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Dense definiteness and boundedness of composition operators in $L^2$-spaces via inductive limitsSep 13 2014The questions of dense definiteness and boundedness of composition operators in $L^2$-spaces are studied by means of inductive limits of operators. Methods based on projective systems of measure spaces and inductive limits of $L^2$-spaces are developed. ... More

Unbounded composition operators via inductive limits: cosubnormals with matrical symbolsFeb 05 2015We prove, by use of inductive techniques, that assorted unbounded composition operators in $L^2$-spaces with matrical symbols are cosubnormal.

New Method for Public Key Distribution Based on Social NetworksMar 11 2015The security of communication in everyday life becomes very important. On the other hand, all existing encryption protocols require from user additional knowledge end resources. In this paper we discuss the problem of public key distribution between interested ... More

Towards autonomous ocean observing systems using Miniature Underwater Gliders with UAV deployment and recovery capabilitiesFeb 08 2019This paper presents preliminary results towards the development of an autonomous ocean observing system using Miniature Underwater Gliders (MUGs) that can operate with the support of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vessels (USVs) ... More

Non-bicolourable Finite Configurations of Rays and Their DeformationsJun 15 2009A new infinite family of examples of finite non-bicolorable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and Kochen-Specker theorem and illustrate ... More

Complex and Unpredictable CardanoJun 03 2008This purely recreational paper is about one of the most colorful characters of the Italian Renaissance, Girolamo Cardano, and the discovery of two basic ingredients of quantum theory, probability and complex numbers. The paper is dedicated to Giuseppe ... More

Density of positive Lyapunov exponents for SL(2,R) cocyclesApr 25 2010We show that SL(2,R) cocycles with a positive Lyapunov exponent are dense in all regularity classes and for all non-periodic dynamical systems. For Schr\"odinger cocycles, we show prevalence of potentials for which the Lyapunov exponent is positive for ... More

The Dirichlet problem for nonlocal Lévy-type operatorsFeb 03 2017May 31 2017We present the theory of the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric L\'evy processes whose L\'evy measures need not be absolutely continuous. We establish basic facts about the Sobolev spaces for ... More

Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisitedApr 12 2008Jan 19 2009We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4\alpha)z z_x, z_t &=& (1-2\alpha)z_{xx} - 4\alpha z w_x + (4-8\alpha)w z_x - (4+8\alpha)w^2 z + (-2+4\alpha)z^3, (*) for which no recursion operator or master symmetry ... More

Representation stability on the cohomology of complements of subspace arrangementsNov 24 2017We study representation stability in the sense of Church and Farb of sequences of cohomology groups of complements of arrangements of linear subspaces in real and complex space as $S_n$-modules. We consider arrangement of linear subspaces defined by sets ... More

Distortion elements in $Diff^\infty(R/Z)$Aug 18 2008We consider the group of smooth diffeomorphisms of the circle. We show that any recurrent $f$ (in the sense that $\{f^n\}_{n \in Z}$ is not discrete) is in fact a distortion element (in the sense that its iterates can be written as short compositions ... More

Infinitesimal perturbations of rational mapsSep 23 2001Feb 16 2002We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restrictions on the behavior of critical points.

Nonlocal and relativistic behavior from a mutual physical base: a toy modelAug 18 2013Sep 19 2013Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of the nature of quantum objects has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could be ... More

JSC : A JavaScript Object SystemDec 15 2009The JSC language is a superset of JavaScript designed to ease the development of large web applications. This language extends JavaScripts own object system by isolating code in a class declaration, simplifying multiple inheritance and using method implementation ... More

Weakly Nonlocal Hamiltonian Structures: Lie Derivative and CompatibilityDec 15 2006Apr 26 2007We show that under certain technical assumptions any weakly nonlocal Hamiltonian structure compatible with a given nondegenerate weakly nonlocal symplectic structure $J$ can be written as the Lie derivative of $J^{-1}$ along a suitably chosen nonlocal ... More

An effective edge--directed frequency filter for removal of aliasing in upsampled imagesSep 04 2006Raster images can have a range of various distortions connected to their raster structure. Upsampling them might in effect substantially yield the raster structure of the original image, known as aliasing. The upsampling itself may introduce aliasing ... More

