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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

Barriers towards no-reference metrics application to compressed video quality analysis: on the example of no-reference metric NIQEJul 08 2019This paper analyses the application of no-reference metric NIQE to the task of video-codec comparison. A number of issues in the metric behaviour on videos was detected and described. The metric has outlying scores on black and solid-coloured frames. ... More

Gravitational field measurement with an equilibrium ensemble of cold atomsMar 21 2005A new approach to the measurement of gravitational fields with an equilibrium ensemble of ultra-cold alkali atoms confined in a cell of volume $V$ is investigated. The proposed model of the gravitational sensor is based on a variation of the density profile ... More

Temperature, Topology and Quantum FieldsSep 05 1996This thesis uses Path Integrals and Green's Functions to study Gravity, Quantum Field Theory and Statistical Mechanics, particularly with respect to: finite temperature quantum systems of different spin in gravitational fields; finite temperature interacting ... More

Borel Reductions and Cub GamesJul 09 2012It is shown that the power set of $\k$ ordered by the subset relation modulo various versions of the non-stationary deal can be embedded into the partial order of Borel equivalence relations on $2^\k$ under Borel reducibility. Here $\k$ is uncountable ... 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

Conceptual Preconditions of Overcoming of Relativistic Intentions in Modern Philosophy of ScienceJul 14 2014Jul 31 2014The paper defends the thesis that it's possible to maintain some conceptual preconditions of overcoming of relativistic intentions in modern philosophy of science ("there are no any general foundations in philosophy of science"). We found two general ... More

A new GPU-accelerated hydrodynamical code for numerical simulation of interacting galaxiesNov 04 2013In this paper a new scalable hydrodynamic code GPUPEGAS (GPU-accelerated PErformance Gas Astrophysic Simulation) for simulation of interacting galaxies is proposed. The code is based on combination of Godunov method as well as on the original implementation ... More

Bose-Einstein condensate in non-homogeneous gravitational fieldMay 15 2002May 22 2002Ground state properties of trapped Bose condensate with repulsive interaction in non-homogeneous gravitational field are studied. Spatial structure of Bose condensate and its momentum distributions in 3-D anisotropic trap are considered by the solution ... More

Possibilities of technologization of philosophical knowledgeJul 10 2014Article purpose is the analysis of a question of possibility of technologization of philosophical knowledge. We understand the organization of cognitive activity which is guided by the set of methods guaranteed bringing to successful (i.e. to precisely ... More

The Size of Generating Sets of PowersApr 08 2015In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the algebra to satisfy ... More

Key (critical) relations preserved by a weak near-unanimity functionJan 19 2015Nov 26 2016In the paper we introduce a notion of a key relation, which is similar to the notion of a critical relation introduced by Keith A.Kearnes and \'Agnes Szendrei. All clones on finite sets can be defined by only key relations. In addition there is a nice ... More

D-affinity and Rational VarietiesNov 21 2018Nov 26 2018We investigate geometry of D-affine varieties. Our main result is that a D-affine uniformly rational projective variety over an algebraically closed field of zero characteristic is a generalised flag variety of a reductive group. This is a partially converse ... More

On factorization of elements in Pimenov algebrasMar 20 2013We consider the operation of division in Pimenov algebras. We obtain necessary and sufficient conditions for prime elements in Pimenov algebras with a number of generators less than five. We adduce examples of the factorization of elements in these algebras. ... More

The proximal point method revisitedDec 17 2017In this short survey, I revisit the role of the proximal point method in large scale optimization. I focus on three recent examples: a proximally guided subgradient method for weakly convex stochastic approximation, the prox-linear algorithm for minimizing ... More

The coloring problem for classes with two small obstructionsJul 01 2013The coloring problem is studied in the paper for graph classes defined by two small forbidden induced subgraphs. We prove some sufficient conditions for effective solvability of the problem in such classes. As their corollary we determine the computational ... More

Formal Languages, Formally and CoinductivelyNov 29 2016Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and elegant proofs ... More

Formal Languages, Formally and CoinductivelyNov 29 2016Sep 18 2017Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and elegant proofs ... More

Algebraic geometry of Hopf-Galois extensionsJul 16 1997Sep 25 1997We continue the study of Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We concentrate on the geometrical side on the subject. We understand how to localize Hopf-Galois extensions and to paste them from local datum. ... More

Miscroscopic origin of de Sitter entropyJan 09 2018It has been argued recently that the entropy of black holes might be associated with soft scalar, graviton and photon states at the event horizon, as number of such possible soft states is proportional to the horizon area. However, the coefficient of ... More

Numerically explicit version of the Pólya--Vinogradov inequalityJul 02 2011In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obtained by C. Pomerance.

