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On pairs, triples and quadruples of points on a cubic surfaceOct 13 2018Apr 22 2019Let $X^{(n)}$ denote $n$-th symmetric power of a cubic surface $X$. We show that $X^{(4)}\times X$ is stably birational to $X^{(3)}\times X$, despite examples when $X^{(4)}$ is not stably birational to $X^{(3)}$.

Degenerations, transitions and quantum cohomologySep 08 2018Sep 11 2018Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations helps with computing Gromov--Witten invariants, and the role of this story in Fanosearch programme. ... More

Apéry constants of homogeneous varietiesApr 15 2016For Fano manifolds we define Ap\'ery constants and Ap\'ery class as particular limits of ratios of coefficients of solutions of the quantum differential equation. We do numerical computations in case of homogeneous varieties. These numbers are identified ... More

Quantum Periods For Certain Four-Dimensional Fano ManifoldsJun 18 2014Dec 02 2014We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all four-dimensional toric Fano manifolds, all four-dimensional products of ... 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

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

Mirror Symmetry and Fano ManifoldsDec 07 2012We consider mirror symmetry for Fano manifolds, and describe how one can recover the classification of 3-dimensional Fano manifolds from the study of their mirrors. We sketch a program to classify 4-dimensional Fano manifolds using these ideas.

Small toric degenerations of Fano threefoldsSep 07 2018We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.

Gamma conjecture via mirror symmetryAug 04 2015The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors claims that the ... More

On pairs, triples and quadruples of points on a cubic surfaceOct 13 2018Let $X^{(n)}$ denote $n$-th symmetric power of a cubic surface $X$. We show that $X^{(4)}\times X$ is stably birational to $X^{(3)}\times X$, despite examples when $X^{(4)}$ is not stably birational to $X^{(3)}$.

On a zeta-function of a dg-categoryJun 18 2015We define a zeta-function of a pre-triangulated dg-category and investigate its relationship with the motivic zeta-function in the geometric case.

The Fano variety of lines and rationality problem for a cubic hypersurfaceMay 20 2014Jun 25 2014We find a relation between a cubic hypersurface $Y$ and its Fano variety of lines $F(Y)$ in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety ... More

Exceptional collections of line bundles on the Beauville surfaceOct 11 2012Jun 10 2013We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface $S$. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal ... More

On pairs, triples and quadruples of points on a cubic surfaceOct 13 2018Apr 15 2019Let $X^{(n)}$ denote $n$-th symmetric power of a cubic surface $X$. We show that $X^{(4)}\times X$ is stably birational to $X^{(3)}\times X$, despite examples when $X^{(4)}$ is not stably birational to $X^{(3)}$.

Upper Bounds for Mutations of PotentialsJan 19 2013In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper bounds from [Berenstein ... More

Acyclicity of non-linearizable line bundles on fake projective planesFeb 19 2016On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-torsion divisors (and usually exists but not unique otherwise). Earlier we ... More

Gamma classes and quantum cohomology of Fano manifolds: Gamma conjecturesApr 25 2014Oct 19 2015We propose Gamma Conjectures for Fano manifolds which can be thought of as a square root of the index theorem. Studying the exponential asymptotics of solutions to the quantum differential equation, we associate a principal asymptotic class A_F to a Fano ... More

Examples violating Golyshev's canonical strip hypothesesJun 20 2018We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomials of polarised varieties. They are given by moduli spaces of rank 2 bundles ... More

Dubrovin's conjecture for $IG(2,6)$May 15 2014We show that the big quantum cohomology of the symplectic isotropic Grassmanian $IG(2,6)$ is generically semisimple, whereas its small quantum cohomology is known to be non-semisimple. This gives yet another case where Dubrovin's conjecture holds and ... More

Quantum Periods for 3-Dimensional Fano ManifoldsMar 13 2013Apr 02 2015The quantum period of a variety X is a generating function for certain Gromov-Witten invariants of X which plays an important role in mirror symmetry. In this paper we compute the quantum periods of all 3-dimensional Fano manifolds. In particular we show ... More