An Algorithm for Transforming Color Images into Tactile GraphicsApr 08 2004This paper presents an algorithm that transforms color visual images, like photographs or paintings, into tactile graphics. In the algorithm, the edges of objects are detected and colors of the objects are estimated. Then, the edges and the colors are ... More

Mesoscopic MechanicsJul 29 2003This article is concerned with the existence, status and description of the so-called emergent phenomena believed to occur in certain principally planar electronic systems. In fact, two distinctly different if inseparable tasks are accomplished. First, ... More

Magnetic Oscillations and Maxwell TheoryNov 26 1996We explore the possibility of using the Kaluza-Klein geometry of Riemannian Submersions to modify the classical Maxwell Theory. We further argue that the resulting modification of Electromagnetism may be interesting in the context of, among other topics, ... More

A Dynamic Approach to Complex Vector Reconstruction from Intensity MeasurementsJul 02 2015Jan 08 2016In this article we propose a dynamic approach to complex vector reconstruction in the context of quantum tomography. There are two underlying assumptions behind our reasoning. The first one claims that the evolution of a d-level pure quantum system is ... More

Some Remarks on Quantum Tomography in Laser CoolingApr 16 2015In this article we take into consideration the evolution model of 3-level quantum systems known as \textit{laser cooling}. The evolution in this model is given by an equation which is a special case of the general Kossakowski-Lindblad master equation. ... More

Microlagrangian manifolds and quasithermodynamic fluctuations of nonequilibrium statesAug 19 2010Dec 23 2010The paper deals with "quantization" and "second quantization" of phenomenological thermodynamics with respect to the Boltzmann's constant. It is suggested to perceive the quasithermodynamic parameter (corresponding to the Boltzmann's constant) as a mathematical ... More

On the Kotani-Last and Schrodinger conjecturesOct 23 2012In the theory of ergodic one-dimensional Schrodinger operators, ac spectrum has been traditionally expected to be very rigid. Two key conjectures in this direction state, on one hand, that ac spectrum demands almost periodicity of the potential, and, ... More

The maximal number of degenerate directions for non-piezoelectric media of trigonal symmetryJun 19 2004Sep 22 2004We show that one can construct positively defined matrix of elastic constants representing medium of trigonal symmetry for which exactly 16 distinct degenerate directions exist.

From quantum-codemaking to quantum code-breakingMar 19 1997This is a semi-popular overview of quantum entanglement as an important physical resource in the field of data security and quantum computing. After a brief outline of entanglement's key role in philosophical debates about the meaning of quantum mechanics ... More

On the regularization of conservative mapsOct 08 2008We show that smooth maps are $C^1$-dense among $C^1$ volume preserving maps.

Convergence of an exact quantization schemeJun 13 2003It has been shown by Voros \cite {V} that the spectrum of the one-dimensional homogeneous anharmonic oscillator (Schr\"odinger operator with potential $q^{2M}$, $M>1$) is a fixed point of an explicit non-linear transformation. We show that this fixed ... More

Endomorphisms of Cuboidal Hamming Graphs, Latin Hypercuboids of Class $r$, and Mixed MDS CodesFeb 17 2016In this paper we investigate the existence of singular endomorphisms of the cuboidal Hamming graph $H(n_1,...,n_d,S)$ over the set $\left[ n_1\right]\times \left[ n_2\right]\times \cdots \times \left[ n_d\right]$, where $\left[ n\right]=\{1,...,n\}$, ... More

Locally small spaces with an applicationMar 03 2019We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)Dec 01 2014Apr 13 2015The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit distance between ... More

Generalized Cauchy identities, trees and multidimensional Brownian motions. Part II: Combinatorial differential calculusAug 25 2007We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements of the considered ... More

Which Regular Expression Patterns are Hard to Match?Nov 22 2015Sep 26 2016Regular expressions constitute a fundamental notion in formal language theory and are frequently used in computer science to define search patterns. A classic algorithm for these problems constructs and simulates a non-deterministic finite automaton corresponding ... More

In medium T matrix with realistic nuclear interactionsDec 06 2002We calculate the self-consistent in-medium T matrix for symmetric nuclear matter using realistic interactions with many partial waves. We find for the interactions used (CDBonn and Nijmegen) very similar results for on-shell quantities. The effective ... More

