### Results for "Victor Liu"

total 31471took 0.13s
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
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
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
$q$-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
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
When Exploiting Individual User Preference Is Beneficial for Caching at Base StationsJan 10 2018Mar 02 2018Most of prior works optimize caching policies based on the following assumptions: 1) every user initiates request according to content popularity, 2) all users are with the same active level, and 3) users are uniformly located in the considered region. ... More
Zero-Resource Neural Machine Translation with Multi-Agent Communication GameFeb 09 2018While end-to-end neural machine translation (NMT) has achieved notable success in the past years in translating a handful of resource-rich language pairs, it still suffers from the data scarcity problem for low-resource language pairs and domains. To ... More
Most Complex Regular Ideal LanguagesOct 31 2015Oct 13 2016A right ideal (left ideal, two-sided ideal) is a non-empty language $L$ over an alphabet $\Sigma$ such that $L=L\Sigma^*$ ($L=\Sigma^*L$, $L=\Sigma^*L\Sigma^*$). Let $k=3$ for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there ... 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
An Asynchronous Parallel Stochastic Coordinate Descent AlgorithmNov 08 2013Nov 10 2014We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong convexity ... More
Where to Go Next: A Spatio-temporal LSTM model for Next POI RecommendationJun 18 2018Next Point-of-Interest (POI) recommendation is of great value for both location-based service providers and users. Recently Recurrent Neural Networks (RNNs) have been proved to be effective on sequential recommendation tasks. However, existing RNN solutions ... 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
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
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
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
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
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
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
Instance Segmentation by Deep ColoringJul 26 2018We propose a new and, arguably, a very simple reduction of instance segmentation to semantic segmentation. This reduction allows to train feed-forward non-recurrent deep instance segmentation systems in an end-to-end fashion using architectures that have ... 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
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
Tensor categories (after P. Deligne)Jan 25 2004These notes give an exposition of Deligne's theorem on the existense of super fiber functor.
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.
Automorphisms of local fields of period $p^M$ and nilpotent class $<p$May 20 2015May 23 2016Suppose $K$ is a finite extension of $\mathbb{Q}_p$ containing a $p^M$-th primitive root of unity. For $1\leqslant s<p$ denote by $K[s,M]$ the maximal $p$-extension of $K$ with the Galois group of period $p^M$ and nilpotent class $s$. We apply the nilpotent ... More
Automorphisms of local fields of period $p$ and nilpotent class $<p$Mar 17 2014Jan 09 2017Suppose $K$ 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
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
Quantum mechanics of time-dependent systems. Construction of pure statesApr 03 1995For time-dependent systems the wavefunction depends explicitly on time and it is not a pure state of the Hamiltonian. We construct operators for which the above wavefunction is a pure state. The method is based on the introduction of conserved quantities ... More
On measures which generate the scalar product in a space of rational functionsFeb 07 2016Feb 12 2016Let $z_1,z_2,\,\ldots\,,z_n$ be pairwise different points of the unit disc and $\mathscr{L}(z_1,z_2,\,\ldots\,z_n)$ be the linear space generated by the rational fractions $\frac{1}{t-z_1} , \frac{1}{t-z_2} , \cdots\ , \frac{1}{t-z_n}\cdot$ Every non-negative ... 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.
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
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
Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square RisksAug 31 2017This paper presents hydrodynamic-like model of business cycles aggregate fluctuations of economic and financial variables. We model macroeconomics as ensemble of economic agents on economic space and agent's risk ratings play role of their coordinates. ... More
Non-Local Macroeconomic Transactions and Credits-Loans Surface-Like WavesMay 29 2017This paper describes surface-like waves of macroeconomic Credits-Loans transactions on economic space. We use agent's risk ratings as their coordinates and describe evolution of macro variables by transactions between agents. Aggregations of agent's variables ... 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
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 2012Mar 28 2017We 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
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
Asymptotics of the ground state energy in the relativistic settingsJul 21 2017Aug 23 2017The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger and relativistic ... 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 phonon nature of a gap in high-temperature superconductorsOct 07 2018The nature of the superconducting gap in high-temperature superconductors is a fundamental problem for understanding the mechanism of this phenomenon, however it has not been fully understood as yet. From the mid of the twentieth century when Bardeen, ... More
Investigations of the limit distribution and the asymptotic behavior of summation arithmetic functionsApr 20 2018The aim of the paper is to study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach based on the use of the axioms of probability theory is used for these purposes. Sufficient conditions are ... More
Resonant properties of finite cracks and their acoustic emission spectraApr 17 2018In this paper, the acoustic emission accompanying the formation of brittle cracks of finite length is investigated theoretically using the approach based on the application of Huygens' principle for elastic solids. In the framework of this approach, the ... More
Lie-Poisson structures over differential algebrasMar 11 2018In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.
