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Compact polyhedral surfaces of an arbitrary genus and determinants of LaplaciansJun 03 2009Compact polyhedral surfaces (or, equivalently, compact Riemann surfaces with conformal flat conical metrics) of an arbitrary genus are considered. After giving a short self-contained survey of their basic spectral properties, we study the zeta-regularized ... More

On the asymptotics of determinant of Laplacian at the principal boundary of the principal stratum of the moduli space of Abelian differentialsAug 11 2009We study the asymptotics of the determinant of Laplacian on a translation surface (a compact Riemann surface equipped with a conformal flat conical metric with trivial holonomy) of genus g with 2g-2 conical points of angle 4\pi as two conical points collide. ... More

DtN isospectrality, flat metrics with non-trivial holonomy and comparison formula for determinants of LaplacianNov 15 2015We study comparison formulas for $\zeta$-regularized determinants of self-adjoint extensions of the Laplacian on flat conical surfaces of genus $g\geq 2$. The cases of trivial and non-trivial holonomy of the metric turn out to differ significantly.

Krein formula and S-matrix for Euclidean Surfaces with Conical SingularitiesNov 23 2010Feb 28 2012We use Krein formula and the S-matrix formalism to give formulas for the zeta-regularized determinant of non-Friedrichs extensions of the Laplacian on Euclidean surfaces with Conical Singularities. This formula involves S(0) and we show that the latter ... More

Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of LaplaciansMay 23 2006Jul 12 2006We prove a formula for the determinant of Laplacian on an arbitrary compact polyhedral surface of genus one. This formula generalizes the well-known Ray-Singer result for a flat torus. A special case of flat conical metrics given by the modulus of a meromorphic ... More

Green function and self-adjoint Laplacians on polyhedral surfacesFeb 08 2019Using Roelcke formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface $X$ and compute the $S$-matrix of $X$ at the zero value of the spectral parameter. We apply these results ... More

Determinant of Laplacian on tori of constant positive curvature with one conical pointDec 13 2017Dec 14 2017We find an explicit expression for the zeta-regularized determinant of (the Friedrichs extension) of the Laplacian on a compact Riemann surface of genus one with conformal metric of curvature $1$ having a single conical singularity of angle $4\pi$.

Determinant of pseudo-laplaciansFeb 17 2012Let X be a compact Riemannian manifold of dimension two or three and let P be a point of X. We derive comparison formulas relating the zeta-regularized determinant of an arbitrary self-adjoint extension of (symmetric) Laplace operator with domain, consisting ... More

Spectral Determinants on Mandelstam DiagramsDec 01 2013We study the regularized determinant of the Laplacian as a functional on the space of Mandelstam diagrams (noncompact translation surfaces glued from finite and semi-infinite cylinders). A Mandelstam diagram can be considered as a compact Riemann surface ... More

Moduli spaces of meromorphic functions and determinant of LaplacianOct 12 2014The Hurwitz space is the moduli space of pairs $(X,f)$ where $X$ is a compact Riemann surface and $f$ is a meromorphic function on $X$. We study the Laplace operator $\Delta^{|df|^2}$ of the flat singular Riemannian manifold $(X,|df|^2)$. We define a ... More

Isomonodromic tau-function of Hurwitz Frobenius manifolds and its applicationsOct 07 2003Mar 23 2005In this work we find the isomonodromic (Jimbo-Miwa) tau-function corresponding to Frobenius manifold structures on Hurwitz spaces. We discuss several applications of this result. First, we get an explicit expression for the G-function (solution of Getzler's ... More

Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formulaMay 04 2004Jul 24 2008Let $w$ be an Abelian differential on compact Riemann surface of genus $g\geq 1$. We obtain an explicit holomorphic factorization formula for $\zeta$-regularized determinant of the Laplacian in flat conical metrics with trivial holonomy $|w|^2$, generalizing ... More

