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Video Distortion Method for VMAF Quality Values IncreasingJul 10 2019Video quality measurement takes an important role in many applications. Full-reference quality metrics which are usually used in video codecs comparisons are expected to reflect any changes in videos. In this article, we consider different colour corrections ... More

On uniquely k-determined permutationsOct 10 2006There are several approaches to study occurrences of consecutive patterns in permutations such as the inclusion-exclusion method, the tree representations of permutations, the spectral approach and others. We propose yet another approach to study occurrences ... More

Partial hyperbolicity and central shadowingDec 19 2011Feb 11 2012We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof is based on ... More

Physical conditions in nearby active galaxies correlated with ultra-high-energy cosmic rays detected by the Pierre Auger ObservatoryAug 04 2008Mar 29 2010We analyze the active-galaxy correlation reported in 2007 by the Pierre Auger Collaboration. The signal diminishes if the correlation-function approach (counting all "source-event" pairs and not only "nearest neighbours") is used, suggesting that the ... More

Zeroes of the spectral density of the periodic Schroedinger operator with Wigner-von Neumann potentialFeb 25 2011We consider the Schroedinger operator L_{\alpha} on the half-line with a periodic background potential and the Wigner-von Neumann potential of Coulomb type: csin(2\omega x+d)/(x+1). It is known that the continuous spectrum of the operator L_{\alpha} has ... More

Generalized Zero Range Potentials and Multi-Channel Electron-Molecule ScatteringSep 09 2002A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges is considered. ... More

Approximate Differentiability of Mappings of Carnot-Carathéodory SpacesJun 22 2012Feb 05 2013We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory spaces. We show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic horizontal vector fields ... More

Inverse shadowing and related measuresJul 15 2019We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along the exact trajectory ... More

Study of internal wave breaking dependence on stratificationJun 26 2012Mixing effect in a stratified fluid is considered and examined. Euler equations for incompressible fluid stratified by a gravity field are applied to state a mathematical problem and describe the effect. It is found out that a system of Euler equations ... More

On the distribution of zeros of the Hermite-Pade polynomials for three algebraic functions $1,f,f^2$ and the global topology of the Stokes lines for some differential equations of the third orderDec 26 2013The paper presents some heuristic results about the distribution of zeros of Hermite-Pade polynomials of first kind for the case of three functions $1,f,f^2$, where $f$ has the form $f(z): = \prod\limits_ {j = 1 } ^3 (z-a_j) ^ {\alpha_j} $, $\alpha_j ... More

Extended Prigozhin theorem: method for universal characterization of complex system evolutionMar 19 2013Jul 27 2014Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, ... More

Moveable objects and applications, based on themApr 04 2009The inner views of all our applications are predetermined by the designers; only some non-significant variations are allowed with the help of adaptive interface. In several programs you can find some moveable objects, but it is an extremely rare thing. ... More

Moving and resizing of the screen objectsSep 05 2008The shape and size of the objects, which we see on the screen, when the application is running, are defined at the design time. By using some sort of adaptive interface, developers give users a chance to resize these objects or on rare occasion even change, ... More

KMS states on the C*-algebras of non-principal groupoidsJun 29 2011Sep 23 2014We describe KMS-states on the C*-algebras of etale groupoids in terms of measurable fields of traces on the C*-algebras of the isotropy groups. We use this description to analyze tracial states on the transformation groupoid C*-algebras and to give a ... More

Smooth crossed products of Rieffel's deformationsJul 08 2013Nov 26 2013Assume A is a Frechet algebra equipped with a smooth isometric action of a vector group V, and consider Rieffel's deformation A_J of A. We construct an explicit isomorphism between the smooth crossed products V\ltimes\A_J and V\ltimes\A. When combined ... More

Twisted Whittaker models for metaplectic groupsSep 08 2015Oct 15 2016Let G be a reductive group (over an algebraically closed field) equipped with the metaplectic data. In this paper we study the corresponding twisted Whittaker category for G. We construct and study a functor from the latter category to the corresponding ... More

