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Construction of Lie algebras with special G2-structuresJul 27 2015Feb 14 2016We give a method to obtain new 7-dimensional Lie algebras endowed with closed and coclosed G2-structures starting from 6-dimensional Lie algebras with symplectic half- at SU(3)-structures and half- at SU(3)- structures, respectively. Finally, we describe ... More

Einstein warped G2 and Spin(7) manifoldsMay 15 2018In this paper most of the classes of G2-structures with Einstein induced metric of negative, null or positive scalar curvature are realized. This is carried out by means of warped G2-structures with fiber an Einstein SU(3) manifold. The torsion forms ... More

Solutions of the Laplacian flow and coflow of a Locally Conformal Parallel $\mathrm{G}_2$-structureNov 23 2017We study the Laplacian flow of a $\mathrm{G}_2$-structure where this latter structure is claimed to be Locally Conformal Parallel. The first examples of long time solutions of this flow with the Locally Conformal Parallel condition are given. These examples ... More

Laplacian coflow for warped $\mathrm{G}_2$-structuresApr 12 2019We consider the Laplacian coflow of a $\mathrm{G}_2$-structure on warped products of the form $M^7= M^6 \times_f S^1$ with $M^6$ a compact 6-manifold endowed with an $\mathrm{SU}(3)$-structure. We give an explicit reinterpretation of this flow as a set ... More

G_2-structures on Einstein solvmanifoldsJul 16 2012Dec 30 2013We study the $G_2$ analogue of the Goldberg conjecture on non-compact solvmanifolds. In contrast to the almost-K\"ahler case we prove that a 7-dimensional solvmanifold cannot admit any left-invariant calibrated $G_2$-structure $\varphi$ such that the ... More

Einstein $\mathrm{SU}(3)$ and $\mathrm{G}_2$ structuresJul 26 2016Jul 27 2016We describe a method to obtain $\mathrm{SU}(3)$-structures and $\mathrm{G}_2$-structures on 6 and 7-dimensional manifolds respectively, such that its associated metric is Einstein. More concretely, we have that different classes of $\mathrm{SU}(2)$ and ... More

Parsing Images of Overlapping Organisms with Deep Singling-Out NetworksDec 19 2016This work is motivated by the mostly unsolved task of parsing biological images with multiple overlapping articulated model organisms (such as worms or larvae). We present a general approach that separates the two main challenges associated with such ... More

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

Laplacian flow of closed $G_2$-structures inducing nilsolitonsOct 07 2013Mar 27 2015We study the existence of left invariant closed $G_2$-structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these $G_2$-structures, we show long time existence and uniqueness of solution for the ... More

Exact and approximate analytical solutions of Weiss equation of ferromagnetism and their experimental relevanceFeb 14 2017The recent progress in the theory of generalized Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical purposes. Precise approximate analytical solutions are ... More

Module categories over representations of $SL_q(2)$ in the non-semisimple caseSep 22 2005Dec 27 2006We classify semisimple module categories over the tensor category of representations of quantum SL(2) extending previous results to the roots of unity and positive characteristic cases.

A remark on cuspidal local systemsDec 09 2003In this note we show that all reductive groups are clean in odd characteristic. In characteristic 2 there are two cuspidal local systems (one for $F_4$ and one for $E_8$) which can not be handled by our method.

Multi-fusion categories of Harish-Chandra bimodulesApr 25 2014We survey some results on tensor products of irreducible Harish-Chandra bimodules. It turns out that such tensor products are semisimple in suitable Serre quotient categories. We explain how to identify the resulting semisimple tensor categories and describe ... More

Pivotal fusion categories of rank 3 (with an Appendix written jointly with Dmitri Nikshych)Sep 18 2013We classify all fusion categories of rank 3 that admit a pivotal structure over an algebraically closed field of characteristic zero. Also in the Appendix (joint with D.Nikshych) we give some restrictions on Grothendieck rings of near-group categories. ... More

Skin Friction in Simple Wall - Bounded Shear Flows in Large Reynolds Number LimitSep 24 2009Feb 09 2010A global approach to analysis of fully developed turbulent flows in pipes/channels and zero pressure gradient boundary layers is proposed. A new dynamic definition of the boundary layer thickness $\delta(x)$, where $x$ is the distance to the plate origin, ... More

Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent FlowsJun 29 2007Small separation between reactants, not exceeding $10^{-8}-10^{-7}cm$, is the necessary condition for various chemical reactions. It is shown that random advection and stretching by turbulence leads to formation of scalar-enriched sheets of {\it strongly ... More

