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Results for "Mikhail Bilenko"

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Schmidt decomposition for non-collinear biphoton angular wave functionsNov 08 2014Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure is described for their separation. Parameters of the Schmidt decomposition are used for evaluation of the degree of biphoton's ... More
Data-driven goodness-of-fit testsAug 01 2007Dec 18 2007We introduce a new general class of statistical tests. The class contains Neyman's smooth tests and data-driven efficient score tests as special examples. We prove general consistency theorems for the tests from the class. The paper shows that the tests ... More
Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmologyNov 02 2005In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly ... More
A question by Alexei Aleksandrov and logarithmic determinantsAug 28 2001We answer negatively to the question posed by Aleksandrov concerning analytic functions of Smirnov's class in the unit disk with pure imaginary boundary values. We also find new sufficient conditions for representations of functions of Smirnov's class ... More
Zeros of Gaussian Analytic FunctionsJul 06 2000We prove and discuss three results on zero distribution of gaussian analytic functions: (i) the Edeleman-Kostlan formula for the expectation of the counting measure; (ii) a variation on the theme of Calabi's rigidity theorem; (iii) Offord's estimate of ... More
Extending the exact sequence of nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modulesAug 26 2016In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modules.
Existence of perfect Morse functions on spaces with semi-free circle actionFeb 15 2002Apr 01 2003Let $M$ be a compact oriented simply-connected manifold of dimension at least 8. Assume $M$ is equipped with a torsion-free semi-free circle action with isolated fixed points. We prove $M$ has a perfect invariant Morse-Smale function. The major ingredient ... More
Marketing features of dropshipping in system of e-commerceMay 10 2015Today dropshipping wins the Internet promptly and transformed to one of the basic tools of marketing in e-commerce. Marketing features, mechanisms and value dropshipping in the conditions of network economy of the XXI century reveal in article. The author ... More
Mathematics of Knowledge Refinement: Probabilistic Arithmetic, with no unknowns and no infinity. Part I. Generalized Probabilistic Arithmetic. Basic definitions and propertiesNov 01 2011May 22 2012An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values, degrees of their ... More
QUBIC ExperimentMay 16 2016QUBIC is a ground-based experiment, currently under construction, that uses the novel bolometric interferometry technology. It is dedicated to measure the primordial B-modes of CMB. As a bolometric interferometer, QUBIC has high sensitivity and good systematics ... More
Surfaces containing two circles through each pointDec 30 2015We find all analytic surfaces in space $\mathbb{R}^3$ such that through each point of the surface one can draw two transversal circular arcs fully contained in the surface. The problem of finding such surfaces traces back to the works of Darboux from ... More
Quasiparticle approach to molecules interacting with quantum solventsOct 05 2016Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here we demonstrate that experimental data collected over the ... More
Dynamics of quadratic polynomials, I: Combinatorics and geometry of the Yoccoz puzzleMar 01 1995This work studies combinatorics and geometry of the Yoccoz puzzle for quadratic polynomials. It is proven that the moduli of the ``principal nest'' of annuli grow at linear rate. As a corollary we obtain complex a priori bounds and local connectivity ... More
On exotic algebraic structures on affine spacesJun 02 1995By an exotic algebraic structure on the affine space ${\bf C}^n$ we mean a smooth affine algebraic variety which is diffeomorphic to ${\bf R}^{2n}$ but not isomorphic to ${\bf C}^n$. This is a survey of the recent developement on the subject, which emphasizes ... More
KISS approach to credit portfolio modelingJul 11 2011A simple, yet reasonably accurate, analytical technique is proposed for multi-factor structural credit portfolio models. The accuracy of the technique is demonstrated by benchmarking against Monte Carlo simulations. The approach presented here may be ... More
On 2-systoles of hyperbolic 3-manifoldsMay 23 2012Jul 08 2012We investigate the geometry of $\pi_1$-injective surfaces in closed hyperbolic 3-manifolds. First we prove that for any $e>0$, if the manifold $M$ has sufficiently large systole $\sys_1(M)$, the genus of any such surface in $M$ is bounded below by $\exp((1/2-e)\sys_1(M))$. ... More
Geodesics, volumes and Lehmer's conjectureJun 09 2011In this report I discuss the relations between systoles and volumes of hyperbolic manifolds and a conjecture of Lehmer about the Mahler measure of non-cyclotomic polynomials.
