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Quantum fluctuation effects on the quench dynamics of thermal quasicondensatesAug 30 2014Feb 12 2016We study the influence of quantum fluctuations on the phase, density, and pair correlations in a trapped quasicondensate after a quench of the interaction strength. To do so, we derive a description similar to the stochastic Gross-Pitaevskii equation ... More

Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybridsMar 06 2009Sep 25 2009A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations ... More

First-principles quantum simulations of many-mode open interacting Bose gases using stochastic gauge methodsJul 01 2005Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with no further ... More

A tractable prescription for large-scale free flight expansion of wavefunctionsFeb 10 2016Mar 06 2016A numerical recipe is given for obtaining the density image of an initially compact quantum mechanical wavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that plague this ... More

Classical field records of a quantum system: their internal consistency and accuracyApr 23 2015Nov 25 2015We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas results carry ... More

Correlation waves after quantum quenches in one- to three-dimensional BECsOct 04 2013We obtain the universal form of spatial density and phase correlations after a quantum quench in dilute ultracold Bose gases, and give compact time-dependent expressions for the most visible effects. A Bogoliubov description in a local density approximation ... More

Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solutionJul 31 2017Number fluctuations in a one-dimensional Bose gas consist of contributions from many smaller independent localized fluctuations, the density grains. We have derived a set of extended integral equations from the Yang-Yang solution for finite temperature ... More

A semiclassical field theory that is freed of the ultraviolet catastropheApr 12 2019A more accurate semiclassical theory for ultracold gases is derived, in which the occupation of high energy modes is dynamically constrained to the Bose-Einstein distribution. This regularized version of the SGPE model preserves the proper nonlinear energy ... More

Comment on "Quantum entangled dark solitons formed by ultracold atoms in optical lattices"Jan 07 2010We demonstrate that knowledge of two body correlation functions like g2(x) is insufficient to draw conclusions about whether solitons fill in or not in individual experimental runs. In our example, g2 is filled in, while the soliton is not.

Correlation evolution in dilute Bose-Einstein condensates after quantum quenchesOct 04 2013Feb 19 2019The universal forms of quantum density and phase correlations after an interaction quench are found for dilute 1d, 2d, and 3d condensates. A Bogoliubov approach in a local density aproximation is used. We obtain compact expressions for the most visible ... More

Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space TechniquesJul 14 2013We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. The new representation ... More

Concurrence in arbitrary dimensionsJul 30 2001We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional generalizations ... More

Contradiction of Quantum Mechanics with Local Hidden Variables for Continuous Variable Quadrature Phase Amplitude MeasurementsOct 06 2000We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous variable quadrature phase amplitude (``position'' and ``momentum'') measurements, by way of a violation of a Bell inequality. For any quantum state, ... More

The time-reversal test for stochastic quantum dynamicsNov 26 2004The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultra-cold atomic Bose-Einstein condensates (BEC) to condensed matter, biology, and even astrophysics. Here we demonstrate ... More

Bogoliubov dynamics of condensate collisions using the positive-P representationMay 06 2011We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-P representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full Bogoliubov description ... More

Mean field effects on the scattered atoms in condensate collisionsJan 28 2011We consider the collision of two Bose Einstein condensates at supersonic velocities and focus on the halo of scattered atoms. This halo is the most important feature for experiments and is also an excellent testing ground for various theoretical approaches. ... More

Anisotropy in s-wave Bose-Einstein condensate collisions and its relationship to superradianceJun 05 2014Aug 30 2014We report the experimental realization of a single-species atomic four-wave mixing process with BEC collisions for which the angular distribution of scattered atom pairs is not isotropic, despite the collisions being in the $s$-wave regime. Theoretical ... More

Solitons as the early stage of quasicondensate formation during evaporative coolingJan 04 2011We calculate the evaporative cooling dynamics of trapped one-dimensional Bose-Einstein condensates for parameters leading to a range of condensates and quasicondensates in the final equilibrium state. We confirm that solitons are created during the evaporation ... More

BPS counting for knots and combinatorics on wordsAug 23 2016We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded ... More

Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond OpticsNov 24 2009May 27 2010We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved ... More

Sub-Poissonian number differences in four-wave mixing of matter wavesAug 04 2010Nov 03 2010We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, ... More