Minisuperspace Models in M-theoryDec 14 2006Jul 22 2007We derive the full canonical formulation of the bosonic sector of 11-dimensional supergravity, and explicitly present the constraint algebra. We then compactify M-theory on a warped product of homogeneous spaces of constant curvature, and construct a ... More

Rare-Event Estimation for Dynamic Fault TreesJan 24 2016Article describes the results of the development and using of Rare-Event Monte-Carlo Simulation Algorithms for Dynamic Fault Trees Estimation. For Fault Trees estimation usually analytical methods are used (Minimal Cut sets, Markov Chains, etc.), but ... More

Is it Correct to Use MLE Method for GRP Parameter Estimation ?Aug 28 2016Sep 05 2016Analysis of repair systems usually uses an As Good As New or As Bad As Old repair assumptions. In practice, repair actions do not result in such extreme situations, but rather in a complex transitional one, that is imperfect maintenance, i.e. Generalized ... More

Computational Bottlenecks of Quantum AnnealingJun 29 2015May 17 2016A promising approach to solving hard binary optimisation problems is quantum adiabatic annealing (QA) in a transverse magnetic field. An instantaneous ground state --- initially a symmetric superposition of all possible assignments of $N$ qubits --- is ... More

Beam Coupling Impedances of Small DiscontinuitiesJan 27 2000A general derivation of the beam coupling impedances produced by small discontinuities on the wall of the vacuum chamber of an accelerator is reviewed. A collection of analytical formulas for the impedances of small obstacles is presented.

Semiinfinite cohomology of Lie-* algebrasMay 22 2000We construct a geometric version of BRST cohomology complex of a chiral module over a Lie-* algebra using the language of differential graded Lie algebroids in the category of D-modules on a compact curve $X$.

Semiinfinite cohomology of associative algebras and bar dualityFeb 05 1996We describe semiinfinite cohomology of associative algebras in terms of Koszul (or bar) duality. Consider an associative algebra $A$ and two its subalgebras $B$ and $N$ such that $A=B\otimes N$ as a vector space. We prove that the endomorphism algebra ... More

A proof of Feigin's conjectureDec 02 1997The paper is devoted to the proof of the following conjecture due to B. Feigin. Let $\frak u_\ell$ be the small quantum group a the primitive $\ell$-th root of unity. Then it is known that the usual $Ext$ algebra of the trivial $\frak u_\ell$-module is ... More

Mass modification of itinerant carriers in RKKY oscillations induced by finite range exchange interactionsMar 16 2010Jun 22 2010We investigate the Ruderman-Kittel-Kasuya-Yosida oscillations of the itinerant carrier spin density in a system where those oscillations appear only due to a finite distribution of a localized spin. The system represents a half-infinite one-dimensional ... More

Ruderman-Kittel-Kasuya-Yosida spin density oscillations: impact of the finite radius of the exchange interactionJan 21 2009Apr 06 2009A non-interacting electron gas on a one-dimensional ring is considered at finite temperatures. The localized spin is embedded at some point on the ring and it is assumed that the interaction between this spin and the electrons is the exchange interaction ... More

Miura type transformations and homogeneous spacesDec 14 2004May 10 2005We relate Miura type transformations (MTs) over an evolution system to its zero-curvature representations with values in Lie algebras g. We prove that certain homogeneous spaces of g produce MTs and show how to distinguish these spaces. For a scalar translation-invariant ... More

Coverings and fundamental algebras for partial differential equationsJan 28 2003May 12 2005Following I. S. Krasilshchik and A. M. Vinogradov, we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs and Backlund ... More

Covariant forms of Lax one-field operators: from Abelian to non-commutativeFeb 22 2003Links of factorization theory, supersymmetry and Darboux transformations as isospectral deformations are considered in the context of quantum theory. The infinite chain equations for factorizing operators for a spectral problem are derived. A closure ... More

