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Fermat-type configurations of lines in $\mathbb P^3$ and the containment problemFeb 07 2017Sep 08 2017The purpose of this note is to show a new series of examples of homogeneous ideals $I$ in ${\mathbb K}[x,y,z,w]$ for which the containment $I^{(3)}\subset I^2$ fails. These ideals are supported on certain arrangements of lines in ${\mathbb P}^3$, which ... More

On codimension two flats in Fermat-type arrangementsMay 01 2017In the present note we study certain arrangements of codimension $2$ flats in projective spaces, we call them "Fermat arrangements". We describe algebraic properties of their defining ideals. In particular, we show that they provide counterexamples to ... More

On a conjecture of Demailly and new bounds on Waldschmidt constants in ${\mathbb P}^N$Jan 17 2017In the present note we prove a conjecture of Demailly for finite sets of sufficiently many very general points in projective spaces. This gives a lower bound on Waldschmidt constants of such sets. Waldschmidt constants are asymptotic invariants of subschemes ... More

New phenomena in the containment problem for simplicial arrangementsDec 11 2018In this note we consider two simplicial arrangements of lines and ideals $I$ of intersection points of these lines. There are $127$ intersection points in both cases and the numbers $t_i$ of points lying on exactly $i$ configuration lines (points of multiplicity ... More

Quartic unexpected curves and surfacesApr 10 2018Our research is motivated by recent work of Cook II, Harbourne, Migliore, and Nagel on configurations of points in the projective plane with properties that are unexpected from the point of view of the postulation theory. In this note, we revisit the ... More

Initial sequences and Waldschmidt constants of planar point configurationsJul 04 2016The purpose of this work is to extend the classification of planar point configurations with low Waldschmidt constants for all values less than $5/2$. As a consequence we prove a conjecture of Dumnicki, Szemberg and Tutaj-Gasi\'nska concerning initial ... More

Points fattening on P^1 x P^1 and symbolic powers of bi-homogeneous idealsApr 21 2013We study symbolic powers of bi-homogeneous ideals of points in the Cartesian product of two projective lines and extend to this setting results on the effect of points fattening obtained by Bocci, Chiantini and Dumnicki, Szemberg, Tutaj-Gasi\'nska. We ... More

On the containment hierarchy for simplicial idealsAug 11 2014Apr 15 2015The purpose of this note is to study containment relations and asymptotic invariants for ideals of fixed codimension skeletons (simplicial ideals) determined by arrangements of $n + 1$ general hyperplanes in the $n-$dimensional projective space over an ... More

Unexpected curves arising from special line arrangementsApr 08 2018In a recent paper arXiv:1602.02300v2, Cook II, Harbourne, Migliore and Nagel related the splitting type of a line arrangement in the projective plane to the number of conditions imposed by a general fat point of multiplicity $j$ to the linear system of ... More

A matrixwise approach to unexpected hypersurfacesJul 10 2019The aim of this note is to give a generalization of some results concerning unexpected hypersurfaces. Unexpected hypersurfaces occur when the actual dimension of the space of forms satisfying certain vanishing data is positive and the imposed vanishing ... More

A counterexample to the containment $I^{(3)}\subset I^2$ over the realsOct 03 2013May 04 2014The purpose of this note is to give counterexamples to the containment $I^{(3)}\subset I^2$ over the real numbers.

Normality of orbit closures for directing modules over tame algebrasNov 15 2004We show that the orbit closures for directing modules over tame algebras are normal and Cohen-Macaulay. The proof is based on deformations to normal toric varieties.

Universal targets for homomorphisms of edge-colored graphsAug 26 2015Nov 21 2016A $k$-edge-colored graph is a finite, simple graph with edges labeled by numbers $1,\ldots,k$. A function from the vertex set of one $k$-edge-colored graph to another is a homomorphism if the endpoints of any edge are mapped to two different vertices ... More

On the Sylvester-Gallai theorem for conicsNov 10 2014In the present note we give a new proof of a result due to Wiseman and Wilson which establishes an analogue of the Sylvester-Gallai theorem valid for curves of degree two. The main ingredients of the proof come from algebraic geometry. Specifically, we ... More

Universal targets for homomorphisms of edge-colored graphsAug 26 2015A $k$-edge-colored graph is a finite, simple graph with edges labeled by numbers $1,\ldots,k$. A function from the vertex set of one $k$-edge-colored graph to another is a homomorphism if the color of every edge is preserved over the mapping. Given a ... More

