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$q$-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

$q$-Analouges of two Ramanujan-type forumlas for $1/π$Feb 06 2018We give $q$-analouges of the following two Ramanujan-type forumlas for $1/\pi$: \begin{align*} \sum_{k=0}^\infty \frac{(6k+1)(\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 ... More

Proof of some conjectures of Z.-W. Sun on the divisibility of certain double-sumsDec 10 2014Z.-W. Sun introduced three kinds of numbers: \begin{align*}S_n=\sum_{k=0}^{n}{n\choose k}^2{2k\choose k}(2k+1),\qquad s_n=\sum_{k=0}^{n}{n\choose k}^2{2k\choose k}\frac{1}{2k-1}, \end{align*} and $S_n^{+}=\sum_{k=0}^{n}{n\choose k}^2{2k\choose k}(2k+1)^2$. ... More

Proof of a conjecture of Z.-W. Sun on the divisibility of a triple sumJan 03 2015The numbers $R_n$ and $W_n$ are defined as \begin{align*} R_n=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}\frac{1}{2k-1},\ \text{and}\ W_n=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}\frac{3}{2k-3}. \end{align*} We prove that, for any positive integer $n$ ... More

Proof of a congruence on sums of powers of $q$-binomial coefficientsApr 20 2015We prove that, if $m,n\geqslant 1$ and $a_1,\ldots,a_m$ are nonnegative integers, then \begin{align*} \frac{[a_1+\cdots+a_m+1]!}{[a_1]!\ldots[a_m]!}\sum^{n-1}_{h=0}q^h\prod_{i=1}^m{h\brack a_i} \equiv 0\pmod{[n]}, \end{align*} where $[n]=\frac{1-q^n}{1-q}$, ... 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

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

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

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

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

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

Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworksJun 19 2000We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient ... More

The Dehn invariants of the Bricard octahedraJan 20 2009We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.

On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curvesOct 16 2011Dec 31 2015We are proving $L^2(\R)\times L^2(\R)\,\rightarrow\,L^1(\R)$ bounds for the bilinear Hilbert transform $H_{\Gamma}$ along curves $\Gamma=(t,-\gamma(t))$ with $\gamma$ being a smooth "non-flat" curve near zero and infinity.

The Polynomial Carleson OperatorMay 19 2011We prove that the generalized Carleson operator with polynomial phase function is of strong type $(p,p)$ for $1<p<\infty$, thus answering a question asked by E. Stein. A key ingredient in this proof is the further extension of the relational time-frequency ... More

Groupoids and the integration of Lie algebroidsApr 13 2000We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators.

Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymersMar 25 2010The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive interactions. Performing ... More

Non-perturbative phenomena in the three-dimensional random field Ising modelMar 27 2006The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to localized in space ... More

Universal RandomnessSep 16 2010Jun 30 2011During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution function which is ... More

Griffiths singularity in the random Ising ferromagnetMay 10 2005The explicit form of the Griffiths singularity in the random ferromagnetic Ising model in external magnetic field is derived. In terms of the continuous random temperature Ginzburg-Landau Hamiltonian it is shown that in the paramagnetic phase away from ... More

Stochastic effects in the growth of dropletsMay 30 2005The effects of stochastic absorption and ejection of molecules by growing droplets have been considered. Both analytical and numerical approaches have been used. They demonstrate the satisfactory coincidence. It is proved that in general case corresponding ... More

Perturbative theory approaches to the metastable phase decayDec 31 2007The perturbative theory of the nucleation kinetics is analyzed. A new improvement is suggested and compared with numerical calculations.

Different scenarios of the late stages of condensationDec 31 2007The late stages of the nucleation have been described analytically. The approximate solution of the Zel'dowich-Folmer-Frenkel equation has been constructed.

Modified proof of a local analogue of the Grothendieck conjectureJul 17 2009A local analogue of the Grothendieck Conjecture is an equivalence of the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p\ne 0$ and the category of absolute Galois groups of fields $K$ together with their ... More

On Transformation of Potapov's Fundamental Matrix InequalityJun 13 2007According to V.P.Potapov, a classical interpolation problem can be reformulated in terms of a so-called Fundamental Matrix Inequality (FMI). To show that every solution of the FMI satisfies the interpolation problem, we usualy have to transform the FMI ... More

A countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoidsJan 22 2013We provide a countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoids.