On fields of definition of arithmetic Kleinian reflection groupsOct 26 2007Apr 01 2008We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.
Enhancement of the electric dipole moment of the electron in the YbF moleculeMay 27 1997We calculate an effective electric field on the unpaired electron in the YbF molecule. This field determines sensitivity of the molecular experiment to the electric dipole moment of the electron. We use experimental value of the spin-doubling constant ... More
On the class of caustic on the moduli space of odd spin curvesSep 08 2015Jan 20 2019Let $C$ be a smooth projective curve of genus $g\geq 3$ and let $\eta$ be an odd theta characteristic on it such that $h^0(C,\eta) = 1$. Pick a point $p$ from the support of $\eta$ and consider the one-dimensional linear system $|\eta + p|$. In general ... More
Polarization spin-tensors in two-spinor formalism and Behrends-Fronsdal spin projection operator for $D$-dimensional caseFeb 07 2019In the work, the recurrent differential relations that connecting the polarization spin-tensor of the wave function of a free massive particle of an arbitrary spin for $D=4$ and new formula of the $D$-dimensional Behrends-Fronsdal spin projection operator ... More
Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impuritiesFeb 05 2019Feb 12 2019We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors ... More
Parallel Algorithm for Frequent Itemset Mining on Intel Many-core SystemsDec 28 2018Frequent itemset mining leads to the discovery of associations and correlations among items in large transactional databases. Apriori is a classical frequent itemset mining algorithm, which employs iterative passes over database combining with generation ... More
$γW$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay SpectrumDec 11 2018Mar 06 2019I consider the $\gamma W$-box correction to superallowed nuclear $\beta$-decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, ... More
Steklov problem on differential formsMay 24 2017In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint on the subspace ... More
Arithmetic Kleinian groups generated by elements of finite orderOct 19 2016Jul 07 2017We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated arithmetic Kleinian ... More
On evolutionary selection of blackjack strategiesNov 16 2017We apply the approach of evolutionary programming to the problem of optimization of the blackjack basic strategy. We demonstrate that the population of initially random blackjack strategies evolves and saturates to a profitable performance in about one ... More
Dimension Theory Approach to the Complexity of Almost Periodic TrajectoriesOct 09 2017We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine dimension is connected ... More
Fluctuations of the aperture-averaged orbital angular momentum after propagation through turbulenceJan 05 2018Jan 09 2018In the recent paper [1] it was shown that for paraxial propagation of scalar waves, the transverse linear momentum and orbital angular momentum (OAM) are related to the wave coherence function. Although both of these quantities are conserved during free-space ... More
Busy beavers and Kolmogorov complexityMar 15 2017The idea to find the "maximal number that can be named" can be traced back to Archimedes (see his Psammit). From the viewpoint of computation theory the natural question is "which number can be described by at most n bits"? This question led to the definition ... More
Derivation of Schrodinger's equationFeb 07 2017In this article, a model of a material particle in chaotic motion (while maintaining a definite size and trajectory) is presented. On the basis of this model, the following is achieved: --to express Planck's constant through the main features of a stationary ... More
Discriminant and Hodge classes on the space of Hitchin's coversMar 31 2019We continue the study of the rational Picard group of the moduli space of Hitchin's spectral covers started in P. Zograf's and D. Korotkin's work [11]. In the first part of the paper we expand the ``boundary'', ``Maxwell stratum'' and ``caustic'' divisors ... More
Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesicsDec 19 2013Apr 04 2014We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that any thick ... More
Proof of Gal's conjecture for the D series of generalized associahedraJun 09 2011In this short note we consider generalized associahedra of type D_n. We prove that these simple flag polytopes are not nestohedra for n > 3, but the statement of Gal's conjecture holds for them.
