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Imaging of interlayer coupling in van der Waals heterostructures using a bright-field optical microscopeDec 23 2016May 01 2017Vertically stacked atomic layers from different layered crystals can be held together by van der Waals forces, which can be used for building novel heterostructures, offering a platform for developing a new generation of atomically thin, transparent and ... More

Resonantly hybridised excitons in moiré superlattices in van der Waals heterostructuresApr 12 2019Atomically-thin layers of two-dimensional materials can be assembled in vertical stacks held together by relatively weak van der Waals forces, allowing for coupling between monolayer crystals with incommensurate lattices and arbitrary mutual rotation. ... More

The Ising version of the t-J modelJul 02 2015The t-J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping ... More

Duplication of Key Frames of Video Streams in Wireless NetworksApr 26 2011In this paper technological solutions for improving the quality of video transfer along wireless networks are investigated. Tools have been developed to allow packets to be duplicated with key frames data. In the paper we tested video streams with duplication ... More

Terahertz optoelectronics of quantum rings and nanohelicesMar 18 2019We outline a range of proposals on using quantum rings and nanohelices for terahertz device implementations. We show that an Aharonov-Bohm quantum ring system and a double-gated quantum ring system both permit control over the polarization properties ... More

Auxiliary tensor fields for Sp(2,R) self-dualityDec 18 2014The coset Sp(2,R)/U(1) is parametrized by two real scalar fields. We generalize the formalism of auxiliary tensor (bispinor) fields in U(1) self-dual nonlinear models of abelian gauge fields to the case of Sp(2,R) self-duality. In this new formulation, ... More

Interpolation and extrapolation of strictly singular operators between $L_p$ spacesJun 27 2017We study the interpolation and extrapolation properties of strictly singular operators between different $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ spaces is analyzed. Among other things, we clarify ... More

BayesSummaryStatLM: An R package for Bayesian Linear Models for Big Data and Data ScienceMar 02 2015Apr 23 2015Recent developments in data science and big data research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on either computer memory or storage capacity. Here, we introduce our R package 'BayesSummaryStatLM' ... More

Superconformal field theory in three dimensions: Correlation functions of conserved currentsMar 17 2015Jul 01 2015For N-extended superconformal field theories in three spacetime dimensions (3D), with N=1,2,3, we compute the two- and three-point correlation functions of the supercurrent and the flavour current multiplets. We demonstrate that supersymmetry imposes ... More

Selective Delamination upon Femtosecond Laser Ablation of Ceramic SurfacesDec 04 2018We report on the experimental observation of selective delamination of semi-transparent materials on the example of yttria-stabilized zirconia ceramics upon femtosecond laser processing of its surface with low numerical aperture lens. The delamination ... More

Open surfaces of small volumeDec 29 2016Jan 31 2017We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1/48 983$ and a log canonical pair $(X,B)$ with a nonempty reduced divisor $B$ and ample $K_X+B$ that has $(K_X+B)^2 = 1/462$. Both examples significantly ... More

ADE surfaces and their moduliDec 21 2017Jan 12 2018We define a class of surfaces and surface pairs corresponding to the ADE root lattices and construct compactifications of their moduli spaces, generalizing Losev-Manin spaces of curves.

Derived categories of Burniat surfaces and exceptional collectionsAug 21 2012Aug 28 2012We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this ... More

Stable spherical varieties and their moduliMay 31 2005We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli space for stable ... More

Moduli of affine schemes with reductive group actionJan 24 2003Sep 15 2003For a connected reductive group G and a finite-dimensional G-module V, we study the invariant Hilbert scheme that parameterizes closed G-stable subschemes of V affording a fixed, multiplicity-finite representation of G in their coordinate ring. We construct ... More

Boundedness of spherical Fano varietiesJan 19 2003We prove that for any e>0, there exists only finitely many e-log terminal spherical Fano varieties of fixed dimension. We also introduce an invariant of a spherical subgroup H in a reductive group G which measures how nice an equivariant Fano compactification ... More

Log surfaces of Picard rank one from four lines in the planeJan 31 2019We derive simple formulas for the basic numerical invariants of a singular surface with Picard number one obtained by blowups and contractions of the four-line configuration in the plane. As an application, we establish the smallest positive volume and ... More

On accumulation points of volumes of log surfacesMar 26 2018Let $\mathcal C\subset(0,1]$ be a set satisfying the descending chain condition. We show that any accumulation point of volumes of log canonical surfaces $(X, B)$ with coefficients in $\mathcal C$ can be realized as the volume of a log canonical surface ... More