On G-function of Frobenius manifolds related to Hurwitz spacesJun 21 2003The semisimple Frobenius manifolds related to the Hurwitz spaces $H_{g,N}(k_1, ..., k_l)$ are considered. We show that the corresponding isomonodromic tau-function $\tau_I$ coincides with $(-1/2)$-power of the Bergmann tau-function which was introduced ... More

A new hierarchy of integrable systems associated to Hurwitz spacesDec 21 2001Jan 29 2004In this paper we introduce a new class of integrable systems, naturally associated to Hurwitz spaces (spaces of meromorphic functions over Riemann surfaces). The critical values of the meromorphic functions play the role of "times". Our systems give a ... More

Normalized Ricci flow on Riemann surfaces and determinants of LaplacianMay 02 2004Jan 10 2009In this note we give a simple proof of the fact that the determinant of Laplace operator in smooth metric over compact Riemann surfaces of arbitrary genus $g$ monotonously grows under the normalized Ricci flow. Together with results of Hamilton that under ... More

On splitting of the normalizer of a maximal torus in $E_l(q)$Dec 30 2018Let $G$ be a finite group of Lie type $E_l$ with $l\in\{6,7,8\}$ over $F_q$ and $W$ be the Weyl group of $G$. We describe all maximal tori $T$ of $G$ such that $T$ has a complement in its algebraic normalizer $N(G,T)$. Let $T$ correspond to an element ... More

On splitting of the normalizer of a maximal torus in $E_6(q)$Jun 07 2018Let $G$ be a finite group of Lie type $E_6$ over $F_q$ (adjoint or simply connected) and $W$ be the Weyl group of $G$. We describe maximal tori $T$ such that $T$ has a complement in its algebraic normalizer $N(G,T)$. It is well known that for each maximal ... More

Tau-function on Hurwitz spacesFeb 25 2002Feb 10 2003We construct a flat holomorphic line bundle over a connected component of the Hurwitz space of branched coverings of the Riemann sphere. A flat holomorphic connection defining the bundle is described in terms of the invariant Wirtinger projective connection ... More

A criterion for left-orthogonality of an effective divisor on a surfaceOct 07 2016We find a criterion for an effective divisor $D$ on a smooth surface to be left-orthogonal or strongly left-orthogonal (i.e. for the pair of line bundles $(\mathcal O,\mathcal O(D))$ to be exceptional or strong exceptional).

Monoid automata for displacement context-free languagesMar 24 2014In 2007 Kambites presented an algebraic interpretation of Chomsky-Schutzenberger theorem for context-free languages. We give an interpretation of the corresponding theorem for the class of displacement context-free languages which are equivalent to well-nested ... More

The quantum mechanics is a non-universal theory. The realistic Schrodinger's and positivistic Born's interpretation of the wave functionNov 18 2013Quantum mechanics describes successfully numerous quantum phenomena both microscopic and macroscopic, such as superconductivity. But the controversies about quantum mechanics, in the old days and present day, reveal fundamental obscurity in quantum mechanics. ... More

Accrual valuation and mark to market adjustmentFeb 18 2016This paper provides intuition on the relationship of accrual and mark-to-market valuation for cash and forward interest rate trades. Discounted cashflow valuation is compared to spread-based valuation for forward trades, which explains the trader's view ... More

Nested Head-Tail Vlasov SolverAug 30 2013Sep 05 2013Nested Head-Tail (NHT) is a Mathematica-based Vlasov solver for transverse oscillations in multi-bunch beams. It takes into account azimuthal, radial, coupled-bunch and beam-beam degrees of freedom, single- and inter-bunch dipole wakes, an arbitrary damper, ... More

Three-beam instability in the LHCJan 03 2013Jan 11 2013In the LHC, a transverse instability is regularly observed at 4TeV right after the beta-squeeze, when the beams are separated by about their ten transverse rms sizes [1-3], and only one of the two beams is seen as oscillating. So far only a single hypothesis ... More

Head-Tail Modes for Strong Space ChargeDec 19 2008Apr 07 2009The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The ... More