On a problem of Dobrowolski--WilliamsJul 02 2011In this paper we prove new upper bounds for the sum $\sum_{n=a+1}^{a+N}f(n)$, for a certain class of arithmetic functions $f$. Our results improve the previous results of G. Bachman and L. Rachakonda.

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-spaceFeb 20 2010Jan 02 2011We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.

Lie algebras in symmetric monoidal categoriesMay 16 2012Jun 18 2013We study algebras defined by identities in symmetric monoidal categories. Our focus is on Lie algebras. Besides usual Lie algebras, there are examples appearing in the study of knot invariants and Rozansky-Witten invariants. Our main result is a proof ... More

Hopf-Galois extensions with central invariantsJul 16 1997Sep 22 1997We study Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We collect general facts about them and discuss some examples arising in the study of restricted Lie algebras and quantum groups at roots of unity. Our focus ... More

A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-spaceAug 14 2012We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).

Weak integral forms and the sixth Kaplansky conjectureJul 04 2019It is a short unpublished note from 1998. I make it public because Cuadra and Meir refer to it in their paper. We precisely state and prove a folklore result that if a finite dimensional semisimple Hopf algebra admits a weak integral form then it is of ... More

D-affinity and Rational VarietiesNov 21 2018May 07 2019We investigate geometry of D-affine varieties. Our main result is that a D-affine rational projective surface over an algebraically closed field is a generalised flag variety of a reductive group.

Cyclic shifts of the van der Corput setNov 12 2008In [13], K. Roth showed that the expected value of the $L^2$ discrepancy of the cyclic shifts of the $N$ point van der Corput set is bounded by a constant multiple of $\sqrt{\log N}$, thus guaranteeing the existence of a shift with asymptotically minimal ... More

Dorronsoro's theorem and a small generalizationJun 21 2015We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

The mean value of Frobenius numbers with three argumentsMar 28 2011We prove an asymptotic formula for the mean value of Frobenius numbers with three arguments. To prove this we use a new method invented by A. Ustinov, Rodseth's algorithm an bounds for exponential sums.

D-affinity and Rational VarietiesNov 21 2018Apr 07 2019We investigate geometry of D-affine varieties. Our main result is that a D-affine uniformly rational projective variety over an algebraically closed field of zero characteristic is a generalised flag variety of a reductive group. This is a partially converse ... More

D-affinity and Rational VarietiesNov 21 2018May 02 2019We investigate geometry of D-affine varieties. Our main result is that a D-affine rational projective surface over an algebraically closed field is a generalised flag variety of a reductive group.

Global solvability of the initial boundary value problem for a model system of one-dimensional equations of polytropic flows of viscous compressible fluid mixturesOct 19 2017Oct 20 2017We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for the strong ... More

Compact domains with prescribed convex boundary metrics in quasi-Fuchsian manifoldsMay 07 2014We show the existence of a convex compact domain in a quasi-Fuchsian manifold such that the induced metric on its boundary coincides with a prescribed surface metric of curvature $K\geq-1$ in the sense of A. D. Alexandrov.

Kac-Moody Groups and Their RepresentationsDec 18 2017Feb 12 2019In this expository paper we review some recent results about representations of Kac-Moody groups. We sketch the construction of these groups. If practical, we present the ideas behind the proofs of theorems. At the end we pose open questions.

On germs of finite morphisms of smooth surfacesDec 08 2018Jan 15 2019Questions related to deformations of germs of finite morphisms of smooth surfaces are discussed. A classification of the four-sheeted germs of finite covers $F: (U,o')\to (V,o)$ is given up to smooth deformations, where $(U,o')$ and $(V,o)$ are two connected ... More

The Hesse curve of a Lefschtz pencil of plane curvesApr 05 2017We prove that for a generic Lefschetz pencil of plane curves of degree $d\geq 3$ there exists a curve $H$ (called the Hesse curve of the pencil) of degree $6(d-1)$ and genus $3(4d^2-13d+8)+1$, and such that: $(i)$ $H$ has $d^2$ singular points of multiplicity ... More

On Chisini's Conjecture. IIOct 11 2006It is proved that if $S\subset \mathbb P^N$ is a smooth projective surface and $f:S\to \mathbb P^2$ is a generic linear projection branched over a cuspidal curve $B\subset \mathbb P^2$, then the surface $S$ is determined uniquely up to an isomorphism ... More

Jacobian Conjecture and Nilpotent MappingsMar 29 1998We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).