Unbounded composition operators via inductive limits: cosubnormal operators with matrix symbols. IIOct 19 2015The paper deals with unbounded composition operators with infinite matrix symbols acting in $L^2$-spaces with respect to the gaussian measure on $\mathbb{R}^\infty$. We introduce weak cohyponormality classes $\EuScript{S}_{n,r}^*$ of unbounded operators ... More

Pauli problem in thermodynamicsAug 14 2012Aug 01 2013A thermodynamic analogue of the Pauli problem (reconstruction of a wavefunction from the position and momentum distributions) is formulated. The coordinates of a quantum system are replaced by the inverse absolute temperature and other intensive quantities, ... More

Quantum Algorithms: Entanglement Enhanced Information ProcessingMar 26 1998We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying ... More

Generic expanding maps without absolutely continuous invariant $σ$-finite measureAug 02 2006We show that a $C^1$-generic expanding map of the circle has no absolutely continuous invariant $\sigma$-finite measure.

Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjectureAug 25 2005We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichm\"uller flow on (any connected component of a stratum of) the moduli space of Abelian differentials on compact Riemann surfaces are all distinct. By previous ... More

Reducibility or non-uniform hyperbolicity for quasiperiodic Schrodinger cocyclesJun 26 2003Apr 26 2007We show that for almost every frequency alpha \in \R \setminus \Q, for every C^omega potential v:\R/\Z \to R, and for almost every energy E the corresponding quasiperiodic Schrodinger cocycle is either reducible or nonuniformly hyperbolic. This result ... More

Towers for commuting endomorphisms, and combinatorial applicationsJul 24 2015Jan 28 2016We give an elementary proof of a generalization of Rokhlin's lemma for commuting non-invertible measure-preserving transformations, and we present several combinatorial applications.

Monotonic cocyclesOct 02 2013We develop a "local theory" of multidimensional quasiperiodic $\SL(2,\R)$ cocycles which are not homotopic to a constant. It describes a $C^1$-open neighborhood of cocycles of rotations and applies irrespective of arithmetic conditions on the frequency, ... More

New Examples of Kochen-Specker Type Configurations on Three QubitsJun 29 2012Oct 30 2012A new example of a saturated Kochen-Specker (KS) type configuration of 64 rays in 8-dimensional space (the Hilbert space of a triple of qubits) is constructed. It is proven that this configuration has a tropical dimension 6 and that it contains a critical ... More

Memory equations as reduced Markov processesApr 06 2018A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory ... More

Inner functions in weak Besov spacesJul 18 2013It is shown that inner functions in weak Besov spaces are precisely the exponential Blaschke products.

An almost-solvable model of complex network dynamicsFeb 26 2019We discuss a specific model, which we refer to as RandLOE, of a large multi-agent network whose dynamic is prescribed via a combination of deterministic local laws and random exogenous factors. The RandLOE approach lies outside the framework of Stochastic ... More

Quasinormal extensions of subnormal operator-weighted composition operators in $\ell^2$-spacesJun 08 2016We prove the subnormality of an operator-weighted composition operator whose symbol is a transformation of a discrete measure space and weights are multiplication operators in $L^2$-spaces under the assumption of existence of a family of probability measures ... More

A uniform dichotomy for generic $SL(2,R)$ cocycles over a minimal baseNov 13 2006Nov 14 2006We consider continuous $SL(2,R)$-cocycles over a minimal homeomorphism of a compact set $K$ of finite dimension. We show that the generic cocycle either is uniformly hyperbolic or has uniform subexponential growth.

