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On the timescale at which statistical stability breaks downJul 10 2018In dynamical systems, understanding statistical properties shared by most orbits and how these properties depend on the system are basic and important questions. Statistical properties may persist as one perturbs the system (\emph{statistical stability} ... More

Superdiffusive limits for deterministic fast-slow dynamical systemsJul 10 2019We consider deterministic fast-slow dynamical systems on $\mathbb{R}^m\times Y$ of the form \[ \begin{cases} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/\alpha} b(x_k^{(n)}) v(y_k)\;,\quad y_{k+1} = f(y_k)\;, \end{cases} \] where $\alpha\in(1,2)$. ... More

Linear response for intermittent maps with summable and nonsummable decay of correlationsAug 26 2015Apr 27 2016We consider a family of Pomeau-Manneville type interval maps $T_\alpha$, parametrized by $\alpha \in (0,1)$, with the unique absolutely continuous invariant probability measures $\nu_\alpha$, and rate of correlations decay $n^{1-1/\alpha}$. We show that ... 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

Deterministic homogenization for discrete-time fast-slow systems under optimal moment assumptionsMar 25 2019We consider discrete-time fast-slow systems of the form $$ X^{(n)}_{k+1} = X^{(n)}_k + n^{-1}a_n(X_k^{(n)},Y_k^{(n)}) + n^{-1/2}b_n(X_k^{(n)},Y_k^{(n)})\;, \quad Y_{k+1}^{(n)} = T_nY_k^{(n)}\;.$$ We give conditions under which the dynamics of the slow ... More

Stable regimes for hard disks in a channel with twisting wallsNov 20 2011Mar 07 2012We study a gas of $N$ hard disks in a box with semi-periodic boundary conditions. The unperturbed gas is hyperbolic and ergodic (these facts are proved for N=2 and expected to be true for all $N\geq 2$). We study various perturbations by twisting the ... More

Some eigenstates for a model associated with solutions of tetrahedron equation. II. A bit of algebraizationFeb 19 1997This paper adds two observations to the work solv-int/9701016 where some eigenstates for a model based on tetrahedron equation have been constructed. The first observation is that there exists a more "algebraic" construction of one-particle states, resembling ... More

Polynomial-valued constant hexagon cohomologyApr 15 2019Hexagon relations are algebraic realizations of four-dimensional Pachner moves. `Constant' -- not depending on a 4-simplex in a triangulation of a 4-manifold -- hexagon relations are proposed, and their polynomial-valued cohomology is constructed. This ... More

Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz GasAug 12 2011We investigate analytically and numerically the spatial structure of the non-equilibrium stationary states (NESS) of a point particle moving in a two dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a constant external electric ... More

Autonomous evolution of electron speeds in a thermostatted system: exact resultsAug 31 2018May 09 2019We investigate a dynamical system consisting of $N$ particles moving on a $d$-dimensional torus under the action of an electric field $E$ with a Gaussian thermostat to keep the total energy constant. The particles are also subject to stochastic collisions ... More

Speed Distribution of N Particles in the Thermostated Periodic Lorentz Gas with a FieldOct 29 2012We study the long time evolution and stationary speed distribution of N point particles in 2D moving under the action of an external field E, and undergoing elastic collisions with either a fixed periodic array of convex scatterers, or with virtual random ... More

Autonomous evolution of electron speeds in a thermostatted system: exact resultsAug 31 2018We investigate a dynamical system consisting of $N$ particles moving on a $d$-dimensional torus under the action of an electric field $E$ with a Gaussian thermostat to keep the total energy constant. The particles are also subject to stochastic collisions ... More

A finite-dimensional TQFT for three-manifolds based on group PSL(2, C) and cross-ratiosSep 24 2008In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its key ingredient ... More

Multiscale systems, homogenization, and rough pathsDec 04 2017Mar 25 2019In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey ... 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

A criterion for left-orthogonality of an effective divisor on a surfaceOct 07 2016Oct 31 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).

