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Some congruences related to a congruence of Van HammeMar 09 2019We establish some supercongruences related to a supercongruence of Van Hamme, such as \begin{align*} \sum_{k=0}^{(p+1)/2} (-1)^k (4k-1)\frac{(-\frac{1}{2})_k^3}{k!^3} &\equiv p(-1)^{(p+1)/2}+p^3(2-E_{p-3})\pmod{p^{4}},\\ \sum_{k=0}^{(p+1)/2} (4k-1)^5 ... More

$q$-Analogues of two Ramanujan-type formulas for $1/π$Feb 06 2018Feb 13 2018We give $q$-analogues of the following two Ramanujan-type formulas for $1/\pi$: \begin{align*} \sum_{k=0}^\infty (6k+1)\frac{(\frac{1}{2})_k^3}{k!^3 4^k} =\frac{4}{\pi} \quad\text{and}\quad \sum_{k=0}^\infty (-1)^k(6k+1)\frac{(\frac{1}{2})_k^3}{k!^3 8^k ... More

Global inequality in energy consumption from 1980 to 2010Dec 22 2013Mar 08 2014We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980-2010. We find that the Lorenz curves have moved up during this time period, and the ... More

Downlink Energy Efficiency of Power Allocation and Wireless Backhaul Bandwidth Allocation in Heterogeneous Small Cell NetworksOct 09 2017The widespread application of wireless services and dense devices access have triggered huge energy consumption. Because of the environmental and financial considerations, energy-efficient design in wireless networks becomes an inevitable trend. To the ... More

Patch Correspondences for Interpreting Pixel-level CNNsNov 29 2017Sep 04 2018We present compositional nearest neighbors (CompNN), a simple approach to visually interpreting distributed representations learned by a convolutional neural network (CNN) for pixel-level tasks (e.g., image synthesis and segmentation). It does so by reconstructing ... More

A Teacher-Student Framework for Zero-Resource Neural Machine TranslationMay 02 2017While end-to-end neural machine translation (NMT) has made remarkable progress recently, it still suffers from the data scarcity problem for low-resource language pairs and domains. In this paper, we propose a method for zero-resource NMT by assuming ... More

Topology optimization of freeform large-area metasurfacesFeb 08 2019We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how topology optimization, ... More

Optimizing Floating Locations in Hard Disk Drive by Solving Max-min OptimizationJan 12 2018Floating operation is very critical in power management in hard disk drive (HDD), during which no control command is applied to the read/write head but a fixed current to counteract actuator flex bias. External disturbance induced drift of head may result ... More

Low Complexity Algorithms for Robust Multigroup Multicast BeamformingMay 14 2019Existing methods for robust multigroup multicast beamforming obtain feasible points using semidefinite relaxation (SDR) and Gaussian randomization, and have high computational complexity. In this letter, we consider the robust multigroup multicast beamforming ... More

Octave-spanning supercontinuum generation in a silicon-rich nitride waveguideJun 02 2016We experimentally show octave-spanning supercontinuum generation in a non-stoichiometric silicon-rich nitride waveguide when pumped by femtosecond pulses from an erbium fiber laser. The pulse energy and bandwidth are comparable to results achieved in ... More

Mixed-Timescale Beamforming and Power Splitting for Massive MIMO Aided SWIPT IoT NetworkAug 20 2019Traditional simultaneous wireless information and power transfer (SWIPT) with power splitting assumes perfect channel state information (CSI), which is difficult to obtain especially in the massive multiple-input-multiple-output (MIMO) regime. In this ... More

Comparison of 2D simulation models to estimate the critical current of a coated superconducting coilJul 26 2018Superconductors have been being applied to a variety of large-scale power applications, including magnets, electric machines, and fault current limiters, because they can enable a compact, lightweight and high efficiency design. In applications such those ... More

Transient Spectroscopy of Glass-Embedded Perovskite Quantum Dots: Novel Structures in an Old WrappingDec 03 2018Semiconductor doped glasses had been used by the research and engineering communities as color filters or saturable absorbers well before it was realized that their optical properties were defined by tiny specs of semiconductor matter known presently ... More

Distributed Virtual Resource Allocation in Small Cell Networks with Full Duplex Self-backhauls and VirtualizationOct 20 2015Wireless network virtualization has attracted great attentions from both academia and industry. Another emerging technology for next generation wireless networks is in-band full duplex (FD) communications. Due to its promising performance, FD communication ... More