Minifolds and PhantomsMay 20 2013Oct 17 2013A minifold is a smooth projective $n$-dimensional variety such that its bounded derived category of coherent sheaves $\D^b(X)$ admits a semi-orthogonal decomposition into an exceptional collection of $n+1$ exceptional objects. In this paper we classify ... More

Minkowski Polynomials and MutationsDec 08 2012Given a Laurent polynomial f, one can form the period of f: this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds. Mutations are a particular class of birational transformations acting on Laurent ... More

Coverage Analysis for Low-Altitude UAV Networks in Urban EnvironmentsApr 15 2017Wireless access points on unmanned aerial vehicles (UAVs) are being considered for mobile service provisioning in commercial networks. To be able to efficiently use these devices in cellular networks it is necessary to first have a qualitative and quantitative ... More

Semileptonic $Ξ_c$ baryon decays in the relativistic quark modelMay 21 2019The form factors of the weak $\Xi_c\to \Xi(\Lambda)$ transitions are calculated in the framework of the relativistic quark model based on the quasipotential approach. All relativistic effects including transformations of the baryon wave functions from ... More

Impact of UAV Antenna Configuration on Wireless Connectivity in Urban EnvironmentsJun 29 2018The growing presence of UAVs has led operators to explore the issue of how to provide wireless service to UAVs. The achieveable service quality will be affected by a number of factors, including the type of antenna that the UAVs are equipped with and ... More

Noctilucent Cloud Particle Size Determination based on Multi-Wavelength All-Sky AnalysisOct 31 2016The article deals with the analysis of color distribution in noctilucent clouds (NLC) in the sky based on multi-wavelength (RGB) CCD-photometry provided with the all-sky camera in Lovozero in the north of Russia (68.0 deg N, 35.1 deg E) during the bright ... More

Termination of Original F5Mar 12 2012Jul 01 2012The original F5 algorithm introduced by Faug\`ere is formulated for any homogeneous polynomial set input. The correctness of output is shown for any input that terminates the algorithm, but the termination itself is proved only for the case of input being ... 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 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

Simple signature-based Groebner basis algorithmMay 28 2012This paper presents an algorithm for computing Groebner bases based upon labeled polynomials and ideas from the algorithm F5. The main highlights of this algorithm compared with analogues are simplicity both of the algorithm and of the its correctness ... 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

Production properties of the Doubly Charmed Baryons at the large Feynman-XJun 16 2014This paper focuses on disagreement between theoretical predictions and the SELEX results of the production properties of Doubly Charmed Baryons. The role of the intrinsic charm mechanism in the SELEX kinematic region is researched. The production ratio ... More

Majorana tunneling entropyJul 01 2015Dec 01 2015In thermodynamics a macroscopic state of a system results from a number of its microscopic states. This number is given by the exponent of the system's entropy $\exp(S)$. In non-interacting systems with discrete energy spectra, such as large scale quantum ... More

Cherenkov sound on a surface of a topological insulatorJul 10 2013Nov 07 2013Topological insulators are currently of considerable interest due to peculiar electronic properties originating from helical states on their surfaces. Here we demonstrate that the sound excited by helical particles on surfaces of topological insulators ... More

On Banach spaces of sequences and free linear logic exponential modalitySep 13 2015Nov 23 2016We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it rigged sequences spaces}, Banach spaces of sequences, with norms defined ... More

Differential approximation for Kelvin-wave turbulenceNov 05 2005Jan 25 2006I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic ... More

Sandpile behaviour in discrete water-wave turbulenceOct 21 2005Jan 16 2006We construct a sandpile model for evolution of the energy spectrum of the water surface waves in finite basins. This model take into account loss of resonant wave interactions in discrete Fourier space and restoration of these interactions at larger nonlinearity ... More

