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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

Linking Things on the Web: A Pragmatic Examination of Linked Data for Libraries, Archives and MuseumsFeb 19 2013Jun 20 2013The Web publishing paradigm of Linked Data has been gaining traction in the cultural heritage sector: libraries, archives and museums. At first glance, the principles of Linked Data seem simple enough. However experienced Web developers, designers and ... More

Permutation Modules associated to the Hyperoctahedron and Group ActionsDec 15 2017Sep 24 2018We investigate the permutation modules associated to the set of $k$-dimensional faces of the hyperoctahedron in dimension $n$, denoted $H^{n}.$ For any $k\leq n$ such a module can be defined over an arbitrary field $F$, it is called a face module of $H^{n}$ ... More

Luminosity and Crab Waist Collision StudiesMay 24 2015In high energy physics, the luminosity is one useful value to characterize the performance of a particle collider. To gain more available data, we need to maximize the luminosity in most collider experiments. With the discussions of tune shift involved ... More

Distributed Model Predictive Consensus via the Alternating Direction Method of MultipliersDec 06 2012We propose a distributed optimization method for solving a distributed model predictive consensus problem. The goal is to design a distributed controller for a network of dynamical systems to optimize a coupled objective function while respecting state ... More

Optimal Sensor and Actuator Placement in Complex Dynamical NetworksJun 11 2013Mar 25 2014Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and ... More

A Model for Generating Relativistic Electrons in the Earth's Inner Magnetosphere Based on Gyroresonant Wave-Particle InteractionsOct 13 1999During the recovery phase of a magnetic storm, fluxes of relativistic ($>1$ MeV) electrons in the inner magnetosphere ($3\le L \le 6$) increase to beyond pre-storm levels, reaching a peak about 4 days after the initiation of the storm. In order to account ... More

Information Structure Design in Team Decision ProblemsJun 17 2017We consider a problem of information structure design in team decision problems and team games. We propose simple, scalable greedy algorithms for adding a set of extra information links to optimize team performance and resilience to non-cooperative and ... More

On Deriving Space-Time From Quantum Observables and StatesApr 21 2003May 07 2003We prove that, under suitable assumptions, operationally motivated data completely determine a space-time in which the quantum systems can be interpreted as evolving. At the same time, the dynamics of the quantum system is also determined. To minimize ... 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

Semiclassical analysis of the schr{ö}dinger equation with conical singularitiesAug 12 2016Aug 17 2016In this article we study the propagation of Wigner measures linked to solutions of the Schr{\"o}dinger equation with potentials presenting conical singularities and show that they are transported by two different Hamiltonian flows, one over the bundle ... More

Zero temperature limit for (1+1) directed polymers with correlated random potentialOct 19 2016Zero temperature limit in (1+1) directed polymers with finite range correlated random potential is studied. In terms of the standard replica technique it is demonstrated that in this limit the considered system reveals the one-step replica symmetry breaking ... More

How many times can the volume of a convex polyhedron be increased by isometric deformations?Jul 22 2016We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c>0$, we construct two oblique triangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvex and intrinsically isometric ... More

Code Generation for Event-BFeb 05 2016Stepwise refinement and Design-by-Contract are two formal approaches for modelling systems. These approaches are widely used in the development of systems. Both approaches have (dis-)advantages. This thesis aims to answer, is it possible to combine both ... More

Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDEDec 02 2015These lectures were given in Session 1: "Vertex algebras, W-algebras, and applications" of INdAM Intensive research period "Perspectives in Lie Theory" at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy, December 9, 2014 -- February 28, ... More

A problem in Pythagorean ArithmeticOct 04 2015Problem 2 at the 56th International Mathematical Olympiad (2015) asks for all triples (a,b,c) of positive integers for which ab-c, bc-a, and ca-b are all powers of 2. We show that this problem requires only a primitive form of arithmetic, going back to ... More