Hultman numbers, polygon gluings and matrix integralsNov 13 2011The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the Hultman numbers: ... More

Equations resolving a conjecture of Rado on partition regularityDec 08 2008Jan 25 2009A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive integer k, there exists a linear equation that is (k-1)-regular but not k-regular. ... More

Majorana neutrinos and other Majorana particles:Theory and experimentDec 10 2014This is a somewhat modified version of Chapter 15 of the book "The Physics of Ettore Majorana", by Salvatore Esposito with contributions by Evgeny Akhmedov (Ch. 15) and Frank Wilczek (Ch. 14), Cambridge University Press, 2014.

Conformal spectral theory for the monodromy matrixDec 11 2006For any $N\ts N$ monodromy matrix we define the Lyapunov function, which is analytic on an associated N-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov function for the Hill operator. The Lyapunov ... More

Geometrical approach to modeling of nonlinear systems from experimental dataFeb 28 2014This monograph presents a geometric modeling method nonlinear dynamical systems from experimental data . basis method is a qualitative approach to the analysis of linear models and construction of the symmetry groups of attractors of dynamical systems ... More

On the strong law of large numbers for L-statistics with dependent dataSep 27 2006The strong law of large numbers for linear combinations of functions of order statistics ($L$-statistics) based on weakly dependent random variables is proven. We also establish the Glivenko--Cantelli theorem for $\phi$-mixing sequences of identically ... More

Thermodynamics of the Binary Symmetric ChannelSep 10 2015We study a hidden Markov process which is the result of a transmission of the binary symmetric Markov source over the memoryless binary symmetric channel. This process has been studied extensively in Information Theory and is often used as a benchmark ... More

The median Genocchi numbers, Q-analogues and continued fractionsNov 03 2011Jun 09 2012The goal of this paper is twofold. First, we review the recently developed geometric approach to the combinatorics of the median Genocchi numbers. The Genocchi numbers appear in this context as Euler characteristics of the degenerate flag varieties. Second, ... More

On critical collapse of gravitational wavesAug 19 2010Dec 23 2010An axisymmetric collapse of non-rotating gravitational waves is numerically investigated in the subcritical regime where no black holes form but where curvature attains a maximum and decreases, following the dispersion of the initial wave packet. We focus ... More

On the base size of a transitive group with solvable point stabilizerNov 19 2010Jun 22 2018We prove that the base size of a transitive group $G$ with solvable point stabilizer and with trivial solvable radical is not greater than $k$ provided the same statement holds for the group of $G$-induced automorphisms of each nonabelian composition ... More

Desingularizations of Schubert varieties in double GrassmanniansAug 22 2006Jul 03 2009Let X be the direct product of two Grassmann varieties of k- and l-planes in a finite-dimensional vector space V, and let B be the isotropy group of a complete flag in V. We consider B-orbits in X, which are an analog to Schubert cells in Grassmannians. ... More

The destiny of constant structure discrete time closed semantic systemsNov 19 2017Constant structure closed semantic systems are the systems each element of which receives its definition through the correspondent unchangeable set of other elements of the system. Discrete time means here that the definitions of the elements change iteratively ... More

Degenerate flag varieties and the median Genocchi numbersJan 10 2011Jan 14 2011We study the $\bG_a^M$ degenerations $\Fl^a_\la$ of the type $A$ flag varieties $\Fl_\la$. We describe these degenerations explicitly as subvarieties in the products of Grassmanians. We construct cell decompositions of $\Fl^a_\la$ and show that for complete ... More

Nuclear Chiral EFT in the Precision EraOct 25 2015Chiral effective field theory has established itself as the method of choice to study nuclear forces and low-energy nuclear dynamics. I review the status and prospects of this approach and discuss ongoing efforts to advance the precision frontier for ... More

Nuclear Physics with Chiral Effective Field Theory: State of the Art and Open ChallengesFeb 13 2013Understanding the properties of atomic nuclei and nuclear dynamics from QCD remains a major challenge. Complementary to first attempts along these lines based on lattice QCD, an effective field theory approach has been developed in the past two decades ... More

On motives of algebraic groups associated to a divsion algebraFeb 14 2012We consider algebraic groups GL_1(A), SL_1(A), where A is a division algebra of prime degree over a field F, and associated motives in the category of motivic complexes DM(F). Following an idea of Suslin, we relate motives of these groups to the motive ... More

