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Heat kernel and Green function estimates on affine buildingsOct 08 2013We obtain the optimal global upper and lower bounds for the transition density $p_n(x,y)$ of a finite range isotropic random walk on affine buildings. We present also sharp estimates for the corresponding Green function.

Pointwise ergodic theorems for some thin subsets of primesMar 15 2018Feb 14 2019We establish pointwise ergodic theorems for operators of Radon type along subsets of prime numbers of the form $\big\{\{ \varphi_1(n)\} < \psi(n)\big\}$. We achieve this by proving $\ell^p(\mathbb{Z})$ boundedness of $r$-variations, where $p > 1$ and ... More

Variational estimates for discrete operators modeled on multi-dimensional polynomial subsets of primesMar 14 2018Nov 06 2018We prove the extensions of Birkhoff's and Cotlar's ergodic theorems to multi-dimensional polynomial subsets of prime numbers $\mathbb{P}^k$. We deduce them from $\ell^p$-boundedness of $r$-variational seminorms for the corresponding discrete operators ... More

Endpoint estimates for the maximal function over prime numbersJul 10 2019Given an ergodic dynamical system $(X, \mathcal{B}, \mu, T)$, we prove that for each function $f$ belonging to the Orlicz space $L(\log L)^2(\log \log L)(X, \mu)$, the ergodic averages \[ \frac{1}{\pi(N)} \sum_{p \in \mathbb{P}_N} f\big(T^p x\big), \] ... More

Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectorsFeb 19 2016Aug 30 2016We study asymptotics of generalized eigenvectors associated with Jacobi matrices. Under weak conditions on the coefficients we identify when the matrices are self-adjoint and show that they satisfy strong non-subordinacy condition.

Limit theorems for random walksApr 07 2015Dec 31 2015We consider a random walk $S_{\tau}$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner's subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau}$ ... More

Heat kernel and Green function estimates on affine buildings of type $\tilde{A}_r$Dec 14 2006We obtain a global estimate of the transition density $p^n(0,x)$ associated to a nearest neighbor random walk, called here "simple", on affine buildings of type $\widetilde{A}_r$. Then we deduce a global estimate of the Green function. This is the analogue ... More

L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimatesDec 23 2015We prove $\ell^p\big(\mathbb Z^d\big)$ bounds for $p\in(1, \infty)$, of $r$-variations $r\in(2, \infty)$, for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with ... More

Long time behaviour of random walks on the integer latticeDec 30 2015We consider an irreducible finite range random walk on the $d$-dimensional integer lattice and study asymptotic behaviour of its transition function $p(n; x)$. In particular, for simple random walk our asymptotic formula is valid as long as $n (n - |x|_1)^{-2}$ ... More

Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficientsFeb 06 2019We study solutions of three-term recurrence relations whose $N$-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more. Namely, we find ... More

Cotlar's ergodic theorem along the prime numbersNov 29 2013The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.

Littlewood-Paley theory for triangle buildingsMar 01 2017For the natural two parameter filtration $(\mathcal{F}_\lambda : \lambda \in P)$ on the boundary of a triangle building we define a maximal function and a square function and show their boundedness on $L^p(\Omega_0)$ for $p \in (1, \infty)$. At the end ... More

Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectorsFeb 19 2016Nov 07 2016We study asymptotics of generalized eigenvectors associated with Jacobi matrices. Under weak conditions on the coefficients we identify when the matrices are self-adjoint and show that they satisfy strong non-subordinacy condition.

Discrete maximal functions in higher dimensions and applications to ergodic theoryMay 21 2014We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1<p<\infty$ and $r>\max\{p, p/(p-1)\}$. ... More

Kink in superconducting cosmic string: exact solutionAug 05 2014Dec 24 2014We solve the equations of motion and find the Lorentz transformation associated with a kink in superconducting cosmic string. The kink velocity does not depend on its amplitude. The kink amplitude cannot be arbitrary but it varies within definite range ... More

Tachyonic Dirac seaJan 27 2012Apr 03 2012We consider a system of many fermions with tachyonic energy spectrum \varepsilon_k=\sqrt{k^2-m^2} and clarify that tachyons with imaginary energy and low momentum (k<m) play the role of Dirac sea in a many-tachyon Fermi system and make contribution to ... More