On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditionsMay 24 2018Jan 10 2019We study the non-autonomously forced Burgers equation $$ u_t(x,t) + u(x,t)u_x(x,t) - u_{xx}(x,t) = f(x,t) $$ on the space interval $(0,1)$ with two sets of the boundary conditions: the Dirichlet and periodic ones. For both situations we prove that there ... More

Hyperbolic geometry for non-differential topologistsJan 22 2018A soft presentation of hyperbolic spaces, free of differential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean ... More

Maxwell-like picture of General Relativity and its Planck limitJan 13 2013Nov 29 2013We show that Geroch decomposition leads us to Maxwell-like representation of gravity in $(3+1)$ metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential $V^\mu$ and gravitational ... More

Information transfer and fidelity in quantum copiersMar 15 2000Apr 12 2000We find that very different quantum copying machines are optimal depending on the indicator used to assess their performance. Several quantum copying machine models acting on non-orthogonal input states are investigated, and assessed according to two ... More

Nonuniform BriberyNov 30 2007We study the concept of bribery in the situation where voters are willing to change their votes as we ask them, but where their prices depend on the nature of the change we request. Our model is an extension of the one of Faliszewski et al. [FHH06], where ... More

Equivariant self-similar wave maps from Minkowski spacetime into 3-sphereOct 17 1999May 25 2000We prove existence of a countable family of spherically symmetric self-similar wave maps from 3+1 Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state wave map found previously by Shatah. The first excitation ... More

Pseudoscalar Meson Temporal Correlation Function in HTL approachAug 11 2006The temporal pseudoscalar meson correlation function in a QCD plasma is investigated in a range of temperatures exceeding $T_c$ and first time for a finite momenta which is of the experimental interest. The imaginary time formalism is employed for the ... More

Event-by-event viscous hydrodynamics for Cu-Au collisions at 200GeVAug 09 2012Sep 24 2012Event-by-event hydrodynamics is applied to Cu-Au collisions at 200GeV. Predictions for charged particle distributions in pseudorapidity, transverse momentum spectra, femtoscopy radii are given. The triangular and elliptic flow coefficients are calculated. ... More

Bulk and shear viscosities of matter created in relativistic heavy-ion collisionsNov 12 2009Mar 08 2010We study the effects of the shear and bulk viscosities in the hadronic phase on the expansion of the fireball and on the particle production in relativistic heavy ion collisions. Comparing simulation with or without viscosity in the hadronic matter we ... More

Early dissipation and viscosityApr 24 2008We consider dissipative phenomena due to the relaxation of an initial anisotropic local pressure in the fireball created in relativistic heavy-ion collisions, both for the Bjorken boost-invariant case and for the azimuthally symmetric radial expansion ... More

Low-energy amplitudes in the non-local chiral quark modelNov 11 2009Jan 19 2010We apply chiral quark model with momentum dependent quark mass to two kinds of non-perturbative objects. These are: photon Distribution Amplitudes which we calculate up to twist-4 in tensor, vector and axial channels and pion-photon Transition Distribution ... More

In-medium ion mass renormalization and lattice vibrations in the neutron star crustDec 30 2003The inner crust of a neutron star consists of nuclei immersed in a superfluid neutron liquid. As these nuclei move through the fermionic medium they bring it into motion as well. As a result their mass is strongly renormalized and the spectrum of the ... More

Deuterium depletion and magnesium enhancement in the local discJul 19 2005Oct 12 2005The local disc deuter is known to be depleted in comparison to the local bubble. We show, that the same lines of sight that are depleted in deuter, are enhanced in magnesium. Heavier elements - Si and Fe do not show any difference in the abundance between ... More

Homotopy Decompositions of Looped Stiefel manifolds, and their ExponentsFeb 20 2010Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0<m<n\leq (p-1)(p-2)$. We give a $p$-local homotopy decomposition for the loop space of the complex Stiefel manifold $W_{n,m}$. Similar decompositions are given for the loop space of the ... More

Evading network-level emulationJun 10 2009Recently more and more attention has been paid to the intrusion detection systems (IDS) which don't rely on signature based detection approach. Such solutions try to increase their defense level by using heuristics detection methods like network-level ... More