Folding a Tree into a MapSep 25 2015Analysis of the retrieval architecture of the highly influential UNIX file system (\cite{Ritchie}\cite{multicsfs}) provides insight into design methods, constraints, and possible alternatives. The basic architecture can be understood in terms of function ... More

Distance-preserving subgraphs of Johnson graphsMar 13 2015Nov 01 2015We give a characterization of distance--preserving subgraphs of Johnson graphs, i.e. of graphs which are isometrically embeddable into Johnson graphs (the Johnson graph $J(m,\Lambda)$ has the subsets of cardinality $m$ of a set $\Lambda$ as the vertex--set ... More

Flexible polyhedra in the Minkowski 3-spaceNov 01 2001Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change its shape ... More

State machine models of timing and circuit designMar 02 2010This paper illustrates a technique for specifying the detailed timing, logical operation, and compositional circuit design of digital circuits in terms of ordinary state machines with output (transducers). The method is illustrated here with specifications ... More

General trends of the late period of evolution in the quasichemical model of nucleationJul 28 2006The periods after the end of the "primary" nucleation are considered. The approximate analytical description is given. The process is split into several periods which form the loop of evolution.

Explicit two cycle model in investigation of stochastic effects in diffusion regime of metastable phase decayOct 24 2004The theory for manifestation of stochastic appearance of embryos in the global decay of metastable phase has been constructed. The regime of droplets growth is supposed to be both free molecular one and diffusion one. The deviation for a mean droplets ... More

A simple method to determine parameters of embryos distribution in homogeneous nucleation under dynamic conditionsJul 22 2002A simple method to get all main characteristics of nucleation process is proposed. The advantage of this method is an applicability to situations with non-linear behavior in time of effective external source of vapor. It is important because already existed ... More

Heterogeneous condensation in dense mediaMar 31 2000The theoretical description of the heterogeneous nucleation kinetics is presented. This description takes into account the perturbation of the vapor phase initiated by the growing droplets. The form of the density profile around the growing droplet is ... More

Effects of stochastic nucleation in the first order phase transitionJul 01 2002The effects of stochastic apppearence of embryos of a new phase are analyzed analytically. A new approach by the similarity of nucleation conditions is proposed. Corrections for a number of droplets are estimated. A comparison with numerical simulation ... More

Dirac variables in gauge theoriesSep 28 2001Sep 30 2001The review is devoted to a relativistic formulation of the first Dirac quantization of QED (1927) and its generalization to the non-Abelian theories (Yang-Mills and QCD) with the topological degeneration of initial data. Using the Dirac variables we give ... More

Automorphisms of local fields of period $p$ and nilpotent class $<p$Mar 17 2014May 17 2016Suppose $K$ is a finite field extension of $\mathbb{Q} _p$ containing a primitive $p$-th root of unity. Let $\Gamma _{<p}$ be the Galois group of a maximal $p$-extension of $K$ with the Galois group of period $p$ and nilpotent class $<p$. In the paper ... More

A restriction theorem for torsion-free sheaves on some elliptic manifoldsDec 27 2012We prove that if $X$ is the total space of an elliptic principal bundle $\pi:X\ra B$ which is non-K\"ahler, then the restriction of any torsion-free sheaf on $X$ to the general fiber of $\pi$ is semi-stable.

Singular integral operators on non-compact manifolds and analysis on polyhedral domainsFeb 19 2004We review the definition of a Lie manifold $(M, \VV)$ and the construction of the algebra $\Psi\sp{\infty}\sb{\VV}(M)$ of pseudodifferential operators on a Lie manifold $(M, \VV)$. We give some concrete Fredholmness conditions for pseudodifferential operators ... More

An index theorem for gauge-invariant families: The case of solvable groupsJan 21 2002We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers of $\GR \to ... More

Distribution function of the endpoint fluctuations of one-dimensional directed polymers in a random potentialSep 27 2012Jan 22 2013The explicit expression for the the probability distribution function of the endpoint fluctuations of one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to ... More

Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in one-dimensional directed polymers with free boundary conditionsSep 17 2012The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions. It is shown ... More

Mean Field Theory of the Three-Dimensional Dipole Superspin GlassesJan 18 2010Sep 16 2010We study the three-dimensional system of magnetic nanoparticle dipoles randomly oriented along quenched easy axes. Directions of the magnetic momenta are described by the Ising variables which allow the momenta to flip along their random orientations. ... More

Mean Field Model of a GlassSep 20 2002In this paper we propose a simple mean-field "toy" model for the liquid-glass phase transition. This is the system of $N$ point-like particles confined in a finite volume of a $D$-dimensional space interacting via infinite-range oscillating potential. ... More

Calculus of the first non-trivial 1-cocycle of the space of long knotsFeb 24 2005Apr 18 2005For the space of long knots in R^3, Vassiliev's theory defines the so called finite order cocycles. Zero degree cocycles are finite type knot invariants. The first non-trivial cocycle of positive dimension in the space of long knots has dimension one ... More

Finite semigroups embed in finitely presented congruence-free monoidsJan 22 2013We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture.

Constraining the two-Higgs doublet models with the LHC dataOct 03 2013Oct 07 2013The recent discovery of a Standard Model-like boson with mass of about 126 GeV seems to be the first direct information on the electroweak symmetry breaking mechanism. Using the available experimental data from the LHC and Tevatron we study the implications ... More

Effects of dead time and after-pulses in photon detector on measured statistics of stochastic radiationNov 19 2013Many physical experiments require analysis of the statistics of fluctuating radiation. In the case of an ideal single-photon detector, the contribution of photon noise to the statistics of the registered signal has been thoroughly examined. However, practical ... More

On primitive idealsFeb 10 2002May 28 2012We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem', to much wider classes of algebras. Our general version of Irreducibility theorem says that if A is ... More

Non-commutative Symplectic Geometry, Quiver varieties, and OperadsMay 17 2000Jun 02 2000Quiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we show that many ... More

Geometric Methods in Representation Theory of Hecke Algebras and Quantum GroupsJan 31 1998Mar 05 1998These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in Representation ... More

The global nilpotent variety is LagrangianApr 10 1997Oct 31 2000The purpose of this note is to present a short elementary proof of a theorem due to Faltings and Laumon, saying that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the moduli space of G-bundles on a complex compact curve. ... More

What are the right values of $\bar Λ$ and the heavy quark kinetic energy?Apr 21 1996May 06 1996The values of two important parameters of the heavy quark effective theory,\, $\bar \Lambda$ and $\mu_\pi^2$ (the mean value of the heavy quark three momentum squared),\, have been determined recently in \cite {GKLW} from the precise CLEO data on the ... More

Properties of {\cal N}=1 SUSY Yang-Mills vacuums and domain wallsAug 16 1998Mar 18 1999It is shown that there is no chirally symmetric vacuum state in the {cal N}=1 supersymmetric Yang-Mills theory. The values of the gluino condensate and the vacuum energy density are found out through a direct instanton calculation. A qualitative picture ... More

Infrared Dynamics in Vector-Like Gauge Theories: QCD and BeyondSep 07 2001Pade-approximant methods are used to extract information about leading positive zeros or poles of QCD and SQCD beta-functions from the known terms of their perturbative series. For QCD, such methods are seen to corroborate the flavour-threshold behaviour ... More

Shape- and topology-dependent heat capacity of few-particle systemsApr 02 2012Thermal properties of few-fermion (n < 5) systems are investigated. The dependence of the heat capacity on the topology and shape of the cavity containing the particles is analyzed. It is found that the maximum of the heat capacity, occuring at low T, ... More

Exact thermodynamics of a planar array of Ginzburg-Landau chains with nn and nnn interactionsOct 01 2007The exact expression of the free energy of a planar array of a Ginzburg-Landau chains with nn and nnn interaction is obtained. The critical behaviour of the specific heat is not qualitatively modified by taking into account the nnn interaction.