Probability Densities in Strong TurbulenceDec 12 2005Dec 14 2005According to modern developments in turbulence theory, the "dissipation" scales (u.v. cut-offs) $\eta$ form a random field related to velocity increments $\delta_{\eta}u$. In this work we, using Mellin's transform combined with the Gaussain large -scale ... More

Mean- Field Approximation and Extended Self-Similarity in TurbulenceAug 17 2001Recent experimental discovery of extended self-similarity (ESS) was one of the most interesting developments, enabling precise determination of the scaling exponents of fully developed turbulence. Here we show that the ESS is consistent with the Navier-Stokes ... More

Two-Dimensional turbulence in the inverse cascade rangeApr 07 1999Apr 28 1999Numerical and physical experiments on the forced two-dimensional Navier-Stokes equations show that transverse velocity differences are described by ``normal'' Kolmogorov scaling $<(\Delta v)^{2n}> \propto r^{2n/3}$ and obey a gaussian statistics. Since ... More

Skin friction in zero-pressure-gradient boundary layersAug 02 2010A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as $Re_{\delta}\rightarrow \infty$, the dynamically defined boundary layer thickness ... More

Semiclassical analysis of the schr{ö}dinger equation with conical singularitiesAug 12 2016Aug 17 2016In this article we study the propagation of Wigner measures linked to solutions of the Schr{\"o}dinger equation with potentials presenting conical singularities and show that they are transported by two different Hamiltonian flows, one over the bundle ... More

Zero temperature limit for (1+1) directed polymers with correlated random potentialOct 19 2016Zero temperature limit in (1+1) directed polymers with finite range correlated random potential is studied. In terms of the standard replica technique it is demonstrated that in this limit the considered system reveals the one-step replica symmetry breaking ... More

How many times can the volume of a convex polyhedron be increased by isometric deformations?Jul 22 2016We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c>0$, we construct two oblique triangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvex and intrinsically isometric ... More

Code Generation for Event-BFeb 05 2016Stepwise refinement and Design-by-Contract are two formal approaches for modelling systems. These approaches are widely used in the development of systems. Both approaches have (dis-)advantages. This thesis aims to answer, is it possible to combine both ... More

Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDEDec 02 2015These lectures were given in Session 1: "Vertex algebras, W-algebras, and applications" of INdAM Intensive research period "Perspectives in Lie Theory" at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy, December 9, 2014 -- February 28, ... More

Folding a Tree into a MapSep 25 2015Analysis of the retrieval architecture of the highly influential UNIX file system (\cite{Ritchie}\cite{multicsfs}) provides insight into design methods, constraints, and possible alternatives. The basic architecture can be understood in terms of function ... More

Distance-preserving subgraphs of Johnson graphsMar 13 2015Nov 01 2015We give a characterization of distance--preserving subgraphs of Johnson graphs, i.e. of graphs which are isometrically embeddable into Johnson graphs (the Johnson graph $J(m,\Lambda)$ has the subsets of cardinality $m$ of a set $\Lambda$ as the vertex--set ... More

State machine models of timing and circuit designMar 02 2010This paper illustrates a technique for specifying the detailed timing, logical operation, and compositional circuit design of digital circuits in terms of ordinary state machines with output (transducers). The method is illustrated here with specifications ... More

General trends of the late period of evolution in the quasichemical model of nucleationJul 28 2006The periods after the end of the "primary" nucleation are considered. The approximate analytical description is given. The process is split into several periods which form the loop of evolution.

Explicit two cycle model in investigation of stochastic effects in diffusion regime of metastable phase decayOct 24 2004The theory for manifestation of stochastic appearance of embryos in the global decay of metastable phase has been constructed. The regime of droplets growth is supposed to be both free molecular one and diffusion one. The deviation for a mean droplets ... More

A simple method to determine parameters of embryos distribution in homogeneous nucleation under dynamic conditionsJul 22 2002A simple method to get all main characteristics of nucleation process is proposed. The advantage of this method is an applicability to situations with non-linear behavior in time of effective external source of vapor. It is important because already existed ... More

Heterogeneous condensation in dense mediaMar 31 2000The theoretical description of the heterogeneous nucleation kinetics is presented. This description takes into account the perturbation of the vapor phase initiated by the growing droplets. The form of the density profile around the growing droplet is ... More

