Results for "Victor Lazarian"
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Cascading of Fast-Mode Balanced and Imbalanced TurbulenceAug 15 2006Jan 28 2007We study the cascading of fast MHD modes in magnetically dominated plasma by performing one-dimensional (1D) dynamical simulations. We find that the cascading becomes more efficient as an angle between wave vector and underlying magnetic field increases ... 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 State machine models of timing and circuit designMar 02 2010This paper illustrates a technique for specifying the detailed timing, logical operation, and compositional circuit design of digital circuits in terms of ordinary state machines with output (transducers). The method is illustrated here with specifications ... More 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 Dirac variables in gauge theoriesSep 28 2001Sep 30 2001The review is devoted to a relativistic formulation of the first Dirac quantization of QED (1927) and its generalization to the non-Abelian theories (Yang-Mills and QCD) with the topological degeneration of initial data. Using the Dirac variables we give ... More Mean Field Model of a GlassSep 20 2002In this paper we propose a simple mean-field "toy" model for the liquid-glass phase transition. This is the system of $N$ point-like particles confined in a finite volume of a $D$-dimensional space interacting via infinite-range oscillating potential. ... More Constraining the two-Higgs doublet models with the LHC dataOct 03 2013Oct 07 2013The recent discovery of a Standard Model-like boson with mass of about 126 GeV seems to be the first direct information on the electroweak symmetry breaking mechanism. Using the available experimental data from the LHC and Tevatron we study the implications ... More 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 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 primitive idealsFeb 10 2002May 28 2012We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem', to much wider classes of algebras. Our general version of Irreducibility theorem says that if A is ... More Non-commutative Symplectic Geometry, Quiver varieties, and OperadsMay 17 2000Jun 02 2000Quiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we show that many ... More The global nilpotent variety is LagrangianApr 10 1997Oct 31 2000The purpose of this note is to present a short elementary proof of a theorem due to Faltings and Laumon, saying that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the moduli space of G-bundles on a complex compact curve. ... More 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 Complete integrable systems with unconfined singularitiesApr 10 2007We prove that any globally periodic rational discrete system in K^k(where K denotes either R or C), has unconfined singularities, zero algebraic entropy and it is complete integrable (that is, it has as many functionally independent first integrals as ... More Electrostatic theory of metal whiskersJan 29 2014Needle shaped whiskers grow on various metal surfaces often across leads of a package causing current leakage or short circuits and raising reliability issues in electronic components. The nature of metal whiskers remains a mystery after several decades ... More 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 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 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 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 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 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 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 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 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 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 Folding a Tree into a MapSep 25 2015Analysis of the retrieval architecture of the highly influential UNIX file system (\cite{Ritchie}\cite{multicsfs}) provides insight into design methods, constraints, and possible alternatives. The basic architecture can be understood in terms of function ... More Distance-preserving subgraphs of Johnson graphsMar 13 2015Nov 01 2015We give a characterization of distance--preserving subgraphs of Johnson graphs, i.e. of graphs which are isometrically embeddable into Johnson graphs (the Johnson graph $J(m,\Lambda)$ has the subsets of cardinality $m$ of a set $\Lambda$ as the vertex--set ... More State 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 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 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 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. 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. 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 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 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 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 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