Superluminal self-interacting neutrinoJan 09 2012The effect of nonlinear self-interaction can be associated with superluminal velocity of neutrino. The power energy spectrum E=p+Cp^a is derived from the nonlinear Dirac equation when interaction term V=\lambda (\psi \gamma_\mu \psi \psi \gamma^\mu \psi)^a ... More

Careful calculation of thermodynamical functions of tachyon gasSep 05 2011Oct 03 2011We analyze several approaches to the thermodynamics of tachyon matter. The energy spectrum of tachyons $\epsilon_k=\sqrt{k^2-m^2}$ is defined at $k\geq m$ and it is not evident how to determine the tachyonic distribution function and calculate its thermodynamical ... More

Dirac tachyons and antitachyons in many-particle systemApr 05 2012A consistent description of charged many-tachyon Fermi system is developed. Tachyons and antitachyons have the same chemical potential \mu+=\mu- because the axial coupling constant g+=g- is invariant under the charge conjugation, in contrast to reversion ... More

Interacting tachyon Fermi gasMar 21 2012Mar 31 2012We consider a system of many fermionic tachyons coupled to a scalar, pseudoscalar, vector and pseudovector fields. The scalar and pseudoscalar fields are responsible for the effective mass, while the pseudovector field is similar to ordinary electromagnetic ... More

Stability of hot tachyon gasAug 24 2011We consider a tachyon gas that obeys Maxwell-Boltzmann statistics. The sound speed is always subluminal and it tends to the limiting minimum value $c_s=1/\sqrt{2}$ in non-relativistic gas (at low temperature), decreasing monotonously with the growth of ... More

Specific heat and entropy of tachyon Fermi gasAug 15 2011We consider an ideal Fermi gas of tachyons and derive a low temperature expansion of its thermodynamical functions. The tachyonic specific heat is linear dependent on temperature $C_V=\epsilon_Fk_FT$ and formally coincides with the specific heat of electron ... More

Tachyon starsOct 11 2011Nov 24 2011We consider a self-gravitating body composed of ideal Fermi gas of tachyons at zero temperature. The Oppenheimer-Volkoff equation is solved for various central densities and various tachyon mass parameter $m$. Although a pure tachyon star has finite mass, ... More

Superluminal neutrino energy spectrum of OPERA and MINOSDec 09 2011Dec 13 2011We analyze the velocity dependence on energy of superluminal neutrino recorded by the OPERA and MINOS collaborations and manage to approximate the energy spectrum by a power law E=p+Cp^a where parameters must be taken in the range a=0.40--1.18 and C=1.5x10^{-5}--4.15x10^{-4} ... More

Asymptotic behaviour and estimates of slowly varying convolution semigroupsJun 13 2016We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on $\mathbb{R} ^d$ under the assumption that its L\'{e}vy--Khintchine exponent varies slowly. We also derive some new estimates ... More

On the Hardy--Littlewood majorant problem for arithmetic setsMay 03 2015The aim of this paper is to exhibit a wide class of sparse deterministic sets, $\mathbf B \subseteq \mathbb{N}$, so that \[ \limsup_{N \to \infty} N^{-1}|\mathbf B \cap [1,N]|= 0, \] for which the Hardy--Littlewood majorant property holds: \[ \sup_{|a_n|\le ... More

Two-parameter version of Bourgain's inequality: Rational frequenciesApr 16 2015Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality on $L^2(\mathbb R^2)$ for the rational frequencies. We achieve this by introducing a variant of a two-parameter Rademacher--Menschov inequality. The method ... More

Asymptotic behavior of densities of unimodal convolution semigroupsApr 30 2015Oct 30 2015We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on $\mathbb{R}^d$ under the assumption that its L\'{e}vy--Khintchine exponent is regularly varying of index between $0$ ... More

Transition densities of subordinatorsDec 17 2018We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Furthermore, we present lower and upper bounds for the density. Sharp estimates ... More

$\ell^p\big(\mathbb Z^d\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimatesDec 23 2015Oct 29 2018We prove $\ell^p\big(\mathbb Z^d\big)$ bounds, for $p\in(1, \infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type, and their applications to pointwise ergodic theory. Our new approach ... More