On the group of automorphisms of Shimura curves and applicationsJun 10 2002Let V_D be the Shimura curve over \Q attached to the indefinite rational quaternion algebra of discriminant D. In this note we investigate the group of automorphisms of V_D and prove that, in many cases, it is the Atkin-Lehner group. Moreover, we determine ... More

Local trace asymptotics in the self-generated magnetic fieldAug 21 2011Dec 23 2011We consider a semiclassical asymptotics of local trace for the 3D-Schroedinger operator with self-generated magnetic field; it is given by Weyl expression with O(h^{-1}) error and under standard condition to Hamiltonian trajectories even o(h^{-1}). In ... More

Sharp Spectral Asymptotics for Operators with Irregular Coefficients. V. Multidimensional Schroedinger operator with a strong magnetic field. Non-Full-rank caseOct 16 2005Aug 02 2011Sharp spectral asymptotics for multidimensional Schroedinger operators with the strong magnetic field are derived under rather weak smoothness conditions. I assume that magnetic intensity matrix has constant defect r>0 at each point. In comparison with ... More

Short Loops and Pointwise Spectral AsymptoticsMay 05 2010We consider pointwise semiclassical spectral asymptotics i.e. asymptotics of $e(x,x,0)$ as $h\to +0$ where $e(x,y,\tau)$ is the Schwartz kernel of the spectral projector and consider two cases when schort loops give contribution above $O(h^{1-d})$: (i) ... More

Sharp Spectral Asymptotics for Operators with Irregular Coefficients. III. Schroedinger operator with a strong magnetic fieldOct 16 2005Apr 01 2011Sharp spectral asymptotics for 2- and 3-dimensional Schroedinger operators with strong magnetic field are derived under rather weak smoothness conditions. In comparison with version 1 of 2005 new results are added and minor errors corrected.

Stratified Picard--Lefschetz theoryMay 11 1995The monodromy action in the homology of level sets of Morse functions on stratified singular analytic varieties is studied. The local variation operators in both the standard and the intersection homology groups defined by the loops around the critical ... More

A Note On Higher Order GrammarOct 03 2009Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar (HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a language is defined entirely in terms of provability in the single logical system. An important ... More

Brownian Super-exponentsDec 06 2006We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a supermartingale ... More

Isospectral commuting variety and the Harish-Chandra D-moduleFeb 17 2010Feb 25 2010Let g be a complex reductive Lie algebra with Cartan algebra h. Hotta and Kashiwara defined a holonomic D-module M, on g x h, called Harish-Chandra module. We give an explicit description of gr(M), the associated graded module with respect to a canonical ... More

Variations on themes of KostantOct 08 2007Jan 09 2008Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form Sym(g^e)/J. Here, J ... More

Fermionization Transform for Certain Higher-Dimensional Quantum Spin ModelsMar 19 2010Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key new steps are to enlarge the Hilbert space of the original model by adding to ... More

On symmetric units in group algebrasSep 01 2000Let $U(KG)$ be the group of units of the group ring $KG$ of the group $G$ over a commutative ring $K$. The anti-automorphism $g\mapsto g\m1$ of $G$ can be extended linearly to an anti-automorphism $a\mapsto a^*$ of $KG$. Let $S_*(KG)=\{x\in U(KG) \mid ... More

Reply to Paris's Comments on Exactification of Stirling's Approximation for the Logarithm of the Gamma FunctionAug 07 2014In a recent paper [arXiv:1406.1320] Paris has made several comments concerning the author's recent work on the exactification of Stirling's approximation for the logarithm of the gamma function, $\ln \Gamma(z)$. Despite acknowledging that the calculations ... More

Exactification of Stirling's Approximation for the Logarithm of the Gamma FunctionApr 10 2014Exactification is the process of obtaining exact values of a function from its complete asymptotic expansion. Here Stirling's approximation for the logarithm of the gamma function or $\ln \Gamma(z)$ is derived completely whereby it is composed of the ... More

The Erdős-Selfridge and the Schinzel-Tijdeman theorems hold in $PA^-$Oct 30 2014Mar 14 2015We show that "The product of consecutive integers is never a power" and several results by Schinzel and Tijdeman on the solutions of the equation $y^m=P(x)$, for $m>1$, $y>1$, and $P(x)$ a polynomial with rational coefficients and with at least two distinct ... More

Reynolds number of transition and large-scale properties of strong turbulenceSep 14 2014A turbulent flow is characterized by velocity fluctuations excited in an extremely broad interval of wave numbers $k> \Lambda_{f}$ where $\Lambda_{f}$ is a relatively small set of the wave-vectors where energy is pumped into fluid by external forces. ... More

