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Bohmian Mechanics, Collapse Models and the emergence of ClassicalityMar 08 2016We discuss the emergence of classical trajectories in Bohmian Mechanics (BM), when a macroscopic object interacts with an external environment. We show that in such a case the conditional wave function of the system follows a dynamics which, under reasonable ... More

Colored and Dissipative Continuous Spontaneous Localization model and Bounds from Matter-Wave InterferometryJan 14 2016Oct 23 2017Matter-wave interferometry is a direct test of the quantum superposition principle for massive systems, and of collapse models. Here we show that the bounds placed by matter-wave interferometry depend weakly on the details of the collapse mechanism. Specifically, ... More

Real-Time Kalman Filter: Cooling of an Optically Levitated NanoparticleDec 21 2017Apr 13 2018We demonstrate that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a Field Programmable Gate Array (FPGA), is sufficient to perform closed-loop parametric feedback cooling of the ... More

Gravity induced wave function collapseJan 09 2017Nov 15 2017Starting from an idea of S.L. Adler~\cite{Adler2015}, we develop a novel model of gravity-induced spontaneous wave-function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, ... More

Bounds on Collapse Models from Matter-Wave Interferometry: Calculational detailsJan 12 2016We present a simple derivation of the interference pattern in matter-wave interferometry as predicted by a class of master equations, by using the density matrix formalism. We apply the obtained formulae to the most relevant collapse models, namely the ... More

Bounds on Collapse Models from Matter-Wave Interferometry: Calculational detailsJan 12 2016May 31 2017We present a simple derivation of the interference pattern in matter-wave interferometry as predicted by a class of master equations, by using the density matrix formalism. We apply the obtained formulae to the most relevant collapse models, namely the ... More

Bounds on Collapse Models from Matter-Wave InterferometryJan 14 2016Jan 15 2016Matter-wave interferometry is a direct test of the quantum superposition principle for massive systems, and of collapse models. This is in contrast to non-interferometric tests, which are currently able to test collapse models more efficiently. However ... More

Wigner Function Reconstruction in Levitated OptomechanicsJul 25 2017Nov 21 2017We demonstrate the reconstruction of the Wigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under ... More

General Galilei Covariant Gaussian MapsMar 16 2017Sep 09 2017We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we characterize translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. ... More

Quantum mechanics for non-inertial observersJan 16 2017A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we show how the center-of-mass ... More

Detection of anisotropic particles in levitated optomechanicsApr 03 2018Jul 17 2018We discuss the detection of an anisotropic particle trapped by an elliptically polarized focused Gaussian laser beam. We obtain the full rotational and translational dynamics, as well as, the measured photo-current in a general-dyne detection. As an example, ... More

Reply to Comment on "Quantum mechanics for non-inertial observers"Apr 07 2017Our recent paper (arXiv:1701.04298 [quant-ph]) discussed the occurrence of a coupling of centre of mass and internal degrees of freedom for complex quantum systems in non-inertial frames. There, we pointed out that an external force supporting the system ... More

Optimal control for feedback cooling in cavityless levitated optomechanicsApr 10 2019We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) ... More

Precession Motion in Levitated OptomechanicsMay 21 2018Jun 29 2018We investigate experimentally the dynamics of a non-spherical levitated nanoparticle in vacuum. In addition to translation and rotation motion, we observe the light torque-induced precession and nutation of the trapped particle. We provide a theoretical ... More

Optimal control for feedback cooling in cavityless levitated optomechanicsApr 10 2019Apr 16 2019We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) ... More

Force sensing with an optically levitated charged nanoparticleJun 29 2017Sep 11 2017Levitated optomechanics is showing potential for precise force measurements. Here, we report a case study, to show experimentally the capacity of such a force sensor. Using an electric field as a tool to detect a Coulomb force applied onto a levitated ... More

Static force characterization with Fano anti-resonance in levitated optomechanicsOct 30 2018Jan 17 2019We demonstrate a classical analogy to the Fano anti-resonance in levitated optomechanics by applying a DC electric field. Specifically, we experimentally tune the Fano parameter by applying a DC voltage from 0~kV to 10~kV on a nearby charged needle tip. ... More

Dynamical model selection near the quantum-classical boundaryNov 27 2017Jun 19 2018We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in post-selection as well as for real-time analysis, and ... More

Dynamical model selection for quantum optomechanical systemsNov 27 2017This paper considers the problem of distinguishing between different dynamical models using continuous weak measurements; that is, whether the evolution is quantum mechanical or given by a classical stochastic differential equation. We examine the conditions ... More

An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapseJul 13 2019Levitated nano-oscillators are seen as promising platforms for testing fundamental physics and testing quantum mechanics in a new high mass regime. Levitation allows extreme isolation from the environment, reducing the decoherence processes that are crucial ... More

Numerical Analysis of the Anderson LocalizationSep 22 2006The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems.