Dynamic Data Flow Analysis via Virtual Code Integration (aka The SpiderPig case)Jun 03 2009Paper addresses the process of dynamic data flow analysis using virtual code integration (VCI), often refered to as dynamic binary rewriting. This article will try to demonstrate all of the techniques that were applied in the SpiderPig project. It will ... More

Clump Distance to the Magellanic Clouds and Anomalous Colors in the Galactic BulgeOct 11 1999Nov 13 1999I demonstrate that the two unexpected results in the local Universe: 1) anomalous intrinsic (V-I)_0 colors of the clump giants and RR Lyrae stars in the Galactic center, and 2) very short distances to the Magellanic Clouds (LMC, SMC) as inferred from ... More

A Complexity of double dummy bridgeSep 23 2013This paper presents an analysis of complexity of double dummy bridge. Values of both, a state-space (search-space) complexity and a game tree complexity have been estimated. ----- Oszacowanie z{\l}o\.zono\'sci problemu rozgrywki w otwarte karty w bryd\.zu ... More

On three dimensional conformally flat almost cosymplectic manifoldsOct 04 2007In the paper there are described new examples of conformally flat three dimensional almost cosymplectic manifolds. All these manifolds form a class which was completely characterized.

Quadratic bosonic and free white noisesMar 20 2003We discuss the meaning of renormalization used for deriving quadratic bosonic commutation relations introduced by Accardi and find a representation of these relations on an interacting Fock space. Also, we investigate classical stochastic processes which ... More

A note on ANR'sJul 07 2011Sep 24 2011It is shown that if for a complete metric space $(X,d)$ there is a constant $\epsilon > 0$ such that the intersection $\bigcap_{j=1}^n B_d(x_j,r_j)$ of open balls is nonempty for every finite system $x_1,...,x_n \in X$ of centers and a corresponding system ... More

Models for subhomogeneous C*-algebrasOct 21 2013A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous C*-algebras and ... More

Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisionsNov 21 2017The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear ... More

On fast bounded locality sensitive hashingApr 19 2017In this paper, we examine the hash functions expressed as scalar products, i.e., $f(x)=<v,x>$, for some bounded random vector $v$. Such hash functions have numerous applications, but often there is a need to optimize the choice of the distribution of ... More

Moduli of $Π$-algebrasMay 16 2017We describe a homotopy-theoretic approach to the moduli of $\Pi$-algebras of Blanc-Dwyer-Goerss using the $\infty$-category $P_{\Sigma}(Sph)$ of product-preserving presheaves on finite-wedges of positive-dimensional spheres, reproving all of their results ... More

Strong isomorphism in Eisert-Wilkens-Lewenstein type quantum gamesJan 19 2017The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate ... More

The one-frequency cohomological equation, Brjuno-like functions and Khintchine-Lévy numbersMar 01 2019In the paper we consider the one-frequency cohomological equation \begin{equation*} (\partial_x + \omega \partial_y) g(x,y) = a(x,y) \end{equation*} on the 2-torus with unknown $g$ and analytic initial data $a$. We identify all the frequencies $\omega$ ... More

On integrands and loop momentum in string and field theoryJan 08 2019Jan 14 2019The notion of a unique integrand does not a priori makes sense in field theory: different Feynman diagrams have different loop momenta and there should be no reason to compare them. In string theory, however, a global integrand is natural and allows, ... More

Applications of semi-definite optimization in quantum information protocolsOct 11 2018This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information science. Our results of the analysis of certain quantum information protocols using this optimization technique are presented, ... More

Quarks, Hadrons, and Emergent SpacetimeSep 12 2018It is argued that important information on the emergence of space is hidden at the quark/hadron level. The arguments follow from the acceptance of the conception that space is an attribute of matter. They involve in particular the discussion of possibly ... More

Total integrals of solutions for the Painlevé II equation and singularity formation in the vortex patch dynamicsAug 27 2018Jan 16 2019In this paper, we establish a formula determining the value of the Cauchy integrals of the real and purely imaginary Ablowitz-Segur solutions for the inhomogeneous second Painlev\'e equation. Our approach relies on the Deift-Zhou steepest descent analysis ... More

Synthetic spectra and the cellular motivic categoryMar 05 2018To any Adams-type homology theory we associate a notion of a synthetic spectrum, this is a spherical sheaf on the site of finite spectra with projective $E$-homology. We show that the $\infty$-category $\mathcal{S}yn_{E}$ of synthetic spectra based on ... More

Transport of the light polarization in the weak gravitational wave backgroundFeb 07 2018The influence of the weak gravitational wave on the light polarization is considered. Oscillations in the direction of the polarization vector is found.