Anomalous Cherenkov spin-orbit soundOct 19 2010Feb 17 2011The Cherenkov effect is a well known phenomenon in the electrodynamics of fast charged particles passing through transparent media. If the particle is faster than the light in a given medium, the medium emits a forward light cone. This beautiful phenomenon ... More

Compactification of *-autonomous categoriesJul 13 2016Jul 20 2016We study the question when a *-autonomous (Mix-)category has a representation as a $*$-autonomous category of a compact one. We prove that necessary and sufficient condition is that weak distributivity maps are monic (or, equivalently epic). For a Mix-category, ... More

Relative Seiberg-Witten and Ozsvath-Szabo 4-dimensional invariants with respect to embedded surfacesJan 26 2004Jul 14 2005We study the invariants of surfaces in 4-manifolds extracted from the Seiberg-Witten and the Ozsvath-Szabo invariants of their fiber sums with auxiliary Lefschetz fibrations. Such invariants involve relative Spin_c structures and can be treated as refinements ... More

Production of the Doubly Heavy Baryons, $B_c$ meson and the Tetra-c-quark at the Fixed-target Experiment at the LHC with double intrinsic heavy approachOct 19 2016Nov 01 2016In the paper we discuss production of the $B_c$ meson, the doubly heavy baryons and the tetra-c-quark at the future fixed-target experiment at the LHC (AFTER@LHC) with the doubly intrinsic heavy mechanism. The production cross sections are present.

On the production properties of the Doubly-Charmed BaryonsMar 02 2014Mar 04 2014This paper focuses on disagreement between theoretical predictions and experimental results of the production properties of Doubly Charmed Baryons. The kinematic dependencies were used to clarify the discrepancy between the SELEX data and the theory. ... More

Relatively free associative algebras of ranks 2 and 3 with Lie nilpotency identity and systems of generators of some T-spacesJan 23 2018We study relatively free associative algebras $F_r^{\left(n\right)}$ of ranks $r=2,3$ with the identity $\left[x_1,\dots,x_n\right]=0$ of Lie nilpotency of step $n\ge3$ over a field $K$ of characteristic $\ne2,3$. First we prove the Theorem about the ... More

On off-shell structure of open string sigma modelApr 04 2001Apr 16 2001We analyze several problems related to off-shell structure of open string sigma model by using a combination of derivative expansion and expansion in powers of the fields. According to the sigma model approach to bosonic open string theory, the tachyon ... More

G2-structures and octonion bundlesOct 14 2015We use a G2-structure on a 7-dimensional Riemannian manifold with a fixed metric to define an octonion bundle with a fiberwise non-associative product. We then define a metric-compatible octonion covariant derivative on this bundle that is compatible ... More

Linear periods of automorphic sheaves for GL_{2n}Mar 04 2019We study, in the framework of the geometric Langlands program, the periods of cuspidal automorphic sheaves for GL_{2n} along the Levi subgroup GL_n\times\GL_n. We solve the corresponding local problem, and discuss the global applications.

Estimates and monotonicity for a heat flow of isometric G2-structuresApr 18 2019Given a $7$-dimensional compact Riemannian manifold $\left( M,g\right) $ that admits $G_{2}$-structure, all the $G_{2}$-structures that are compatible with the metric $g$ are parametrized by unit sections of an octonion bundle over $M$. We define a natural ... More

Particle with internal dynamical asymmetry: chaotic self-propulsion and turningJul 24 2000We consider model of a complex particle that consists of a rigid shell and a nucleus with spatial asymmetric interaction. The particle's dynamics with the nucleus driven by a periodic excitation is considered. It is shown that unidirectional self-propulsed ... More

Ranks for families of theories and their spectraJan 24 2019We define ranks and degrees for families of theories, similar to Morley rank and degree, as well as Cantor-Bendixson rank and degree, and the notion of totally transcendental family of theories. Bounds for $e$-spectra with respect to ranks and degrees ... More

Darboux-covariant differential-difference operators and dressing chainsApr 01 2005The general approach to chain equations derivation for the function generated by a Miura transformation analog is developing to account evolution (second Lax equation) and illustrated for Sturm-Liouville differential and difference operators. Polynomial ... More