Exponential decay of correlations for the Rauzy-Veech-Zorich induction mapOct 20 2006We prove exponential mixing for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations (Theorem 3)

Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical CouplingNov 27 2007We show that the integrated density of states of the almost Mathieu operator is absolutely continuous if and only if the coupling is non-critical. We deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase, ... More

Simplicity of Lyapunov spectra: a sufficient criterionJul 28 2006We exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. This builds on work of Guivarc'h-Raugi and Gol'dsheid-Margulis, who considered products of random matrices, and of Bonatti-Viana, ... More

Generic singular continuous spectrum for ergodic Schrödinger operatorsSep 06 2004We consider Schr\"odinger operators with ergodic potential $V_\omega(n)=f(T^n(\omega))$, $n \in \Z$, $\omega \in \Omega$, where $T:\Omega \to \Omega$ is a non-periodic homeomorphism. We show that for generic $f \in C(\Omega)$, the spectrum has no absolutely ... More

Bornological quasi-metrizability in generalized topologyMay 17 2015Oct 17 2018A concept of quasi-metrizability with respect to a bornology of a generalized topological space in the sense of Delfs and Knebusch is introduced. Quasi-metrization theorems for generalized bornological universes are deduced. A uniform quasi-metrizability ... More

Nanoscale plasmonic circulatorFeb 21 2013Here, we propose a conceptual approach for design of an ultracompact nanoscale passive optical circulator based on the excitation of plasmonic resonances. We study a three-port Y-junction with a deep subwavelength plasmonic nanorod structure integrated ... More

On time-dependent symmetries and formal symmetries of evolution equationsJan 31 1999We present the explicit formulae, describing the structure of symmetries and formal symmetries of any scalar (1+1)-dimensional evolution equation. Using these results, the formulae for the leading terms of commutators of two symmetries and two formal ... More

Anisotropic evolution of energy gap in Bi2212 superconductorAug 03 2016We present a systematic analysis of the energy gap in underdoped Bi2212 superconductor as a function of temperature and hole doping level. Within the framework of the theoretical model containing the electron-phonon and electron-electron-phonon pairing ... More

The local power of the gradient testApr 30 2010Jul 12 2010The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample size. Comparisons ... More

Fluctuations of intensive quantities in statistical thermodynamicsSep 17 2013Nov 12 2013In phenomenological thermodynamics, the canonical coordinates of a physical system split in pairs with each pair consisting of an extensive quantity and an intensive one. In the present paper, the quasi-thermodynamic fluctuation theory of a model system ... More

A generic $C^1$ map has no absolutely continuous invariant probability measureMay 29 2006Oct 18 2006Let $M$ be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension $d \ge 1$. We consider the set of $C^1$ maps $f:M\to M$ which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show ... More

Compactness and compactifications in generalized topologyFeb 06 2014A generalized topology in a set $X$ is a collection $\text{Cov}_X$ of families of subsets of $X$ such that the triple $(X,\bigcup \text{Cov}_X,\text{Cov}_X)$ is a generalized topological space in the sense of Delfs and Knebusch. In this work, notions ... More

A log-Birnbaum-Saunders Regression Model with Asymmetric ErrorsSep 05 2010The paper by Leiva et al. (2010) introduced a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum-Saunders distribution associated with this distribution. In this paper, we introduce ... More

Speckle observations of binary stars with a 0.5 m telescopeJun 08 2005We present 36 observations of 17 visual binaries of moderate separation (range from 0.15'' to 0.79'') made with the 50 cm Cassegrain telescope of the Jagiellonian University in Cracow. The speckle interferometry technique was combined with modest optical ... More

Exploiting Spontaneous Transmissions for Broadcasting and Leader Election in Radio NetworksMar 06 2017We study two fundamental communication primitives: broadcasting and leader election in the classical model of multi-hop radio networks with unknown topology and without collision detection mechanisms. It has been known for almost 20 years that in undirected ... More

Optimal leader election in multi-hop radio networksMay 22 2015We present two optimal randomized leader election algorithms for multi-hop radio networks, which run in expected time asymptotically equal to the time required to broadcast one message to the entire network. We first observe that, under certain assumptions, ... More

Convergence of multiple Fourier series of functions of bounded generalized variationOct 07 2012The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series

Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operatorsDec 16 2009We establish sharp results on the modulus of continuity of the distribution of the spectral measure for one-frequency Schrodinger operators with Diophantine frequencies in the region of absolutely continuous spectrum. More precisely, we establish 1/2-Holder ... More

Almost localization and almost reducibilityMay 12 2008We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schr\"odinger cocycles associated to a non-perturbatively small analytic potential and Diophantine frequency. In particular, we establish ... More