The closure of the set of periodic modules over a concealed canonical algebra is regular in codimension oneDec 29 2016Let A be a concealed canonical algebra and d the dimension vector of an A-module which is periodic respect to the action of the Auslander-Reiten translation In the paper, we investigate the union of the closures of the orbits of the periodic A-modules ... More

Line arrangements with the maximal number of triple pointsJun 25 2014The purpose of this note is to study configurations of lines in projective planes over arbitrary fields having the maximal number of intersection points where three lines meet. We give precise conditions on ground fields F over which such extremal configurations ... More

Periodic perturbations of unbounded Jacobi matrices II: Formulas for densityFeb 22 2016Aug 30 2016We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately scaled Tur\'an determinants or Christoffel functions. Exact asymptotics of ... More

Domain shape dependence of semiclassical corrections to energyAug 09 2016Stationary solution of one-dimensional Sine-Gordon system is embedded in a multidimensional theory with explicitly finite domain in the added spatial dimensions. Semiclassical corrections to energy are calculated for static kink solution with emphasis ... More

Wild Kernels and divisibility in K-groups of global fieldsAug 10 2012In this paper we study the divisibility and the wild kernels in algebraic K-theory of global fields $F.$ We extend the notion of the wild kernel to all K-groups of global fields and prove that Quillen-Lichtenbaum conjecture for $F$ is equivalent to the ... More

On resolvent kernels on real hyperbolic spaceFeb 02 2015Consider the $\lambda$-Green function and the $\lambda$-Poisson kernel of a Lipschitz domain $U\subset \mathbb H^n=\{x\in\mathbb R^n:x_n>0\}$ for hyperbolic Brownian motion with drift. We investigate a relationship between these objects and those for ... More

Periodic perturbations of unbounded Jacobi matrices III: The soft edge regimeJul 20 2017Feb 04 2018We present pretty detailed spectral analysis of Jacobi matrices with periodically modulated entries in the case when $0$ lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that the studied operators ... More

The derived equivalence classification of gentle two-cycle algebrasSep 29 2015We complete the derived equivalence classification of the gentle two-cycle algebras initiated in earlier papers by Avella-Alaminos and Bobinski-Malicki.

Normal forms of modules over admissible algebras with formal two-ray modulesMar 24 2005Aug 02 2005The aim of the paper is to classify the indecomposable modules and describe the Auslander--Reiten sequences for admissible algebras with formal two-ray modules.

On potential theory of hyperbolic Brownian motion with driftFeb 02 2015Jul 10 2019Consider the $\lambda$-Green function and the $\lambda$-Poisson kernel of a Lipschitz domain $U\subset \mathbb H^n=\left\{x\in\mathbb R^n:x_n>0\right\}$ for hyperbolic Brownian motion with drift. We provide several relationships that facilitate studying ... More

The model of closed-loop control by thermostats: properties and numerical simulationsMay 23 2013Jun 27 2013A closed-loop control of a reaction-diffusion type process is introduced. The control system consist of a finite number of control and measurement devices. The measurement devices collect information about the current state of the process. The control ... More

On uniqueness of dissipative solutions of the Camassa-Holm equationNov 01 2016Feb 27 2019We prove that dissipative weak solutions of the Camassa-Holm equation are unique. Thus we complete the global well-posedness theory of this celebrated model of shallow water, initiated by a general proof of existence in [Z. Xin, P. Zhang Comm. Pure Appl. ... More

Transfer of energy in Camassa-Holm and related models by use of nonunique characteristicsMay 10 2016Nov 09 2016We study the propagation of energy density in finite-energy weak solutions of the Camassa-Holm and related equations. Developing the methods based on generalized nonunique characteristics, we show that the parts of energy related to positive and negative ... More

Measure-transmission metric and stability of structured population modelsApr 16 2014In [Gwiazda, Jamr\'oz, Marciniak-Czochra 2012] a framework for studying cell differentiation processes based on measure-valued solutions of transport equations was introduced. Under application of the so-called measure-transmission conditions it enabled ... More

Symbolic inductive bias for visually grounded learning of spoken languageDec 21 2018A widespread approach to processing spoken language is to first automatically transcribe it into text. An alternative is to use an end-to-end approach: recent works have proposed to learn semantic embeddings of spoken language from images with spoken ... More

Mode-coupling theory and beyond: a diagrammatic approachSep 28 2012For almost thirty years, mode-coupling theory has been the most widely discussed and used but also the most controversial theory of the glass transition. In this paper we briefly review the reasons for both its popularity and its controversy. We emphasize ... More

On some expansions for the Euler Gamma function and the Riemann Zeta functionJul 12 2010Feb 13 2013In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Fa\'a di Bruno formula, Bell polynomials, potential polynomials, Mittag-Leffler polynomials, ... More

Fluctuations, correlations and non-extensivityOct 23 2006Feb 15 2007The present status of investigations on fluctuations and correlations seen in high energy multiparticle production processes made using the notion of nonextensivity is reviewed.