Cosmic particles with energies above 10^19 eV: a brief review of resultsJan 10 2013Experimental results on ultra-high-energy cosmic rays are briefly reviewed and their interpretation is discussed. The results related to principal observables (arrival directions, energies and composition) of primary particles of extended air showers ... More

Supermassive dark-matter Q-balls in galactic centers?Oct 24 2015Nov 10 2016Though widely accepted, it is not proven that supermassive compact objects (SMCOs) residing in galactic centers are black holes. In particular, the Milky Way's SMCO can be a giant nontopological soliton, Q-ball, made of a scalar field: this fits perfectly ... More

Lax Pair for Strings in Lunin-Maldacena BackgroundMar 25 2005May 25 2005Recently Lunin and Maldacena used an SL(3,R) transformation of the AdS_5 x S^5 background to generate a supergravity solution dual to a so-called beta-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation ... More

Normative properties of multi-criteria choice procedures and their superpositions: INov 02 2016We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that show how the ... More

A dynamical theory of speciation on holey adaptive landscapesJul 27 1998The metaphor of holey adaptive landscapes provides a pictorial representation of the process of speciation as a consequence of genetic divergence. In this metaphor, biological populations diverge along connected clusters of well-fit genotypes in a multidimensional ... More

Accurate transport cross sections for the Lennard-Jones potentialApr 22 2014Oct 08 2014Physically motivated expressions for the transport cross sections describing classical scattering in the Lennard-Jones potential are proposed. These expressions, which agree with the numerical results better than to within $\pm 1%$, can be easy implemented ... More

Notes on the biextension of Chow groupsFeb 11 2008Mar 07 2009The paper discusses four approaches to the biextension of Chow groups and their equivalences. These are the following: an explicit construction given by S.Bloch, a construction in terms of the Poincare biextension of dual intermediate Jacobians, a construction ... More

Improved Monotone Circuit Depth Upper Bound for Directed Graph ReachabilitySep 22 2008We prove that the directed graph reachability problem (transitive closure) can be solved by monotone fan-in 2 boolean circuits of depth (1/2+o(1))(log n)^2, where n is the number of nodes. This improves the previous known upper bound (1+o(1))(log n)^2. ... More

On the Plaque Expansivity ConjectureNov 27 2013Dec 21 2015It is one of the main properties of uniformly hyperbolic dynamics that points of two distinct trajectories cannot be uniformly close one to another. This characteristics of hyperbolic dynamics is called expansivity. Hirsch, Pugh and Shub, 1977, formulated ... More

Taylor and minimal resolutions of homogeneous polynomial idealsMay 20 1999We give a necessary and sufficient condition on a homogeneous polynomial ideal for its Taylor complex to be exact. Then we give a combinatorial construction of a minimal resolution for ideals satisfying the above condition (in particular for monomial ... More

Extended Fokker Planck model: properties and solutionsJan 20 2014In the current paper Fokker Planck model of random walks has been extended to non conservative cases characterized by explicit dependence of diffusion and energy on time. A given generalization allows describing of such non equilibrium processes as Levy ... More

Interface Transformation from Ruling to ObedienceFeb 15 2015This article is about one feature which was partly introduced 30 years ago with the development of multi windows operating systems. It is about the movability of screen objects not according to some predetermined algorithm but by the direct user action. ... More

Interface Between Market and ScienceOct 02 2015At the beginning, programming was inspired by the search of the best solutions. At that time some fundamental stones like famous languages and object oriented and structured programming were laid. It was found later that applications could generate huge ... More

World of Movable Objects. Part 1Nov 18 2010This book is about the transformation of screen objects into movable and resizable and about the design of applications entirely on the basis of such elements. The screen objects have a wide variety of shapes; they can be either graphical objects or controls; ... More

Excerpt from the book World of Movable ObjectsNov 09 2010This book is about the transformation of screen objects into movable and resizable and about the design of applications entirely on the basis of such elements. The screen objects have a wide variety of shapes; they can be either graphical objects or controls; ... More