Weak mixing properties of interval exchange transformations and translation flowsMay 10 2016Feb 05 2017Let $d >1$. In this paper we show that for an irreducible permutation $\pi$ which is not a rotation, the set of $[\lambda]\in \mathbb{P}_+^{d-1}$ such that the interval exchange transformation $f([\lambda],\pi)$ is not weakly mixing does not have full ... More

Improving Viterbi is Hard: Better Runtimes Imply Faster Clique AlgorithmsJul 14 2016The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations. It runs in time $O(Tn^2)$ given a sequence of $T$ observations from a HMM with $n$ states. Despite significant ... More

Optical vortex coronagraphy from soft spin-orbit masksSep 19 2016We report on a soft route towards optical vortex coronagraphy based on self-engineered electrically tunable vortex masks based on liquid crystal topological defects. These results suggest that a Nature-assisted technological approach to the fabrication ... More

Entropy and density of states from isoenergetic nonequilibrium processesAug 03 2004Apr 05 2005Two identities in statistical mechanics involving entropy differences (or ratios of density of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C. Jarzynski, Phys. ... More

Does the Boltzmann principle need a dynamical correction?Apr 27 2002Jun 10 2004In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived [M. Bianucci, R. Mannella, B. J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)] which ... More

Weak mixing properties of interval exchange transformations and translation flowsMay 10 2016Nov 02 2016Let $d >1$. In this paper we show that for an irreducible permutation $\pi$ which is not a rotation, the set of $[\lambda]\in \mathbb{P}_+^{d-1}$ such that the interval exchange transformation $f([\lambda],\pi)$ is not weakly mixing does not have full ... More

Huygens' principle and anomalously small radiation tailsJan 14 2008This is a short account of recent joint work with T. Chmaj and A. Rostworowski on asymptotic behavior of linear and nonlinear waves, as presented at the conference devoted to Myron Mathisson held at the Banach Center, Warsaw 2007.

An unusual eigenvalue problemNov 10 2004We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires special methods ... More

Harmonic maps between three-spheresJul 21 1994It is shown that smooth maps $f: S^3 \rightarrow S^3$ contain two countable families of harmonic representatives in the homotopy classes of degree zero and one.

Saddle points of stringy actionApr 28 1993It is shown that Einstein-Yang-Mills-dilaton theory has a countable family of static globally regular solutions which are purely magnetic but uncharged. The discrete spectrum of masses of these solutions is bounded from above by the mass of extremal Gibbons-Maeda ... More

Parametric Dynamics of Level Spacings in Quantum ChaosJun 04 2001We identify parametric (radial) Bessel-Ornstein-Uhlenbeck stochastic processes as primitive dynamical models of energy level repulsion in irregular quantum systems. Familiar GOE, GUE, GSE and non-Hermitian Ginibre universality classes of spacing distributions ... More

Information dynamics: Temporal behavior of uncertainty measuresMar 06 2007Dec 05 2007We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities ... More

Entropy methods in random motionOct 20 2005We analyze a contrasting dynamical behavior of Gibbs-Shannon and conditional Kullback-Leibler entropies, induced by time-evolution of continuous probability distributions. The question of predominantly purpose-dependent entropy definition for non-equilibrium ... More

Shannon versus Kullback-Leibler Entropies in Nonequilibrium Random MotionApr 05 2005We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler ... More

Stochastic modelling of nonlinear dynamical systemsOct 20 1999We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium (related to driving ... More

Viscous evolution of the rapidity distribution of matter created in relativistic heavy-ion collisionsDec 20 2007Longitudinal hydrodynamic expansion of the fluid created in relativistic heavy-collisions is considered taking into account shear viscosity. Both a on-vanishing viscosity and a soft equation of state make particle distributions in rapidity narrower. The ... More

Hydrodynamic flow from RHIC to LHCNov 18 2011The hydrodynamic model for the expansion of the fireball in relativistic heavy-ion collisions is presented. Calculations using relativistic hydrodynamics of a fluid with small viscosity yield a satisfactory description of the experimental data on the ... More

Spectra, flow and HBT in Pb-Pb collisions at the LHCJun 29 2011The transverse momentum spectra, elliptic flow and interferometry radii for Pb-Pb collisions at the LHC are calculated in relativistic viscous hydrodynamics. For Glauber model initial conditions, we find that the data can be described using a small value ... More

