ingredient in this proof is the further extension of the relational time-frequency ... More

Groupoids and the integration of Lie algebroidsApr 13 2000We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators.

Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymersMar 25 2010The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive interactions. Performing ... More

Non-perturbative phenomena in the three-dimensional random field Ising modelMar 27 2006The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to localized in space ... More

Universal RandomnessSep 16 2010Jun 30 2011During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution function which is ... More

Griffiths singularity in the random Ising ferromagnetMay 10 2005The explicit form of the Griffiths singularity in the random ferromagnetic Ising model in external magnetic field is derived. In terms of the continuous random temperature Ginzburg-Landau Hamiltonian it is shown that in the paramagnetic phase away from ... More

Stochastic effects in the growth of dropletsMay 30 2005The effects of stochastic absorption and ejection of molecules by growing droplets have been considered. Both analytical and numerical approaches have been used. They demonstrate the satisfactory coincidence. It is proved that in general case corresponding ... More

Perturbative theory approaches to the metastable phase decayDec 31 2007The perturbative theory of the nucleation kinetics is analyzed. A new improvement is suggested and compared with numerical calculations.

Different scenarios of the late stages of condensationDec 31 2007The late stages of the nucleation have been described analytically. The approximate solution of the Zel'dowich-Folmer-Frenkel equation has been constructed.

Stratified Picard--Lefschetz theoryMay 11 1995The monodromy action in the homology of level sets of Morse functions on stratified singular analytic varieties is studied. The local variation operators in both the standard and the intersection homology groups defined by the loops around the critical ... More