Minimal generating sets of directed oriented Reidemeister movesJan 04 2016Sep 13 2016Polyak proved that the set $\{\Omega1a,\Omega1b,\Omega2a,\Omega3a\}$ is a minimal generating set of oriented Reidemeister moves. One may distinguish between forward and backward moves, obtaining $32$ different types of moves, which we call directed oriented ... More

Local $C^r$-right equivalence of $C^{r+1}$ functionsJun 08 2015Jun 21 2015Let $f,g:(\mathbb{R}^n,0)\rightarrow (\mathbb{R},0)$ be $C^{r+1}$ functions, $r\in \mathbb{N}$. We will show that if $\nabla f(0)=0$ and there exist a neigbourhood $U$ of $0\in \mathbb{R}^n$ and a constant $C>0$ such that $$ \left|\partial^m(g-f)(x)\right|\leq ... More

Functor of continuation in Hilbert cube and Hilbert spaceJul 07 2011A $Z$-set in a metric space $X$ is a closed subset $K$ of $X$ such that each map of the Hilbert cube $Q$ into $X$ can uniformly be approximated by maps of $Q$ into $X \setminus K$. The aim of the paper is to show that there exists a functor of extension ... More

Combinatorics of asymptotic representation theoryMar 29 2012The representation theory of the symmetric groups S_n is intimately related to combinatorics: combinatorial objects such as Young tableaux and combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n tends to infinity, the structure ... More

Asymptotics of characters of symmetric groups, genus expansion and free probabilityNov 30 2004Oct 21 2005The 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

A remark on the dimension of the Bergman space of some Hartogs domainsApr 08 2009Let D be a Hartogs domain of the form D={(z,w) \in CxC^N : |w| < e^{-u(z)}} where u is a subharmonic function on C. We prove that the Bergman space of holomorphic and square integrable functions on D is either trivial or infinite dimensional.

Short and biased introduction to groupoidsNov 15 2013The algebraic part of approach to groupoids started by S. Zakrzewski is presented.

Some properties of the moment estimator of shape parameter for the gamma distributionAug 17 2011Exact distribution of the moment estimator of shape parameter for the gamma distribution for small samples is derived. Order preserving properties of this estimator are presented.

Pseudoquotient extensions of measure spacesMay 30 2018A space of pseudoquotients $\mathcal P (X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and $(x,f) \sim (y,g)$ ... More

Functional calculus for diagonalizable matricesNov 30 2012For an arbitrary function f:\Omega \rightarrow C (where \Omega is a subset of the field C) and a positive integer k let f act on all diagonalizable complex matrices whose all eigenvalues lie in Omega in the following way: f[P Diag(z1,...,zk) P-1] = P ... More

Hausdorff dimension of elliptic functions with critical values approaching infinityMay 05 2011May 06 2011We consider the escaping parameters in the family $\beta\wp_\Lambda$, i.e. these parameters for which the orbits of critical values of $\beta\wp_\Lambda$ approach infinity, where $\wp_\Lambda$ is the Weierstrass function. Unlike to the exponential map ... More

Information Based Method for Approximate Solving Stochastic Control ProblemsApr 12 2019An information based method for solving stochastic control problems with partial observation has been proposed. First, the information-theoretic lower bounds of the cost function has been analysed. It has been shown, under rather weak assumptions, that ... More

Rank of Jacobi operator and existence of quadratic parallel differential form, with applications to geometry of almost para-contact metric manifoldsJun 14 2018Oct 12 2018It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such obstacle follows ... More

On a class of immersions between almost para-Hermitian manifoldsOct 03 2017Oct 26 2017Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost para-Hermitian manifolds. ... More