Elliptic flow in proton-proton collisions at 7 TeVOct 03 2010Oct 26 2010The angular correlations measured in proton-proton collisions at 7 TeV are decomposed into contributions from back to back emission and elliptic flow. Modeling the dominant term in the correlation functions as a momentum conservation effect or as an effect ... More

Interplay of the emission from thermal and direct sources in relativistic heavy ion collisionsNov 12 2008The separation of the source created in ultrarelativistic heavy-ion collisions into a thermalized dense core and an outer mantle consisting of independent nucleon-nucleon collisions is discussed. Evidence for such a two component picture is found in transverse ... More

The balance functions in azimuthal angle is a measure of the transverse flowDec 20 2004The charge or barion number balance function in the relative azimuthal angle of a pair of particles emitted in ultrarelativistic heavy ion collisions is studied. The pi+pi- and ppbar balance functions are computed using thermal models with two different ... More

Functional calculus in finite type I von Neumann algebrasOct 21 2013A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded sequences f_1,f_2,... ... More

Krasnosel'skii type formula and translation along trajectories method on the scale of fractional spacesApr 13 2014Oct 30 2015We provide global continuation principle of periodic solutions for the equation $\dot u = - Au + F(t,u)$, where $A:D(A)\to X$ is a sectorial operator on a Banach space $X$ and $F:[0,+\infty)\times X^\alpha\to X$ is a nonlinear map defined on fractional ... More

Thom polynomials and Schur functions: the singularities I_{2,2}(-)May 09 2007We give the Thom polynomials for the singularities $I_{2,2}$ associated with maps $({\bf C}^{\bullet},0) \to ({\bf C}^{\bullet+k},0)$ with parameter $k\ge 0$. Our computations combine the characterization of Thom polynomials via the ``method of restriction ... More

Symmetric groups and random matricesJan 26 2003Dec 18 2006The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves many conjugacy ... More

Free probability and representations of large symmetric groupsApr 19 2003Dec 18 2006We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys--Murphy elements--or equivalently--of the transition measure associated with a Young diagram. We express these cumulants in terms of ... More

Sobolev mappings: Lipschitz density is not an isometric invariant of the targetSep 21 2011If $M$ is a compact smooth manifold and $X$ is a compact metric space, the Sobolev space $W^{1,p}(M,X)$ is defined through an isometric embedding of $X$ into a Banach space. We prove that the answer to the question whether Lipschitz mappings ${\rm Lip}\,(M,X)$ ... More

Some Representation Theorem for nonreflexive Banach space ultrapowers under the Continuum HypothesisJul 08 2011In this paper it will be shown that assuming the Continuum Hypothesis (CH) every nonreflexive Banach space ultrapower is isometrically isomorphic to the space of continuous, bounded and real-valued functions on the Parovicenko space. This Representation ... More

A Gysin formula for Hall-Littlewood polynomialsMar 04 2014Apr 06 2016We give a formula for pushing forward the classes of Hall-Littlewood polynomials in Grassmann bundles, generalizing Gysin formulas for Schur S- and Q-functions.

Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensionsJul 02 2007Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in $\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either a standard Poisson random field ... More

Five dimensional almost para-cosymplectic manifolds with contact Ricci potentialAug 29 2013There are studied in details 5-dimensional pseudo-Riemannian manifolds equipped with the structure analogous to the almost cosymplectic (almost coKaehler) structure. The curvature by assumption commutes with the structure affinor and all these manifolds ... More

Sewing cells in almost cosymplectic and almost Kenmotsu geometryMar 21 2012Mar 30 2012For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form $\eta$ is described a construction of an almost contact metric manifold, where the members of the family are building blocks - cells. Obtained manifold ... More

Structure coefficients for Jack characters: approximate factorization propertyMar 14 2016Dec 06 2018Jack characters are a generalization of the characters of the symmetric groups; a generalization that is related to Jack symmetric functions. We investigate the structure coefficients for Jack characters; they are a generalization of the connection coefficients ... More

Saddle point solutions in Yang-Mills-dilaton theorySep 26 1992The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analitical and numerical methods. In the abelian sector of the theory there are finite-energy ... More