Inverse resonance scattering for Jacobi operatorsAug 20 2008We consider the Jacobi operator $(Jf)_n= a_{n-1}f_{n-1}+a_nf_{n+1}+b_nf_n$ on $\Z$ with a real compactly supported sequences $(a_n-1)_{n\in\Z}$ and $(b_n)_{n\in\Z}$. We give the solution of two inverse problems (including characterization): $ (a,b)\to ... More

Swing amplification and global modes reciprocity in models with cuspsAug 05 2016Using 3D N-body simulations we analyse an onset of the bar in cuspy models, and argue that role of swing amplification is twofold. Amplified shot noise due to disc discreteness hampers bar formation, while induced resonance perturbations allow bar amplitude ... More

Atmospheric neutrinos, $nu_e-nu_s$ oscillations, and a novel neutrino evolution equationJun 23 2016Sep 28 2016If a sterile neutrino nu_s with an eV-scale mass and a sizeable mixing to the electron neutrino exists, as indicated by the reactor and gallium neutrino anomalies, a strong resonance enhancement of nu_e-nu_s oscillations of atmospheric neutrinos should ... More

Bispectrality for the quantum open Toda chainJun 03 2013An alternative to Babelon's (2003) construction of dual variables for the quantum open Toda chain is proposed that is based on the 2x2 Lax matrix and the corresponding quadratic R-matrix algebra.

Dehn surgeries on the figure eight knot: an upper bound for the complexityJul 05 2010We establish an upper bound $\omega(p/q)$ on the complexity of manifolds obtained by $p/q$-surgeries on the figure eight knot. It turns out that if $\omega(p/q)\leqslant 12$, the bound is sharp.

A priori estimates for the Hill and Dirac operatorsJan 16 2007Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps $\g_n,n\ge 1$ with length $|\g_n|\ge 0$. We obtain ... More

Classification of log del Pezzo surfaces of index $\le 2$Jun 25 2004Jun 10 2006This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all exceptional curves ... More

Non-rational centers of log canonical singularitiesSep 19 2011Jun 28 2012We show that if $(X,B)$ is a log canonical pair with $\dim X\geq d+2$, whose non-klt centers have dimension $\geq d$, then $X$ is has depth $\ge d+2$ at every closed point.

Hyperbolic Metamaterials with Bragg PolaritonsSep 10 2014Jan 12 2015We propose a novel mechanism for designing quantum hyperbolic metamaterials with use of semi-conductor Bragg mirrors containing periodically arrangedquantum wells. The hyperbolic dispersion of exciton-polariton modes is realized near the top of the first ... More

Long and short range multi-locus QTL interactions in a complex trait of yeastMar 19 2015We analyse interactions of Quantitative Trait Loci (QTL) in heat selected yeast by comparing them to an unselected pool of random individuals. Here we re-examine data on individual F12 progeny selected for heat tolerance, which have been genotyped at ... More

Extreme thermodynamics with polymer gel tori: harnessing thermodynamic instabilities to induce large-scale deformationsJun 28 2018When a swollen, thermoresponsive polymer gel is heated in a solvent bath, it expels solvent and deswells. When this heating is slow, deswelling proceeds homogeneously, as observed in a toroid-shaped gel that changes volume whilst maintaining its toroidal ... More

Investigation of scaling properties of a thin current sheet by means of particle trajectories studyJun 17 2015A thin current sheet (TCS), with the width of an order of thermal proton gyroradius, appears a fundamental physical object which plays an important role in structuring of major magnetospheric current systems (magnetotail, magnetodisk, etc.). The TCSs ... More

On minimal colorings without monochromatic solutions to a linear equationSep 21 2010For a ring R and system L of linear homogeneous equations, we call a coloring of the nonzero elements of R minimal for L if there are no monochromatic solutions to L and the coloring uses as few colors as possible. For a rational number q and positive ... More

Spectral estimates for Schrödinger operator with periodic matrix potentials on the real lineAug 29 2005We consider the Schr\"odinger operator on the real line with a $N\ts N$ matrix valued periodic potential, N>1. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov function, which is ... More

Inverse problem for the discrete 1D Schrödinger operator with small periodic potentialsJul 14 2005Consider the discrete 1D Schr\"odinger operator on $\Z$ with an odd $2k$ periodic potential $q$. For small potentials we show that the mapping: $q\to $ heights of vertical slits on the quasi-momentum domain (similar to the Marchenko-Ostrovski maping for ... More