User-driven applicationsApr 03 2010User-driven applications are the programs, in which the full control is given to the users. Designers of such programs are responsible only for developing an instrument for solving some task, but they do not enforce users to work with this instrument ... More

User driven applications - new design paradigmJun 28 2007Programs for complicated engineering and scientific tasks always have to deal with a problem of showing numerous graphical results. The limits of the screen space and often opposite requirements from different users are the cause of the infinite discussions ... More

Modeling multistage decision processes with Reflexive Game TheoryMar 11 2012This paper introduces application of Reflexive Game Theory to the matter of multistage decision making processes. The idea behind is that each decision making session has certain parameters like "when the session is taking place", "who are the group members ... More

Inertial manifolds and finite-dimensional reduction for dissipative PDEsMar 19 2013These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called Man\'e projection ... More

Finite Bases with Respect to the Superposition in Classes of Elementary Recursive Functions, dissertationNov 14 2016This is a thesis that was defended in 2009 at Lomonosov Moscow State University. In Chapter 1: 1. It is proved that that the class of lower elementary functions (also known as Skolem elementary functions) is the set of all functions that can be obtained ... More

How do curved spheres intersect in 3-space?Oct 27 2012Jun 11 2013The following problem was proposed in 2010 by S. Lando. Let $M$ and $N$ be two unions of the same number of disjoint circles in a sphere. Do there always exist two spheres in 3-space such that their intersection is transversal and is a union of disjoint ... More

CKM Phase MeasurementsSep 07 2004Sep 08 2004Recent experimental results on CP violation in the B sector from BABAR and BELLE, experiments at asymmetric e+e- B-Factories, are summarized in these proceedings. The constraint on the position of the apex of the unitary triangle, obtained from these ... More

Semiinfinite cohomology of Tate Lie algebrasMar 02 2000In this note we give a definition of semiinfinite cohomology for Tate Lie algebras using the language of Differential Graded Lie algebroids with Curvature (CDG Lie algebroids).

Generality of inflation in closed FRW modelsOct 14 2003We investigate the generality of inflation in closed FRW models for a wide class of quintessence potentials. It is shown that inflation is not suppressed for most of them for a wide class of their parameters. This allows us to decide if inflation is common ... More

Lax Pair Covariance and Integrability of Compatibility ConditionJan 17 2001We continue to study Lax (L-A, U-V) pairs (LP) joint covariance with respect to Darboux transformations (DT) as a classification principle. The scheme is based on a comparison of general expressions for the transformed coefficients of LP and its Frechet ... More

Onset of negative dispersion in one-component-plasma revisitedOct 14 2016A simple approach to describe the long-wavelength dispersion of the longitudinal (plasmon) mode of the classical one-component-plasma (OCP), with the main objective to correctly capture the onset of negative dispersion, is proposed. The approach is applicable ... More

Finite Bases with Respect to the Superposition in Classes of Elementary Recursive Functions, dissertationNov 14 2016Nov 20 2016This is a thesis that was defended in 2009 at Lomonosov Moscow State University. In Chapter 1: 1. It is proved that that the class of lower (Skolem) elementary functions is the set of all polynomial-bounded functions that can be obtained by a composition ... More

Limiting distribution of particles near the frontier in the catalytic branching Brownian motionMar 17 2019We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and give an explicit ... More

Distributions of countable models of disjoint unions of Ehrenfeucht theoriesFeb 23 2018We describe Rudin-Keisler preorders and distribution functions of numbers of limit models for disjoint unions of Ehrenfeucht theories. Decomposition formulas for these distributions are found.