Effects of stochastic nucleation in the first order phase transitionJul 01 2002The effects of stochastic apppearence of embryos of a new phase are analyzed analytically. A new approach by the similarity of nucleation conditions is proposed. Corrections for a number of droplets are estimated. A comparison with numerical simulation ... More

Dirac variables in gauge theoriesSep 28 2001Sep 30 2001The review is devoted to a relativistic formulation of the first Dirac quantization of QED (1927) and its generalization to the non-Abelian theories (Yang-Mills and QCD) with the topological degeneration of initial data. Using the Dirac variables we give ... More

Automorphisms of local fields of period $p$ and nilpotent class $<p$Mar 17 2014May 17 2016Suppose $K$ is a finite field extension of $\mathbb{Q} _p$ containing a primitive $p$-th root of unity. Let $\Gamma _{<p}$ be the Galois group of a maximal $p$-extension of $K$ with the Galois group of period $p$ and nilpotent class $<p$. In the paper ... More

A restriction theorem for torsion-free sheaves on some elliptic manifoldsDec 27 2012We prove that if $X$ is the total space of an elliptic principal bundle $\pi:X\ra B$ which is non-K\"ahler, then the restriction of any torsion-free sheaf on $X$ to the general fiber of $\pi$ is semi-stable.

Singular integral operators on non-compact manifolds and analysis on polyhedral domainsFeb 19 2004We review the definition of a Lie manifold $(M, \VV)$ and the construction of the algebra $\Psi\sp{\infty}\sb{\VV}(M)$ of pseudodifferential operators on a Lie manifold $(M, \VV)$. We give some concrete Fredholmness conditions for pseudodifferential operators ... More

An index theorem for gauge-invariant families: The case of solvable groupsJan 21 2002We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers of $\GR \to ... More

Distribution function of the endpoint fluctuations of one-dimensional directed polymers in a random potentialSep 27 2012Jan 22 2013The explicit expression for the the probability distribution function of the endpoint fluctuations of one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to ... More

Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in one-dimensional directed polymers with free boundary conditionsSep 17 2012The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions. It is shown ... More

Mean Field Theory of the Three-Dimensional Dipole Superspin GlassesJan 18 2010Sep 16 2010We study the three-dimensional system of magnetic nanoparticle dipoles randomly oriented along quenched easy axes. Directions of the magnetic momenta are described by the Ising variables which allow the momenta to flip along their random orientations. ... More

Mean Field Model of a GlassSep 20 2002In this paper we propose a simple mean-field "toy" model for the liquid-glass phase transition. This is the system of $N$ point-like particles confined in a finite volume of a $D$-dimensional space interacting via infinite-range oscillating potential. ... More

Calculus of the first non-trivial 1-cocycle of the space of long knotsFeb 24 2005Apr 18 2005For the space of long knots in R^3, Vassiliev's theory defines the so called finite order cocycles. Zero degree cocycles are finite type knot invariants. The first non-trivial cocycle of positive dimension in the space of long knots has dimension one ... More

Constraining the two-Higgs doublet models with the LHC dataOct 03 2013Oct 07 2013The recent discovery of a Standard Model-like boson with mass of about 126 GeV seems to be the first direct information on the electroweak symmetry breaking mechanism. Using the available experimental data from the LHC and Tevatron we study the implications ... More

Effects of dead time and after-pulses in photon detector on measured statistics of stochastic radiationNov 19 2013Many physical experiments require analysis of the statistics of fluctuating radiation. In the case of an ideal single-photon detector, the contribution of photon noise to the statistics of the registered signal has been thoroughly examined. However, practical ... More

On primitive idealsFeb 10 2002May 28 2012We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem', to much wider classes of algebras. Our general version of Irreducibility theorem says that if A is ... More

Non-commutative Symplectic Geometry, Quiver varieties, and OperadsMay 17 2000Jun 02 2000Quiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we show that many ... More

Geometric Methods in Representation Theory of Hecke Algebras and Quantum GroupsJan 31 1998Mar 05 1998These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in Representation ... More

The global nilpotent variety is LagrangianApr 10 1997Oct 31 2000The purpose of this note is to present a short elementary proof of a theorem due to Faltings and Laumon, saying that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the moduli space of G-bundles on a complex compact curve. ... More

Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reductionOct 02 2013Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We present here ... More

Complete integrable systems with unconfined singularitiesApr 10 2007We prove that any globally periodic rational discrete system in K^k(where K denotes either R or C), has unconfined singularities, zero algebraic entropy and it is complete integrable (that is, it has as many functionally independent first integrals as ... More