Minimax Error of Interpolation and Optimal Design of Experiments for Variable Fidelity DataOct 21 2016Engineering problems often involve data sources of variable fidelity with different costs of obtaining an observation. In particular, one can use both a cheap low fidelity function (e.g. a computational experiment with a CFD code) and an expensive high ... More

Impact of continuous particle injection on generation and decay of the magnetic field in collisionless shocksMar 25 2016Jun 03 2016We present numerical simulations of the magnetic field turbulence in collisionless electron-positron plasma with continuous injection of new pairs, which maintains anisotropy in the particle distribution over long time. {With these simulations we follow ... More

Casimir electromotive force in periodic configurationsJan 24 2016The possibility in principle of the existence of Casimir electromotive force (EMF) is shown for nonparallel nanosized metal plates arranged in the form of a periodic structure. It is found that EMF does not appear in strictly periodic structures with ... More

Stability of a vacuum nonsingular black holeSep 12 2004This is the first of series of papers in which we investigate stability of the spherically symmetric space-time with de Sitter center. Geometry, asymptotically Schwarzschild for large $r$ and asymptotically de Sitter as $r\to 0$, describes a vacuum nonsingular ... More

Generalized Weyl modules for twisted current algebrasJun 16 2016We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we compute the ... More

A weighted binary average of point-normal pairs with application to subdivision schemesAug 14 2016Subdivision is a well-known and established method for generating smooth curves and surfaces from discrete data by repeated refinements. The typical input for such a process is a mesh of vertices. In this work we propose to refine 2D data consisting of ... More

A Factorization Method and Monotonicity Bounds in Inverse Medium Scattering for Contrasts with Fixed Sign on the BoundaryFeb 09 2016Aug 04 2016We generalize the factorization method for inverse medium scattering using a particular factorization of the difference of two far field operators. Whilst the factorization method been used so far mainly to identify the shape of a scatterer's support, ... More

Resonances of 4-th Order Differential OperatorsMar 06 2017Dec 12 2017We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We determine asymptotics of the number of resonances in complex discs at large radius. We consider resonances of an Euler-Bernoulli operator on ... More

k-Normal surfacesJun 05 2006Following Matveev, a k-normal surface in a triangulated 3-manifold is a generalization of both normal and (octagonal) almost normal surfaces. Using spines, complexity, and Turaev-Viro invariants of 3-manifolds, we prove the following results: 1) a minimal ... More

Springer fiber components in the two columns case for types A and D are normalJul 03 2009Sep 13 2010We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N^2=0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible ... More

Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graphMar 28 2019The periodic Schrodinger operator $ H $ on a discrete periodic graph is considered. We estimate the discrete spectrum of the perturbed operator $ H _ {-} (t) = H-tV $, $ t> 0 $, where the potential $ V \ ge 0 $ is decreasing and $t>0$ is the coupling ... More

On variants of $H$-measures and compensated compactnessMar 25 2014We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we present new compensated ... More

Distance-2 MDS codes and latin colorings in the Doob graphsOct 06 2015The maximum independent sets in the Doob graphs D(m,n) are analogs of the distance-2 MDS codes in Hamming graphs and of the latin hypercubes. We prove the characterization of these sets stating that every such set is semilinear or reducible. As related ... More

On a test on switching separability of graphs modulo $q$Dec 09 2014We consider the graphs whose edges are marked by the integers (weights) from $0$ to $q-1$ (zero corresponds to no-edge). Such graph is called additive if its vertices can be marked in such a way that the weight of every edge is equal to the modulo-$q$ ... More

Integrable Hierarchy of the Quantum Benjamin-Ono EquationSep 25 2013Dec 08 2013A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables $x_1,x_2,\ldots$. This ... More

Zeta-invariants of the Steklov spectrum for a planar domainApr 08 2014The classical inverse problem of recovering a simply connected smooth planar domain from the Steklov spectrum \cite{E} is equivalent to the problem of recovering, up to a conformal equivalence, a positive function $a\in C^\infty({\mathbb S})$ on the unit ... More

Number of Sylow subgroups in finite groupsSep 01 2017Denote by $\nu_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that $\nu_p(H)\leq\nu_p(G)$ for $H\leq G$, however $\nu_p(H)$ does not divide $\nu_p(G)$ in general. In this paper we reduce the question whether $\nu_p(H)$ divides ... More

On decay of entropy solutions to multidimensional conservation lawsApr 02 2019Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.