Metallic phase in a two-dimensional disordered Fermi system with singular interactionsJul 30 2005Oct 12 2005We consider a disordered system of gapless fermions interacting with a singular transverse (2+1)-dimensional gauge-field. We study quantum corrections to fermion conductivity and show that they are very different from those in a Fermi liquid with non-singular ... More

State Space Methods for Granger-Geweke Causality MeasuresJan 19 2015At least two recent developments have put the spotlight on some significant gaps in the theory of multivariate time series. The recent interest in the dynamics of networks; and the advent, across a range of applications, of measuring modalities that operate ... More

Ramification filtration of the Galois group of a local field via deformationsJan 09 2017Dec 21 2018Let $\mathcal K$ be a field of formal Laurent series with coefficients in a finite field of characteristic $p$, $\mathcal G_{<p}$ --- the maximal quotient of $\operatorname{Gal} (\mathcal K_{sep}/\mathcal K)$ of period $p$ and nilpotent class $<p$ and ... More

Analytical evaluation and asymptotic evaluation of Dawson's integral and related functions in mathematical physicsMar 14 2017Dawson's integral and related functions in mathematical physics that include the complex error function (Faddeeva's integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev's integral are analytically evaluated ... More

Algebra versus analysis in the theory of flexible polyhedraFeb 02 2009Jul 06 2010Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used ... More

Minimal polynomials of simple highest weight modules over classical Lie algebrasNov 15 2013We completely determine the minimal polynomial of an arbitrary simple highest weight module $L(\lambda)$ over a complex classical Lie algebra $\mathfrak{g}\subseteq\mathfrak{gl}_N$ relative to its defining module $\pi=\mathbb{C}^{N}$. These results are ... More

The (weak-$L^2$) Boundedness of The Quadratic Carleson OperatorOct 11 2007Sep 06 2008We prove that the generalized Carleson operator with polynomial phase function of degree two is of weak type (2,2). For this, we introduce a new approach to the time-frequency analysis of the quadratic phase.

A Note on the Polynomial Carleson Operator in higher dimensionsDec 08 2017We prove the $L^p$-boundedness, $1<p<\infty$, of the Polynomial Carleson operator in general dimension. This follows the author's resolution of the one dimensional case as well as the work of Zorin-Kranich on the higher dimensional case in the setting ... More

Modular group algebras with almost maximal Lie nilpotency indices, IIJul 06 2006Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that, if KG is Lie nilpotent, then its upper (or lower) Lie nilpotency index is at most |G'|+1, where |G'| is the order of the commutator subgroup. Previously ... More

Minimax theorem for the spectral radius of the product of non-negative matricesMar 17 2016Dec 26 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

The Berger-Wang formula for the Markovian joint spectral radiusJan 13 2014May 07 2014The Berger-Wang formula establishes equality between the joint and generalized spectral radii of a set of matrices. For matrix products whose multipliers are applied not arbitrarily but in accordance with some Markovian law, there are also known analogs ... More

On the roots of a hyperbolic polynomial pencilApr 27 2016May 01 2016Let $\nu_0(t),\nu_1(t),\,\ldots\,,\nu_n(t)$ be the roots of the equation $R(z)=t$, where $R(z)$ is a rational function of the form \[R(z)=z+\sum\limits_{k=1}^n\frac{\alpha_k}{z-\mu_k},\] $\mu_k$ are pairwise different real numbers, $\alpha_k>0,\,1\leq{}k\leq{}n$. ... More

On a special case of the Herbert Stahl theoremJun 22 2016The BMV conjecture states that for $n\times n$ Hermitian matrices $A$ and $B$ the function $f_{A,B}(t)=trace{\, } e^{tA+B}$ is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is based on ingenious ... More

