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In-plane field-induced vortex liquid correlations in underdoped Bi_2Sr_2CaCu_2O_8+δJul 24 2006Jun 25 2007The effect of a magnetic field component parallel to the superconducting layers on longitudinal Josephson plasma oscillations in the layered high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ is shown to depend on the thermodynamic state ... More

Vortex liquid correlations induced by in-plane field in underdoped Bi2Sr2CaCu2O8+dJul 27 2006By measuring the Josephson Plasma Resonance, we have probed the influence of an in-plane magnetic field on the pancake vortex correlations along the c-axis in heavily underdoped Bi2Sr2CaCu2O8+d (Tc = 72.4 +/- 0.6 K) single crystals both in the vortex ... More

Submillimeter - sized proximity effect in graphite and bismuthFeb 08 2019In this work, we probe the electrical properties of macroscopic graphite and bismuth in which the electrical current is injected via superconducting electrodes, few millimeters apart from each other. Results reveal the induction of a partial superconducting-like ... More

Nature of c-axis coupling in underdoped Bi2Sr2CaCu2O8 with varying degrees of disorderJan 07 2008The dependence of the Josephson Plasma Resonance (JPR) frequency in heavily underdoped Bi2Sr2CaCu2O8+\delta on temperature and controlled pointlike disorder, introduced by high-energy electron irradiation, is cross-correlated and compared to the behavior ... More

Electron irradiation of Co, Ni, and P-doped BaFe2As2 - type iron-based superconductorsSep 17 2012Nov 14 2012High energy electron irradiation is used to controllably introduce atomic-scale point defects into single crystalline Ba(Fe_1-xCo_x)_2As_2, Ba(Fe_1-xNi_x)_2As_2, and BaFe_2(As_1-xP_x)_2. The appearance of the collective pinning contribution to the critical ... 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

Approximating the MaxCover Problem with Bounded Frequencies in FPT TimeSep 17 2013We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The goal is to find ... More

Approximate nearest neighbors search without false negatives for $l_2$ for $c>\sqrt{\log\log{n}}$Aug 21 2017Sep 13 2017In this paper, we report progress on answering the open problem presented by Pagh~[14], who considered the nearest neighbor search without false negatives for the Hamming distance. We show new data structures for solving the $c$-approximate nearest neighbors ... 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

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

Gravity as field - field oriented framework reproducing General RelativityApr 13 2014Sep 21 2015In the last article we have created foundations for gravitational field oriented framework (DaF) that reproduces GR. In this article we show, that using DaF approach, we can reproduce Schwarzschild solution with orbit equations, effective potential and ... More

A note on symmetries in the path integral formulation of the Langevin dynamicsMar 23 2017Dec 30 2018We study a dissipative Langevin dynamics in the path integral formulation using the Martin-Siggia-Rose formalism. The effective action is supersymmetric and we identify the supercharges. In addition we study the transformations generated by superderivatives, ... 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

Levy flights, dynamical duality and fractional quantum mechanicsNov 24 2008Mar 21 2009We discuss dual time evolution scenarios which, albeit running according to the same real time clock, in each considered case may be mapped among each other by means of an analytic continuation in time. This dynamical duality is a generic feature of diffusion-type ... More

Modular Schrödinger equation and dynamical dualityMay 11 2008Aug 08 2008We discuss quite surprising properties of the one-parameter family of modular (Auberson and Sabatier (1994)) nonlinear Schr\"{o}dinger equations. We develop a unified theoretical framework for this family. Special attention is paid to the emergent \it ... More

Comment on "Time-dependent entropy of simple quantum model systems"Sep 30 2005In the above mentioned paper by J. Dunkel and S. A. Trigger [Phys. Rev. {\bf A 71}, 052102, (2005)] a hypothesis has been pursued that the loss of information associated with the quantum evolution of pure states, quantified in terms of an increase in ... 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

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

Some topological invariants and biorthogonal systems in Banach spacesSep 19 2012We consider topological invariants on compact spaces related to the sizes of discrete subspaces (spread), densities of subspaces, Lindelof degree of subspaces, irredundant families of clopen sets and others and look at the following associations 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