Population protocols with unreliable communicationFeb 26 2019Mar 06 2019Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities occur nondeterministically, ... More
The defect of weak approximation for homogeneous spaces. IIApr 30 2008May 10 2008Let X be a homogeneous space of a connected linear algebraic group G' over a number field k, containing a k-point x. Assume that the stabilizer of x in G' is connected. Using the notion of a quasi-trivial group, recently introduced by Colliot-Th\'el\`ene, ... More
On distinguishability of hypothesesAug 20 2013Oct 23 2013We consider the problems of hypothesis testing on a probability measure of independent sample, on solution of ill-posed problem, on deconvolution problem and on Poisson mean measure. For all these setups necessary conditions and sufficient conditions ... More
When is the set of embeddings finite up to isotopy?Jun 09 2011Dec 27 2015Given a manifold N and a number m, we study the following question: is the set of isotopy classes of embeddings N->S^m finite? In case when the manifold N is a sphere the answer was given by A. Haefliger in 1966. In case when the manifold N is a disjoint ... More
Continuity of the Mixing OperatorAug 16 2005Oct 03 2005Mixed distributions are considered as a results of application of a linear operator, which maps mixing measures to mixed measures. The main result is a proof of continuity of this mixing operator. Corollaries for parametric families of distributions (usually ... More
Heisenberg algebra and a graphical calculusSep 16 2010A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg ... More
The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation ProbabilitiesJun 07 2012For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the lower bound ... More
Parshin Residues via Coboundary OperatorsJul 25 2007Dec 05 2010The article consist of two main parts: an analog of the Leray Theory for Singular Varieties and its application to the Theory of Parshin's Residues. The first part is independent from the second. It uses the theory of Whitney stratifications. The second ... More
Link homology and Frobenius extensionsNov 20 2004Feb 20 2006We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant.
NilCoxeter algebras categorify the Weyl algebraJun 24 1999We show that induction and restriction functors for inclusions of nilCoxeter algebras provide a categorical realization of the algebra of polynomial differential operators in one variable.
A categorification of the Jones polynomialAug 30 1999Aug 30 1999We construct a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial.
New approach to low energy Virtual Compton Scattering and generalized polarizabilities of the nucleonMay 27 2009Sep 21 2009Virtual Compton scattering off the nucleon (VCS) is studied in the regime of low energy of the outgoing real photon. This regime allows one to directly access the generalized polarizabilities of the nucleon in a VCS experiment. In the derivation of the ... More
Doubly virtual Compton scattering and the beam normal spin asymmetryDec 08 2005Jan 17 2006We construct an invariant basis for Compton scattering with two virtual photons (VVCS). The basis tensors are chosen to be gauge invariant and orthogonal to each other. The properties of the corresponding 18 invariant amplitudes are studied in detail. ... More
Theoretical ecology without speciesApr 10 2015Apr 14 2016Ecosystems are commonly conceptualized as networks of interacting species. However, partitioning natural diversity of organisms into discrete units is notoriously problematic, and mounting experimental evidence raises the intriguing question whether this ... More
Manipulating scattering of ultracold atoms with light-induced dissipationJul 30 2013Recently it has been shown that pairs of atoms can form metastable bonds due to non-conservative forces induced by dissipation [Lemeshko&Weimer, Nature Comm. 4, 2230 (2013)]. Here we study the dynamics of interaction-induced coherent population trapping ... More
Teichmüller space of Fibonacci mapsNov 27 1993According to Sullivan, a space ${\cal E}$ of unimodal maps with the same combinatorics (modulo smooth conjugacy) should be treated as an infinitely-dimensional Teichm\"{u}ller space. This is a basic idea in Sullivan's approach to the Renormalization Conjecture. ... More
Geometry of quadratic polynomials: moduli, rigidity and local connectivitySep 04 1993A while ago MLC (the conjecture that the Mandelbrot set is locally connected) was proven for quasi-hyperbolic points by Douady and Hubbard, and for boundaries of hyperbolic components by Yoccoz. More recently Yoccoz proved MLC for all at most finitely ... More
Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch TheoryOct 18 2009May 31 2010The classical Floquet theory deals with Floquet-Bloch solutions of periodic PDEs (see e.g., P. Kuchment. Floquet Theory for Partial Differential Equations. Basel: Birkhauser, 1993). Peter Kuchment developed as well a discrete version of this theory for ... More
Membranes and higher groupoidsFeb 22 2015We study the dg-Lie algebra f_n generated by the coefficients of the universal translation invariant flat dg-connection on the n-dimensional affine space. We describe its "semiabelianization" (in particular, the universal quotient which is a crossed module ... More
Resonance Gyrons and Quantum GeometryNov 07 2005We describe irreducible representations, coherent states and star-products for algebras of integrals of motions (symmetries) of two-dimensional resonance oscillators. We demonstrate how the quantum geometry (quantum K\"ahler form, metric, quantum Ricci ... More
Generalization of Schensted insertion algorithm to the cases of hooks and semi-shufflesJun 05 2002Given an rc-graph $R$ of permutation $w$ and an rc-graph $Y$ of permutation $v$, we provide an insertion algorithm, which defines an rc-graph $R\leftarrow Y$ in the case when $v$ is a shuffle with the descent at $r$ and $w$ has no descents greater than ... More
Coupling of microwave magnetic dynamics in thin ferromagnetic films to stripline transducers in the geometry of the broadband stripline ferromagnetic resonanceNov 04 2015We constructed a quasi-analytical self-consistent model of the stripline-based broadband ferromagnetic resonance (FMR) measurements of ferromagnetic films. Exchange-free description of magnetization dynamics in the films allowed us to obtain simple analytical ... More
ITEP Lectures in Particle PhysicsOct 24 1995Introduction to the Lecture Note Volume "ITEP Lectures in Particle Physics", including 25 years of personal reminiscences.