Dimension dependence of the conductance distribution in the non-metallic regimesSep 17 2000Jan 18 2002We study numerically the form of the conductance distribution in the non-metallic regime for (1) weakly disordered systems which become insulating due to increase of the system length and (2) cubic d-dimensional systems, in which localization occours ... More

Metal-insulator transition in system with topological disorderNov 25 1999Nov 26 1999Metal-insulator transition in anisotropic disordered Anderson model with both topological and diagonal disorder is investigated numerically. For four sets of the model parameters we found the critical disorder and the critical exponent and prove that ... More

Notes on Leibniz thought experimentSep 03 2013Leibniz thought experiment of perception, sensing, and thinking is reconsidered. We try to understand Leibniz picture in view of our knowledge of basic neuroscience. In particular we can see how the emergence of consciousness could in principle be understood. ... More

Fano resonances in dielectric, metallic and metamaterial photonic structuresAug 27 2016We investigate numerically Fano resonances excited in periodic arrays of dielectric, metallic and left-handed cylinders. Of particular interest are Fano resonances excited in the linear array of cylin- ders. We analyze spatial distribution and symmetry ... More

The number of roots of full supportFeb 26 2016Chapoton has observed a simple product formula for the number of reflections in a finite Coxeter group that have full support. We give a uniform proof of his formula for Weyl groups.

Asymptotic expansion for inverse moments of binomial and Poisson distributionsNov 09 2005An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous results, a single ... More

New Categorifications of the Chromatic and the Dichromatic Polynomials for GraphsJul 14 2005May 22 2006In this paper, for each graph $G$, we def\mbox{}ine a chain complex of graded modules over the ring of polynomials, whose graded Euler characteristic is equal to the chromatic polynomial of $G$. Furthermore, we def\mbox{}ine a chain complex of doubly-graded ... More

Single-solution Random 3-SAT InstancesApr 25 2005Aug 18 2005We study a class of random 3-SAT instances having exactly one solution. The properties of this ensemble considerably differ from those of a random 3-SAT ensemble. It is numerically shown that the running time of several complete and stochastic local search ... More

Stability of Quantum DynamicsJun 17 2004The stability of quantum systems to perturbations of the Hamiltonian is studied. This stability is quantified by the fidelity. Dependence of fidelity on the initial state as well as on the dynamical properties of the system is considered. In particular, ... More

Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebrasAug 31 2016Let $G=GL(m|n)$ be the general linear supergroup over an algebraically closed field $K$ of characteristic zero and let $G_{ev}=GL(m)\times GL(n)$ be its even subsupergroup. The induced supermodule $H^0_G(\lambda)$, corresponding to a dominant weight $\lambda$ ... More

The number of roots of full supportFeb 26 2016Jan 30 2017Chapoton has observed a simple product formula for the number of reflections in a finite Coxeter group that have full support. We give a uniform proof of his formula for Weyl groups. We furthermore refine his formula by the length of the roots.

Relaxation times of dissipative many-body quantum systemsJul 28 2015Oct 29 2015We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number ... More

Quasi-asymptotically almost periodic functions and applicationsSep 25 2018The main aim of this paper is to consider the classes of quasi-asymptotically almost periodic functions and Stepanov quasi-asymptotically almost periodic functions in Banach spaces. These classes extend the well known classes of asymptotically almost ... More

Entanglement in a dephasing model and many-body localizationMar 07 2018Jun 05 2018We study entanglement dynamics in a diagonal dephasing model in which the strength of interaction decays exponentially with distance -- the so-called l-bit model of many-body localization. We calculate the exact expression for entanglement growth with ... More

Multi-directed graph complexes and quasi-isomorphisms between them II: Sourced graphsDec 04 2017Feb 13 2018We prove that the inclusion from oriented graph complex into graph complex with at least one source is a quasi-isomorphism, showing that homology of the "sourced" graph complex is also equal to the homology of standard Kontsevich's graph complex. This ... More