Asymptotic properties of zeta functions over finite fieldsOct 23 2013Oct 28 2013In this paper we study asymptotic properties of families of zeta and $L$-functions over finite fields. We do it in the context of three main problems: the basic inequality, the Brauer--Siegel type results and the results on distribution of zeroes. We ... More

Measurement of the charged-pion polarisability at COMPASSNov 09 2015The electric (${\alpha}_{\pi}$) and the magnetic (${\beta}_{\pi}$) polarisabilities are fundamental properties of the pion characterising the rigidity of its internal structure. They have been precisely measured at the COMPASS experiment at CERN with ... More

A search for x-ray counterparts of gamma-ray bursts with the ROSAT PSPCAug 01 1998We search for faint X-ray bursts with duration 10--300 seconds in the ROSAT PSPC pointed observations with a total exposure of 1.6e7 seconds. We do not detect any events shorter than ~100s, i.e. those that could be related to the classic gamma-ray bursts. ... More

Equality cases in Viterbo's conjecture related to permutohedraDec 05 2015In this note we show, using the billiard technique, that the product of a regular permutohedron and a regular simplex delivers an equality in Viterbo's conjecture.

The Supersymmetric Axion and CosmologyJul 21 2003May 13 2005In this lecture we review several cosmological issues associated with the axion. Axion solves the strong CP problem and is a good candidate for the dark matter. Limits, which are imposed by the value of isocurvature fluctuations fraction in the observed ... More

Thermal Effects And Flat Direction BaryogenesisNov 19 2001Jan 23 2003In this paper we provide a detailed numerical study of the influence of thermal effects on the original picture of AD baryogenesis. These effects are found to modify the results greatly in some cases. We estimate the baryon/entropy ratio and provide numerical ... More

On the monodromy group of confluenting linear equationsApr 17 2003We consider a linear analytic ordinary differential equation with complex time having a nonresonant irregular singular point. We study it as a limit of a generic family of equations with confluenting Fuchsian singularities. In 1984 V.I.Arnold asked the ... More

Solving the mystery integralJul 27 2016We give a direct evaluation of a curious integral identity, which follows from the work of Ismail and Valent on the Nevanlinna parametrization of solutions to a certain indeterminate moment problem.

A note on LU decomposition of the Discrete Fourier Transform matrixJul 02 2015We describe some properties of the lower triangular Toeplitz matrix $T_q$ with coefficients $t_{i,j}=1/(q;q)_{i-j}$, where $(z;q)_k$ is the q-Pochhammer symbol. We identify explicitly the inverse of $T_q$ and show that both this matrix and its transpose ... More

Some properties of antistochastic stringsSep 12 2014Mar 09 2016Antistochastic strings are those strings that lack any reasonable statistical explanations. We establish the follow property of such strings: every absolutely non-stochastic string $x$ is "holographic" in the sense that it can be restored by a short program ... More

Bounds of some parameters of elliptic curve on finite fieldJul 02 2013I prove lower bounds of some parameters of elliptic curve over finite field. There parameters are closely interrelated with cryptographic stability of elliptic curve.

The central limit theorem for extremal characters of the infinite symmetric groupMay 08 2011Jul 14 2011The asymptotics of the first rows and columns of random Young diagrams corresponding to extremal characters of the infinite symmetric group is studied. We consider rows and columns with linear growth in $n$, the number of boxes of random diagrams, and ... More

Bounded reductive subalgebras of sl(n)Jul 08 2010Mar 15 2011Let $\mathfrak g$ be a semisimple Lie algebra and $\mathfrak k\subset\mathfrak g$ be a reductive in $\mathfrak g$ subalgebra. A $(\mathfrak g, \mathfrak k)$-module is a $\mathfrak g$-module which after restriction to $\mathfrak k$ becomes a direct sum ... More

On extrema of stable processesJan 07 2010Apr 08 2011We study the Wiener--Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener--Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such as infinite ... More

On the convergence of the Gaver-Stehfest algorithmMay 03 2013Jul 11 2013The Gaver-Stehfest algorithm for numerical inversion of Laplace transform was developed in the late 1960s. Due to its simplicity and good performance it is becoming increasingly more popular in such diverse areas as Geophysics, Operations Research and ... More

