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The evolution of electron dispersion in the series of rare-earth tritelluride compounds obtained from their charge-density-wave properties and susceptibility calculationsJul 10 2019We calculated electron susceptibility of rare-earth tritelluride compounds RTe$_3$ as a function of temperature, wave vector and electron-dispersion parameters. Comparison of results obtained with the available experimental data on the transition temperature ... More

Precision measurement of the proton charge radius in electron proton scatteringApr 23 2019This report presents a project of an experiment for precision studies of the elastic electron proton scattering in the low momentum transfer region. The project is based on an innovative experimental method which allows for detection of recoil protons ... More

Oblique propagation of longitudinal spin-electron acoustic waves under the influence of the Coulomb exchange interaction and the quantum Bohm potentialNov 30 2017Influence of the exchange interaction on the properties of the spin-electron acoustic waves at the oblique propagation of waves relatively to the external magnetic field in the magnetically ordered metals is studied. The spectra of the Langmuir wave and ... More

Kinetic description of the oblique propagating spin-electron acoustic waves in degenerate plasmasOct 22 2017Oblique propagation of the spin-electron acoustic waves in degenerate magnetized plasmas is considered in terms of quantum kinetics with the separate spin evolution, where the spin-up electrons and the spin-down electrons are considered as two different ... More

Coulomb-induced instabilities of nodal surfacesJul 24 2018Dec 14 2018We consider the stability of nodal surfaces in fermionic band systems with respect to the Coulomb repulsion. It is shown that nodal surfaces at the Fermi level are gapped out at low temperatures due to emergent particle-hole orders. Energy dispersion ... More

Addendum: Virtually Free pro-$p$ groups whose Torsion Elements have finite CentralizerApr 28 2012We fill details in the proof of Lemma 13 in Bull.London.Math.Soc 40 (2008) (that is Lemma 3.2 in arXiv:0712.4244v1).

Evolution and surface abundances of red giants experiencing deep mixingFeb 14 2000We have calculated the evolution of low metallicity red giant stars under the assumption of deep mixing between the convective envelope and the hydrogen burning shell. We find that the extent of the observed abundance anomalies, and in particular the ... More

A representing system generated by the Szegö kernel for the Hardy spaceMar 14 2018In this paper we give an explicit construction of a representing system generated by the Szeg\"{o} kernel for the Hardy space. Thus we answer an open question posed by Fricain, Khoi and Lef\`evre. We use frame theory to prove the main result.

Bifurcation Diagram of One Generalized Integrable Model of Vortex DynamicsApr 20 2019The article is devoted to the results of a phase topology research on a generalized mathematical model, which covers such two problems as dynamics of two point vortices enclosed in a harmonic trap in a Bose-Einstein condensate and dynamics of two point ... More

Simple singularities of multigerms of curvesDec 06 2000We classify stably simple reducible curve singularities in complex spaces of any dimension. This extends the same classification of of irreducible curve singularities obtained by V.I.Arnold. The proof is essentially based on the method of complete transversals ... More

Collective stimulated Brillouin backscatterOct 02 2007We develop the statistical theory of the stimulated Brillouin backscatter (BSBS) instability of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new regime of BSBS which has a much larger threshold ... More

Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard ModelJun 15 2015Nov 05 2015We continue our research Nucl.Phys B888, 92 (2014); Int. J. Mod. Phys. A29, 1450159 (2014); Phys. Lett. B739, 110 (2014); Int. J. Mod. Phys. A30, 1550021 (2015) and extend the class of finite BRST-antiBRST transformations with odd-valued parameters $\lambda_{a}$, ... More

Finite BRST-antiBRST Transformations in Lagrangian FormalismJun 01 2014Jul 05 2014We continue the study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [arXiv:1405.0790[hep-th]], with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters, and find an explicit ... More

Non-equilibrium critical relaxation of the 3D Heisenberg magnets with long-range correlated disorderOct 04 2012Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Heisenberg model with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are ... More

Comparative analysis of finite field-dependent BRST transformationsApr 11 2016Jul 21 2016We present a review of our recent study (A. Reshetnyak, IJMPA 29 (2014) 1450128; P. Moshin, A. Reshetnyak, Nucl. Phys. B 888 (2014) 92; Phys. Lett B 739 (2014) 110; IJMPA 29 (2014) 1450159; IJMPA 30 (2015) 1550021; IJMPA 31 (2016) 1650111), in which the ... More

Optimum Branching Problem RevisitedNov 15 2006Given a digraph $G = (V_G, A_G)$, a \emph{branching} in $G$ is a set of arcs $B \subseteq A_G$ such that the underlying undirected graph spanned by $B$ is acyclic and each node in $G$ is entered (\emph{covered}) by at most one arc from $B$. Tarjan developed ... More