Optimal Hybrid Beamforming for Multiuser Massive MIMO Systems With Individual SINR ConstraintsNov 22 2018In this letter, we consider optimal hybrid beamforming design to minimize the transmission power under individual signal-to-interference-plus-noise ratio (SINR) constraints in a multiuser massive multiple-input-multiple-output (MIMO) system. This results ... 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

Frequency Comb Assisted Broadband Precision Spectroscopy with Cascaded Diode LasersApr 18 2016Frequency comb assisted diode laser spectroscopy, employing both the accuracy of an optical frequency comb and the broad wavelength tuning range of a tunable diode laser, has been widely used in many applications. In this letter we present a novel method ... More

Adsorption structures and energetics of molecules on metal surfaces: Bridging experiment and theoryMay 18 2016Adsorption geometry and stability of organic molecules on surfaces are key parameters that determine the observable properties and functions of hybrid inorganic/organic systems (HIOSs). Despite many recent advances in precise experimental characterization ... 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

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

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

Construction of Sources for Majumdar-Papapetrou SpacetimesJan 22 2002We study Majumdar-Papapetrou solutions for the 3+1 Einstein-Maxwell equations, with charged dust acting as the external source for the fields. The spherically symmetric solution of G\"{u}rses is considered in detail. We introduce new parameters that simplify ... 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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

On Wiener - Hopf factorization of scalar polynomialJun 05 2018In the work we propose an algorithm for a Wiener -- Hopf factorization of scalar polynomials based on notions of indices and essential polynomials. The algorithm uses computations with finite Toeplitz matrices and permits to obtain coefficients of both ... 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.

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

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

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.

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

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

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

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

The Berger-Wang formula for the Markovian joint spectral radiusJan 13 2014May 07 2014The Berger-Wang formula establishes equality between the joint and generalized spectral radii of a set of matrices. For matrix products whose multipliers are applied not arbitrarily but in accordance with some Markovian law, there are also known analogs ... 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

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

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

Entropic theory of GravitationFeb 08 2017We construct a manifestly Machian theory of gravitation on the foundation that information in the universe cannot be destroyed (Landauer's principle). If no bit of information in the Universe is lost, than the sum of the entropies of the geometric and ... More

Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domainsOct 21 2011We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum or acoustically-soft ... More

Weighted Hardy-Sobolev spaces and complex scaling of differential equations with operator coefficientsJan 12 2009In this paper we study weighted Hardy-Sobolev spaces of vector valued functions analytic on double-napped cones of the complex plane. We introduce these spaces as a tool for complex scaling of linear ordinary differential equations with dilation analytic ... More

Minkowski-type and Alexandrov-type theorems for polyhedral herissonsNov 19 2002Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a class of nonconvex ... More

Primitive Recursive Presentations of Automata and their ProductsJul 23 2009Jan 10 2010Methods for specifying Moore type state machines (transducers) abstractly via primitive recursive functions and for defining parallel composition via simultaneous primitive recursion are discussed. The method is mostly of interest as a concise and convenient ... More

Topological Unconstrained QCDNov 15 2000"Equivalent unconstrained systems" for QCD obtained by resolving the Gauss law are discussed. We show that the effects of hadronization, confinement, spontaneous chiral symmetry breaking and $\eta_0$-meson mass can be hidden in solutions of the non-Abelian ... More

Le trading algorithmiqueOct 22 2008Mar 19 2009The algorithmic trading comes from digitalisation of the processing of trading assets on financial markets. Since 1980 the computerization of the stock market offers real time processing of financial information. This technological revolution has offered ... More

One more discussion of the replica trick: the examples of exact solutionsOct 19 2010A systematic replica field theory calculations are analysed using the examples of two particular one-dimensional "toy" random models with Gaussian disorder. Due to apparent simplicity of the model the replica trick calculations can be followed here step ... More

On the homology of the spaces of long knotsMay 16 2001This paper is a little more detailed version of math-QA/0010017 "Sur l'homologie des espaces de n\oe uds non-compacts", where the first term of the Vassiliev spectral sequence (computing the homology of the space of long knots in ${\mathbb R}^d$, $d\ge ... More

Steiner-Minkowski Polynomials of Convex Sets in High Dimension, and Limit Entire FunctionsSep 01 2007For a convex set (K) of the (n)-dimensional Euclidean space, the Steiner-Minkowski polynomial (M_K(t)) is defined as the (n)-dimensional Euclidean volume of the neighborhood of the radius (t). Being defined for positive (t), the Steiner-Minkowski polynomials ... More

On the spaces of polynomial knotsMay 05 1995Homology groups of spaces of nonsingular polynomial embeddings ${\bf R}^1 \to {\bf R}^n$ of degrees $\le 4$ are calculated. A general algebraic technique of such calculations for spaces of polynomial knots of arbitrary degrees is described.