Software Testing Models Against Information Security RequirementsJun 08 2013An overview and classification of software testing models are done. Recommendations on the choice of models are proposed

Conservative curved systems and free functional modelApr 30 2005We introduce conservative curved systems over multiply connected domains and study relationships of such systems with related notions of functional model, characteristic function, and transfer function. In contrast to standard theory for the unit disk, ... More

Self-adjointness of Cauchy singular integral operatorJun 24 2005Sep 11 2005We extend Krupnik's criterion of self-adjointness of the Cauchy singular integral operator to the case of finitely connected domains. The main aim of the paper is to present a new approach for proof of the criterion.

Soft factors for double parton scattering at NNLOAug 17 2016Dec 05 2016We show at NNLO that the soft factors for double parton scattering (DPS) for both integrated and unintegrated kinematics, can be presented entirely in the terms of the soft factor for single Drell-Yan process, i.e. the transverse momentum dependent (TMD) ... More

On quadrilateral orbits in complex algebraic planar billiardsSep 07 2013Jan 27 2014The famous conjecture of V.Ya.Ivrii (1978) says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study the complex algebraic version of Ivrii's conjecture ... More

A nice limaçon-like spiralSep 22 2013Oct 07 2013A lima\c{c}on-like curve, allowing 2{\pi}-transition with monotone curvature between concentric curvature elements, is presented. The curve is 4th degree algebraic, 4th degree rational, and shares other common features with Pascal's lima\c{c}on.

Asymptotic approximations to the Hardy-Littlewood functionApr 09 2012The function $Q(x):=\sum_{n\ge 1} (1/n) \sin(x/n)$ was introduced by Hardy and Littlewood [10] in their study of Lambert summability, and since then it has attracted attention of many researchers. In particular, this function has made a surprising appearance ... More

On the distribution of exponential functionals for Levy processes with jumps of rational transformNov 16 2010Jan 27 2012We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou on the processes with hyper-exponential jumps [N. Cai ... More

Difference integrability conditions for parameterized linear difference and differential equationsMay 02 2013Dec 23 2013This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference isomonodromic with respect ... More

Differential Tannakian CategoriesJul 16 2008Feb 24 2009We define a differential Tannakian category and show that under a natural assumption it has a fibre functor. If in addition this category is neutral, that is, the target category for the fibre functor are finite dimensional vector spaces over the base ... More

On 4-reflective complex analytic planar billiardsMay 23 2014Dec 17 2015The famous conjecture of V.Ya.Ivrii says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study its complex analytic version for quadrilateral orbits ... More

The Galois closure of the Garcia-Stichtenoth towerApr 21 2005We describe the Galois closure of the Garcia-Stichtenoth tower and prove that it is optimal.

On transversal connecting orbits of Lagrangian systems in non-stationary force field: Newton-Kantorovich approachApr 02 2019We consider a natural Lagrangian system defined on a complete Riemannian manifold being subjected to the action of a non-stationary force field with potential $U(q,t) = f(t)V(q)$. It is assumed that the factor $f(t)$ tends to $\infty$ as $t\to \pm\infty$ ... More

Stability of fully discrete variational schemes for elastodynamics with a polyconvex stored energyNov 09 2016In this article we develop a fully discrete variational scheme that approximates the equations of three dimensional elastodynamics with polyconvex stored energy. The fully discrete scheme is based on a time-discrete variational scheme developed by S.~Demoulini, ... More

Stable operations and cooperations in derived Witt theory with rational coefficientsApr 19 2015Mar 06 2017The algebras of stable operations and cooperations in derived Witt theory with rational coefficients are computed and an additive description of cooperations in derived Witt theory is given. The answer is parallel to the well-known case of K-theory of ... More

On intersection of two embedded spheres in 3-spaceNov 03 2011Dec 10 2011This article is covered by the article arxiv.1012.0925 We study intersection of two polyhedral spheres without self-intersections in 3-space. We find necessary and sufficient conditions on sequences x = x_1,x_2,...,x_n, y = y_1,y_2,...,y_n of positive ... More

Optimal curves of low genus over finite fieldsJun 28 2007Aug 31 2011The Hasse-Weil-Serre bound is improved for curves of low genera over finite fields with discriminant in {-3,-4,-7,-8,-11,-19} by studying optimal curves.