On long time behavior of periodic entropy solutions of a degenerate non-linear parabolic equationFeb 12 2018We prove the asymptotic convergence of a space-periodic entropy solution of a one-dimensional degenerate parabolic equation to a traveling wave. It is also shown that on a segment containing the essential range of the limit profile the flux function is ... More

Quantum toroidal algebra associated with $\mathfrak{gl}_{m|n}$Apr 15 2019We introduce and study the quantum toroidal algebra $\mathcal{E}_{m|n}(q_1,q_2,q_3)$ associated with the superalgebra $\mathfrak{gl}_{m|n}$ with $m\neq n$, where the parameters satisfy $q_1q_2q_3=1$. We give an evaluation map. The evaluation map is a ... More

Asymptotic properties of parallel Bayesian kernel density estimatorsNov 09 2016Mar 26 2017In this article we perform an asymptotic analysis of Bayesian parallel kernel density estimators introduced by Neiswanger, Wang and Xing (2014). We derive the asymptotic expansion of the mean integrated squared error for the full data posterior estimator ... More

Graphs with multiple sheeted pluripolar hullsMar 16 2005In this paper we study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.

Moduli of holomorphic functions and logarithmically convex radial weightsJan 26 2013Apr 01 2015Let $H(D)$ denote the space of holomorphic functions on the unit disk $D$. We characterize those radial weights $w$ on $D$, for which there exist functions $f, g \in H(D)$ such that the sum $|f| + |g|$ is equivalent to $w$. Also, we obtain similar results ... More

First steps in stable Hamiltonian topologyMar 26 2010Dec 17 2010In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; there exist stable Hamiltonian structures ... More

Generalized Weyl modules, alcove paths and Macdonald polynomialsDec 10 2015Sep 06 2016Classical local Weyl modules for a simple Lie algebra are labeled by dominant weights. We generalize the definition to the case of arbitrary weights and study the properties of the generalized modules. We prove that the representation theory of the generalized ... More

Zhu's algebra and the $C_2$-algebra in the symplectic and the orthogonal casesNov 16 2009We prove that Zhu's algebra and the $C_2$-algebra of type ${\tt C}_m$ have the same dimension, and we compute the graded character of the latter. Maximal parabolic subalgebras of the symplectic algebra play a central role in our construction. For the ... More

Generalized Weyl modules for twisted current algebrasJun 16 2016Nov 25 2016We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we compute the ... More

Initial Data for Black Holes and Black Strings in 5dNov 22 2002Mar 05 2003We explore time-symmetric hypersurfaces containing apparent horizons of black objects in a 5d spacetime with one coordinate compactified on a circle. We find a phase transition within the family of such hypersurfaces: the horizon has different topology ... More

Miura Opers and Critical Points of Master FunctionsDec 22 2003Oct 12 2004Critical points of a master function associated to a simple Lie algebra \g come in families called the populations [MV1]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra \g^t. The proof is based on the correspondence ... More

Remarks on critical points of phase functions and norms of Bethe vectorsOct 14 1998We consider a tensor product of a Verma module and the linear representation of $sl(n+1)$. We prove that the corresponding phase function, which is used in the solutions of the KZ equation with values in the tensor product, has a unique critical point ... More

Periodic Jacobi operator with finitely supported perturbationsJun 08 2010We describe the spectral properties of the Jacobi operator $(Hy)_n= a_{n-1} y_{n-1}+a_{n}y_{n+1}+b_ny_n,$ $n\in\Z,$ with $a_n=a_n^0+ u_n,$ $b_n= b_n^0+ v_n,$ where sequences $a_n^0>0,$ $b_n^0\in\R$ are periodic with period $q$, and sequences $ u_n,$ $ ... More

Resonances for the radial Dirac operatorsApr 24 2014May 21 2014We consider the radial Dirac operator with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: 1) asymptotics ... More

Harmonic Space Construction of the Quaternionic Taub-NUT metricOct 01 1998Oct 07 1998We present details of the harmonic space construction of a quaternionic extension of the four-dimensional Taub-NUT metric. As the main merit of the harmonic space approach, the metric is obtained in an explicit form following a generic set of rules. It ... More

Light-Front Bootstrap for Chern-Simons Matter TheoriesNov 29 2018Nov 30 2018We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the large-$N$ as a simple ... More

Helium-like atoms. The Green's function approach to the Fock expansion calculationsMay 25 2017The renewed Green's function approach to calculating the angular Fock coefficients, $\psi_{k,p}(\alpha,\theta)$ is presented. The final formulas are simplified and specified to be applicable for analytical as well as numerical calculations. The Green's ... More