Reiterative $m_{n}$-distributional chaos of type $s$ in Fr\' echet spacesFeb 09 2019May 20 2019The main aim of this paper is to consider various notions of (dense) $m_{n}$-distributional chaos of type $s$ and (dense) reiterative $m_{n}$-distributional chaos of type $s$ for general sequences of linear not necessarily continuous operators in Fr\' ... More

Disjoint distributionally chaotic abstract PDE'sDec 21 2018In this paper, we analyze disjoint distributionally chaotic abstract non-degenerate partial differential equations in Fr\' echet spaces, with integer or Caputo time-fractional derivatives. We present several illustrative examples and applications of our ... More

Distributional chaos and Li-Yorke chaos in metric spacesJan 08 2019Jan 22 2019In this paper, we introduce several new types and generalizations of the concepts distributional chaos and Li-Yorke chaos. We consider the general sequences of binary relations acting between metric spaces, while in a separate section we focus our attention ... More

Homological thickness and stability of torus knotsNov 21 2005Sep 28 2006In this paper we show that the non-alternating torus knots are homologically thick, i.e. that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot without changing ... More

On the H-triangle of generalised nonnesting partitionsMay 02 2013Oct 31 2013To a crystallographic root system \Phi, and a positive integer k, there are associated two Fuss-Catalan objects, the set of nonnesting partitions NN^(k)(\Phi), and the cluster complex \Delta^(k)(\Phi). These posess a number of enumerative coincidences, ... More

On complex points of codimension 2 submanifoldsDec 08 2013In this paper we study the structure of complex points of codimension 2 real submanifolds in complex $n$ dimensional manifolds. We show that the local structure of a complex point up to isotopy only depends on their type (either elliptic or hyperbolic). ... More

Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representationNov 03 2010Jan 12 2011We study a 1-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in [J.Stat.Mech., L05002 (2010)] ... More

Khovanov homology of links and graphsMay 22 2006In this thesis we work with Khovanov homology of links and its generalizations, as well as with the homology of graphs. Khovanov homology of links consists of graded chain complexes which are link invariants, up to chain homotopy, with graded Euler characteristic ... More

Elementary epistemological features of machine intelligenceDec 04 2008Jun 30 2017Theoretical analysis of machine intelligence (MI) is useful for defining a common platform in both theoretical and applied artificial intelligence (AI). The goal of this paper is to set canonical definitions that can assist pragmatic research in both ... More

Wonderful Compactifications in Quantum Field TheoryNov 20 2014Jan 07 2016This article reviews the use of DeConcini-Procesi wonderful models in renormalization of ultraviolet divergences in position space as introduced by Bergbauer, Brunetti and Kreimer. In contrast to the exposition there we employ a slightly different approach; ... More

Multivariate normal mixture modeling, clustering and classification with the rebmix packageJan 26 2018The rebmix package provides R functions for random univariate and multivariate finite mixture model generation, estimation, clustering and classification. The paper is focused on multivariate normal mixture models with unrestricted variance-covariance ... More

Negentropy concept revisited: Standard thermodynamic properties of 16 bacteria, fungi and algae speciesJan 01 2019Standard molar and specific (per gram) enthalpy of formation, entropy and Gibbs free energy of formation of biomatter have been determined for 16 microorganism species, including Methylococcus capsulatus, Klebsiella aerogenes, Paracoccus denitrificans, ... More

Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,A)Dec 20 2012Jun 14 2013Let A be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. Let \pi be an irreducible unitary representation of M and \phi (not necessarily unitary) character ... More

Remark on representation theory of general linear groups over a non-archimedean local division algebraJan 27 2016In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the irreducible square ... More

Circulant matrices: norm, powers, and positivityMar 26 2018Apr 23 2018In their recent paper "The spectral norm of a Horadam circulant matrix", Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the spectral norm of a general real circulant matrix ${\bf C}$ equals the modulus of its row/column sum. ... More

Definite Sums as Solutions of Linear Recurrences With Polynomial CoefficientsApr 09 2018We present an algorithm which, given a linear recurrence operator $L$ with polynomial coefficients, $m \in \mathbb{N}\setminus\{0\}$, $a_1,a_2,\ldots,a_m \in \mathbb{N}\setminus\{0\}$ and $b_1,b_2,\ldots,b_m \in \mathbb{K}$, returns a linear recurrence ... More