Researh Note: Stokes-Einstein relation in simple fluids revisitedMay 29 2019In this Research Note the Zwanzig's formulation of the Stokes-Einstein (SE) relation for simple atomistic fluids is re-examined. It is shown that the value of the coefficient in SE relation depends on the ratio of the transverse and longitudinal sound ... More

Global geometrised Rankin-Selberg method for GL(n)Aug 30 2001We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. We show that the geometric Langlands conjecture for an irreducible unramified local system $E$ of rank $n$ on a ... More

Eulerian and Newtonian dynamics of quantum particlesJan 20 2013Feb 12 2013We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and described by ... More

Hadronic resonance production with ALICE at the LHCDec 06 2017We present recent results on short-lived hadronic resonances obtained by the ALICE experiment in pp, p-Pb and Pb-Pb collisions at LHC energies, including the most recent measurements of $\Lambda(1520)$ and $\Xi(1530)^{0}$ resonances.

Median and Mode in First Passage under RestartJun 13 2019Restart -- interrupting a stochastic process followed by a new start -- is known to improve the mean time to its completion, and the general conditions under which such an improvement is achieved are now well understood. Here, we explore how restart affects ... More

On parabolic Whittaker functions IIJul 15 2011We derive a Givental-type stationary phase integral representation for the specified $\Gr_{m,N}$-Whittaker function introduced in \cite{GLO2}, which presumably describes the $S^1\times U_N$-equivariant Gromov-Witten invariants of Grassmann variety $\Gr_{m,N}$. ... More

G2-structure deformations and warped productsOct 20 2011Jun 13 2012We overview the properties of non-infinitesimal deformations of G2-structures on seven-manifolds, and in particular, focus on deformations that lie in the seven-dimensional representation of G2 and are thus defined by a vector. We then consider deformations ... More

1+1-dimensional Yang-Mills equations and mass via quasiclassical correction to actionDec 07 2016Two-dimensional Yang-Mills models in a pseudo-euclidean space are considered from a point of view of a class of nonlinear Klein-Gordon-Fock equations. It is shown that the Nahm reduction does not work, another choice is proposed and investigated. A quasiclassical ... More

Truth problem in the context of interpretations of quantum logicJul 10 2014The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a context of modal ... More

Twisted Whittaker models for metaplectic groupsSep 08 2015Jun 23 2017Let G be a reductive group (over an algebraically closed field) equipped with the metaplectic data. In this paper we study the corresponding twisted Whittaker category for G. We construct and study a functor from the latter category to the corresponding ... More

Geometric theta-lifting for the dual pair GSp_{2n}, GO_{2m}Feb 04 2008Let X be a smooth projective curve over an algebraically closed field of characteristic >2. Consider the dual pair H=GO_{2m}, G=GSp_{2n} over X, where H splits over an etale two-sheeted covering of X. Write Bun_G and Bun_H for the stacks of G-torsors ... More

Rademacher functions in weighted symmetric spacesAug 04 2015Aug 06 2015The closed span of Rademacher functions is investigated in the weighted spaces X(w), where X is a symmetric space on [0,1] and w is a positive measurable function on [0,1]. By using the notion and properties of the Rademacher multiplicator space of a ... More

Short-time behaviour of a modified Laplacian coflow of G2-structuresSep 19 2012Sep 08 2013We modify the Laplacian coflow of co-closed G2-structures - $\frac{d}{dt}\psi =\Delta \psi $ where $\psi $ is the closed dual 4-form of a $G_{2}$-structure $\varphi $. The modified flow is now parabolic in the direction of closed forms upto diffeomorphisms. ... More

Degenerate billiards in celestial mechanicsDec 28 2016In an ordinary billiard trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is degenerate. Degenerate ... More

Entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to quasi-free statesFeb 10 2000We compute the dynamical entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to arbitrary gauge-invariant quasi-free states. This completes the research started by Stormer and Voiculescu, and continued in works of Narnhofer-Thirring ... More