What are the right values of $\bar Λ$ and the heavy quark kinetic energy?Apr 21 1996May 06 1996The values of two important parameters of the heavy quark effective theory,\, $\bar \Lambda$ and $\mu_\pi^2$ (the mean value of the heavy quark three momentum squared),\, have been determined recently in \cite {GKLW} from the precise CLEO data on the ... More

Properties of {\cal N}=1 SUSY Yang-Mills vacuums and domain wallsAug 16 1998Mar 18 1999It is shown that there is no chirally symmetric vacuum state in the {cal N}=1 supersymmetric Yang-Mills theory. The values of the gluino condensate and the vacuum energy density are found out through a direct instanton calculation. A qualitative picture ... More

Electrostatic theory of metal whiskersJan 29 2014Needle shaped whiskers grow on various metal surfaces often across leads of a package causing current leakage or short circuits and raising reliability issues in electronic components. The nature of metal whiskers remains a mystery after several decades ... More

Shape- and topology-dependent heat capacity of few-particle systemsApr 02 2012Thermal properties of few-fermion (n < 5) systems are investigated. The dependence of the heat capacity on the topology and shape of the cavity containing the particles is analyzed. It is found that the maximum of the heat capacity, occuring at low T, ... More

Exact thermodynamics of a planar array of Ginzburg-Landau chains with nn and nnn interactionsOct 01 2007The exact expression of the free energy of a planar array of a Ginzburg-Landau chains with nn and nnn interaction is obtained. The critical behaviour of the specific heat is not qualitatively modified by taking into account the nnn interaction.

Metallic phase in a two-dimensional disordered Fermi system with singular interactionsJul 30 2005Oct 12 2005We consider a disordered system of gapless fermions interacting with a singular transverse (2+1)-dimensional gauge-field. We study quantum corrections to fermion conductivity and show that they are very different from those in a Fermi liquid with non-singular ... More

New applications of the Lambert and generalized Lambert functions in ferromagnetism and quantum mechanicsNov 03 2016The applications of the recent results obtained in the theory of generalized Lambert functions, to the mean field theory of ferromagnetism are presented. As a consequence, all the predictions of the Weiss theory of ferromagnetism can be explicitly and ... More

A Hypergraph Dictatorship Test with Perfect CompletenessNov 12 2008Apr 11 2009A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based $\PCP$ construction. Such a test has oracle access to a collection of functions and determines whether all the functions ... More

The (weak-$L^2$) Boundedness of The Quadratic Carleson OperatorOct 11 2007Sep 06 2008We prove that the generalized Carleson operator with polynomial phase function of degree two is of weak type (2,2). For this, we introduce a new approach to the time-frequency analysis of the quadratic phase.

Econophysics Macroeconomic ModelJan 20 2017This paper presents macroeconomic model that is based on parallels between macroeconomic multi-agent systems and multi-particle systems. We use risk ratings of economic agents as their coordinates on economic space. Aggregates of economic or financial ... More

Coordinate System, Temperature and GravityJul 09 2001We discuss the problem of applicability of Coordinate Systems (or Frames) that determine (t,x,y,z) values - the initial notions for most physical theories. Equipment that measure these values - Clocks and Meters - are based at Reference System and are ... More

State Space Methods for Granger-Geweke Causality MeasuresJan 19 2015At least two recent developments have put the spotlight on some significant gaps in the theory of multivariate time series. The recent interest in the dynamics of networks; and the advent, across a range of applications, of measuring modalities that operate ... More

Polynomial reformulation of the Kuo criteria for v-sufficiency of map-germsJul 03 2009Jan 03 2011In the paper a set of necessary and sufficient conditions for \textit{v-}sufficiency (equiv. \textit{sv-}sufficiency) of jets of map-germs $f:(\mathbb{R}^{n},0)\to (\mathbb{R}^{m},0)$ is proved which generalize both the Kuiper-Kuo and the Thom conditions ... More

Infrared Dynamics in Vector-Like Gauge Theories: QCD and BeyondSep 07 2001Pade-approximant methods are used to extract information about leading positive zeros or poles of QCD and SQCD beta-functions from the known terms of their perturbative series. For QCD, such methods are seen to corroborate the flavour-threshold behaviour ... More