Modeling complex points up to isotopyNov 19 2011In this paper we examine the structure of complex points of real 4-manifolds embedded into complex 3-manifolds up to isotopy. We show that there are only two types of complex points up to isotopy and as a consequence, show that any such embedding can ... More

On Stein Neighborhood Basis of Real SurfacesSep 12 2003In this paper, we show that a compact real surface embedded in a complex surface has a regular Stein neighborhood basis, provided that there are only finitely many complex points on the surface, and that they are all flat and hyperbolic. An application ... More

On extended graphical calculus for categorified quantum $sl(n)$May 22 2016We study the properties of the extended graphical calculus for categorified quantum $sl(n)$. The main results include proofs of Reidemeister 2 and Reidemeister 3-like moves involving strands corresponding to arbitrary thicknesses and arbitrary colors ... More

The existence and uniqueness of almost periodic and asymptotically almost periodic solutions of semilinear Cauchy inclusionsAug 08 2018The main aim of this paper is to investigate almost periodicity and asymptotic almost periodicity of abstract semilinear Cauchy inclusions of first order with (asymptotically) Stepanov almost periodic coefficients. To achieve our goal, we employ fixed ... More

Elementary epistemological features of machine intelligenceDec 04 2008Feb 09 2013Theoretical analysis of machine intelligence (MI) is useful for defining a common platform in both theoretical and applied artificial intelligence (AI). The goal of this paper is to set canonical definitions that can assist pragmatic research in both ... More

Categorification of the Dichromatic Polynomial for GraphsApr 12 2005Sep 06 2005For each graph and each positive integer $n$, we define a chain complex whose graded Euler characteristic is equal to an appropriate $n$-specialization of the dichromatic polynomial. This also gives a categorification of $n$-specializations of the Tutte ... More

Scaling of running time of quantum adiabatic algorithm for propositional satisfiabilityFeb 14 2005We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows exponentially ... More

Fano resonances and band structure of two dimensional photonic structuresSep 18 2015We show that the frequency spectrum of two dimensional photonic crystals is strongly influenced by Fano resonances which can be excited already in the linear array of dielectric cylinders. To support this claim, we calculate the transmission of electromagnetic ... More

Comment on the paper I. M. Suslov: Finite Size Scaling from the Self Consistent Theory of LocalizationMay 03 2012In the recent paper [I.M.Suslov, JETP {\bf 114} (2012) 107] a new scaling theory of electron localization was proposed. We show that numerical data for the quasi-one dimensional Anderson model do not support predictions of this theory.

Random Matrix Theory with Non-integer Beta-parameterSep 17 2000We show that the random matrix theory with non-integer "symmetry parameter" beta describes the statistics of transport parameters of strongly disordered two dimensional systems.

Photonic crystal with left-handed componentsOct 19 2015We show that the periodic array of left-handed cylinders possesses a rich spectrum of guided modes when the negative permeability of cylinders equals exactly to minus value of permeability of embedding media. These resonances strongly influences propagation ... More

Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponentsJul 27 1999Nov 17 1999Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling supports the hypothesis ... More

$m_{n}$-Distributional chaos in Fr\' echet spacesFeb 09 2019The main aim of this paper is to introduce the concepts of $m_{n}$-distributional chaos and $\lambda$-distributional chaos for linear continuous operators and their sequences in Fr\' echet spaces ($\lambda \in (0,1]$), as well as their continuous analogues ... More

On Minkowski space and finite geometryOct 08 2014The main aim of this interdisciplinary paper is to characterize all maps on finite Minkowski space of arbitrary dimension $n$ that map pairs of distinct light-like events into pairs of distinct light-like events. Neither bijectivity of maps nor preservation ... More

A Polling Model with Reneging at Polling InstantsAug 01 2014In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that we consider ... More

Upper Bound for Critical Probability of Site Percolation on Triangular LatticeAug 21 2013In site percolation, vertices (sites) of a graph are open with probability p, and there is critical p, for which open vertices form an open path the long way across a graph, so a vertex at the origin is a part of an infinite connected open vertex set. ... More

Cosine problem in EPRL/FK spinfoam modelJul 19 2013Dec 11 2013We calculate the classical limit effective action of the EPRL/FK spinfoam model of quantum gravity coupled to matter fields. By employing the standard QFT background field method adapted to the spinfoam setting, we find that the model has many different ... More