Pontryagin's principle of stabilizationDec 28 2006Mar 09 2007The paper presents necessary and sufficient conditions for a nonlinear system to be stabilized by a feedback. The conditions are based on the ideas related to the well-known Pontryagin's maximum principle. That allows us to formulate the results in terms ... More

Banach Analytic Sets and a Non-Linear Version of the Levi Extension TheoremMar 07 2012Dec 18 2012We prove a certain non-linear version of the Levi extension theorem for meromorphic functions. This means that the meromorphic function in question is supposed to be extendable along a sequence of complex curves, which are arbitrary, not necessarily straight ... More

Limiting behavior of trajectories of complex polynomial vector fieldsApr 15 2010We prove that every trajectory of a polynomial vector field on the complex projective plane accumulates to the singular locus of the vector field. This statement represents a holomorphic version of the Poincare-Bendixson theorem and solves the complex ... More

On fixed points of rational self-maps of complex projective planeNov 27 2009Feb 27 2010For any given natural $d\ge 1$ we provide examples of rational self-maps of complex projective plane $\pp^2$ of degree $d$ without (holomorphic) fixed points. This makes a contrast with the situation in one dimension. We also prove that the set of fixed ... More

Invariant measures for interval translations and some other piecewise continuous mapsDec 11 2018Apr 22 2019We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation maps), a Borel ... More

Fermionic forms and quiver varietiesOct 02 2006Oct 11 2007We prove a formula relating the fermionic forms and the Poincare polynomials of quiver varieties associated to a finite quiver. Applied to quivers of type ADE, our result implies a version of the fermionic conjecture of Lusztig.

A computational criterion for the Kac conjectureAug 13 2006Aug 09 2007We give a criterion for the Kac conjecture asserting that the free term of the polynomial counting the absolutely indecomposable representations of a quiver over a finite field of given dimension coincides with the corresponding root multiplicity of the ... More

Metrizable DH-spaces with a dense complete subsetJan 15 2016It is proved that for an h-homogeneous space X the following conditions are equivalent: 1) X is a densely homogeneous space with a dense complete subspace; 2) X is $\sigma$-discretely controlled.

On Singular Value Inequalities for the Sum of Two MatricesJul 08 2015A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.

Genus two Veech surfaces arising from general quadratic differentialsApr 09 2005We study Veech surfaces of genus 2 arising from quadratic differentials that are not squares of abelian differentials. We prove that all such surfaces of type (2,2) and (2,1,1) are arithmetic. In (1,1,1,1) case, we reduce the question to abelian differentials ... More

On asymptotically free action of permutation groups on subsets and multisetsDec 24 2013Dec 02 2014Let $G$ be a permutation group acting on a finite set $\Omega$ of cardinality $n$. The number of orbits of the induced action of $G$ on the set $\Omega_m$ of all size $m$ subsets of $\Omega$ satisfies the trivial inequalities $|\Omega_m|/|G|\leq |\Omega_m/G|\leq ... More

Large Fourier Quasicrystals and Wiener's TheoremJan 22 2017We find new simple conditions for support of a discrete measure on Euclidean space to be a finite union of translated lattices. The arguments are based on a local analog of Wiener's Theorem on absolutely convergent trigonometric series and theory of almost ... More

Fano-Mathieu correspondenceSep 08 2018We show that $G$-Fano threefolds are mirror-modular. 1. Mirror maps are inversed reversed Hauptmoduln for moonshine subgroups of $SL_2(\mathbb{R})$. 2. Quantum periods, shifted by an integer constant (eigenvalue of quantum operator on primitive cohomology) ... More

Subsystem codes with spatially local generatorsAug 05 2010We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both proportional to ... More

Classical scattering in strongly attractive potentialsMar 24 2014Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angles scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and exponential), which are ... More