Limit theorems for random walksApr 07 2015Feb 20 2017We consider a random walk $S_{\tau}$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner's subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau}$ ... More

Analytic theory of discontinuities in current-carrying cosmic stringsDec 02 2013Aug 04 2014We formulate an analytic method to study the discontinuities in superconducting cosmic strings. Equations of discontinuities and conditions of their existence are derived from the intrinsic and extrinsic equations of motion. It is the fundamental for ... More

L^p(Z^d)-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimatesDec 23 2015We show $\ell^p\big(\mathbb Z^d\big)$ boundedness, for $p\in(1, \infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type. We shall present a new approach which allows us to handle these ... More

The Maximal Function and Square Function Control the Variation: An Elementary ProofAug 06 2014Sep 21 2015In this note we prove the following good-$\lambda$ inequality, for $r>2$, all $\lambda > 0$, $\delta \in \big(0, \frac{1}{2} \big)$ \[ \nu\big\{ V_r(f) > 3 \lambda ; \mathcal{M}(f) \leq \delta \lambda\big\} \leq 4 \nu\{s(f) > \delta \lambda\} + {\delta^2 ... More

Variational estimates for averages and truncated singular integrals along the prime numbersOct 13 2014We prove, in a unified way, $r$-variational estimates, $r>2$, on $\ell^{s}(\mathbb{Z})$ spaces, $s \in (1, \infty)$, for averages and truncated singular integrals along the set of prime numbers.

Effects of relaxation processes during deposition of anisotropic grains on a flat substrateNov 29 2004The ballistic deposition on a one dimensional substrate of grains with one degree of freedom, called spin, is studied with respect to relaxation processes during deposition. The "spin" represents the grain anisotropy, e.g. its longest axis with respect ... More

Clusters in a magnetic toy model for binary granular pilesMar 05 2004Results on a generalized magnetically controlled ballistic deposition (MBD) model of granular piles are reported in order to search for the effect of "spin flip" probability q in building a granular pile. Two different regimes of spin cluster site distributions ... More

Magnetically controlled ballistic deposition. A model of polydisperse granular packingMar 25 2003The flow and deposition of polydisperse granular materials is simulated through the Magnetic Diffusion Limited Aggregation (MDLA) model. The random walk undergone by an entity in the MDLA model is modified such that the trajectories are ballistic in nature, ... More

Interaction and heat exchange in two-component relativistic fluidAug 03 2011Aug 12 2011A model of two-component relativistic fluid is considered, and the thermal nature of coupling between the fluid constituents is outlined. This thermal coupling is responsible for non-ideality of the fluid composite where the components are not fully independent. ... More

Thermodynamics of exotic matter with constant w=P/EAug 03 2011Aug 04 2011We consider a substance with equation of state $P=wE$ at constant $w$ and find that it is an ideal gas of quasi-particles with the energy spectrum $\epsilon_p\sim p^{wq}$ that can constitute either regular matter (when $w>0$) or exotic matter (when $w<0$) ... More

Shock waves in superconducting cosmic strings: growth of currentFeb 28 2011May 22 2012Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term \chi. The hypersurface of discontinuity propagates at finite velocity determined by finite increment ... More

Thermodynamics of absolute stiff matterJul 09 2011Oct 04 2011The 'absolute stiff' matter ($P=E$) can be a Fermi or Bose gas of particles with the energy spectrum $\epsilon_p \sim p^q$ in $q$-dimensional space, particularly $\epsilon_p =p^3/m^2$ in 3-dimensional space. We obtain its pressure, particle number density ... More

Reply to Comment on "Acoustics of tachyon Fermi gas"Dec 05 2013In a paper appearing in this issue of Physical Review D, Burmistrov raises some critical comments on the thermodynamics of a cold tachyon Fermi gas [E. Trojan and G. V. Vlasov, Phys. Rev. D 83, 124013 (2011)]. However, apart from any possible theoretical ... More

Acoustics of tachyon Fermi gasMar 11 2011Jun 03 2011We consider a Fermi gas of free tachyons as a continuous medium and find whether it satisfies the causality condition. There is no stable tachyon matter with the particle density below critical value $n_T$ and the Fermi momentum $k_F<\sqrt{\frac 32}m$ ... More