Coexistence of diffusive and ballistic transport in a simple spin ladderFeb 22 2013We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the transport is ... More

The parallel TASEP, fixed particle number and weighted Motzkin pathsNov 11 2013In this paper the totally asymmetric exclusion process (TASEP) with parallel update on an open lattice of size $L$ is considered in the maximum-current region. A formal expression for the generating function for the weight of configurations with $N$ particles ... More

Transport in a one-dimensional isotropic Heisenberg model at high temperatureDec 12 2011Magnetization transport in a one-dimensional isotropic spin 1/2 Heisenberg model is studied. It is shown that in a nonequilibrium steady state at high temperature and constant small driving the magnetization current depends on the system length L as 1/L^{0.5}, ... More

Dephasing-induced diffusive transport in anisotropic Heisenberg modelDec 01 2009Apr 01 2010We study transport properties of anisotropic Heisenberg model in a disordered magnetic field experiencing dephasing due to external degrees of freedom. In the absence of dephasing the model can display, depending on parameter values, the whole range of ... More

Hochschild homology of certain Soergel bimodulesOct 20 2008In this paper we compute Hochschild homology of certain Soergel bimodules. Moreover, we describe explicitly the graded bimodule maps between Soergel bimodules. This computations are motivated by the categorifications of the colored HOMFLY-PT polynomial ... More

Exact convergence times for generation of random bipartite entanglementSep 03 2008Sep 26 2008We calculate exact convergence times to reach random bipartite entanglement for various random protocols. The eigenproblem of a Markovian chain governing the process is mapped to a spin chain, thereby obtaining exact expression for the gap of the Markov ... More

Calculating the probability of detecting radio signals from alien civilizationsJun 29 2007Jul 14 2007Although it might not be self-evident, it is in fact entirely possible to calculate the probability of detecting alien radio signals by understanding what types of extraterrestrial radio emissions can be expected and what properties these emissions can ... More

Homology of torus linksJun 26 2006Aug 15 2007In this paper we show that there is a cut-off in the Khovanov homology of $(2k,2kn)$-torus links, namely that the maximal homological degree of non-zero homology group of $(2k,2kn)$-torus link is $2k^2n$. Furthermore, we calculate explicitely the homology ... More

Properties of Khovanov homology for positive braid knotsNov 21 2005In this paper we solve one open problem from \cite{pat} and give some generalizations. Namely, we prove that the first homology group of positive braid knot is trivial. Also, we show that the same is true for the Khovanov-Rozansky homology \cite{kovroz} ... More

Disjoint Li-Yorke chaos in Fréchet spacesMay 10 2019Jun 02 2019The main aim of this paper is to consider various notions of (dense) disjoint Li-Yorke chaos for general sequences of multivalued linear operators in Fr\' echet spaces. We also consider continuous analogues of introduced notions and provide certain applications ... More

On the strong approximations of partial sums of f(nkx)Sep 27 2015We prove a strong invariance principle for the sums PN k=1 f(nkx), where f is a smooth periodic function on R and (nk)k?1 is an increasing random sequence. Our results show that in contrast to the classical Salem-Zygmund theory, the asymptotic properties ... More

On unitarity of some representatations of classical p-adic groups IJan 26 2017In the case of p-adic general linear groups, each irreducible representation is parabolically induced by a tensor product of irreducible representations supported by cuspidal lines. One gets in this way a parameterization of the irreducible representations ... More

Unitarizability in generalized rank three for classical p-adic groupsSep 02 2017In an earlier paper we propose an approach to the unitarizability problem in the case of classical groups over a p-adic field of characteristic zero based on cuspidal reducibility points. We have reduced earlier the unitarizability for these groups to ... More

Some bounds on unitary duals of classical groups - non-archimeden caseJan 27 2016In the first part of the paper we give some bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical p-adic groups. Roughly, it can show up only if the central character of the inducing ... More

Feynman amplitudes on moduli spaces of graphsSep 02 2017Jul 24 2018This article introduces moduli spaces of coloured graphs on which Feynman amplitudes can be viewed as 'discrete' volume densities. The basic idea behind this construction is that these moduli spaces decompose into disjoint unions of open cells on which ... More

Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and normJun 14 2007Nov 21 2007Let $\F_q$ ($q=p^r$) be a finite field. In this paper the number of irreducible polynomials of degree $m$ in $\F_q[x]$ with prescribed trace and norm coefficients is calculated in certain special cases and a general bound for that number is obtained improving ... More