Efficient generation of distant atom entanglementSep 13 2004We show how the entanglement of two atoms, trapped in distant separate cavities, can be generated with arbitrarily high probability of success. The scheme proposed employs sudden excitation of the atoms proving that the weakly driven condition is not ... More

Hyperbolicity is dense in the real quadratic familyJul 06 1992It is shown that for non-hyperbolic real quadratic polynomials topological and quasisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that hyperbolic maps ... More

Specific Heat of Disordered Superconductors Induced by Negative CentersDec 28 2003We show that superconductors with inhomogeneous order parameters can show similar features as anisotropic ones. In this paper we study the low temperature specific heat dependence in such a system and we show that the disorder associated with randomly ... More

Kinetic Theory Approach to the SK Spin Glass Model with Glauber DynamicsJun 18 1997I present a new method to analyze Glauber dynamics of the Sherrington-Kirkpatrick (SK) spin glass model. The method is based on ideas used in the classical kinetic theory of fluids. I apply it to study spin correlations in the high temperature phase ($T\ge ... More

Quantum harmonic oscillator, entanglement in the vacuum and its geometric interpretationJun 12 2018Nov 29 2018Starting with a formalism of operators in extended Hilbert space we reformulate a two dimensional quantum harmonic oscillator in such a way the ground state is explicitly maximally entangled. Being a vector in the Hilbert space, it has also a non-trivial ... More

A theory for the dynamics of glassy mixtures with particle size swapsMay 07 2018Oct 20 2018We present a theory for the dynamics of a binary mixture with particle size swaps. The theory is based on a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. The theory shows that, in accordance with ... More

A Method of Generating Random Weights and Biases in Feedforward Neural Networks with Random Hidden NodesOct 13 2017Neural networks with random hidden nodes have gained increasing interest from researchers and practical applications. This is due to their unique features such as very fast training and universal approximation property. In these networks the weights and ... More

On measures of accretion and dissipation for solutions of the Camassa-Holm equationNov 30 2016We investigate the measures of dissipation and accretion related to the weak solutions of the Camassa-Holm equation. Demonstrating certain properties of nonunique characteristics, we prove a new representation formula for these measures and conclude about ... More

High fidelity state mapping performed in a V-type level structure via stimulated Raman transitionDec 30 2013Feb 19 2015It is proved that a qubit encoded in excited states of a V-type quantum system cannot be perfectly transferred to the state of the cavity field mode using a single rectangular laser pulse. This obstacle can be overcome by using a two-stage protocol, in ... More

Relational parsing: a clean, fast parsing strategy for all context-free languagesFeb 18 2019We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state of the art: ... More

On Krull-Gabriel dimension and Galois coveringsJan 18 2018Assume that $K$ is an algebraically closed field, $R$ a locally support-finite locally bounded $K$-category, $G$ a torsion-free admissible group of $K$-linear automorphisms of $R$ and $A=R\slash G$. We show that the Krull-Gabriel dimension $KG(R)$ of ... More

Density quantization method in the optimal portfolio choice with partial observation of stochastic volatilitySep 29 2010Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - density quantization - is introduced which reduces the original ... More

Algebras with irreducible module varieties III: Birkhoff varietiesOct 29 2018We study a family of affine varieties arising from a version of an old problem due to Birkhoff asking for the classification of embeddings of finite abelian p-groups. We show that all of these varieties are irreducible and have a dense orbit.

Exit times densities of Bessel processMay 28 2015We examine the density functions of the first exit times of the Bessel process from the intervals [0,1) and (0,1). First, we express them by means of the transition density function of the killed process. Using that relationship we provide precise estimates ... More

Projections of del Pezzo surfaces and Calabi--Yau threefoldsOct 19 2010Mar 04 2015We study the syzygetic structure of projections of del Pezzo surfaces in order to construct singular Calabi-Yau threefolds. By smoothing those threefolds, we obtain new examples of Calabi-Yau threefolds with Picard group of rank 1. We also give an example ... More

The almost split triangles for perfect complexes over gentle algebrasMar 30 2009In the paper we describe the almost split sequences in the homotopy category of perfect complexes over a gentle algebra.