On the BMV conjecture for 2\times2 matrices and the exponential convexity of the function \cosh(\sqrt{at^2+b})May 01 2015Nov 01 2015The BMV conjecture states that for \(n\times n\) Hermitian matrices \(A\) and \(B\) the function \(f_{A,B}(t)=\tr e^{tA+B}\) is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is based on ingenious ... More

Contradictions in some primes conjecturesJul 22 2014This paper demonstrates that from the Cramer's, Hardy-Littlewood's and Bateman-Horn's conjectures (suggest that the probability of a large positive integer being $x$ a prime - $\frac {1} {\ln(x)}$) it follows that the events consisting in a positive integer ... More

Fredholm criteria for pseudodifferential operators and induced representations of groupoid algebrasFeb 15 2016We characterize the groupoids for which an operator is Fredholm if, and only if, its principal symbol and all its boundary restrictions are invertible. A groupoid with this property is called {\em Fredholm}. Using results on the Effros-Hahn conjecture, ... More

Desingularization of Lie groupoids and pseudodifferential operators on singular spacesDec 29 2015We introduce and study a "desingularization" of a Lie groupoid $G$ along an "$A(G)$-tame" submanifold $L$ of the space of units $M$. An $A(G)$-tame submanifold $L \subset M$ is one that has, by definition, a tubular neighborhood on which $A(G)$ becomes ... More

2D- and 3DMagnetic Schroedinger Operators: Short Loops, Pointwise Spectral Asymptotics and Asymptotics of Dirac EnergyAug 21 2010Dec 07 2010We consider 2- and 3-dimensional Schr\"odinger or generalized Schr\"odinger-Pauli operators with the non-degenerating magnetic field in the open domain under certain non-degeneracy assumptions we derive pointwise spectral asymptotics. We also consider ... More

Schroedinger Operator with Strong Magnetic Field: Propagation of singularities and sharper asymptoticsMay 04 2010We consider 2-dimensional Schr\"odinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o(\mu^{-1}h^{-1})$ or better. We also consider 3-dimensional Schr\"odinger operator with the non-degenerating ... More

Complete Differentiable Semiclassical Spectral AsymptoticsSep 19 2018For an operator $A:= A_h= A^0(hD) + V(x,hD)$ with a "potential" $V$ decaying as $|x|\to \infty$ we establish under certain assumptions the complete and differentiable with respect to $\tau$ asymptotics of $e_h(x,x,\tau)$ where $e_h(x,y,\tau)$ is the Schwartz ... More

Badly approximable points on manifoldsApr 02 2013Mar 30 2016This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of the sets of weighted ... More

Gromov-Witten invariants of Fano threefolds of genera 6 and 8Oct 13 2004Jan 07 2007The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$. This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. More precisely, we find counting matrices ... More

Quantum cohomology of smooth complete intersections in weighted projective spaces and singular toric varietiesJul 12 2005Jul 25 2007We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\geq 3$, which are complete intersections in weighted projective spaces ... More

New manifestations of the Darboux's rotation and translation fields of a surfaceOct 27 2009We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal bending) and ... More

Exponential Decay of Eigenfunctions and Accumulation of Eigenvalues on Manifolds with Axial Analytic Asymptotically Cylindrical EndsJul 25 2010In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling method and the Phragm\'{e}n-Lindel\"{o}f principle we prove exponential decay ... More

Universal Higher Order GrammarFeb 25 2011We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities. This class is ... More

Econophysics Macroeconomic ModelJan 20 2017This paper presents macroeconomic model that is based on parallels between macroeconomic multi-agent systems and multi-particle systems. We use risk ratings of economic agents as their coordinates on economic space. Aggregates of economic or financial ... More

Coordinate System, Temperature and GravityJul 09 2001We discuss the problem of applicability of Coordinate Systems (or Frames) that determine (t,x,y,z) values - the initial notions for most physical theories. Equipment that measure these values - Clocks and Meters - are based at Reference System and are ... 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

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.

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