Non-factorisation of Arf-Kervaire classes through ${\mathbb RP}^{\infty} \wedge {\mathbb RP}^{\infty}$Feb 25 2010As an application of the upper triangular technology method of (V.P. Snaith: {\em Stable homotopy -- around the Arf-Kervaire invariant}; Birkh\"{a}user Progress on Math. Series vol. 273 (April 2009)) it is shown that there do not exist stable homotopy ... More

Relative K_0, annihilators, Fitting ideals and the Stickelberger phenomenaMar 01 2002When $G$ is abelian and $l$ is a prime we show how elements of the relative K-group $K_{0}({\bf Z}_{l}[G], {\bf Q}_{l})$ give rise to annihilator/Fitting ideal relations of certain associated ${\bf Z}[G]$-modules. Examples of this phenomenon are ubiquitous. ... More

NLCertify: A Tool for Formal Nonlinear OptimizationMay 22 2014NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic optimization techniques with approximation methods for transcendental functions, ... More

Error Bounds for Polynomial Optimization over the Hypercube using Putinar type RepresentationsApr 24 2014Consider the optimization problem $p_{\min, Q} := \min_{\mathbf{x} \in Q} p(\mathbf{x})$, where $p$ is a degree $m$ multivariate polynomial and $Q := [0, 1]^n$ is the hypercube. We provide explicit degree and error bounds for the sums of squares approximations ... More

Sternberg astronomical institute activities on site testing programsJan 12 2011Recent Sternberg astronomical institute activities on site testing programs and technique are presented. The main attention is paid to the new modifications of MASS and DIMM data processing developed by SAI team. Four important unresolved questions affected ... More

Lectures on Nakajima's Quiver VarietiesMay 05 2009May 05 2009This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).

Harish-Chandra bimodules for quantized Slodowy slicesJul 02 2008May 05 2009The Slodowy slice is an especially nice slice to a given nilpotent conjugacy class in a semisimple Lie algebra. Premet introduced noncommutative quantizaions of the Poisson algebra of polynomial functions on the Slodowy slice. In this paper, we define ... More

Double derivations and Cyclic homologyMay 12 2005Aug 11 2005We give a new construction of cyclic homology of an associative algebra A that does not involve Connes' differential. Our approach is based on an extended version of the complex \Omega A, of noncommutative differential forms on A, and is similar in spirit ... More

Loop Grassmannian cohomology, the principal nilpotent and Kostant theoremMar 30 1998Apr 02 1998Given a complex projective algebraic variety, write H(X) for its cohomology with complex coefficients and IH(X) for its Intersection cohomology. We first show that, under some fairly general conditions, the canonical map H(X)\to IH(X) is injective. Now ... More

Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic ApproachDec 13 2010Jun 02 2011We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first part of the ... More

The internal Josephson effect in a Fermi gas near a Feshbach resonanceApr 06 2004We consider a two-component system of Fermi atoms and molecular bosons in the vicinity of a Feshbash resonance. We derive an effective action for the system, which has a term describing coherent tunneling of the molecular bosons into Cooper pairs and ... More

Nucleation and growth of metal whiskersSep 16 2013Sep 22 2013The existence of metal whiskers is attributed to the energy gain due to electrostatic polarization of needle shaped metal filaments in the electric field induced by surface imperfections: contaminations, oxide states, etc. A proposed theory provides closed ... More

Square wells, quantum wells and ultra-thin metallic filmsJul 09 2013The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these results in the ... More

Minimal Gromov--Witten ringOct 22 2007We build the abstract theory of Gromov-Witten invariants of genus 0 for quantum minimal Fano varieties (a minimal natural (with respect to Gromov-Witten theory) class of varieties). In particular, we consider ``the minimal Gromov-Witten ring'', i. e. ... More

Asymptotic of summation arithmetic functions, the limit for which is the law of normal distributionFeb 08 2019Apr 16 2019Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.