On the zero set of semi-invariants for regular modules over tame canonical algebrasNov 25 2006Oct 23 2007We investigate sets of the common zeros of non-constant semi-invariants for regular modules over canonical algebras. In particular, we show that if the considered algebra is tame then for big enough vectors these sets are complete intersections.

Singularities of orbit closures in module varieties and cones over rational normal curvesJul 28 2005Let $N$ be a point of an orbit closure $\bar{O_M}$ in a module variety such that its orbit $O_N$ has codimension two in $\bar{O_M}$. We show that under some additional conditions the pointed variety $(\bar{O_M},N)$ is smoothly equivalent to a cone over ... More

Geometry of regular modules over canonical algebrasJul 01 2005Oct 04 2005We classify canonical algebras such that for every dimension vector of a regular module the corresponding module variety is normal (respectively, a complete intersection). We also prove that for the dimension vectors of regular modules normality is equivalent ... More

Evaluating linear response in active systems with no perturbing fieldJul 01 2016We present a method for the evaluation of time-dependent linear response functions for systems of active Ornstein-Uhlenbeck particles from unperturbed simulations. The method is inspired by the Malliavin weights sampling method proposed by Warren and ... More

On ascending chains of ideals in the polynomial ringMay 20 2016Assume that $K$ is a field and $I_{1}\subsetneq ...\subsetneq I_{t}$ is an ascending chain (of length $t$) of ideals in the polynomial ring $K[x_{1},,...,x_{m}]$, for some $m\geq 1$. Suppose that $I_{j}$ is generated by polynomials of degrees less or ... More

Wide-field variability survey of the globular cluster NGC 4833Jan 20 2014We present preliminary results of the variability survey in the field of the glo bular cluster NGC 4833. We observed all 34 variable stars known in the cluster. In add ition, we have found two new SX Phoenicis stars, one new RR Lyrae star, twelve new ... More

A self-propelled particle in an external potential: is there an effective temperature?Apr 03 2014We study a stationary state of a single self-propelled, athermal particle in linear and quadratic external potentials. The self-propulsion is modeled as a fluctuating force evolving according to the Ornstein-Uhlenbeck process, independently of the state ... More

Portfolio Management Approach in Trade Credit Decision MakingJan 16 2013The basic financial purpose of an enterprise is maximization of its value. Trade credit management should also contribute to realization of this fundamental aim. Many of the current asset management models that are found in financial management literature ... More

Text segmentation with character-level text embeddingsSep 18 2013Learning word representations has recently seen much success in computational linguistics. However, assuming sequences of word tokens as input to linguistic analysis is often unjustified. For many languages word segmentation is a non-trivial task and ... More

Planning Optimal From the Firm Value Creation Perspective Levels of Operating Cash InvestmentsJan 16 2013The basic financial purpose of corporation is creation of its value. Liquidity management should also contribute to realization of this fundamental aim. Many of the current asset management models that are found in financial management literature assume ... More

Primitive contractions of Calabi-Yau threefolds IIJul 17 2007Sep 25 2008We construct 16 new examples of Calabi--Yau threefolds with Picard group of rank 1. Each of these examples is obtained by smoothing the image of a primitive contraction with exceptional divisor being a del Pezzo surface of degree 6, 7 or $\mathbb{P}^1\times ... More

Divergent four-point dynamic density correlation function of a glassy colloidal suspension: a diagrammatic approachMay 30 2008We use a recently derived diagrammatic formulation of the dynamics of interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)] to study a four-point dynamic density correlation function. We re-sum a class of diagrams which separate ... More

Variations of Pairing Potential and Charge Distribution in Presence of a Non-magnetic ImpurityNov 08 2004Using an attractive Hubbard model we examine spatial variations of superconducting order parameter and local charge on a two dimensional lattice. For various band filling we show the effect of destruction of the order parameter around a non-magnetic impurity. ... More

Is a "homogeneous" description of dynamic heterogeneities possible?Jul 20 2004We study the simplest model of dynamic heterogeneities in glass forming liquids: one-spin facilitated kinetic Ising model introduced by Fredrickson and Andersen [G.H. Fredrickson and H.C. Andersen, Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 83, ... More