Shock waves in superconducting cosmic strings: instability to extrinsic perturbationsMar 03 2011May 22 2012Superconducting cosmic string may admit shock-like discontinuities of the current when the latter is spacelike ("magnetic" regime), while no shock at timelike current ("electric" regime) was discovered in numerical simulations. We find that the necessary ... More

Tachyonic thermal excitations and causalityJun 29 2011Oct 08 2011We consider an ideal Fermi gas of tachyonic thermal excitations as a continuous medium and establish when it satisfies the causality condition. At high temperature the sound speed is always subluminal $c_s<1$, but there is no stable form of tachyon matter ... More

The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearitiesFeb 01 2018We look for solutions to a fractional Schr\"odinger equation of the following form $$ (-\Delta)^{\alpha / 2} u + \left( V(x) - \frac{\mu}{|x|^{\alpha}} \right) u = f(x,u)-K(x)|u|^{q-2}u\hbox{ on }\mathbb{R}^N \setminus \{0\}, $$ where $V$ is bounded and ... More

The Matsumoto--Yor Property and Its Converse on Symmetric ConesSep 18 2014Oct 01 2015The Matsumoto--Yor (MY) property of the generalized inverse Gaussian and gamma distributions has many generalizations. As it was observed in (Letac and Weso{\l}owski in Ann Probab 28:1371--1383, 2000) the natural framework for the multivariate MY property ... More

A deterministic version of Pollard's p-1 algorithmJul 27 2007May 12 2009In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard's $p-1$ algorithm, which finds in random polynomial time the prime divisors $p$ of an ... More

On higher congruences between cusp forms and Eisenstein seriesJun 08 2012Jun 29 2013In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properties of the prime ideals and their relation to the weights. ... More

Logarithmic tails of sums of products of positive random variables bounded by oneOct 05 2015May 26 2017In this paper we show under weak assumptions that for $R\stackrel{d}{=}1+M_1+M_1M_2+\ldots$, where $P(M\in[0,1])=1$ and $M_i$ are independent copies of $M$, we have $\ln P(R>x)\sim C\, x\ln P(M>1-\frac1x)$ as $x\to\infty$. The constant $C$ is given explicitly ... More

Constraints on radio source clustering towards galaxy clusters: application for cm-wavelength simulations of blind sky surveysApr 16 2015We constrain radio source clustering towards $Planck$-selected galaxy clusters using the NVSS point source catalogue. The constraint can be utilised for generating realistic Sunyaev-Zeldovich effect (SZE) mocks, and for predicting detectable clusters ... More

Hemispherical power asymmetry: parameter estimation from CMB WMAP5 dataAug 21 2008Nov 10 2008We reexamine the evidence of the hemispherical power asymmetry, detected in the CMB WMAP data using a new method. At first, we analyze the hemispherical variance ratios and compare these with simulated distributions. Secondly, working within a previously-proposed ... More

Using the smoothness of p-1 for computing roots modulo pMar 04 2008We prove, without recourse to the Extended Riemann Hypothesis, that the projection modulo $p$ of any prefixed polynomial with integer coefficients can be completely factored in deterministic polynomial time if $p-1$ has a $(\ln p)^{O(1)}$-smooth divisor ... More

Potential and Sobolev Spaces Related to Symmetrized Jacobi ExpansionsMay 07 2015May 02 2016We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among further results, ... More

On potential spaces related to Jacobi expansionsOct 24 2014We investigate potential spaces associated with Jacobi expansions. We prove structural and Sobolev-type embedding theorems for these spaces. We also establish their characterizations in terms of suitably defined fractional square functions. Finally, we ... More

On a certain hypergeometric motive of weight 2 and rank 3Feb 24 2017May 17 2017We study a family of hypergeometric motives $H(\alpha,\beta|t)$ attached to a pair of tuples $\alpha=(1/4,1/2,3/4)$, $\beta=(0,0,0)$. To each such motive we can attach a system of $\ell$--adic realisations with the trace of geometric Frobenius given by ... More