On a scenario of onset of strongly dissipative mixed dynamicsDec 30 2017Jan 09 2018In this paper we present the scenario of the occurrence of strongly dissipative mixed dynamics in two-dimensional reversible diffeomorphisms, using as an example the system describing a motion of two point vortices under the influence of wave perturbation ... More

Faster Polynomial Multiplication via Discrete Fourier TransformsOct 06 2010We study the complexity of polynomial multiplication over arbitrary fields. We present a unified approach that generalizes all known asymptotically fastest algorithms for this problem. In particular, the well-known algorithm for multiplication of polynomials ... More

Instability of nondiscrete free subgroups in Lie groupsSep 28 2004Feb 07 2011We study finitely-generated nondiscrete free subgroups in Lie groups. We address the following question first raised by \'Etienne Ghys: is it always possible to make arbitrarily small perturbation of the generators of the free subgroup in such a way that ... More

Actions of Ore extensions and growth of polynomial $H$-identitiesMay 12 2015May 17 2017We show that if $A$ is a finite dimensional associative $H$-module algebra for an arbitrary Hopf algebra $H$, then the proof of the analog of Amitsur's conjecture for $H$-codimensions of $A$ can be reduced to the case when $A$ is $H$-simple. (Here we ... More

Open--constructible functionsFeb 08 2013Jan 11 2014We prove that if a continuous function $f : X \to f(X)$ takes open sets into elements of the Boolean algebra generated by open and closed subsets in $f(X)$, then there exist $X_n \subset X,$ $(n \in \omega)$ such that $f$ is open on every $X_n$ and $f(X_n)$ ... More

General Slit Stochastic Löwner Evolution and Conformal Field TheoryOct 14 2015Jun 02 2016This monograph is dedicated to a generalization of the L\"owner equation in its stochastic form known as SLE and to its coupling with the Gaussian free field, ultimately aiming at the construction of a boundary conformal field theory with one free scalar ... More

Coupled-Beam and Coupled-Bunch InstabilitiesJun 23 2016A problem of coupled-beam instability is solved for two multibunch beams with slightly different revolution frequencies, as in the Fermilab Recycler Ring (RR). Sharing of the inter-bunch growth rates between the intra-bunch modes is described. The general ... More

Antiproton Stacking in the RecyclerJul 09 2003Possibilities to accumulate antiprotons in the Recycler are considered for three different cases: with current stochastic cooling, with upgraded stochastic cooling and with electron cooling. With stochastic cooling only, even upgraded, Recycler looks ... More

Lower bounds for the simplexity of the n-cubeOct 21 2009Dec 23 2012In this paper we prove a new asymptotic lower bound for the minimal number of simplices in simplicial dissections of $n$-dimensional cubes. In particular we show that the number of simplices in dissections of $n$-cubes without additional vertices is at ... More

An Upper Bound on the Minimum Distance of LDPC Codes over GF(q)Feb 24 2015In [1] a syndrome counting based upper bound on the minimum distance of regular binary LDPC codes is given. In this paper we extend the bound to the case of irregular and generalized LDPC codes over GF(q). The comparison to the lower bound for LDPC codes ... More

Symmetric measures via momentsJun 09 2004May 14 2008Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection, namely, one between ... More

Asymptotic properties of Dedekind zeta functions in families of number fieldsDec 02 2009The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $\Re s > 1/2$ in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization ... More

On density of horospheres in dynamical laminationsMay 24 2006Feb 11 2010In 1985 D.Sullivan had introduced a dictionary between two domains of complex dynamics: iterations of rational functions on the Riemann sphere and Kleinian groups. The latters are discrete subgroups of the group of conformal automorphisms of the Riemann ... More