On a special case of the Herbert Stahl theoremJun 22 2016The BMV conjecture states that for $n\times n$ Hermitian matrices $A$ and $B$ the function $f_{A,B}(t)=trace{\, } e^{tA+B}$ is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is based on ingenious ... More

On the BMV conjecture for 2\times2 matrices and the exponential convexity of the function \cosh(\sqrt{at^2+b})May 01 2015Nov 01 2015The BMV conjecture states that for \(n\times n\) Hermitian matrices \(A\) and \(B\) the function \(f_{A,B}(t)=\tr e^{tA+B}\) is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is based on ingenious ... More

The index of operators on foliated bundlesJul 03 1996We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses techniques for analizing ... More

Ramification filtration of the Galois group of a local field via deformationsJan 09 2017Dec 21 2018Let $\mathcal K$ be a field of formal Laurent series with coefficients in a finite field of characteristic $p$, $\mathcal G_{<p}$ --- the maximal quotient of $\operatorname{Gal} (\mathcal K_{sep}/\mathcal K)$ of period $p$ and nilpotent class $<p$ and ... More

Contradictions in some primes conjecturesJul 22 2014This paper demonstrates that from the Cramer's, Hardy-Littlewood's and Bateman-Horn's conjectures (suggest that the probability of a large positive integer being $x$ a prime - $\frac {1} {\ln(x)}$) it follows that the events consisting in a positive integer ... More

Badly approximable points on manifoldsApr 02 2013Mar 30 2016This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of the sets of weighted ... More

A relaxation scheme for computation of the joint spectral radius of matrix setsOct 23 2008Feb 17 2010The problem of computation of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In the paper an iteration procedure is considered that allows to build numerically Barabanov norms for the irreducible ... More

On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formulaOct 13 2008Feb 17 2010In various problems of control theory, non-autonomous and multivalued dynamical systems, wavelet theory and other fields of mathematics information about the rate of growth of matrix products with factors taken from some matrix set plays a key role. One ... More

Universal Higher Order GrammarFeb 25 2011We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities. This class is ... More

Minimax theorem for the spectral radius of the product of non-negative matricesMar 17 2016Dec 26 2016We prove the minimax equality for the spectral radius $\rho(AB)$ of the product of matrices $A\in\mathcal{A}$ and $B\in\mathcal{B}$, where $\mathcal{A}$ and $\mathcal{B}$ are compact sets of non-negative matrices of dimensions $N\times M$ and $M\times ... More

Modular group algebras with almost maximal Lie nilpotency indices, IIJul 06 2006Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that, if KG is Lie nilpotent, then its upper (or lower) Lie nilpotency index is at most |G'|+1, where |G'| is the order of the commutator subgroup. Previously ... More

A Note on the Polynomial Carleson Operator in higher dimensionsDec 08 2017We prove the $L^p$-boundedness, $1<p<\infty$, of the Polynomial Carleson operator in general dimension. This follows the author's resolution of the one dimensional case as well as the work of Zorin-Kranich on the higher dimensional case in the setting ... More

Exact inversion of Funk-Radon transforms with non-algebraic geometriesNov 28 2017Any even function defined on 2-sphere is reconstructed from its integrals over big circles by means of the classical Funk formula. For the non-geodesic Funk transform on the sphere of arbitrary dimension, there is the explicit inversion formula similar ... More

On the total mean curvature of non-rigid surfacesNov 29 2008Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean ... More

Exponential Decay of Eigenfunctions and Accumulation of Eigenvalues on Manifolds with Axial Analytic Asymptotically Cylindrical EndsJul 25 2010In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling method and the Phragm\'{e}n-Lindel\"{o}f principle we prove exponential decay ... More

Delooping totalization of a multiplicative operadDec 29 2010Dec 30 2010The paper shows that under some conditions the totalization of a cosimplicial space obtained from a multiplicative operad is a double loop space of the space of derived morphisms from the associative operad to the operad itself.

Minimal polynomials of simple highest weight modules over classical Lie algebrasNov 15 2013We completely determine the minimal polynomial of an arbitrary simple highest weight module $L(\lambda)$ over a complex classical Lie algebra $\mathfrak{g}\subseteq\mathfrak{gl}_N$ relative to its defining module $\pi=\mathbb{C}^{N}$. These results are ... More

Symmetric representations of distributions over $\mathbb{R}^2$ by distributions with not more than three-point supportsMar 01 2011We construct symmetric representations of distributions over two-dimensional plane with given mean values as convex combinations of distributions with supports containing not more than three points and with the same mean values.

