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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Growth of graph powersMay 14 2010For a graph G, its rth power is constructed by placing an edge between two vertices if they are within distance r of each other. In this note we study the amount of edges added to a graph by taking its rth power. In particular we obtain that either the ... 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

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

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

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

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

On approximation of planar curves by circular arcs with length preservationApr 25 2016Jul 03 2016The method for approximation of planar curve by circular arcs with length preservation, proposed by I.Kh. Sabitov and A.V. Slovesnov, is analyzed. We extend the applicability of the method, and consider some corollaries, not related to the approximation ... More

Lie algebras simple with respect to a Taft algebra actionMay 16 2017Oct 12 2018We classify finite dimensional $H_{m^2}(\zeta)$-simple $H_{m^2}(\zeta)$-module Lie algebras $L$ over an algebraically closed field of characteristic $0$ where $H_{m^2}(\zeta)$ is the $m$th Taft algebra. As an application, we show that despite the fact ... 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

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

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

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

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

Computing the truncated theta function via Mordell integralJun 18 2013Mar 24 2014Hiary [3] has presented an algorithm which allows to evaluate the truncated theta function $\sum_{k=0}^n \exp(2\pi \i (zk+\tau k^2))$ to within $\pm \epsilon$ in $O(\ln(\tfrac{n}{\epsilon})^{\kappa})$ arithmetic operations for any real $z$ and $\tau$. ... More

Operations on t-structures and perverse coherent sheavesAug 12 2013The notions of consistent pairs and consistent chains of t-structures are introduced. A theorem that two consistent chains of t-structures generate a distributive lattice is proven. The technique developed is then applied to the pairs of chains obtained ... More

Identifier Namespaces in Mathematical NotationJan 13 2016In this thesis, we look at the problem of assigning each identifier of a document to a namespace. At the moment, there does not exist a special dataset where all identifiers are grouped to namespaces, and therefore we need to create such a dataset ourselves. ... More

Argument shift method and sectional operators: applications to differential geometryFeb 09 2016This paper does not contain any new results, it is just an attempt to present, in a systematic way, one construction which establishes an interesting relationship between some ideas and notions well-known in the theory of integrable systems on Lie algebras ... More

Finitely generated infinite simple groups of infinite commutator widthAug 28 2006Sep 12 2009It is shown that there exists a finitely generated infinite simple group of infinite commutator width, and that the commutator width of a finitely generated infinite boundedly simple group can be arbitrarily large. Besides, such groups can be constructed ... More

On the relation of special linear algebraic cobordism to Witt groupsDec 23 2012Oct 23 2015We reconstruct derived Witt groups via special linear algebraic cobordism. There is a morphism of ring cohomology theories which sends the canonical Thom class in special linear cobordism to the Thom class in the derived Witt groups. We show that for ... More

The geometric meaning of Zhelobenko operatorsJun 18 2012Aug 16 2013Let g be the complex semisimple Lie algebra associated to a complex semisimple algebraic group G, b a Borel subalgebra of g, h the Cartan sublagebra contained in b and N the unipotent subgroup of G corresponding to the nilradical n of b. We show that ... More

Explicit Hermite-type eigenvectors of the discrete Fourier transformJan 30 2015The search for a canonical set of eigenvectors of the discrete Fourier transform has been ongoing for more than three decades. The goal is to find an orthogonal basis of eigenvectors which would approximate Hermite functions -- the eigenfunctions of the ... More

Predicting Single-Temperature Fit to Multi-Component Thermal Plasma SpectraApr 05 2005Nov 25 2005Observed X-ray spectra of hot gas in clusters, groups, and individual galaxies are commonly fit with a single-temperature thermal plasma model even though the beam may contain emission from components with different temperatures. Recently, Mazzotta et ... More

Upper bounds of topology of complex polynomials in two variablesSep 30 2005The paper deals with a complex polynomial $H$ in two variables having - a generic highest homogeneous part (without multiple zero lines), - nonconstant lower terms. In particular, under these conditions the polynomial $H$ has at least two distinct critical ... More

Note on the best approximation in $L^1$ metricJul 18 2016We present one of the approaches to find the best approximation of the given function by trigonometric polynomials in $L^1$ metric and applied it to find the optimal constants in the Nikolsky's type inequality, concerning approximation of Lipschitz functions ... More