Note on classical notion of Lee formOct 29 2014This note is devoted to partial study of recurrent equation $d\omega=\beta \wedge \omega$, based on linear algebra of exterior forms. Such equation was considered by Lee, for non-degenerate 2-form. In this note we approach general case, when $\omega$ ... More

Irreducible Jacobian derivations in positive characteristicJun 20 2013We prove that an irreducible polynomial derivation in positive characteristic is a Jacobian derivation if and only if there exists an n-1-element p-basis of its ring of constants. In the case of two variables we characterize these derivations in terms ... More

A characterization of p-bases of rings of constantsJun 15 2012We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a UFD of characteristic p>0. One of these conditions involves jacobians, and the second - some properties ... More

Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identitiesDec 02 2004Jun 13 2006In this series of articles we study connections between combinatorics of multidimensional generalizations of Cauchy identity and continuous objects such as multidimensional Brownian motions and Brownian bridges. In Part I of the series we present a bijective ... More

Multinomial identities arising from the free probability theoryFeb 08 2002Feb 24 2003We prove a family of new identities fulfilled by multinomial coefficients, which were conjectured by Dykema and Haagerup. Our method bases on a study of the, so-called, triangular operator T by the means of the free probability theory.

Effect of resonance on the existence of periodic solutions for strongly damped wave equationOct 25 2013Oct 30 2015We are interested in the differential equation $\ddot u(t) = -A u(t) - c A \dot u(t) + \lambda u(t) + F(t,u(t))$, where $c > 0$ is a damping factor, $A$ is a sectorial operator and $F$ is a continuous map. We consider the situation where the equation ... More

Central points and measures and dense subsets of compact metric spacesMay 28 2011For every nonempty compact convex subset $K$ of a normed linear space a (unique) point $c_K \in K$, called the generalized Chebyshev center, is distinguished. It is shown that $c_K$ is a common fixed point for the isometry group of the metric space $K$. ... More

Norm closures of orbits of bounded operatorsJul 07 2011To every bounded linear operator $A$ between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$ three cardinals $\iota_r(A)$, $\iota_i(A)$ and $\iota_f(A)$ and a binary number $\iota_b(A)$ are assigned in terms of which the descriptions of the norm closures ... More

Hirzebruch-type inequalities and plane curve configurationsOct 17 2016Jan 20 2017In this paper we come back to a problem proposed by F. Hirzebruch in the 1980's, namely whether there exists a configuration of smooth conics in the complex projective plane such that the associated desingularization of the Kummer extension is a ball ... More

The orbifold Langer-Miyaoka-Yau inequality and Hirzebruch-type inequalitiesDec 15 2016Mar 29 2017Using Langer's variation on the Bogomolov-Miyaoka-Yau inequality \cite[Theorem 0.1]{Langer} we provide some Hirzebruch-type inequalities for curve arrangements in the complex projective plane.

Blowup versus global in time existence of solutions for nonlinear heat equationsMay 10 2017May 18 2017This note is devoted to a simple proof of blowup of solutions for a nonlinear heat equation. The criterion for a blowup is expressed in terms of a Morrey space norm and is in a sense complementary to conditions guaranteeing the global in time existence ... More

Positivity of Thom polynomials and Schubert calculusApr 09 2013Oct 08 2016We describe the positivity of Thom polynomials of singularities of maps, Lagrangian Thom polynomials and Legendrian Thom polynomials. We show that these positivities come from Schubert calculus.

A note on generalization of Zermelo navigation problem on Riemannian manifolds with strong perturbationJun 03 2016We generalize the Zermelo navigation problem and its solution on Riemannian manifolds $(M, h)$ admitting a space dependence of a ship's speed $0<|u(x)|_h\leq1$ in the presence of a perturbation $\tilde{W}$ determined by a strong velocity vector field ... More

Occupation time fluctuation limits of infinite variance equilibrium branching systemsFeb 01 2008We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The branching law is ... More

Generic identities for finite group actionsApr 16 2019Apr 24 2019Let $G$ be a finite group of order $n$, and $Z_G=\mathbb{Z}\langle\zeta_{i,g}\mid g\in G,\ i=1,2,\dots,n\rangle$ be the free generic algebra, with canonical action of $G$ according to $(\zeta_{i,g})^x=\zeta_{i,x^{-1}g}$. It is proved that there exists ... More

A mathematical model of the Mafia gameSep 06 2010Mar 12 2013Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a certain set ... 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

Geometria nieortodoksyjnaJun 18 2001This is an introductory text to differential geometry (written in Polish) aimed for high-school students.