Magnetic Schrödinger operators on armchair nanotubesApr 01 2008We consider the Schr\"odinger operator with a periodic potential on a quasi 1D continuous periodic model of armchair nanotubes in $\R^3$ in a uniform magnetic field (with amplitude $B\in \R$), which is parallel to the axis of the nanotube. The spectrum ... More

Nanoribbons in external electric fieldsMar 19 2008We consider the Schr\"odinger operator on nanoribbons (tight-binding models) in an external electric potentials $V$. The corresponding electric field is perpendicular to the axis of the nanoribbon. If V=0, then the spectrum of the Schr\"odinger operator ... More

Volterra type operators on growth Fock spacesNov 13 2016Let $\omega$ be an unbounded radial weight on $\mathbb{C}^d$, $d\ge 1$. Using results related to approximation of $\omega$ by entire maps, we investigate Volterra type and weighted composition operators defined on the growth space $\mathcal{A}^\omega(\mathbb{C}^d)$. ... More

Even order periodic operators on the real lineOct 06 2010We consider $2p\ge 4$ order differential operator on the real line with a periodic coefficients. The spectrum of this operator is absolutely continuous and is a union of spectral bands separated by gaps. We define the Lyapunov function, which is analytic ... More

Lax operator for Macdonald symmetric functionsNov 05 2014Jun 23 2015Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters $q,t$ are their eigenfunctions. We express our operators in terms of ... More

Uniform exponential-power estimate for the solution to a family of the Cauchy problems for linear differential equationsFeb 26 2018We consider a solution to a parametric family of the Cauchy problems for $m$th-order linear differential equations with constant coefficients. Parameters of the family are the coefficients of the differential equation and the initial values of the solution ... More

Coulomb branch of a multiloop quiver gauge theoryMar 14 2019We compute the Coulomb branch of a multiloop quiver gauge theory for the quiver with a single vertex, $r$ loops, one-dimensional framing, and $\dim V=2$. We identify it with a Slodowy slice in the nilpotent cone of the symplectic Lie algebra of rank $r$. ... More

On decay of almost periodic viscosity solutions to Hamilton-Jacobi equationsNov 08 2017We establish that a viscosity solution to a multidimensional Hamilton-Jacobi equation with a convex non-degenerate hamiltonian and Bohr almost periodic initial data decays to its infimum as time $t\to+\infty$.

Wave turbulence of a liquid surface in an external tangential electric fieldApr 17 2019A direct numerical simulation of the interaction of plane capillary waves on the surface of a liquid dielectric in an external tangential electric field taking into account viscous forces has been performed. It has been shown that the interaction of counter-propagating ... More

Simultaneous two-dimensional best Diophantine approximations in the Euclidean normFeb 13 2010We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.

On the long time behavior of almost periodic entropy solutions to scalar conservation lawsJan 07 2017We found the precise condition for the decay as $t\to\infty$ of Besicovitch almost periodic entropy solutions of multidimensional scalar conservation laws. Moreover, in the case of one space variable we establish asymptotic convergence of the entropy ... More

On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions: global well-posedness and decay propertyJun 18 2014Jun 19 2014We study the Cauchy problem for a multidimensional scalar conservation law with merely continuous flux vector in the class of Besicovitch almost periodic functions. The existence and uniqueness of entropy solutions are established. We propose also the ... More

Determinantal identities for flagged Schur and Schubert polynomialsOct 25 2014Sep 28 2015We prove new determinantal identities for a family of flagged Schur polynomials. As a corollary of these identities we obtain determinantal expressions of Schubert polynomials for certain vexillary permutations.

A braid group action on parking functionsDec 02 2011Sep 20 2013We construct an action of the braid group on $n$ strands on the set of parking functions of $n$ cars such that elementary braids have orbits of length 2 or 3. The construction is motivated by a theorem of Lyashko and Looijenga stating that the number ... More

LG (Landau-Ginzburg) in GL (Gregory-Laflamme)Apr 04 2006Jun 22 2006This paper continues the study of the Gregory-Laflamme instability of black strings, or more precisely of the order of the transition, being either first or second order, and the critical dimension which separates the two cases. First, we describe a novel ... More

Effects of Pair Creation on Charged Gravitational CollapseSep 28 2000Dec 05 2000We investigate the effects of pair creation on the internal geometry of a black hole, which forms during the gravitational collapse of a charged massless scalar field. Classically, strong central Schwarzschild-like singularity forms, and a null, weak, ... More