QSOs and the hard x-ray backgroundAug 06 1995We calculate the contribution to the cosmic x-ray background (CXB) of a population of power law spectrum sources with spectral indices distributed over a broad range of values. The composite spectrum of this source population is significantly harder than ... More

Algorithmic statistics: normal objects and universal modelsDec 14 2015Kolmogorov suggested to measure quality of a statistical hypothesis $P$ for a data $x$ by two parameters: Kolmogorov complexity $C(P)$ of the hypothesis and the probability $P(x)$ of $x$ with respect to $P$. P. G\'acs, J. Tromp, P.M.B. Vit\'anyi discovered ... More

Note on the covering theorem for complex polynomialsOct 24 2014In this note we give the answer to the question posed by V. N. Dubinin concerning covering properties of complex polynomials

On tractrices of planar curvesJul 15 2012Tractrices of planar curves, in particular, a family of tractrices of a circle, are considered. Some new observations (including arc-length parametrization, Chezaro equation) and corrected reference informations are provided. The article is written in ... More

Kerov's interlacing sequences and random matricesNov 07 2012To a $N \times N$ real symmetric matrix Kerov assigns a piecewise linear function whose local minima are the eigenvalues of this matrix and whose local maxima are the eigenvalues of its $(N-1) \times (N-1)$ submatrix. We study the scaling limit of Kerov's ... More

Quantum memory for light using extended atomic ensembles in a tunable cavityAug 19 2008Sep 22 2008Cavity-assisted storage and retrieval of single-photon wave packets in optically thin spatially extended resonant materials are analyzed. It is shown that the use of cavity tuning allows one to store and recall time-symmetric double-sided exponential ... More

Geometric Description of Epimorphic SubgroupsJul 08 2010Oct 30 2010Let $G$ be an affine algebraic group over an algrebraically closed field $\mathbb K$ of characteristic 0 and $H$ be a subgroup of $G$. The stabilizer of all the set of all vector-functions of $\mathbb K[G]^H$ with respect to the right action of $H$ is ... More

Dependence of transport through carbon nanotubes on local Coulomb potentialAug 03 2006In this paper, we present the results of helium temperature transport measurements through carbon nanotubes using an AFM conductive tip as a mobile gate. In semiconducting nanotubes we observe shifting of the conductance peaks with changing of the AFM ... More

Global attractors of evolutionary systemsSep 13 2006An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes equations ... More

Simple proofs of uniformization theoremsOct 04 2005The measurable Riemann mapping theorem proved by Morrey and in some particular cases by Ahlfors, Lavrentiev and Vekua, says that any measurable almost complex structure on $\rd$ ($S^2$) with bounded dilatation is integrable: there is a quasiconformal ... More

Elliptic law for real random matricesJan 08 2012Aug 05 2012In this paper we consider ensemble of random matrices $\X_n$ with independent identically distributed vectors $(X_{ij}, X_{ji})_{i \neq j}$ of entries. Under assumption of finite fourth moment of matrix entries it is proved that empirical spectral distribution ... More

On curves with Poritsky propertyJan 07 2019For a given closed convex planar curve $\gamma$ with smooth boundary and a given $p>0$, the string construction yields a family of curves $\Gamma_p$ for which $\gamma$ is a caustic. The action of the reflection $T_p$ on the tangent lines to $\gamma\simeq ... More

Modelling Solutions to the Kdv-Burgers Equation in the Case of Non-homogeneous Dissipative MediaJul 12 2017We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with finite dissipation. The modelling included the case of a finite dissipative layer similar to a wave passing through the air-glass-air as well ... More

Tannakian categories, linear differential algebraic groups, and parameterized linear differential equationsMar 14 2007Sep 16 2008We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations ... More

On odd-periodic orbits in complex planar billiardsSep 07 2013The famous conjecture of V.Ya.Ivrii (1978) says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study the complex version of Ivrii's conjecture for ... More

Herman's Theory Revisited (Extension)Jun 30 2007Oct 13 2007We prove that a $C^{3+\beta}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\beta<\delta<1$, is $C^{2+\beta-\delta}$-smoothly conjugate to a rigid rotation.