Reynolds Number of Transition as a Dynamic Constraint on Statistical Theory of TurbulenceAug 20 2013Iterative coarse-graining procedure based on Wyld's perturbation expansion is applied to the problem of Navier-Stokes turbulence. It is shown that the low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$ (coupling constant) almost identical ... More

Statistics of Transverse Velocity Differences in TurbulenceSep 09 1999An unusual symmetry of the equation for the generating function of transverse velocity differences $\Delta v=v(x+r)-v(x)$ is used to obtain a closed equation for the probability density function $P(\Delta v,r)$ in strong three-dimensional turbulence. ... More

A positivity property of a Quantum Anharmonic Oscillator suggested by the BMV conjectureOct 18 2014Oct 21 2014In this work an observation concerning a positivity property of the quantum anharmonic oscillator is made. This positivity property is suggested by the BMV conjecture.

Tensor categories (after P. Deligne)Jan 25 2004These notes give an exposition of Deligne's theorem on the existense of super fiber functor.

Asymptotics of the ground state energy of heavy atoms and molecules in combined magnetic fieldDec 29 2013Mar 27 2014We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$H=((D-A)\cdot\boldsymbol{\sigma})^2-V$$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a corresponding ... More

Asymptotics of the ground state energy of heavy molecules and related topics. IIOct 04 2012Jan 23 2013We consider asymptotics of the ground state energy of heavy atoms and molecules in the strong external magnetic field and derive it including Schwinger and Dirac corrections (if magnetic field is not too strong). We also consider related topics: an excessive ... More

Asymptotics of the ground state energy of heavy molecules and related topicsOct 03 2012We consider asymptotics of the ground state energy of heavy atoms and molecules and derive it including Schwinger and Dirac corrections. We consider also related topics: an excessive negative charge, ionization energy and excessive negative charge when ... More

On filtered multiplicative bases of group algebras IIFeb 13 2001We give an explicit list of all p-groups G with a cyclic subgroup of index p^2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also proved that such a K-basis does not exist for the group ... More

An analytical approach to the Rational Simplex ProblemApr 28 2013May 08 2013In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples ... More

Déformations isospectrales non compactes et théorie quantique des champsJul 21 2005Nov 02 2005The aim of this thesis is to study the isopectral deformations from the point of view of Alain Connes' noncommutative geometry. This class of quantum spaces constituts a curved space generalisation of Moyal planes and noncommutative tori. First of all, ... More

Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation ManifoldsDec 20 2004May 23 2005We work out the general features of perturbative field theory on noncommutative manifolds defined by isospectral deformation. These (in general curved) `quantum spaces', generalizing Moyal planes and noncommutative tori, are constructed using Rieffel's ... More

A. Cormack's last inversion formula and a FBP reconstructionJul 31 2014A reconstruction of a function from integrals over the family of confocal paraboloids is given by a FBP formula.

Cell decompositions of double Bott-Samelson varietiesOct 17 2013Nov 18 2013Let G be a connected complex semisimple Lie group. Webster and Yakimov have constructed partitions of the double flag variety G/B x G/B_, where (B, B_) is a pair of opposite Borel subgroups of G, generalizing the Deodhar decompositions of G/B. We show ... More

Integer conversions and estimation of the number of integer solutions of algebraic Diophantine equationsNov 17 2016The paper assesses the top number of integer solutions of algebraic Diophantine Thue diagonal equation with the degree $n \geq 2$ and number of variables $k > 2$ and equations with explicit variable in the case when the coefficients of the equation have ... More

Analysis of Perfectly Matched Layer operators for acoustic scattering on manifolds with quasicylindrical endsDec 22 2012We prove stability and exponential convergence of the Perfectly Matched Layer (PML) method for acoustic scattering on manifolds with axial analytic quasicylindrical ends. These manifolds model long-range geometric perturbations (e.g. bending or stretching) ... More

On the Pauli principle violation in QFTJun 27 2007We propose a new mechanism for a ''small" violation of Pauli Principle in the framework of Quantum Field Theory. Instead of modification of algebra - commutation relations for fields - we introduce spontaneous violation of Pauli Principle which is proportional ... More

Dyer-Lashof-Cohen operations in Hochschild cohomologyApr 01 2005Apr 17 2009We give explicit formulae for operations in Hochschild cohomology which are analogous to the operations in the homology of double loop spaces. As a corollary we obtain that any brace algebra in finite characteristic is always a restricted Lie algebra. ... More