Descent theory for semiorthogonal decompositionsJun 13 2012In this paper a method of constructing a semiorthogonal decomposition of the derived category of $G$-equivariant sheaves on a variety $X$ is described, provided that the derived category of sheaves on $X$ admits a semiorthogonal decomposition, whose components ... More

Cohomological descent theory for a morphism of stacks and for equivariant derived categoriesMar 16 2011In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As a corollary, ... More

Search for exclusive photoproduction of $Z_c(3900)$ at COMPASSNov 09 2015The $Z_{c}(3900)$ hadron state has been found by the BES-III and Belle experiments in the decay of the hadron state with higher mass. The first attempt to search for the direct exclusive production of the $Z_c^{\pm}(3900)$ hadron by virtual photons has ... More

#P- and $\oplus$P- completeness of counting roots of a sparse polynomialAug 08 2016We improve and simplify the result of the part 4 of "Counting curves and their projections" (Joachim von zur Gathen, Marek Karpinski, Igor Shparlinski) by showing that counting roots of a sparse polynomial over $\mathbb{F}_{2^n}$ is #P- and $\oplus$P-complete ... More

A Step from Probabilistic Programming to Cognitive ArchitecturesMay 04 2016Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive architectures for extending ... More

Normal forms for linear displacement context-free grammarsJul 30 2015In this paper we prove several results on normal forms for linear displacement context-free grammars. The results themselves are rather simple and use well-known techniques, but they are extensively used in more complex constructions. Therefore this article ... More

On Helly number for crystals and cut-and-project setsMay 25 2016May 26 2016We prove existence of Helly numbers for crystals and for cut-and-project sets with convex window. Also we show that for a two-dimensional crystal consisting of $k$ copies of a single lattice the Helly number does not exceed $k+6$.

Generalization of Deuring Reduction TheoremSep 24 2012In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety $A$, arising after reduction of an Abelian variety with complex multiplication by a CM field $K$ over ... More

Geometric mesoscopic correlations in quasi-one dimensionJun 10 2007We study analytically and numerically field/intensity correlations in wave transport through volume-disordered waveguide. The obtained channel and spacial correlations deviate from those found in framework of Dorokhov-Mello-Pereyra-Kumar (DMPK) formalism, ... More

Bounds for Bilinear Complexity of Noncommutative Group AlgebrasMar 24 2010We study the complexity of multiplication in noncommutative group algebras which is closely related to the complexity of matrix multiplication. We characterize such semisimple group algebras of the minimal bilinear complexity and show nontrivial lower ... More

Complex wave dynamics in a rugby microballs with semiconductor active mirrorsJul 11 2003Feb 26 2007The optical implementation of complex network is considered for laser cavity formed by active mirrors deposited on the surface of ellipsoidal semiconductor microball having size of about 1 mm, whose eccentricity close to 0.5 and equivalent optical circuit, ... More

Structure of rapidity divergences in soft factorsJul 24 2017Sep 28 2017We discuss the structure of rapidity divergences that are presented in the soft factors of transverse momentum dependent (TMD) factorization theorems. To provide the discussion on the most general level we consider soft factors for multi-parton scattering. ... More

Proof of the List Coloring Conjecture for line perfect multigraphsApr 14 2019We prove that for a line perfect multigraph the chromatic index is equal to the list chromatic index. This is a generalization of Galvin's result on bipartite multigraphs.

Transverse Instabilities of a Bunch with Space Charge, Wake and FeedbackSep 18 2018When a resistive feedback and single-bunch wake act together, it is known that some head-tail modes may become unstable even without space charge. This feedback-wake instability, FWI, modified by space charge to a certain degree, is shown to have a special ... More

Convective Instabilities of Bunched Beams with Space ChargeJul 13 2018Apr 07 2019For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI. For sufficiently ... More

SL-oriented cohomology theoriesJan 06 2019We show that a representable motivic cohomology theory admits a unique normalized SL^c-orientation if the zeroth cohomology presheaf is a Zariski sheaf. We also construct Thom isomorphisms in SL-oriented cohomology for SL^c-bundles and obtain new results ... More