On the extra phase correction to the semiclassical spin coherent-state propagatorApr 04 2003Jan 12 2004The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. ... More
PICsar: A 2.5D Axisymmetric, Relativistic, Electromagnetic, Particle in Cell Code with a Radiation Absorbing BoundaryJul 07 2014Jun 01 2016We present PICsar -- a new Particle in Cell code geared towards efficiently simulating the magnetosphere of the aligned rotator. PICsar is a special relativistic, electromagnetic, charge conservative code that can be used to simulate arbitrary electromagnetics ... More
On the specialization to the asymptotic coneMay 07 1998Let X be a smooth, connected, closed subvariety of a complex vector space V. The asymptotic cone as(X) is naturally equipped with a nearby cycles sheaf P coming from the specialization of X to as(X). We show that if X is transverse to infinity in a suitable ... More
On spaces in countable webJun 26 2000We show that a Tychonoff discretely star-Lindelof space can have arbitrarily big extent and note that there are consistent examples of normal discretely star-Lindelof spaces with uncountable extent.
Nonlinear supersymmetry: from classical to quantum mechanicsFeb 03 2004Feb 06 2004Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum level. With ... More
Nonlinear superconformal symmetryDec 31 2003Jan 07 2004We discuss two different nonlinear generalizations of the osp(2|2) supersymmetry which arise in superconformal mechanics and fermion-monopole models.
Magnetic behaviour of dirty multiband superconductors near the upper critical fieldMar 19 2016Magnetic properties of dirty multiband superconductors near the upper critical field are studied. The parameter $\kappa_2$ characterizing magnetization slope is shown to have a significant temperature variation which is quite sensitive to the pairing ... More
An upper bound for the Hales-Jewett number HJ(4,2)Apr 10 2015We show that for $n$ at least $10^{11}$, any 2-coloring of the $n$-dimensional grid $[4]^n$ contains a monochromatic combinatorial line. This is a special case of the Hales-Jewett Theorem, to which the best known general upper bound is due to Shelah; ... More
Gorenstein models of del Pezzo surfaces of degree 1 over Dedekind schemesMar 24 2000Let R be a Dedekind scheme, $\nu$ its generic point, X and V del Pezzo surfaces of degree 1 over R that are Gorenstein Mori fiber spaces (as 3-folds germs over the ground field). We study birational maps $\phi:X\dasharrow V$ over R which are isomorphisms ... More
Slowly Synchronizing Automata with Idempotent Letters of Low RankJul 18 2018We use a semigroup-theoretic construction by Peter Higgins in order to produce, for each even $n$, an $n$-state and 3-letter synchronizing automaton with the following two features: 1) all its input letters act as idempotent selfmaps of rank at most $\dfrac{n}2$; ... More
Axiomatization of the Choquet integral for 2-dimensional heterogeneous product setsJul 15 2015Mar 26 2016We prove a representation theorem for the Choquet integral model. The preference relation is defined on a two-dimensional heterogeneous product set $X = X_1 \times X_2$ where elements of $X_1$ and $X_2$ are not necessarily comparable with each other. ... More
Asymptotic distribution of capital in a model of an investment market with competitionNov 29 2018We consider a stochastic game-theoretic model of an investment market in continuous time where investors compete for dividend income from several assets. Asset prices are determined endogenously from the equality of supply and demand. The main results ... More
Transverse linear and orbital angular momenta of beam waves and propagation in random mediaMay 13 2017For paraxial propagation of scalar waves the classic electromagnetic theory definition of transverse linear (TLM) and orbital angular (OAM) momenta of the beam wave are represented in terms of the coherence function. We show in examples that neither the ... More
Choquet integral in decision analysis - lessons from the axiomatizationNov 29 2016The Choquet integral is a powerful aggregation operator which lists many well-known models as its special cases. We look at these special cases and provide their axiomatic analysis. In cases where an axiomatization has been previously given in the literature, ... More
Analogue of Pontryagin's maximum principle for multiple integrals minimization problemsOct 26 2016The theorem like Pontryagin's maximum principle for multiple integrals is proved. Unlike the usual maximum principle, the maximum should be taken not over all matrices, but only on matrices of rank one. Examples are given.