Cauchy flights in confining potentialsJul 05 2009Oct 24 2009We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process whose target ... More

Entropy and time: Thermodynamics of diffusion processesApr 24 2006Apr 29 2008We give meaning to the first and second laws of thermodynamics in case of mesoscopic out-of-equilibrium systems which are driven by diffusion processes. The notion of the entropy production is analyzed. The role of the Helmholtz extremum principle is ... More

Comment on ``Connection between the Burgers equation with an elastic forcing term and a stochastic process''May 21 2006In the above mentioned paper by E. Moreau and O. Vall\'{e}e [Phys. Rev. {\bf E 73}, 016112, (2006)], the one-dimensional Burgers equation with an elastic (attractive) forcing term has been claimed to be connected with the Ornstein-Uhlenbeck process. We ... More

Random Dynamics, Entropy Production and Fisher InformationNov 18 2002Jul 01 2003We analyze a specific role of probability density gradients in the theory of irreversible transport processes. The classic Fisher information and information entropy production concepts are found to be intrinsically entangled with the very notion of the ... More

Noise perturbations in the Brownian motion and quantum dynamicsApr 23 1999The third Newton law for mean velocity fields is utilised to generate anomalous (enhanced) or non-dispersive diffusion-type processes which, in particular, can be interpreted as a probabilistic counterpart of the Schr\"{o}dinger picture quantum dynamics. ... More

Interstellar H2 toward HD 37903Feb 26 2010Mar 14 2011We present an analysis of interstellar H2 toward HD 37903, which is a hot, B 1.5 V star located in the NGC 2023 reflection nebula. Meyer et al. (2001) have used a rich spectrum of vibrationally excited H2 observed by the HST to calculate a model of the ... More

On Value at Risk for foreign exchange rates - the copula approachAug 18 2006The aim of this paper is to determine the Value at Risk (VaR) of the portfolio consisting of long positions in foreign currencies on an emerging market. Basing on empirical data we restrict ourselves to the case when the tail parts of distributions of ... More

The Distance to the Large Magellanic CloudJan 31 2000I demonstrate that the two unexpected results in the local Universe: anomalous intrinsic (V-I)_0 colors of RR Lyrae stars and clump giants in the Galactic center, and very short distances to Magellanic Clouds inferred from clump giants, can be at least ... More

Harmonizing the RR Lyrae and Clump Distance Scales - Stretching the Short Distance Scale to Intermediate Ranges?Jan 26 2000Sep 26 2000I explore the consequences of making the RR Lyrae and clump giant distance scales consistent in the solar neighborhood, Galactic bulge and Large Magellanic Cloud (LMC). I employ two major assumptions: 1) that the absolute magnitude - metallicity, M_V(RR) ... More

Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spacesMay 28 2011An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with respect to ideals) ... More

Weak convergence of the sequences of homogeneous Young measures associated with a class of oscillating functionsJul 11 2018Feb 12 2019We consider the sequences of oscillating functions which are sums of the functions having continuously differentiable inverses. We show that if the total slopes of the elements of these sequences form monotonic sequence then the sequence of the respective ... More

On a certain family of U(b)-modulesMar 01 2016Oct 08 2016We report on results of Kra\'skiewicz and the author, and Watanabe on KP modules materializing Schubert polynomials, and filtrations having KP modules as their subquotients. We discuss applications of KP filtrations and ample KP bundles to positivity, ... More

Consistency of modified versions of Bayesian Information Criterion in sparse linear regression with subgaussian errorsNov 15 2014May 29 2018We consider a sparse linear regression model, when the number of available predictors, $p$, is much larger than the sample size, $n$, and the number of non-zero coefficients, $p_0$, is small. To choose the regression model in this situation, we cannot ... More

Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the targetFeb 01 2006We study a question of density of Lipschitz mappings in the Sobolev class of mappings from a closed manifold into a singular space. The main result of the paper shows that if we change the metric in the target space to a bi-Lipschitz equivalent one, than ... More