Structure Function and Variability Mechanism of Quasars from SDSS Stripe 82Jul 21 2011Aug 30 2011Theoretical predictions for the ensemble quasar structure function are tested using multi-epoch observations of Stripe 82 collected by the Sloan Digital Sky Survey. We reanalyze the entire available volume of the g-band imaging data using difference image ... More

An approximate version of a conjecture of Aharoni and BergerSep 20 2016Aharoni and Berger conjectured that in every proper edge-colouring of a bipartite multigraph by $n$ colours with at least $n+1$ edges of each colour there is a rainbow matching using every colour. Here an approximate version of this conjecture is proved ... More

A geometric approach to (g, k)-modules of finite typeMay 25 2011Let $g$ be a semisimple Lie algebra over $\mathbb C$ and $k$ be a reductive in $g$ subalgebra. We say that a simple $g$-module $M$ is a $(g; k)$-module if as a $k$-module $M$ is a direct sum of finite-dimensional $k$-modules. We say that a simple $(g; ... More

Wiener-Hopf factorization for a family of Levy processes related to theta functionsJan 27 2012In this paper we study the Wiener-Hopf factorization for a class of L\'evy processes with double-sided jumps, characterized by the fact that the density of the L\'evy measure is given by an infinite series of exponential functions with positive coefficients. ... More

Zigzag algebras and finite-dimensional representations of minimal nilpotent W-algebrasOct 11 2016Let $\frak g$ be a simple finite-dimensional Lie algebra over an algebraically closed field $\mathbb F$ of characteristic 0. We denote by $\operatorname{U}(\frak g)$ the universal enveloping algebra of $\frak g$. To any nilpotent element $e\in \frak g$ ... More

First, Second and Third Massive Stars in Open ClustersDec 20 2010The goal of this paper is to study possibilities of using first, second and third massive stars in open clusters to estimate total cluster mass and membership. We built estimator functions with the use of numerical simulations and analytical approximations ... More

On nonlinear superposition of shock waves for the KdV-Burgers equationApr 02 2016Superposition of explicit (analytic) monotone non-increasing shock waves for the KdV-Burgers equation is studied, modelled numerically and graphically presented. Initial profile chosen as a sum of two such shock waves gradually transforms into a single ... More

6-dimensional FJRW theories of the simple-elliptic singularitiesOct 24 2016We give explicitly in the closed formulae the genus zero primary potentials of the three 6-dimensional FJRW theories of the simple-elliptic singularity $\tilde E_7$ with the non-maximal symmetry groups. For each of these FJRW theories we establish the ... More

Two-point G$^2$ Hermite interpolation with spirals by inversion of conics: summaryJan 29 2014Feb 01 2014The article completes the research of two-point G$^2$ Hermite interpolation problem with spirals by inversion of conics. A simple algorithm is proposed to construct a family of 4th degree rational spirals, matching given G$^2$ Hermite data. A possibility ... More

Countable open and closed functionsFeb 09 2011Nov 24 2011We define two natural classes of functions, called 2-open and 2-closed, that are closest to open and closed functions. We show that they have the following property: there are $X_i \subset X$ $ (i=1,2,...$) such that $f|X_i$ are open or closed functions ... More

Equidistribution for nonuniformly expanding dynamical systems, and application to the almost sure invariance principleJan 13 2017Nov 08 2017Let $T \colon M \to M$ be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let $v \colon M \to \mathbb{R}^d$ be an observable and $v_n = \sum_{k=0}^{n-1} v \circ T^k$ denote the Birkhoff sums. Given a probability measure ... More

Partitioning a graph into a cycle and a sparse graphJul 12 2016Jul 25 2016In this paper we investigate results of the form "every graph $G$ has a cycle $C$ such that the induced subgraph of $G$ on $V(G)\setminus V(C)$ has small maximum degree." Such results haven't been studied before, but are motivated by the Bessy and Thomass\'e ... More

On consistency of optimal pricing algorithms in repeated posted-price auctions with strategic buyerJul 17 2017Feb 08 2018We study revenue optimization learning algorithms for repeated posted-price auctions where a seller interacts with a single strategic buyer that holds a fixed private valuation for a good and seeks to maximize his cumulative discounted surplus. For this ... 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

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

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

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

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

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.

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

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.

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.

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.

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

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.

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

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

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

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