Estimating of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficientsAug 11 2016Aug 12 2016This paper investigates the upper bound of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients without a free member via the circle method of Hardy and Littlewood. Author found ... More

Hodge decomposition in the homology of long knotsDec 01 2008Dec 06 2008The paper describes a natural splitting in the rational homology and homotopy of the spaces of long knots. This decomposition presumably arises from the cabling maps in the same way as a natural decomposition in the homology of loop spaces arises from ... More

Weak Landau-Ginzburg models for smooth Fano threefoldsFeb 26 2009Oct 23 2012The paper is joined with arXiv:0911.5428 and improved. We prove that Landau-Ginzburg models for all 17 smooth Fano threefolds with Picard rank 1 can be represented as Laurent polynomials in 3 variables exhibiting them case by case. We check that these ... More

Quasigroup based crypto-algorithmsJan 14 2012Modifications of Markovski quasigroup based crypto-algorithm have been proposed. Some of these modifications are based on the systems of orthogonal n-ary groupoids. T-quasigroups based stream ciphers have been constructed.

Generalized Cosecant Numbers and the Hurwitz Zeta FunctionFeb 14 2017Aug 09 2018This announcement paper summarises recent development concerning the generalized cosecant numbers $c_{\rho,k}$, which represent the coefficients of the power series expansion for the important fundamental function $z^{\rho}/\sin^{\rho} z$. These coefficients ... More

Matrix products with constraints on the sliding block relative frequencies of different factorsMar 20 2014May 28 2014One of fundamental results of the theory of joint/generalized spectral radius, the Berger-Wang theorem, establishes equality between the joint and generalized spectral radii of a set of matrices. Generalization of this theorem on products of matrices ... More

Physical applications of a new method of solving the quintic equationOct 15 2009Oct 27 2009Some physical applications of the Passare-Tsikh solution of a principal quintic equation are discussed. As an example, a quintic equation of state is solved in detail. This approach provides analytical approximations for several problems admitting until ... 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

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

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

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

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

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

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

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 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

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

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.

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

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

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.

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

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

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

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

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

The pointwise convergence of Fourier Series (II). Strong $L^1$ case for the lacunary Carleson operatorFeb 10 2019We prove that the lacunary Carleson operator is bounded from $L \log L$ to $L^{1}$. This result is sharp. The proof is based on two newly introduced concepts: 1) the \emph{time-frequency regularization of a measurable set} and 2) the \emph{set-resolution ... More

Perfectly matched layers for the stationary Schrodinger equation in a periodic structureJun 12 2008We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show ... More

Corrections to the book ``Vertex algebras for beginners'', second edition, by Victor KacJan 18 1999These are corrections to the second edition of the book ``Vertex algebras for beginners'', University Lecture Series, 10, American Mathematical Society, Providence, RI, 1998.

The meaning of concurrent programsOct 07 2008The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on event sequences ... More

Using boundaries to find smooth normsNov 06 2013Apr 28 2014The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with $C^k$ smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of $B_{X^*}$, namely boundaries. Of interest ... More

Hori--Vafa mirror models for complete intersections in weighted projective spaces and weak Landau--Ginzburg modelsMar 26 2010Jul 12 2011We prove that Hori--Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials.

Astrophysical Data and Conformal Unified TheoryOct 31 2002Astrophysical data reformulated in the units of the relative Paris meter and running Planck mass are used for restoration of a conformal version of the unified theory where the absolute Planck mass belongs to ordinary initial data (like the absolute Ptolemaeus ... More

Non stationary nucleation: the model with averaged velocityFeb 01 2013A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. The key characteristic which arises in frames of this theory is the mean ... More

Late periods of the condensation processNov 15 2010The full evolution during the late periods of the condensation process is described in the analytical form. The process is split into several periods and for every period the simple approximate solution is given.

Different approaches to describe depletion regions in first order phase transition kineticsJul 31 2002The theory of nucleation with depletion zones is discussed. The approach of stochastic effects of solitary droplet is analyzed. The negative features of a solution with fixed boundary are outlined. A new solution with effective fixed boundary is proposed. ... More

Non stationary nucleation: the model with minimal environmentJan 06 2013A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. As the result the free energy has to be recalculated which brings a new ... More

Variations of parameters in nucleation process under different external conditionsAug 21 2008The nucleation process under different external conditions is considered. It is shown that the duration of this process can be connected with the microscopic corrections to the free energy of the critical embryo. Connection between variations in the value ... More

Some properties of evolution equation for homogeneous nucleation period under the smooth behavior of initial conditionsMar 10 2005The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated ... More