On Hamiltonian operators in differential algebrasMar 11 2018Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of equations (suitable ... More
On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves. The Banach triangle case ($L^r,\: 1\leq r<\infty$)Dec 31 2015Apr 27 2016We show that the bilinear Hilbert transform $H_{\Gamma}$ along curves $\Gamma=(t,-\gamma(t))$ with $\gamma\in\mathcal{N}\mathcal{F}^{C}$ is bounded from $L^{p}(\mathbb{R})\times L^{q}(\mathbb{R})\,\rightarrow\,L^{r}(\mathbb{R})$ where $p,\,q,\,r$ are ... More
Detecting Cross-Lingual Plagiarism Using Simulated Word EmbeddingsDec 29 2017Jan 03 2018Cross-lingual plagiarism (CLP) occurs when texts written in one language are translated into a different language and used without acknowledging the original sources. One of the most common methods for detecting CLP requires online machine translators ... More
Density of States under non-local interactions III. N-particle Bernoulli--Anderson modelNov 09 2017Following [7,8], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions and arbitrary nontrivial probability ... More
An investigation of the asymptotic behavior of the Mertens functionDec 13 2017Dec 15 2017The limiting distribution function for the Mobius function is found in the paper. It is proved also the relation: $\lim_{n \to \infty} {P(S_n/\sqrt {2pn}<y)}=G(y)$, where $S_n$ is the sum of random variables having the distribution of the Mobius function, ... More
Teichmuller TQFT vs Chern-Simons TheoryOct 12 2017Oct 19 2017Teichm\"uller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence ... More
A functional model for the Fourier--Plancherel operator truncated on the positive half-axisOct 30 2017Jul 17 2018The truncated Fourier operator $\mathscr{F}_{\mathbb{R^{+}}}$, $$(\mathscr{F}_{\mathbb{R^{+}}}x)(t)=\frac{1}{\sqrt{2\pi}} \int\limits_{\mathbb{R^{+}}}x(\xi)e^{it\xi}\,d\xi\,,\ \ \ t\in{}{\mathbb{R^{+}}},$$ is studied. The operator $\mathscr{F}_{\mathbb{R^{+}}}$ ... More
Beware of DOI! A "bibliographic detective story" of the era of digitalizationMar 08 2019Mar 11 2019An example of inconsistencies in information provided by popular bibliographic services is described, and the reasons for such inconsistencies are discussed.
Asymptotic of summation arithmetic functions, the limit for which is the law of normal distributionFeb 08 2019Feb 13 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.
Spectral stability and semiclassical measures for renormalized KAM systemsNov 29 2018Feb 12 2019An exact semiclassical version of the classical KAM theorem about small perturbations of vector fields on the torus is given. Moreover, a renormalization theorem based on counterterms for some semiclassical systems that are close to completely integrable ... More
Sinai's condition for real valued Lévy processesMay 24 2005We prove that the upward ladder height subordinator $H$ associated to a real valued L\'{e}vy process $\xi$ has Laplace exponent $\phi$ that varies regularly at $\infty$ (resp. at 0) if and only if the underlying L\'{e}vy process $\xi$ satisfies Sinai's ... More
Rational points near manifolds and metric Diophantine approximationApr 02 2009Jun 03 2009This work is motivated by problems on simultaneous Diophantine approximation on manifolds, namely, establishing Khintchine and Jarnik type theorems for submanifolds of R^n. These problems have attracted a lot of interest since Kleinbock and Margulis proved ... More
An analogue of a van der Waerden's theorem and its application to two-distance preserving mappingsApr 15 2015Apr 17 2015The van der Waerden's theorem reads that an equilateral pentagon in Euclidean 3-space $\Bbb E^3$ with all diagonals of the same length is necessarily planar and its vertex set coincides with the vertex set of some convex regular pentagon. We prove the ... 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 $S_*(KG)=\{x\in U(KG) \mid ... More Hodge decomposition in the homology of long knotsDec 01 2008Dec 06 2008The paper describes a natural splitting in the rational homology and homotopy of the spaces of long knots. This decomposition presumably arises from the cabling maps in the same way as a natural decomposition in the homology of loop spaces arises from ... More The Erdős-Selfridge and the Schinzel-Tijdeman theorems hold in$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)$a polynomial with rational coefficients and with at least two distinct ... More On filtered multiplicative bases of group algebras IIFeb 13 2001We give an explicit list of all p-groups G with a cyclic subgroup of index p^2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also proved that such a K-basis does not exist for the group ... More Estimating