Instance Segmentation of Biological Images Using Harmonic EmbeddingsApr 10 2019We present a new instance segmentation approach tailored to biological images, where instances may correspond to individual cells, organisms or plant parts. Unlike instance segmentation for user photographs or road scenes, in biological data object instances ... More

On the Galois groups of the dualizing coverings for plane curvesMar 06 2014Let $C_1$ be an irreducible component of a reduced projective curve $C\subset \mathbb P^2$ defined over the field $\mathbb C$, $\mathrm{deg} C_1\geq 2$, and let $T$ be the set of lines $l\subset \mathbb P^2$ meeting $C$ transversally. In the article, ... More

Factorizations in finite groupsMay 10 2011A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each conjugacy class ... More

On the Alexander polynomials of Hurwitz curvesDec 23 2004Properties of the Alexander polynomials of Hurwitz curves are investigated. A complete description of the set of the Alexander polynomials of irreducible Hurwitz curves in the terms of their roots is given.

Duality of planar and spacial curves: new insightDec 05 2014Jun 26 2015We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (degree of the dual curve). Our main observation is that the use of duality ... More

On complete degenerations of surfaces with ordinary singularities in $\mathbb P^3$Feb 24 2009We investigate the problem of existence of degenerations of surfaces in $\mathbb P^3$ with ordinary singularities into plane arrangements in general position.

Comparison theorems for the position-dependent mass Schroedinger equationAug 13 2011The following comparison rules for the discrete spectrum of the position-dependent mass (PDM) Schroedinger equation are established. (i) If a constant mass $m_0$ and a PDM $m(x)$ are ordered everywhere, that is either $m_0\leq m(x)$ or $m_0\geq m(x)$, ... More

On a Chisini ConjectureMar 29 1998Chisini's conjecture asserts that for a cuspidal curve $B\subset \mathbb P^2$ a generic morphism $f$ of a smooth projective surface onto $\mathbb P^2$ of degree $\geq 5$, branched along $B$, is unique up to isomorphism. We prove that if $\deg f$ is greater ... More

On the variety of the inflection points of plane cubic curvesOct 03 2018In the paper, we investigate properties of the nine-dimensional variety of the inflection points of the plane cubic curves. The description of local monodromy groups of the set of inflection points near singular cubic curves is given. Also, it is given ... More

On Σ^1_1-complete Equivalence Relations on the Generalized Baire SpaceSep 18 2012Working with uncountable structures of fixed cardinality, we investigate the complexity of certain equivalence relations and show that if V = L, then many of them are \Sigma^1_1-complete, in particular the isomorphism relation of dense linear orders. ... More

Factorization semigroups and irreducible components of Hurwitz spaceMar 15 2010We introduce a natural structure of a semigroup (isomorphic to a factorization semigroup of the unity in the symmetric group) on the set of irreducible components of Hurwitz space of marked degree $d$ coverings of $\mathbb P^1$ of fixed ramification types. ... More

Alexander modules of irreducible $C$-groupsMar 07 2006A complete description of the Alexander modules of knotted $n$-manifolds in the sphere $S^{n+2}$, $n\geq 2$, and irreducible Hurwitz curves is given. This description is applied to investigate properties of the first homology groups of cyclic coverings ... More

On Boris Moishezon's multiple planesJul 27 1998The text of the talk on Workshop on Topology of Algebraic Varieties in honour of Boris Moishezon, Bonn, MPI, Monday July 27, 1998.