Spatial limit theorem for interval exchange transformationsJan 17 2019We prove a spatial limit theorem for generic interval exchange transformations (IETs): for a generic IET the normalized ergodic sums of a sufficiently regular (e.g., Lipschitz) function have the same asymptotic behavior of distributions as the behaviour ... More

PIT for depth-$4$ circuits and Sylvester-Gallai conjecture for polynomialsFeb 19 2019This text is a development of a preprint of Ankit Gupta. We present an approach for devising a deterministic polynomial time blackbox identity testing (PIT) algorithm for depth-$4$ circuits with bounded top fanin. This approach is similar to Kayal-Shubhangi ... More

On commuting billiards in higher dimensionsJul 27 2018Aug 07 2018We consider two nested billiards in $\mathbb R^n$, $n\geq3$, with smooth strictly convex boundaries. We prove that if the corresponding actions by reflections on the space of oriented lines commute, then the billiards are confocal ellipsoids. This together ... More

Covering by homothets and illuminating convex bodiesMay 25 2019The paper is devoted to coverings by translative homothets and illuminations of convex bodies. For a given positive number $\alpha$ and a convex body $B$, $g_{\alpha}(B)$ is the infimum of $\alpha$-powers of finitely many homothety coefficients less than ... More

Milnor Attractors of Skew Products with the Fiber a CircleAug 10 2015Jul 15 2016We prove that for a generic skew product with circle fiber over an Anosov diffeomorphism the Milnor attractor (also called the likely limit set) coincides with the statistical attractor, is Lyapunov stable, and either has zero Lebesgue measure or coincides ... More

Covering by homothets and illuminating convex bodiesMay 25 2019Jun 02 2019The paper is devoted to coverings by translative homothets and illuminations of convex bodies. For a given positive number $\alpha$ and a convex body $B$, $g_{\alpha}(B)$ is the infimum of $\alpha$-powers of finitely many homothety coefficients less than ... More

On π-surfaces of four-dimensional parallelohedraSep 29 2013We show that every four-dimensional parallelohedron P satisfies a recently found condition of Garber, Gavrilyuk & Magazinov sufficient for the Voronoi conjecture being true for P. Namely we show that for every four-dimensional parallelohedron P the group ... More

An approximate version of a conjecture of Aharoni and BergerSep 20 2016May 24 2018Aharoni 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. This conjecture generalizes a longstanding problem of ... More

The special linear version of the projective bundle theoremMay 28 2012Jun 25 2013A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). For a representable ring cohomology theory A(-) with a special linear orientation and invertible stable ... More

The Brauer-Siegel and Tsfasman-Vladut Theorems for Almost Normal Extensions of Number FieldsNov 04 2004The classical Brauer-Siegel theorem states that if $k$ runs through the sequence of normal extensions of $\mathbb{Q}$ such that $n_k/\log|D_k|\to 0,$ then $\log h_k R_k/\log \sqrt{|D_k|}\to 1.$ First, in this paper we obtain the generalization of the ... More

Edge disjoint Hamiltonian cycles in highly connected tournamentsJun 29 2014Thomassen conjectured that there is a function $f(k)$ such that every strongly $f(k)$-connected tournament contains $k$ edge-disjoint Hamiltonian cycles. This conjecture was recently proved by K\"uhn, Lapinskas, Osthus, and Patel who showed that $f(k)\leq ... More

On Dirichlet series and functional equationsMar 26 2017Apr 07 2017There exist many explicit evaluations of Dirichlet series. Most of them are constructed via the same approach: by taking products or powers of Dirichlet series with a known Euler product representation. In this paper we derive a result of a new flavour: ... More

Finite-dimensional representations of minimal nilpotent W-algebras and zigzag algebrasOct 11 2016Dec 24 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

On intersection of two embedded spheres in 3-spaceDec 04 2010Jun 13 2013We 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 integers, for existence of 2-dimensional polyhedra f,g ... More