An Inverse Problem for Sturm-Liouville Operators on the Half-line Having Bessel-type Singularity in an Interior PointNov 11 2012We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution ... More

On free regular and Bondesson convolution semigroupsOct 16 2018Free regular convolution semigroups describe the distribution of free subortinators, while Bondesson class convolution semigroups correspond to classical subordinators with completely monotone Levy density. We show that these two classes of convolution ... More

Estimating the Distribution of DisplacementsDec 28 2016Feb 06 2018In this paper, we propose a method for estimating the distribution of time differences between connected events (such as ad impressions and corresponding customer calls). A special feature of this method is that it does not require matching those connected ... More

On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of double confluent Heun equationMay 07 2018Jun 21 2018We will discuss the model of the overdamped Josephson junction in superconductivity, which is given by a family of first order non-linear ordinary differential equations on two-torus depending on three parameters: a fixed parameter $\omega$ (the frequency); ... More

On the density of the supremum of a stable processDec 19 2011We study the density of the supremum of a strictly stable L\'evy process. As was proved recently in F. Hubalek and A. Kuznetsov "A convergent series representation for the density of the supremum of a stable process" (Elect. Comm. in Probab., 16, 84-95, ... More

Series representations and asymptotic expansions for the density of the supremum of a stable processFeb 02 2010Jun 14 2010We derive explicit asymptotic expansions of the density of the supremum of a strictly stable process when the index $\alpha$ is not rational. In the case when parameters $\alpha$ and $\rho=\p(X_1>0)$ satisfy $\rho+k=l/\alpha$ for some integers $k,l \ge ... More

Average estimate for additive energy in prime fieldJul 23 2011Assume that $A\subseteq \Fp, B\subseteq \Fp^{*}$, $\1/4\leqslant\frac{|B|}{|A|},$ $|A|=p^{\alpha}, |B|=p^{\beta}$. We will prove that for $p\geqslant p_0(\beta)$ one has $$\sum_{b\in B}E_{+}(A, bA)\leqslant 15 p^{-\frac{\min\{\beta, 1-\alpha\}}{308}}|A|^3|B|.$$ ... More

Additive properties of product sets in an arbitrary finite fieldJan 14 2008It is proved that for any two subsets $A$ and $B$ of an arbitrary finite field $\Fq$ such that $|A||B|>q$ the identity $16AB=\Fq$ holds. Moreover, it is established that for every subsets $X, Y\subset \Fq$ with the property $|X||Y|\geqslant 2q$ the equality ... More

Finitely generated infinite simple groups of infinite square width and vanishing stable commutator lengthSep 14 2009Sep 07 2010It is shown that there exist finitely generated infinite simple groups of infinite commutator width and infinite square width on which there exists no stably unbounded conjugation-invariant norm, and in particular stable commutator length vanishes. Moreover, ... More

On the push-forwards for motivic cohomology theories with invertible stable Hopf elementJun 11 2014Oct 23 2015We present a geometric construction of push-forward maps along projective morphisms for cohomology theories representable in the stable motivic homotopy category assuming that the element corresponding to the stable Hopf map is inverted in the coefficient ... More

Non-invertibility in Some Heteroscedastic ModelsApr 17 2011Dec 16 2012In order to calculate the unobserved volatility in conditional heteroscedastic time series models, the natural recursive approximation is very often used. Following \cite{StraumannMikosch2006}, we will call the model \emph{invertible} if this approximation ... More

Why state of quantum system is fully defined by density matrixJan 29 2016We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in the density ... More

A linear bound on the Manickam-Miklos-Singhi ConjectureAug 09 2013Suppose that we have a set of numbers x_1, ..., x_n which have nonnegative sum. How many subsets of k numbers from {x_1, ..., x_n} must have nonnegative sum? Manickam, Miklos, and Singhi conjectured that for n at least 4k the answer is (n-1 \choose k-1). ... More