Colloidal glass transition: Beyond mode-coupling theoryMay 27 2003A new theory for dynamics of concentrated colloidal suspensions and the colloidal glass transition is proposed. The starting point is the memory function representation of the density correlation function. The memory function can be expressed in terms ... More

On the Dirichlet problem in billiard spacesApr 24 2015Jul 01 2015The constrained Dirichlet boundary value problem $\ddot x=f(t,x)$, $x(0)=x(T)$, is studied in billiard spaces, where impacts occur in boundary points. Therefore we develop the research on impulsive Dirichlet problems with state-dependent impulses. Inspiring ... More

Semi-invariants for concealed-canonical algebrasDec 17 2012In the paper is we generalize known descriptions of rings of semi-invariants for regular modules over Euclidean and canonical algebras to arbitrary concealed-canonical algebras.

Normality of maximal orbit closures for Euclidean quiversSep 12 2011Let Delta be an Euclidean quiver. We prove that the closures of the maximal orbits in the varieties of representations of Delta are normal and Cohen--Macaulay (even complete intersections). Moreover, we give a generalization of this result for the tame ... More

Canonical tilting modules over shod algebras are regular in codimension oneJul 14 2008We show that for a class of modules over shod algebras, including the canonical tilting modules, the closures of the corresponding orbits in module varieties are regular in codimension one.

A characterization of admissible algebras with formal two-ray modulesMar 17 2005Jul 06 2005In the paper we characterize, in terms of quivers and relations, the admissible algebras with formal two-ray modules introduced by G. Bobi\'nski and A. Skowro\'nski [Cent. Eur. J.Math.1 (2003), 457--476].

Orbit closures for representations of Dynkin quivers are regular in codimension twoNov 14 2004We develop reductions for classifications of singularities of orbit closures in module varieties. Then we show that the orbit closures for representations of Dynkin quivers are regular in codimension two.

An analytic approach to special numbers and polynomialsFeb 13 2013The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains some new elements. ... More

On uniqueness of dissipative solutions of the Camassa-Holm equationNov 01 2016Jul 15 2018We prove that dissipative weak solutions of the Camassa-Holm equation are unique. Thus we complete the global well-posedness theory of this celebrated model of shallow water, initiated by a general proof of existence in [Z. Xin, P. Zhang Comm. Pure Appl. ... More

A note on product of measuresOct 26 2018A slight modification to Halmos' definition of product of measures yields a uniquely characterized associative product. The operation applies to arbitrary (not necessarily $\sigma-$finite) measures and is consistent with the Fubini--Tonelli theorem.

On isomorphisms of Banach spaces of continuous functionsFeb 13 2013Sep 19 2013We prove that if $K$ and $L$ are compact spaces and $C(K)$ and $C(L)$ are isomorphic as Banach spaces then $K$ has a $\pi$-base consisting of open sets $U$ such that $\bar{U}$ is a continuous image of some compact subspace of $L$. This gives some information ... More

Dynamics of interacting Brownian particles: a diagrammatic formulationMay 24 2007Jun 21 2007We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion we introduce a basis that consists of orthogonalized ... More

Elliptic flow of Lambda hyperons in Pb+Pb collisions at 158 AGeVOct 24 2005The elliptic flow of Lambda hyperons has been measured by the NA49 experiment in semi-central Pb+Pb collisions at 158 AGeV. The standard method of correlating particles with an event plane has been used. Measurements of v2 near mid-rapidity are reported ... More

One-dimensional maps and Poincaré metricAug 12 1990Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show that the joint ... More

Effect of Disorder on a D-wave SuperconductorJun 16 2001We apply the Coherent Potential Approximation (CPA) to an extended Hubbard model to describe disordered superconductors with d-wave pairing. We discuss the pair-breaking effect caused by non-magneticdisorder in presence of Van Hove Singularity.

Complexity of Finding Perfect Bipartite Matchings Minimizing the Number of Intersecting EdgesSep 20 2017Dec 22 2017Consider a problem where we are given a bipartite graph H with vertices arranged on two horizontal lines in the plane, such that the two sets of vertices placed on the two lines form a bipartition of H. We additionally require that H admits a perfect ... More

Domain shape dependence of semiclassical corrections to energyAug 09 2016Jun 02 2017Stationary solution of one-dimensional Sine-Gordon system is embedded in a multidimensional theory with explicitly finite domain in the added spatial dimensions. Semiclassical corrections to energy are calculated for static kink solution with emphasis ... More