Calculating Ramsey numbers by partitioning coloured graphsSep 16 2013In this paper we prove a new result about partitioning coloured complete graphs and use it to determine certain Ramsey numbers exactly. The partitioning theorem we prove is that for k at least 1, in every edge colouring of a complete graph with the colours ... More

Partitioning edge-coloured complete graphs into monochromatic cycles and pathsMay 24 2012A conjecture of Erd\H{o}s, Gy\'arf\'as, and Pyber says that in any edge-colouring of a complete graph with r colours, it is possible to cover all the vertices with r vertex-disjoint monochromatic cycles. So far, this conjecture has been proven only for ... More

Stochastic calculus of variations for general Lévy processes and its applications to jump-type SDE's with non-degenerated driftJun 18 2006Jan 25 2007We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of the noise, ... More

Majorana Dark MatterDec 04 2006Jan 09 2007In this letter in the framework of a simple see-saw scenario with two (or three) quasi degenerate Majorana neutrinos we propose that one of these neutrinos can be very weakly coupled, yet there is a mechanism of the generation of the abundance of such ... More

Wiener-Hopf factorization and distribution of extrema for a family of Lévy processesNov 08 2010In this paper we introduce a ten-parameter family of L\'{e}vy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes ... More

On torsion-free groups with finite regular file basesApr 21 2005Apr 20 2007The following question was asked by V. V. Bludov in The Kourovka Notebook in 1995: If a torsion-free group $G$ has a finite system of generators $a_1$, ..., $a_n$ such that every element of $G$ has a unique presentation in the form $a_1^{k_1}... a_n^{k_n}$ ... More

Diagrams with Selection and Method for Constructing Boundedly Generated and Boundedly Simple GroupsApr 26 2004Feb 18 2006The existence of an infinite simple boundedly generated 2-generated group and the existence of a boundedly simple 2-generated group containing a free non-cyclic subgroup are proved.

Blow-up in finite time for the dyadic model of the Navier-Stokes equationsJan 04 2006Jun 08 2006We study the dyadic model of the Navier-Stokes equations introduced by Katz and Pavlovi\'c. They showed a finite time blow-up in the case where the dissipation degree $\alpha$ is less than 1/4. In this paper we prove the existence of weak solutions for ... More

Factorizations and invariant subspaces for weighted Schur classesOct 07 2005We study factorizations of operator valued functions of weighted Schur classes over multiply-connected domains. There is a correspondence between functions from weighted Schur classes and so-called ``conservative curved'' systems introduced in the paper. ... 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

Efficiency of feedbacks for suppression of transverse instabilities of bunched beamsMay 20 2016Which gain and phase have to be set for a bunch-by-bunch transverse damper, and at which chromaticity it is better to stay? These questions are considered for three models: the two-particle model with possible quadrupole wake, the author's Nested Head-Tail ... More

Transverse modes for flat inter-bunch wakesJan 08 2013If inter-bunch wake fields are flat, i.e. their variations over a bunch length can be neglected, all coherent modes have the same coupled-bunch structure, provided the bunches can be treated as identical by their inner qualities (train theorem). If a ... 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

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

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

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

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

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

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

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

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

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 polynomially integrable Birkhoff billiards on surfaces of constant curvatureJun 13 2017Feb 22 2019We present a solution of the algebraic version of Birkhoff Conjecture on integrable billiards. Namely we show that every polynomially integrable real bounded convex planar billiard with smooth boundary is an ellipse. We extend this result to billiards ... 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

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

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

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 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

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

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

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

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

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

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 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

On the Extremal Maximum Agreement Subtree ProblemDec 17 2018Given two phylogenetic trees with the $\{1, \ldots, n\}$ leaf-set the maximum agreement subtree problem asks what is the maximum size of the subset $A \subseteq \{1, \ldots, n\}$ such that the two trees are equivalent when restricted to $A$. The long-standing ... More

On the optimal focusing of solitons and breathers in long wave modelsAug 29 2018Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to other long-wave ... 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