Quasiparticle approach to molecules interacting with quantum solventsOct 05 2016Feb 15 2017Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here we demonstrate that experimental data collected over the ... More
On the Dimensional-like Characteristics Arising From Linear Inhomogeneous ApproximationsMar 13 2018Jul 27 2018As it follows from the theory of almost periodic functions the set of integer solutions $q$ to the Kronecker system $|\omega_{j} q - \theta_{j}| < \varepsilon \pmod 1$, $j=1,\ldots,m$, where $1,\omega_{1},\ldots,\omega_{m}$ are linearly independent over ... More
Studying superconformal symmetry enhancement through indicesAug 28 2017Jan 13 2019In this note we classify the necessary and the sufficient conditions that an index of a superconformal theory in $3\leq d \leq 6$ must obey for the theory to have enhanced supersymmetry. We do that by noting that the index distinguishes a superconformal ... More
Height transitions, shape evolution, and coarsening of equilibrating quantum nanoislandsAug 24 2017Morphology evolution and coarsening of metal nanoislands is computed within the framework of a surface diffusion-type model that includes the effects of the electron energy confinement within the film, the charge spillage at the film/substrate interface, ... More
On the accuracy of the poissonisation in the infinite occupancy schemeDec 10 2017We obtain asymptotic accuracy of the poissonisation in the infinite occupancy scheme. All results are obtained for integer-valued random variables having a regularly varying distribution.
Searches for sterile neutrinos at very short baseline reactor experimentsDec 10 2018For a long time there were 3 main experimental indications in favor of the existence of sterile neutrinos: $\bar{\nu_e}$ appearance in the $\bar{\nu_\mu}$ beam in the LSND experiment, $\bar{\nu_e}$ flux deficit in comparison with theoretical expectations ... More
Symmetry of the triple octonionic productJun 14 2018The Hermitian decomposition of a linear operator is generalized to the case of two or more operations. An additive expansion of the product of three octonions into three parts is constructed, wherein each part either preserve or change the sign under ... More
On self-play computation of equilibrium in pokerMay 23 2018We compare performance of the genetic algorithm and the counterfactual regret minimization algorithm in computing the near-equilibrium strategies in the simplified poker games. We focus on the von Neumann poker and the simplified version of the Texas ... More
A space with a Lusin $π$-base whose square has no Lusin $π$-baseDec 09 2018We construct a space ${X}$ that has a Lusin $\pi$-base and such that ${X}^{2}$ has no Lusin $\pi$-base.
Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifoldsJul 04 2000Jul 30 2001We prove essential self-adjointness for semi-bounded below magnetic Schr\"odinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are ... More
On approximability by embeddings of cycles in the planeAug 08 2008We obtain a criterion for approximability by embeddings of piecewise linear maps of a circle to the plane, analogous to the one proved by Minc for maps of a segment to the plane. Theorem. Let S be a triangulation of a circle with s vertices. Let f be ... More
On the stability of some Erdős--Ko--Rado type resultsSep 30 2015Consider classical Kneser's graph $K(n,r)$: for two natural numbers $ r, n $ such that $r \le n / 2$, its vertices are all the subsets of $[n]=\{1,2,\ldots,n\}$ of size $r$, and two such vertices are adjacent if the corresponding subsets are disjoint. ... More
Finiteness theorems for congruence reflection groupsAug 05 2010Mar 14 2011This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible application ... More
Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphsDec 17 2013We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups. We compare characterizations of superreflexivity in terms of diamond graphs and binary trees. We show that there exist sequences of series-parallel ... More
Hyperbolic surfaces in ${\bf P}^3$: examplesNov 24 2003Apr 30 2004This is a recent conference report on the Kobayashi Problem on hyperbolicity of generic projective hypersurfaces. As an appendix, a (non-updated) author's survey article of 1992 on the same subject, published in an edition with a limited distribution, ... More
Interpolation by periods in planar domainNov 22 2015Let $\Omega\subset\mathbb R^2$ be a countably connected domain. To any closed differential form of degree $1$ in $\Omega$ with components in $L^2(\Omega)$ one associates the sequence of its periods around holes in $\Omega$, that is around bounded connected ... More
Interplay of Quantum Size Effect, Anisotropy and Surface Stress Shapes the Instability of Thin Metal FilmsMar 15 2016Aug 11 2016Morphological instability of a planar surface ([111], [011], or [001]) of an ultra-thin metal film is studied in a parameter space formed by three major effects (the quantum size effect, the surface energy anisotropy and the surface stress) that influence ... More
Aloff-Wallach Spaces: Volumes, Curvatures, Injectivity RadiiNov 24 2005In this paper, we obtain two-sided bounds for the volumes of the Aloff-Wallach spaces $W(p,q),$ compute maximal and minimal sectional curvature for the spaces $W(n,n+1),$ and use this information to estimate the injectivity radii: We derive an upper bound ... More
On metric characterizations of some classes of Banach spacesFeb 24 2011The paper contains the following results and observations: (1) There exists a sequence of unweighted graphs $\{G_n\}_n$ with maximum degree 3 such that a Banach space $X$ has no nontrivial cotype iff $\{G_n\}_n$ admit uniformly bilipschitz embeddings ... More
Crossingless matchings and the cohomology of (n,n) Springer varietiesFeb 12 2002The sequence of rings $H^n, n\ge 0,$ introduced in math.QA/0103190, controls categorification of the quantum sl(2) invariant of tangles. We prove that the center of $H^n$ is isomorphic to the cohomology ring of the (n,n) Springer variety and show that ... More
Non-rationality of a three-dimensional Fano variety of index 2 and degree 1Apr 22 2003We describe the set of Mori structures for a Fano 3-fold of index 2 and degree 1 (the double cone over the Veronese surface). In partiular, it is proved that such a Fano variety is not rational, the group of birational automorphisms coincides with the ... More
Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologiesDec 05 2012Jan 04 2013A PDE-based model combining surface electromigration and wetting is developed for the analysis of morphological stability of ultrathin solid films. Adatom mobility is assumed anisotropic, and two directions of the electric field (parallel and perpendicular ... More
Golod-Shafarevich groups: a surveyJun 03 2012In this paper we survey the main results about Golod-Shafarevich groups and their applications in algebra, number theory and topology.
Self-interlacing polynomials II: Matrices with self-interlacing spectrumDec 05 2016An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows $$ \lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0. $$ A method for constructing sign definite matrices ... More
sl(3) link homologyApr 24 2003Nov 27 2004We define a bigraded homology theory whose Euler characteristic is the quantum sl(3) link invariant.
Categorifications from planar diagrammaticsAug 30 2010A diagrammatic presentation of functors and natural transformations and the virtues of biadjointness are discussed. We then review a graphical description of the category of Soergel bimodules and a diagrammatic categorification of positive halves of quantum ... More
How to categorify one-half of quantum gl(1|2)Jul 20 2010Jul 25 2010We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra gl(1|2).
Model for computing kinetics of the graphene edge epitaxial growth on copperJan 24 2016Jun 29 2016A basic kinetic model that incorporates a coupled dynamics of the carbon atoms and dimers on a copper surface is used to compute growth of a single-layer graphene island. The speed of the island's edge advancement on Cu[111] and Cu[100] surfaces is computed ... More