Old and new examples of surfaces of general type with $p_g=0$Apr 06 2004Apr 13 2004Surfaces of general type with geometric genus $p_g=0$, which can be given as Galois covering of the projective plane branched over an arrangement of lines with Galois group $G=(\mathbb Z/q\mathbb Z)^k$, where $k\geq 2$ and $q$ is a prime number, are investigated. ... More

Factorization semigroups and irreducible components of Hurwitz space. IINov 16 2010Dec 06 2011This article is a continuation of the article with the same title (see arXiv:1003.2953v1). Let {\rm $\text{HUR}_{d,t}^{G}(\mathbb P^1)$} be the Hurwitz space of degree $d$ coverings of the projective line $\mathbb P^1$ with Galois group $\mathcal S_d$ ... More

Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flowsJul 05 2016An approach for constructing a low-dissipation numerical method is described. The method is based on a combination of the operator-splitting method, Godunov method, and piecewise-parabolic method on the local stencil. Numerical method was tested on a ... More

Braid Monodromy Factorization and Diffeomorphism TypesMay 20 1999In this manuscript we prove that if two cuspidal plane curves have equivalent braid monodromy factorizations, then they are smoothly isotopic in the plane. As a consequence of this and the Chisini conjecture, we obtain that if two discriminant curves ... More

Amazing examples of nonrational smooth spectral surfacesOct 16 2017Jan 29 2018In this paper we construct first examples of smooth projective surfaces of general type satisfying the following conditions: there are 1) an ample integral curve $C$ with $C^2=1$ and $h^0(X,O_X(C))=1$; \quad 2) a divisor $D$ with $(D, C)_X=g(C)-1$, $h^i(X,O_X(D))=0$, ... More

Distribution of the first particle in discrete orthogonal polynomial ensemblesApr 01 2002We show that the distribution function of the first particle in a discrete orthogonal polynomial ensemble can be obtained through a certain recurrence procedure, if the (difference or q-) log-derivative of the weight function is rational. In a number ... More

Pointwise best approximation results for Galerkin finite element solutions of parabolic problemsAug 05 2015Feb 17 2016In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method uses of continuous ... More

Optimal a priori error estimates of parabolic optimal control problems with a moving point controlJan 11 2017Mar 06 2017In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear finite elements ... More

Kac-Moody Groups and Cosheaves on Davis BuildingApr 25 2017Sep 07 2018We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on projective dimension, ... More

Cascade Connections of Linear Systems and Factorizations of Holomorphic Operator Functions Around a Multiple Zero in Several VariablesFeb 04 2000We show that the factorization problem $\theta (z)=\theta_2(z)\theta_1(z)$ is solvable in the class of Hilbert space operator-valued functions holomorphic on some neighbourhood of $z=0$ in $\nspace{C}{N}$ and having a zero at $z=0$ (here $\theta (z)$ ... More

Multiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete CaseApr 28 1998Mar 24 1999We propose the new generalization of linear stationary dynamical systems with discrete time $t\in\mathbb{Z}$ to the case $t\in\nspace{Z}{N}$. The dynamics of such a system can be reproduced by means of its associated multiparametric Lax-Phillips semigroup. ... More

BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimensionNov 21 2014Jul 09 2015In the current paper we obtain discrepancy estimates in exponential Orlicz and BMO spaces in arbitrary dimension $d \ge 3$. In particular, we use dyadic harmonic analysis to prove that for the so-called digital nets of order $2$ the BMO${}^d$ and $\exp ... More

A Deterministic Approximation Algorithm for Computing a Permanent of a 0,1 matrixFeb 02 2007We construct a deterministic approximation algorithm for computing a permanent of a $0,1$ $n$ by $n$ matrix to within a multiplicative factor $(1+\epsilon)^n$, for arbitrary $\epsilon>0$. When the graph underlying the matrix is a constant degree expander ... More

Graphical Convergence of Subgradients in Nonconvex Optimization and LearningOct 17 2018Dec 17 2018We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such losses. We ... More

Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functionsFeb 08 2018Feb 19 2018We prove that the proximal stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. As a consequence, we resolve an open question on the convergence rate of the proximal ... More

Relative velocity of dark matter and baryonic fluids and the formation of the first structuresMay 13 2010Oct 18 2010At the time of recombination, baryons and photons decoupled and the sound speed in the baryonic fluid dropped from relativistic to the thermal velocities of the hydrogen atoms. This is less than the relative velocities of baryons and dark matter computed ... More

Correlation Functions in N=3 Superconformal TheoryJun 17 2010Jan 31 2011Using a superspace representation of the N=3 Neveau-Schwarz super Virasoro algebra, we find solutions of N=3 super Ward identities. Global transformations generated by the non-abelian supercurrent require not only superfields, but also functions of Grassmann ... More