Locally coalgebra-Galois extensionsDec 07 2005The paper introduces the notion of a locally coalgebra-Galois extension and, as its special case, a locally cleft extension. The necessary and sufficient conditions for a locally coalgebra-Galois extension to be a (global) coalgebra-Galois extension are ... More

The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearitiesFeb 01 2018Jun 13 2018We look for solutions to a fractional Schr\"odinger equation of the following form $$ (-\Delta)^{\alpha / 2} u + \left( V(x) - \frac{\mu}{|x|^{\alpha}} \right) u = f(x,u)-K(x)|u|^{q-2}u\hbox{ on }\mathbb{R}^N \setminus \{0\}, $$ where $V$ is bounded and ... More

Solutions of fractional Schrödinger equation with sign-changing nonlinearitySep 29 2016We look for a solutions to a nonlinear, fractional Schr\"odinger equation $$(-\Delta)^{\alpha / 2}u + V(x)u = f(x,u)-\Gamma(x)|u|^{q-2}u\hbox{ on }\mathbb{R}^N,$$ where potential $V$ is coercive or $V=V_{per} + V_{loc}$ is a sum of periodic in $x$ potential ... More

The Lukacs-Olkin-Rubin theorem on symmetric cones without invariance of the "quotient"Mar 02 2014Dec 02 2014We prove the Lukacs-Olkin-Rubin theorem without invariance of the distribution of the "quotient", which was the key assumption in the original proof of [Olkin--Rubin, Ann. Math. Stat. 33 (1962), 1272--1280]. Instead we assume existence of strictly positive ... More

On perpetuities with light tailsNov 24 2017Dec 10 2018In the paper we consider the asymptotics of logarithmic tails of a perpetuity $$R \stackrel{d}{=}\sum_{j=1}^\infty Q_j \prod_{k=1}^{j-1}M_k,\qquad(M_n,Q_n)_{n=1}^\infty \mbox{ are i.i.d. copies of }(M,Q),$$ in the case when $\mathbb{P}(M\in[0,1))=1$ and ... More

Harmonic analysis operators related to symmetrized Jacobi expansions for all admissible parametersDec 30 2015This is an ultimate completion of our earlier paper [Acta.\ Math.\ Hungar.\ 140 (2013), 248--292] where mapping properties of several fundamental harmonic analysis operators in the setting of symmetrized Jacobi trigonometric expansions were investigated ... More

Exploding Markov operatorsJan 04 2019A special class of doubly stochastic (Markov) operators is constructed. These operators come from measure preserving transformations and inherit some of their properties, namely ergodicity and positivity of entropy, yet they may have no pointwise factors. ... More

Cotensor products of quantum principal bundlesJan 11 2005Mar 11 2005A cotensor product A\Box_H P of an H-Hopf Galois extension A and a C-coalgebra Galois extension P, such that P is an (H,C)-bicomodule, is analyzed. Conditions are stated, when A\Box_H P is a C-coalgebra Galois extension and when there exists a strong ... More

Distribution of Mordell--Weil ranks of families of elliptic curvesSep 15 2016We discuss the distribution of Mordell--Weil ranks of the family of elliptic curves $y^2=(x+\alpha f^2)(x+\beta b g^2)(x+\gamma h^2)$ where $f,g,h$ are coprime polynomials that parametrize the projective smooth conic $a^2+b^2=c^2$ and $\alpha,\beta,\gamma$ ... More

Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic formsSep 15 2016We prove results on the Mordell--Weil rank of elliptic curves $y^2=x(x-\alpha a^2)(x-\beta b^2)$ parametrized by binary quadratic forms $\alpha a^2+\beta b^2=\gamma c^2$. We express our explicit lower bounds over number fields and offer a detailed description ... More

Asymmetric truncated Toeplitz operators on finite-dimensional spaces IINov 04 2016In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be characterized using ... More

Bose-Einstein correlations and b-bbar correlations in pp collisions with LHCbSep 26 2018Bose-Einstein correlations for same-sign charged pions and kinematic b-bbar correlations in proton-proton collisions at a center-of-mass energy of 7 and 8 TeV are studied by the LHCb experiment. The dependence of Bose-Einstein correlation parameters on ... More

MSSM with gauged baryon and lepton numbersMar 31 2015Jul 07 2015A simple extension of the minimal supersymmetric standard model in which baryon and lepton numbers are local gauge symmetries spontaneously broken at the supersymmetry scale is reported. This theory provides a natural explanation for proton stability. ... More

The generalized fundamental equation of information on symmetric conesJan 12 2015In this paper we generalize the fundamental equation of information to the symmetric cone domain and find general solution under the assumption of continuity of respective functions.