Adelic resolution for homology sheavesMay 17 2007Feb 11 2008A generalization of the usual ideles group is proposed, namely, we construct certain adelic complexes for sheaves of $K$-groups on schemes. More generally, such complexes are defined for any abelian sheaf on a scheme. We focus on the case when the sheaf ... More

Production of the Doubly Heavy Baryons, $B_c$ meson and the Tetra-c-quark at the Fixed-target Experiment at the LHC with double intrinsic heavy approachOct 19 2016In the paper we discuss production of the $B_c$ meson, the doubly heavy baryons and the tetra-c-quark at the future fixed-target experiment at the LHC (AFTER@LHC) with the doubly intrinsic heavy mechanism. The production cross sections are present.

Poincare biextension and ideles on the algebraic curveNov 25 2005May 16 2007Arbarello, de Concini, and Kac have constructed a central extension of the ideles group on a smooth projective algebraic curve. We show a relation of this central extension with the theta-bundle and the Poincare biextension of the Jacobian of the curve. ... More

A distribution on triples with maximum entropy marginalJul 31 2016We construct an $S_3$-symmetric probability distribution on $\{(a,b,c) \in \mathbb{Z}_{\geq 0}^3 \: : \: a+b+c =n \}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\ldots,n\}$ with mean $n/3$. Existence ... More

Subtraction Procedure for Calculation of Anomalous Magnetic Moment of Electron in QED and its Application to Numerical Computation at 3-loop LevelJul 23 2015Jul 28 2016A new subtraction procedure for removal both ultraviolet and infrared divergences in Feynman integrals is proposed. This method is developed for computation of QED corrections to the electron anomalous magnetic moment. The procedure is formulated in the ... More

Dynamics of clade diversification on the morphological hypercubeSep 15 1998Understanding the relationship between taxonomic and morphological changes is important in identifying the reasons for accelerated morphological diversification early in the history of animal phyla. Here, a simple general model describing the joint dynamics ... More

On absolute nonshadowability of transitive mapsJun 24 2016We study shadowing property for random infinite pseudotrajectories of a continuous map $f$ of a compact metric space. For the cases of transitive maps and transitive attractors we prove a dichotomy: either $f$ satisfies shadowing property or random pseudotrajectory ... More

Extended foundations of stochastic predictionAug 17 2012Jun 28 2014The basic purpose of this work was to suggest universal quantitative description of ergodic system intermediate bifurcation and obligatory conditions of this transition. Conditions for existence of phase state and first order phase transition were introduced ... More

Bifurcation patterns of market regime transitionJul 11 2015Jan 05 2016In this paper mechanisms of reversion - momentum transition are considered. Two basic nonlinear mechanisms are highlighted: a slow and fast bifurcation. A slow bifurcation leads to the equilibrium evolution, preceded by stability loss delay of a control ... More

Design of moveable and resizable graphicsSep 22 2007We are communicating with computers on two different levels. On upper level we have a very flexible system of windows: we can move them, resize, overlap or put side by side. At any moment we decide what would be the best view and reorganize the whole ... More

Rejecting Adaptive InterfaceSep 14 2011Programs have to be designed in such a way as to make them looking good and being handy for all users. Adaptive interface, with all the numerous achievements throughout 30 years of its history, contains and in reality is based on one fundamental flaw ... More

Personal applications, based on moveable / resizable elementsJun 17 2009All the modern day applications have the interface, absolutely defined by the developers. The use of adaptive interface or dynamic layout allows some variations, but even all of them are predetermined on the design stage, because the best reaction (from ... More

The conifold pointApr 29 2014Consider a Laurent polynomial with real positive coefficients such that the origin is strictly inside its Newton polytope. Then it is strongly convex as a function of real positive argument. So it has a distinguished Morse critical point --- the unique ... More

DG-modules over de Rham DG-algebraNov 29 2013For a morphism of smooth schemes over a regular affine base we define functors of derived direct image and extraordinary inverse image on coderived categories of DG-modules over de Rham DG-algebras. Positselski proved that for a smooth algebraic variety ... More