Femtoscopy analysis of d-Au interactions at $\sqrt{s}=200$GeVAug 06 2014The femtoscopy correlation radii for d-Au collisions at $200$GeV are calculated in the hydrodynamic model and compared to PHENIX collaboration data. For asymmetric systems, such as d-Au or p-Pb collisions, the correlation radius $R_{out-long}$ is estimated ... More

Wilson lines and gauge invariant off-shell amplitudesMar 19 2014Apr 24 2014We study matrix elements of Fourier-transformed straight infinite Wilson lines as a way to calculate gauge invariant tree-level amplitudes with off-shell gluons. The off-shell gluons are assigned "polarization vectors" which (in the Feynman gauge) are ... More

Arcs intersecting at most onceFeb 07 2014Aug 26 2014We prove that on a punctured oriented surface with Euler characteristic chi < 0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersecting at most once is 2|chi|(|chi|+1). This gives a cubic estimate in ... More

On one-loop corrections to matching conditions of Lattice HQET including 1/m_b termsDec 09 2013HQET is an effective theory for QCD with N_f light quarks and a massive valence quark if the mass of the latter is much bigger than Lambda_QCD. As any effective theory, HQET is predictive only when a set of parameters has been determined through a process ... More

Top degree of Jack characters and enumeration of mapsJun 21 2015Mar 16 2016Jack characters are (suitably normalized) coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. These quantities have been introduced recently by Lassalle who formulated some challenging conjectures about ... More

Wild binary segmentation for multiple change-point detectionNov 04 2014We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to ... More

Combining Fuzzy Cognitive Maps and Discrete Random VariablesDec 29 2015In this paper we propose an extension to the Fuzzy Cognitive Maps (FCMs) that aims at aggregating a number of reasoning tasks into a one parallel run. The described approach consists in replacing real-valued activation levels of concepts (and further ... More

Connecting orbits for nonlinear differential equations at resonanceMay 01 2015Nov 02 2015We study the existence of orbits connecting stationary points for the first order differential equations being at resonance at infinity, where the right hand side is the perturbations of a sectorial operator. Our aim is to prove an index formula expressing ... More

The CLS 2+1 flavor simulationsDec 31 2014We report on the status of large volume simulations with 2+1 dynamical fermions which are being performed by the CLS initiative. The algorithmic details include: open boundary conditions, twisted mass reweighting and RHMC, whereas the main feature of ... More

Weak consistency of modified versions of Bayesian Information Criterion in a sparse linear regression with non-normal error termNov 15 2014We consider a sparse linear regression model, when the number of available predictors $p$ is much bigger 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 use classical ... 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 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

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

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

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

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.

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.

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.

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

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

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

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

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

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.

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

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

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

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.

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

The Hopf type theorem for equivariant gradient local mapsOct 01 2015Feb 23 2016We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant ... 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

Key User Extraction Based on Telecommunication Data (aka. Key Users in Social Network. How to find them?)Feb 06 2013Feb 11 2013The number of systems that collect vast amount of data about users rapidly grow during last few years. Many of these systems contain data not only about people characteristics but also about their relationships with other system users. From this kind ... More

Transverse momentum-flow correlations in relativistic heavy-ion collisionsJan 18 2016Mar 17 2016The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow ... More

On the problem of compact totally disconnected reflection of nonmetrizabilitySep 17 2015We construct a ZFC example of a nonmetrizable compact space $K$ such that every totally disconnected closed subspace $L\subseteq K$ is metrizable. In fact, the construction can be arranged so that every nonmetrizable compact subspace may be of fixed big ... More

Symmetries and self-similarity of many-body wavefunctionsDec 21 2014This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states, visualization schemes ... More

Hirzebruch-type inequalities and plane curve configurationsOct 17 2016Nov 07 2016In 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 on the complex projective plane such that the associated desingularization of the Kummer extension is a ball ... More

Uncountable equilateral sets in Banach spaces of the form $C(K)$Mar 21 2015Apr 20 2015The paper is concerned with the problem whether a nonseparable Banach space must contain an uncountable set of vectors such that the distances between every two distinct vectors of the set are the same. Such sets are called equilateral. We show that Martin's ... More

Quantum coherence and correlations in cold atom systemsFeb 04 2015Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical" and "quantum" ... More