Effect of anisotropy distribution on local nucleation field in bistable ferromagntic microwiresMar 23 2017Jun 03 2019Critical parameters defining the local nucleation field in amorphous ferromagnetic microwires with positive magnetostriction are obtained analytically through scaling procedures. Exact value of the nucleation field is obtained numerically as a function ... More

A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACFJul 19 2016Assume that $ACF$ denotes the theory of algebraically closed fields. The renowned theorem of A. Tarski states that $ACF$ admits quantifier elimination. In this paper we give a constructive proof of Tarski's theorem on quantifier elimination in $ACF$. ... More

Evaluating linear response in active systems with no perturbing fieldJul 01 2016Apr 10 2017We present a method for the evaluation of time-dependent linear response functions for systems of active Ornstein-Uhlenbeck particles from unperturbed simulations. The method is inspired by the Malliavin weights sampling method proposed by Warren and ... More

Irreducible Green Functions Method applied to nanoscopic systemsMar 08 2016The equation of motion method (EOM) for Green functions is one of the tools used in the analysis of quantum dot system coupled with metallic and superconducting leads. We investigate modified EOM, based on differentiation of double-time temperature dependent ... More

A theory for the dynamics of dense systems of athermal self-propelled particlesJul 16 2015Dec 11 2015We present a derivation of a recently proposed theory for the time dependence of density fluctuations in stationary states of strongly interacting, athermal, self-propelled particles. The derivation consists of two steps. First, we start from the equation ... More

A-manifolds on a principal torus bundle over an A-manifold baseJun 10 2014Jun 11 2014We construct new examples of manifolds with cyclic-parallel Ricci tensor, so called A-manifolds, on a r-torus bundle over a product of almost Hodge A-manifolds.

An in-place, subquadratic algorithm for permutation inversionJan 07 2019We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time with a simple ... More

Statistical test for fractional Brownian motion based on detrending moving average algorithmMar 22 2018Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on detrending ... More

Construction of an A-manifold on a principal torus bundleMay 31 2012Dec 26 2012We construct a new example of an A-manifold, i.e. a Riemannian manifold with a cyclic-parallel Ricci tensor, which can be viewed as a generalization of the Einstein condition. The underlying manifold for our construction is a principal torus bundle over ... More

The Ellis group conjecture and variants of definable amenabilityOct 30 2017We consider definable topological dynamics for $NIP$ groups admitting certain decompositions in terms of specific classes of definably amenable groups. For such a group, we find a description of the Ellis group of its universal definable flow. This description ... More

A normal measure on a compact connected spaceJul 10 2015We present a construction of a compact connected space which supports a normal probability measure.

Periodic perturbations of unbounded Jacobi matrices II: Formulas for densityFeb 22 2016Nov 07 2016We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately scaled Tur\'an determinants or Christoffel functions. Exact asymptotics of ... More

Spectral properties of block Jacobi matricesMay 17 2017Jan 30 2018We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous. Uniform ... More

A characterization of representation infinite quiver settingsMar 12 2019We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this result to the ... More

Orbit closures of directing modules are regular in codimension oneDec 07 2007We show that the orbit closure of a directing module is regular in codimension one. In particular, this result gives information about a distinguished irreducible component of a module variety.

Codimension two singularities for representations of extended Dynkin quiversMar 29 2006Let M and N be two representations of an extended Dynkin quiver such that the orbit O_N of N is contained in the orbit closure \bar{O_M} and has codimension two. We show that the pointed variety $(\bar{O_M},N)$ is smoothly equivalent to a simple surface ... More

Modeling a coronal loop heated by MHD-turbulence nanoflaresJun 28 2005We model the hydrodynamic evolution of the plasma confined in a coronal loop, 30000 km long, subject to the heating of nanoflares due to intermittent magnetic dissipative events in the MHD turbulence produced by loop footpoint motions. We use the time-dependent ... More

On uniqueness of dissipative solutions of the Camassa-Holm equationNov 01 2016We prove that dissipative weak solutions of the Camassa-Holm equation are unique.

Transfer of energy in Camassa-Holm and related models by use of nonunique characteristicsMay 10 2016Aug 01 2016We study the propagation of energy density in finite-energy weak solutions of the Camassa-Holm and related equations. Developing the methods based on generalized nonunique characteristics, we show that the parts of energy related to positive and negative ... More

On uniqueness of dissipative solutions of the Camassa-Holm equationNov 01 2016Nov 07 2016We prove that dissipative weak solutions of the Camassa-Holm equation are unique.