Generating functions partitioning algorithm for computing power indices in weighted voting gamesNov 30 2010Jan 22 2011In this paper new algorithm for calculating power indices is described. The complexity class of the problem is #P-complete and even calculating power index of the biggest player is NP-hard task. Constructed algorithm is a mix of ideas of two algorithms: ... More

Nearly invariant subspaces of de Branges spacesFeb 27 2019We prove that the nearly invariant subspaces of a de Branges space which have no common zeros are precisely of the form an exponential function times a de Branges space.

Recent results and future of the NA61/SHINE strong interactions programNov 07 2017Apr 13 2018NA61/SHINE is a fixed target experiment at the CERN Super-Proton- Synchrotron. The main goals of the experiment are to discover the critical point of strongly interacting matter and study the properties of the onset of deconfnement. In order to reach ... More

Two-particle correlations in azimuthal angle and pseudorapidity in Be+BeJan 03 2018The NA61/SHINE experiment aims to discover the critical point of strongly interacting matter and study the properties of the onset of deconfinement. These goals are to be achieved by performing a two dimensional phase diagram $(T-\mu_B)$ scan by measurements ... More

Convex geometry of quantum resource quantificationJul 19 2017Apr 24 2019We introduce a framework unifying the mathematical characterisation of different measures of general quantum resources and allowing for a systematic way to define a variety of faithful quantifiers for any given convex quantum resource theory. The approach ... More

Dark Matter and Baryogenesis from Non-Abelian Gauged Lepton NumberMay 20 2017A simple model is constructed based on the gauge symmetry $SU(3)_c \times SU(2)_L \times U(1)_Y \times SU(2)_\ell$, with only the leptons transforming nontrivially under $SU(2)_\ell$. The extended symmetry is broken down to the Standard Model gauge group ... More

The left tail of renewal measureJan 10 2017Jul 31 2017In the paper, we find exact asymptotics of the left tail of renewal measure for a broad class of two-sided random walks. We only require that an exponential moment of the left tail is finite. Through a simple change of measure approach, our result turns ... More

Multiplicative Cauchy functional equation on symmetric conesJul 15 2013Nov 25 2014We solve the multiplicative Cauchy functional equation on symmetric cones with respect to two different multiplication algorithms. We impose no regularity assumptions on respective functions.

The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theoremJun 26 2012Sep 24 2013We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Weso{\l}owski, Studia Math. 152 (2002), 147-160]. ... More

Asymmetric truncated Toeplitz operators on finite-dimensional spaces IINov 04 2016Dec 09 2016In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be characterized using ... More

Triangle-free geometric intersection graphs with no large independent setsApr 01 2014Dec 26 2014It is proved that there are triangle-free intersection graphs of line segments in the plane with arbitrarily small ratio between the maximum size of an independent set and the total number of vertices.

Sobolev spaces associated with Jacobi expansionsDec 27 2013We define and study Sobolev spaces associated with Jacobi expansions. We prove that these Sobolev spaces are isomorphic to Jacobi potential spaces. As a technical tool, we also show some approximation properties of Poisson-Jacobi integrals.

Divisibility sequences of polynomials and heights estimatesSep 15 2016In this note we compute a constant $N$ that bounds the number of non--primitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a result of Ingram--Mah{\'e}--Silverman--Stange--Streng, 2012, and we show ... More

The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equationsFeb 20 2017In this paper we focus on finding all the factorials expressible as a product of a fixed number of $2k$-nacci numbers with $k \geq 2$. We derive the 2-adic valuation of the $2k$-nacci sequence and use it to establish bounds on the solutions of the initial ... More

Infinite family of elliptic curves of rank at least 4Sep 18 2009Nov 14 2009We investigate $\mathbb{Q}$-ranks of the elliptic curve $E_t$: $y^2+txy=x^3+tx^2-x+1$ where $t$ is a rational parameter. We prove that for infinitely many values of $t$ the rank of $E_t(\mathbb{Q})$ is at least 4.