of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficientsAug 11 2016Aug 12 2016This paper investigates the upper bound of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients without a free member via the circle method of Hardy and Littlewood. Author found ... More Quasigroup based crypto-algorithmsJan 14 2012Modifications of Markovski quasigroup based crypto-algorithm have been proposed. Some of these modifications are based on the systems of orthogonal n-ary groupoids. T-quasigroups based stream ciphers have been constructed. Generalized Cosecant Numbers and the Hurwitz Zeta FunctionFeb 14 2017Aug 09 2018This announcement paper summarises recent development concerning the generalized cosecant numbers$c_{\rho,k}$, which represent the coefficients of the power series expansion for the important fundamental function$z^{\rho}/\sin^{\rho} z$. These coefficients ... More Cell decompositions of double Bott-Samelson varietiesOct 17 2013Nov 18 2013Let G be a connected complex semisimple Lie group. Webster and Yakimov have constructed partitions of the double flag variety G/B x G/B_, where (B, B_) is a pair of opposite Borel subgroups of G, generalizing the Deodhar decompositions of G/B. We show ... More Extremal quantile regressionMay 30 2005Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower ... More An analytical approach to the Rational Simplex ProblemApr 28 2013May 08 2013In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples ... More Exponential scaling limit of the single-particle Anderson model via adaptive feedback scalingMar 09 2015Aug 12 2015We propose a reformulation of the bootstrap version of the Multi-Scale Analysis (BMSA), developed by Germinet and Klein, to make explicit the fact that BMSA implies asymptotically exponential decay of eigenfunctions (EFs) and of EF correlators (EFCs), ... More Minimax joint spectral radius and stabilizability of discrete-time linear switching control systemsDec 19 2017Dec 21 2017To estimate the growth rate of matrix products$A_{n}\cdots A_{1}$with factors from some set of matrices$\mathcal{A}$, such numeric quantities as the joint spectral radius$\rho(\mathcal{A})$and the lower spectral radius$\check{\rho}(\mathcal{A})$... More Dyer-Lashof-Cohen operations in Hochschild cohomologyApr 01 2005Apr 17 2009We give explicit formulae for operations in Hochschild cohomology which are analogous to the operations in the homology of double loop spaces. As a corollary we obtain that any brace algebra in finite characteristic is always a restricted Lie algebra. ... More Brownian Super-exponentsDec 06 2006We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a supermartingale ... More The matrix function$e^{tA+B}$is representable as the Laplace transform of a matrix measureSep 13 2016Oct 04 2016Given a pair$A,B$of matrices of size$n\times n$, we consider the matrix function$e^{At+B}$of the variable$t\in\mathbb{C}$. If the matrix$A$is Hermitian, the matrix function$e^{At+B}$is representable as the bilateral Laplace transform of a matrix-valued ... More On the group of automorphisms of Shimura curves and applicationsJun 10 2002Let V_D be the Shimura curve over \Q attached to the indefinite rational quaternion algebra of discriminant D. In this note we investigate the group of automorphisms of V_D and prove that, in many cases, it is the Atkin-Lehner group. Moreover, we determine ... More On the Properties of the Cayley Graph of Richard Thompson's Group FNov 26 2002We study some properties of the Cayley graph of the R.Thompson's group F in generators$x_0$,$x_1$. We show that the density of this graph, that is, the least upper bound of the average vertex degree of its finite subgraphs is at least 3. It is known ... More Iterative building of Barabanov norms and computation of the joint spectral radius for matrix setsOct 13 2008Mar 02 2010The problem of construction of Barabanov norms for analysis of properties of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. The method of Barabanov norms was the key instrument in disproving the ... 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 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. 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 Hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non-negative matricesJul 02 2015Oct 19 2015Recently Blondel, Nesterov and Protasov proved that the finiteness conjecture holds for the generalized and the lower spectral radii of the sets of non-negative matrices with independent row/column uncertainty. We show that this result can be obtained ... 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 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 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