Numerical calculation of 5-loop QED contributions to the electron anomalous magnetic momentMay 20 2019Preliminary numerical results of calculating the 5-loop QED contributions to the electron (and muon) anomalous magnetic moment are presented. The results include the total contribution of the 5-loop Feynman diagrams without lepton loops and the contributions ... More

On centrality of $K_2$ for Chevalley groups of type $E_l$Feb 09 2015Oct 14 2016For a root system $\Phi$ of type $E_l$ and arbitrary commutative ring $R$ we show that the group $K_2(\Phi, R)$ is contained in the centre of the Steinberg group $St(\Phi, R)$. In course of the proof we also demonstrate an analogue of Quillen---Suslin ... More

Moduli of metaplectic bundles on curves and Theta-sheavesMay 02 2004Jul 26 2005We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program. For a smooth projective curve X we introduce an algebraic stack \tilde\Bun_G of metaplectic bundles ... More

Covariant forms of Lax one-field operatorsJun 01 2004Polynomials in differentiation operators are considered. The Darboux transformations covariance determines non-Abelian entries to form the coefficients of the polynomials. Joint covariance of a pair of such polynomials (Lax pair) as a function of one-field ... More

Counterexamples for Frobenius primality testJul 30 2013At present one can not find a single counterexample to even a simplest version of Frobenius primality test. The assessment of probability of the mistake, presented in [I.B. Damgard and G.S.Frandsen, Journal of Cryptology, 2006] is strongly overestimated. ... More

Analysis of Voros criterion: what derivatives involving the logarithm of the Riemann xi-function at z=1/2 should be non-negative for the Riemann hypothesis holds trueJul 22 2014Recently, Voros has found the sums involving certain powers of z-1/2, which, when taken over Riemann xi-function zeroes /rho, must be positive for the Riemann hypothesis holds true and vice versa. Here we analyze these sums, write them as expressions ... More

Coxeter groups of stellar manifoldsFeb 21 2004It is well known that a compact two dimensional surface is homeomorphic to a polygon with the edges identified in pairs. This paper not only presents a new proof of this statement but also generalizes it to any connected $n$-dimensional stellar manifold ... More

On piecewise continuous mappings of metrizable spacesAug 01 2016Let $f \colon X \rightarrow Y$ be a resolvable-measurable mapping of a metrizable space $X$ to a regular space $Y$. Then $f$ is piecewise continuous. Additionally, for a metrizable completely Baire space $X$, it is proved that $f$ is resolvable-measurable ... More

Weyl-Titchmarsh type formula for Hermite operator with small perturbationMar 18 2010Small perturbations of the Jacobi matrix with weights \sqrt n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical Weyl-Titchmarsh ... More

Strong Uniform Attractors for Non-Autonomous Dissipative PDEs with non translation-compact external forcesApr 22 2014We give a comprehensive study of strong uniform attractors of non-autonomous dissipative systems for the case where the external forces are not translation compact. We introduce several new classes of external forces which are not translation compact, ... More

Black hole entropy: statistical mechanics agrees thermodynamicsJan 29 1996Jul 21 1996We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical ... More

Klein Group And Four Color TheoremJun 02 2010Jun 03 2010In this work methods of construction of cubic graphs are analyzed and a theorem of existence of a colored disc traversing each pair of linked edges belonging to an elementary cycle of a planar cubic graph is proved.

Loop-erased walks and total positivityApr 12 2000We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights with nonnegative ... More

Infinite Energy Solutions for Damped Navier-Stokes Equations in R2Mar 26 2012Apr 19 2012We study the so-called damped Navier-Stokes equations in the whole 2D space. The global well-posedness, dissipativity and further regularity of weak solutions of this problem in the uniformly-local spaces are verified based on the further development ... More

Universal derivative-free optimization method with quadratic convergenceFeb 07 2011A new universal derivative-free optimization method CDOS (Conjugate Direction with Orthogonal Shift) is proposed. The CDOS method was specially developed to solve optimization tasks where the objective function and constraints are black boxes. The method ... More

Parametrized symmetric groups and the second homology of a groupMay 31 2017We introduce the notion of a symmetric group parametrized by elements of a group. We show that this group is an extension of a subgroup of the wreath product $G \wr S_n$ by $\mathrm{H}_2(G, \mathbb{Z})$. We also discuss the motivation behind this construction. ... 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

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