Minors and dimensionJul 15 2014Apr 05 2016It has been known for 30 years that posets with bounded height and with cover graphs of bounded maximum degree have bounded dimension. Recently, Streib and Trotter proved that dimension is bounded for posets with bounded height and planar cover graphs, ... More

Logarithmic tails of sums of products of positive random variables bounded by oneOct 05 2015In this paper we show under weak assumptions that for $R\stackrel{d}{=}1+M_1+M_1M_2+\ldots$, where $P(M\in[0,1])=1$ and $M_i$ are independent copies of $M$, we have $\ln P(R>x)\sim C\, x\ln P(M>1-\frac1x)$ as $x\to\infty$. The constant $C$ is given explicitly ... More

Convex geometry of quantum resource quantificationJul 19 2017Dec 20 2017We introduce a framework unifying the mathematical characterisation of different measures of general quantum resources and allowing for a systematic way to define a variety of faithful quantifiers for any given convex quantum resource theory. The approach ... More

Is There a Sign of New Physics in Beryllium Transitions?Jul 31 2017We discuss the current status of the anomaly in beryllium-8 nuclear transitions recently reported in the angular distribution of internal conversion electron-positron pairs. We present a phenomenological analysis of the signal and review the models proposed ... More

Piecewise Principal Coactions of Co-Commutative Hopf AlgebrasMar 30 2014Aug 19 2014Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a ... More

On higher congruences between cusp forms and Eisenstein series. IIOct 04 2018We study congruences between cuspidal modular forms and Eisenstein series at levels which are square-free integers and for equal even weights. This generalizes our previous results from Naskr\k{e}cki [17] for prime levels and provides further evidence ... More

Schrödinger-type equations with sign-changing nonlinearities: a surveyOct 01 2018We are looking for solutions to nonlinear Schr\"odinger-type equations of the form $$ (-\Delta)^{\alpha / 2} u (x) + V(x) u(x) = h (x,u(x)), \quad x \in \mathbb{R}^N, $$ where $V : \mathbb{R}^N \rightarrow \mathbb{R}$ is an external potential (bounded, ... More

A mechanism of synaptic clock underlying subjective time perceptionOct 08 2018Temporal resolution of visual information processing is thought to be an important factor in predator-prey interactions, shaped in the course of evolution by animals' ecology. Here I show that light can be considered to have a dual role of a source of ... More

A Matsumoto-Yor characterization for Kummer and Wishart random matricesSep 29 2017Feb 15 2018In the paper we resolve positively the conjecture on a characterization of matrix Kummer and Wishart laws through independence property, which was posed in [Koudou, Statist. Probab. Lett. 82 (2012), 1903--1907] . Apart from the probabilistic result, we ... More

Improving pointing of Toruń 32-m radio telescope: effects of rail surface irregularitiesJul 27 2017Jan 31 2018Over the last few years a number of software and hardware improvements have been implemented to the 32-m Cassegrain radio telescope located near Toru\'n. The 19-bit angle encoders have been upgraded to 29-bit in azimuth and elevation axes. The control ... More

Real space tests of the statistical isotropy and Gaussianity of the WMAP CMB dataMar 10 2008Aug 10 2008ABRIDGED: We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the WMAP CMB foreground reduced, temperature maps, and cross-channel difference maps. We divide the sky into regions of varying size and shape ... More

Harmonic analysis operators related to symmetrized Jacobi expansionsOct 04 2012Following a symmetrization procedure proposed recently by Nowak and Stempak, we consider the setting of symmetrized Jacobi expansions. In this framework we investigate mapping properties of several fundamental harmonic analysis operators, including Riesz ... More

Minors and dimensionJul 15 2014Dec 09 2018It has been known for 30 years that posets with bounded height and with cover graphs of bounded maximum degree have bounded dimension. Recently, Streib and Trotter proved that dimension is bounded for posets with bounded height and planar cover graphs, ... More

Exponential and power law distribution of mass clusters in a (magnetic-like) deposition model of elongated grains in 2D pilesApr 06 2004A generalized so called magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, ... More