Equidistribution of the Sequence [m]P in Elliptic CurvesMar 24 2019Apr 29 2019Major controversy surrounds the use of Elliptic Curves in finite fields as Random Number Generators. There is little information however concerning the "randomness" of different procedures on Elliptic Curves defined over fields of characteristic $0$. ... More

Asymptotically almost periodic and asymptotically almost automorphic vector-valued generalized functionsAug 08 2018The main purpose of this paper is to introduce the notion of an asymptotically almost periodic ultradistribution and asymptotically almost automorphic ultradistribution with values in a Banach space, as well as to further analyze the classes of asymptotically ... More

${\mathcal F}$-Hypercyclic and disjoint ${\mathcal F}$-hypercyclic properties of binary relations over topological spacesAug 08 2018In this paper, we examine various types of ${\mathcal F}$-hypercyclic (${\mathcal F}$-topologically transitive) and disjoint ${\mathcal F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties of binary relations over topological ... More

Two stable modifications of the finite section methodFeb 24 2010In this article we demonstrate and compare two modified versions of the classical finite section method for band-dominated operators in case the latter is not stable. For both methods we give explicit criteria for their applicability.

DGP Brane as a Gravity ConductorMar 14 2002We study how the DGP (Dvali-Gabadadze-Porrati) brane affects particle dynamics in linearized approximation. We find that once the particle is removed from the brane it is repelled to the bulk. Assuming that the cutoff for gravitational interaction is ... More

An external approach to unitary representationsApr 01 1993The main aim of this paper is to present the ideas which lead first to the solution of the unitarizability problem for $\GL(n)$ over nonarchimedean local fields and to the recognition that the same result holds over archimedean local fields, a result ... More

Conductance statistics near the Anderson transitionNov 02 2002Paper reviews recent numerical data for the conductance distribution of disordered systems in the critical regime and in the localized regime. Of particular interest is the non-analytical form of the critical conductance distribution in the 3D and 4D ... More

Electronic transport in strongly anisotropic disordered systems: model for the random matrix theory with non-integer betaSep 17 2000Jan 18 2002We study numerically an electronic transport in strongly anisotropic weakly disorderd two-dimensional systems. We find that the conductance distribution is gaussian but the conductance fluctuations increase when anisotropy becomes stronger. We interpret ... More

Guided modes in photonic structures with left-handed componentsJan 21 2015The spectrum of guided modes of linear chain of dielectric and left-handed cylinders is analyzed. The structure of eigenfrequences is much more richer if cylinders are made from the left-handed material with both permittivity and permeability negative. ... More

Two-dimensional electron systems beyond the diffusive regimeMay 03 2010Jul 21 2010Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of the spatial ... More

Irreducibility of induced modules for general linear supergroupsSep 02 2013In this note we determine when is an induced module H^0_G(\lambda), corresponding to a dominant integral highest weight \lambda of the general linear supergroup G=GL(m|n) irreducible. Using the contravariant duality given by the supertrace we obtain a ... More

Adjacency preservers on invertible hermitian matrices IJul 10 2013Hua's fundamental theorem of geometry of hermitian matrices characterizes all bijective maps on the space of all hermitian matrices, which preserve adjacency in both directions. In this and subsequent paper we characterize maps on the set of all invertible ... More

Exact Site and Bond Percolation Probability on Lattice-like GraphsOct 01 2013I calculated the exact site and bond percolation probability on lattice-like graphs for given dimension d: site percolation probability is 1/d and bond percolation probability is 0.5(d-1)^{-1/2}

Second comment on "Dense and nanometric electronic excitations induced by swift heavy ions in an ionic CaF2 crystal: Evidence for two thresholds of damage creation"Sep 06 2013Controversy over nature and existence of the velocity effect [G. Szenes, Phys. Rev. B 87, 056101 (2013)], [M. Toulemonde et al., Phys. Rev. B 87, 056102 (2013)] reignited after new experimental data on swift heavy ion tracks in CaF2 was reported recently ... More

S^1-equivariant Morse cohomologyApr 12 2012We construct a deformed Morse complex computing the equivariant cohomology of a manifold M endowed with a smooth S^1-action. The deformation of the coboundary operator is given by counting gradient flow lines of a Morse function f that are allowed to ... More