An accelerated algorithm for minimizing convex compositionsApr 30 2016We describe a new proximal algorithm for minimizing compositions of finite-valued convex functions with smooth mappings. When applied to convex optimization problems having an additive composite form, the algorithm reduces to FISTA. The method both realizes ... More

The two-dimensional small ball inequality and binary netsNov 23 2015In the current paper we present a new proof of the small ball inequality in two dimensions. More importantly, this new argument, based on an approach inspired by lacunary Fourier series, reveals the first formal connection between this inequality and ... More

Stability of Skorokhod problem is undecidableJul 10 2010Skorokhod problem arises in studying Reflected Brownian Motion (RBM) on an non-negative orthant, specifically in the context of queueing networks in the heavy traffic regime. One of the key problems is identifying conditions for stability of a Skorokhod ... More

Regular bipartite graphs and intersecting familiesNov 09 2016Oct 18 2017In this paper we present a simple unifying approach to prove several statements about intersecting and cross-intersecting families, including the Erd\H os--Ko--Rado theorem, the Hilton--Milner theorem, a theorem due to Frankl concerning the size of intersecting ... More

Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Stochastic Partial Differential EquationsMay 09 2019Jun 26 2019We consider a method for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with ... More

Multiparametric Passive Linear Stationary Dynamical Scattering Systems: Discrete Case, II: Existence of Conservative DilationsOct 19 1998Mar 28 1999In the present paper we introduce the notion of dilation of a multiparametric linear stationary dynamical system (systems of this type, in particular passive, and conservative scattering ones were first introduced in func-an/9804130). We establish the ... More

Solvability of a steady boundary-value problem for the equations of one-temperature viscous compressible heat-conducting bifluidsOct 18 2017We consider a boundary-value problem describing the steady motion of a two-component mixture of viscous compressible heat-conducting fluids in a bounded domain. We make no simplifying assumptions except for postulating the coincidence of phase temperatures ... More

Global unique solvability of the initial-boundary value problem for the equations of one-dimensional polytropic flows of viscous compressible multifluidsSep 18 2018We consider the equations which describe polytropic one-dimensional flows of viscous compressible multifluids. We prove global existence and uniqueness of a solution to the initial-boundary value problem which corresponds to the flow in a bounded space ... More

Switchability and collapsibility of Gap AlgebrasOct 21 2015Let A be an idempotent algebra on a 3-element domain D that omits a G-set for a factor. Suppose A is not \alpha\beta-projective (for some alpha, beta subsets of D) and is not collapsible. It follows that A is switchable. We prove that, for every finite ... More

The Connes character formula for locally compact spectral triplesMar 05 2018May 04 2018A fundamental tool in noncommutative geometry is Connes' character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterisation of manifolds. A non-compact space ... More

Dark matter in a Simplest Little Higgs with T-parity modelMar 27 2009Little Higgs models may provide a viable alternative to supersymmetry as an extension of the Standard Model. After the introduction of a discrete $Z_2$ symmetry, dubbed T-parity into Little Higgs models they also contain a promising dark matter candidate. ... More

Global and interior pointwise best approximation results for the gradient of Galerkin solutions for parabolic problemsJun 20 2016In this paper we establish best approximation property of fully discrete Galerkin solutions of the second parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method consists of ... More

Discrete maximal parabolic regularity for Galerkin finite element methodsMay 18 2015Feb 05 2016The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the time discontinuous Galerkin solution of linear parabolic equations. Such estimates have many applications. They are essential, ... More

Parametric interaction and intensification of nonlinear Kelvin wavesJul 03 2008Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\omega_t$ or the inertial -- $\omega_i$ frequency and oscillations of synoptic -- $\Omega $ frequency of the background coastal current ... More

A Note on Application of the Method of Approximation of Iterated Stochastic Ito integrals Based on Generalized Multiple Fourier Series to the Numerical Integration of Stochastic Partial Differential EquationsMay 09 2019We consider a way for approximation of iterated stochastic Ito integrals with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with respect to finite-dimensional Wiener process ... More

A Note on Application of the Method of Approximation of Iterated Stochastic Ito integrals Based on Generalized Multiple Fourier Series to the Numerical Integration of Stochastic Partial Differential EquationsMay 09 2019May 12 2019We consider a way for approximation of iterated stochastic Ito integrals with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with respect to finite-dimensional Wiener process ... More

Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Stochastic Partial Differential EquationsMay 09 2019Jul 03 2019We consider a method for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with ... More

Expansion of Multiple Stratonovich Stochastic Integrals of Fifth Multiplicity, Based on Generalized Multiple Fourier SeriesFeb 02 2018This article is devoted to the expansion of multiple Stratonovich stochastic integrals of fifth multiplicity, based on the method of generalized multiple Fourier series. We consider the expansion of multiple Ito stochastic integrals of fifth multiplicity ... More

Expansion of Multiple Stratonovich Stochastic Integrals of Multiplicity 2, Based on Double Fourier-Legendre Series, Summarized by Prinsheim MethodJan 06 2018The article is devoted to the expansion of multiple Stratonovich stochastic integrals of multiplicity 2 into double series of standard Gaussian random variables. The proof of the expansion is based on application of double Fourier-Legendre series, summarized ... More

Application of the Fourier Method to the Mean-Square Approximation of Multiple Ito and Stratonovich Stochastic IntegralsDec 25 2017Jun 07 2018The article is devoted to the mean-square approximation of multiple Ito and Stratonovich stochastic integrals in the context of numerical integration of Ito stochastic differential equations. The expansion of multiple Ito stochastic integrals of any arbitrary ... More

New Representation of Levy Stochastic Area, Based on Legendre polynomialsJul 01 2018The article is devoted to obtainment a new representation of Levy stochastic area, based on Legengre polynomials. We use expansion of multiple Ito stochastic integrals, based on multiple Fourier-Legendre series converging in the mean. The mentioned new ... More

To Numerical Modeling With Strong Orders 1.5 and 2.0 of Convergence for Multidimensional Dynamical Systems With Random DisturbancesFeb 03 2018Jun 06 2018The article is devoted to numerical methods with strong orders 1.5 and 2.0 of convergence for multidimensional dynamical systems with random disturbances. We consider explicit one-step numerical methods for Ito stochastic differential equations. For numerical ... More

Expansions of Multiple Stratonovich Stochastic Integrals From the Taylor-Stratonovich Expansion, Based on Multiple Trigonometric Fourier Series. Comparison With the Milstein ExpansionJan 25 2018Jun 17 2018The article is devoted to comparison of the Milstein expansion of multiple stochastic integrals with the method of expansion of multiple stochastic integrals, based on generalized multiple Fourier series. We consider some practical material connected ... More

Expansion of Triple Stratonovich Stochastic Integrals, Based on Generalized Multiple Fourier Series, Converging in the Mean: General Case of Series SummationJan 04 2018The article is devoted to the development of the method of expansion and mean-square approximation of multiple Ito stochastic integrals, based on generalized multiple Fourier series, converging in the mean. We adapt this method for the triple Stratonovich ... More

Expansion of Multiple Ito Stochastic Integrals of Arbitrary Multiplicity, Based on Generalized Multiple Fourier Series, Converging in the MeanDec 28 2017Aug 19 2018The article is devoted to expansions of multiple Ito stochastic integrals, based on generalized multiple Fourier series converging in the mean. The method of generalized multiple Fourier series for expansions and mean-square approximations of multiple ... More

Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Stochastic Partial Differential EquationsMay 09 2019Jul 08 2019We consider a method for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with ... More

Cascade Connection of Multiparametric Linear Systems and a Conservative Realization of Decomposable Inner Operator Functions in BidiskFeb 25 2000We introduce the notion of cascade connection of multiparametric discrete time-invariant linear dynamical systems with unit delay. This allows us to construct the explicit example of conservative realization of a decomposable operator-valued function ... More

Learning Patient Representations from TextMay 05 2018Mining electronic health records for patients who satisfy a set of predefined criteria is known in medical informatics as phenotyping. Phenotyping has numerous applications such as outcome prediction, clinical trial recruitment, and retrospective studies. ... More

Modeling viscous compressible barotropic multi-fluid flowsAug 24 2017Aug 25 2017We study the system of equations which describes barotropic (isentropic) flows of viscous compressible multi-fluids (mixtures of fluids). We study the relations between pressure, densities, concentrations, viscosities and other parameters of the flow ... More

Global solvability of 1D equations of viscous compressible multi-fluidsAug 25 2017We consider the model of viscous compressible multi-fluids with multiple velocities. We review different formulations of the model and the existence results for boundary value problems. We analyze crucial mathematical difficulties which arise during the ... More