An Application of the EM-algorithm to Approximate Empirical Distributions of Financial Indices with the Gaussian MixturesJun 29 2016In this study I briefly illustrate application of the Gaussian mixtures to approximate empirical distributions of financial indices (DAX, Dow Jones, Nikkei, RTSI, S&P 500). The resulting distributions illustrate very high quality of approximation as evaluated ... More

Socializing Autonomous Units with the Reflexive Game Theory and Resonate-and-Fire neuronsApr 19 2015In this study the concept of reflexia is applied to modeling behavior of autonomous units. The relationship between reflexia, on the one hand, and mirror neuron system and perception of emotions, on the other hand, is introduced. The main method of using ... More

Betti numbers of a class of barely G2 manifoldsSep 25 2009We calculate explicitly the Betti numbers of a class of barely G2 manifolds - that is, G2 manifolds that are realised as a product of a Calabi-Yau manifold and a circle, modulo an involution. The particular class which we consider are those spaces where ... More

Analytic Methods to Calculate Fault Trees with Loops - Restrictions of Application and Solution UniquenessFeb 11 2016One of the important tasks of the Reliability Estimation is Analysis of the Fault Tree. A problem of Fault Trees analysis is considered one of the most complex ones, since structure of such trees is characterized by a considerable number of interconnections. ... More

Improved Upper Bound for the Redundancy of Fix-Free CodesAug 05 2004A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise and speed ... More

Resolving Two Beams in Beam Splitters with a Beam Position MonitorMay 23 2002The beam transport system for the Advanced Hydrotest Facility (AHF) anticipates multiple beam splitters [1]. Monitoring two separated beams in a common beam pipe in the splitter sections imposes certain requirements on diagnostics for these sections. ... More

Algebraic construction of contragradient quasi-Verma modules in positive characteristicMay 05 2001In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of the global Grothendieck-Cousin ... More

Semiinfinite cohomology of quantum groupsJan 24 1996In this paper we develop a new homology theory of associative algebras called semiinfinite cohomology in a derived category setting. We show that in the case of small quantum groups the zeroth semiinfinite cohomology of the trivial module is closely related ... More

Semiinfinite cohomology of contragradient Weyl modules over small quantum groupsJun 11 1999In this paper we construct some quantum analogues of the global Cousin complex for the flag variety in positive characteristic. Just like in the positive characteristic case, we obtain some remarkable resolutions of the contragradient modules over the ... More

Rare Phi Decays and Exotic HadronsOct 27 1999The results of the experimental study of the reactions e+e-->\pi\pi\gamma, \eta\pi\gamma, \eta'\gamma, \omega\pi,... at VEPP-2M collider with CMD-2 and SND detectors are presented. The branching ratios of \phi, \rho, \omega rare decays were measured. ... More

Faster Algorithms for Rigidity in the PlaneNov 19 2007Feb 29 2008In [1], a new construction called red-black hierarchy characterizing Laman graphs and an algorithm for computing it were presented. For a Laman graph G=(V,E) with n vertices it runs in O(n^2) time assuming that a partition of (V,E+e) into two spanning ... More

Solutions of the motivic ADHM recursion formulaApr 29 2011We give an explicit solution of the ADHM recursion formula conjectured by Chuang, Diaconescu, and Pan. This solution is closely related to the formula for the Hodge polynomials of Higgs moduli spaces conjectured by Hausel and Rodriguez-Villegas. We solve ... More

Wall-crossing formulas for framed objectsApr 21 2011We prove wall-crossing formulas for the motivic invariants of the moduli spaces of framed objects in the ind-constructible abelian categories. Developed techniques are applied in the case of the motivic Donaldson-Thomas invariants of quivers with potentials. ... More

On the motivic Donaldson-Thomas invariants of quivers with potentialsMar 15 2011We study motivic Donaldson-Thomas invariants for a class of quivers with potentials using the strategy of Behrend, Bryan, and Szendroi. This class includes quivers with potentials arising from consistent brane tilings and quivers with zero potential. ... More