On the roots of a hyperbolic polynomial pencilApr 27 2016May 01 2016Let $\nu_0(t),\nu_1(t),\,\ldots\,,\nu_n(t)$ be the roots of the equation $R(z)=t$, where $R(z)$ is a rational function of the form \[R(z)=z+\sum\limits_{k=1}^n\frac{\alpha_k}{z-\mu_k},\] $\mu_k$ are pairwise different real numbers, $\alpha_k>0,\,1\leq{}k\leq{}n$. ... More

A problem in Pythagorean ArithmeticOct 04 2015Problem 2 at the 56th International Mathematical Olympiad (2015) asks for all triples (a,b,c) of positive integers for which ab-c, bc-a, and ca-b are all powers of 2. We show that this problem requires only a primitive form of arithmetic, going back to ... More

Quantum cohomology of smooth complete intersections in weighted projective spaces and singular toric varietiesJul 12 2005Jul 25 2007We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\geq 3$, which are complete intersections in weighted projective spaces ... More

Gromov-Witten invariants of Fano threefolds of genera 6 and 8Oct 13 2004Jan 07 2007The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$. This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. More precisely, we find counting matrices ... More

New manifestations of the Darboux's rotation and translation fields of a surfaceOct 27 2009We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal bending) and ... More

Blowing-up points on l.c. K. manifoldsJun 09 2009It is a classical result, due to F. Tricceri, that the blow-up of a manifold of locally conformally K\"ahler (l.c.K. for short) type at some point is again of l.c.K. type. However, the proof given in \cite{Tric} is somehow unclear. We give a different ... More

Fredholm criteria for pseudodifferential operators and induced representations of groupoid algebrasFeb 15 2016We characterize the groupoids for which an operator is Fredholm if, and only if, its principal symbol and all its boundary restrictions are invertible. A groupoid with this property is called {\em Fredholm}. Using results on the Effros-Hahn conjecture, ... More

Desingularization of Lie groupoids and pseudodifferential operators on singular spacesDec 29 2015We introduce and study a "desingularization" of a Lie groupoid $G$ along an "$A(G)$-tame" submanifold $L$ of the space of units $M$. An $A(G)$-tame submanifold $L \subset M$ is one that has, by definition, a tubular neighborhood on which $A(G)$ becomes ... More

Flexible polyhedra in the Minkowski 3-spaceNov 01 2001Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change its shape ... More

Upper Estimates for Electronic Density in Heavy Atoms and MoleculesJun 03 2019We derive an upper estimate for electronic density in heavy atoms and molecules.

Complete Differentiable Semiclassical Spectral AsymptoticsSep 19 2018For an operator $A:= A_h= A^0(hD) + V(x,hD)$ with a "potential" $V$ decaying as $|x|\to \infty$ we establish under certain assumptions the complete and differentiable with respect to $\tau$ asymptotics of $e_h(x,x,\tau)$ where $e_h(x,y,\tau)$ is the Schwartz ... More

2D- and 3DMagnetic Schroedinger Operators: Short Loops, Pointwise Spectral Asymptotics and Asymptotics of Dirac EnergyAug 21 2010Dec 07 2010We consider 2- and 3-dimensional Schr\"odinger or generalized Schr\"odinger-Pauli operators with the non-degenerating magnetic field in the open domain under certain non-degeneracy assumptions we derive pointwise spectral asymptotics. We also consider ... More

Schroedinger Operator with Strong Magnetic Field: Propagation of singularities and sharper asymptoticsMay 04 2010We consider 2-dimensional Schr\"odinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o(\mu^{-1}h^{-1})$ or better. We also consider 3-dimensional Schr\"odinger operator with the non-degenerating ... More

Finite semigroups embed in finitely presented congruence-free monoidsJan 22 2013We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture.

Algebra versus analysis in the theory of flexible polyhedraFeb 02 2009Jul 06 2010Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used ... More

Analytical evaluation and asymptotic evaluation of Dawson's integral and related functions in mathematical physicsMar 14 2017Dawson's integral and related functions in mathematical physics that include the complex error function (Faddeeva's integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev's integral are analytically evaluated ... More

Summation arithmetic functions with asymptotically independent summandsNov 29 2018Mar 18 2019The summation arithmetic functions with asymptotically independent summands are studied in the paper. We prove statements about the condition under which the summation arithmetic functions have asymptotically independent summands. It is also prove that ... More