Gaze-based, Context-aware Robotic System for Assisted Reaching and GraspingSep 21 2018Mar 06 2019Assistive robotic systems endeavour to support those with movement disabilities, enabling them to move again and regain functionality. Main issue with these systems is the complexity of their low-level control, and how to translate this to simpler, higher ... More

Representing systems of dilations and translations in symmetric spacesMar 17 2019Let $X$ be an arbitrary separable symmetric space on $[0,1]$. By using a combination of the frame approach and the notion of the multiplicator space $\mathscr{M}(X)$ of $X$ with respect to the tensor product, we investigate the problem when the sequence ... More

Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger TheoriesMay 05 2014Sep 14 2014We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang--Mills ... More

On the Groundstate of Yang-Mills Quantum MechanicsMay 13 1999Jun 22 1999A systematic method to calculate the low energy spectrum of SU(2) Yang-Mills quantum mechanics with high precision is given and applied to obtain the energies of the groundstate and the first few excited states.

Finite BRST-antiBRST Transformations for the Theories with Gauge GroupNov 30 2014Following our recent study [P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888 (2014) 92], we discuss the notion of finite BRST-antiBRST transformations, with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting (both global and field-dependent) Grassmann ... More

Instability Versus Equilibrium Propagation of Laser Beam in PlasmaDec 09 2003We obtain, for the first time, an analytic theory of the forward stimulated Brillouin scattering instability of a spatially and temporally incoherent laser beam, that controls the transition between statistical equilibrium and non-equilibrium (unstable) ... More

How much laser power can propagate through fusion plasma?Dec 30 2005Mar 28 2006Propagation of intense laser beams is crucial for inertial confinement fusion, which requires precise beam control to achieve the compression and heating necessary to ignite the fusion reaction. The National Ignition Facility (NIF), where fusion will ... More

Threshold Disjunctive CodesJan 25 2016Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the circuit is said ... More

Interplay between electron band-anticrossing and charge-density-wave instabilitiesJun 26 2019Our measurements of the Hall coefficient in rare-earth tritelluride compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We show that this effect ... More

Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivityFeb 21 2012Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents ... More

Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulationsOct 19 2016Mar 17 2017A nonlinear Langmuir wave in the kinetic regime $k\lambda_D\gtrsim0.2$ may have a filamentation instability, where $k$ is the wavenumber and $\lambda_D$ is the Debye length. The nonlinear stage of that instability develops into the filamentation of Langmuir ... More

Langmuir wave filamentation in the kinetic regimeOct 19 2016Nonlinear Langmuir wave in the kinetic regime $k\lambda_D\gtrsim0.2$ has a transverse instability, where $k$ is the wavenumber and $\lambda_D$ is the Debye length. The nonlinear stage of that instability development leads to the filamentation of Langmuir ... More

On a consistent macroscopic description for a spin quantum plasma with interparticle interactionsApr 21 2013Quantum mechanical averaging of the particle concentration operator is an effective starting point for derivation of the many-particle quantum hydrodynamic equations. In many-particle quantum systems, we have to separate the ordered motion of the local ... More

New symmetric families of silicon quantum dots and their conglomerates as a tunable source of photoluminescence in nanodevicesSep 14 2007We propose a new variety of silicon quantum dots containing fullerene-derived hollows of nearly arbitrary symmetry. Conglomerate structures are designed by connecting the quantum dots through two kinds of junctions. The quantum confinement effect is investigated ... More

Multiterminal Nanowire Junctions of Silicon: A Theoretical Prediction of Atomic Structure and Electronic PropertiesSep 14 2007Using empirical scheme, atomic structure of a new exotic class of silicon nanoclusters was elaborated upon the central icosahedral core (Si-IC) and pentagonal petals (Si-PP) growing from Si-IC vertexes. It was shown that Si-IC/Si-PP interface formation ... More

Lie group classification of first-order delay ordinary differential equationsDec 07 2017A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which consists of linear ... More

A Weakly Coordinating Anion Substantially Enhances Carbon Dioxide Fixation by Calcium and Barium SaltsJun 27 2017Carbon dioxide fixation and storage constitute a drastically important problem for the humanity nowadays. We hereby publish a new solution based on the alkaline earth salts with a weakly coordinating anion, tetrakis(pentafluorophenyl)borate. The proposed ... More

s+is superconductivity with incipient bands: doping dependence and STM signaturesApr 26 2017Jul 26 2017Motivated by the recent observations of small Fermi energies and comparatively large superconducting gaps, present also on bands not crossing the Fermi energy (incipient bands) in iron-based superconductors, we analyse the doping evolution of superconductivity ... More

Probing Quantum Chaos in many-body quantum systems by the induced dissipationApr 25 2019We theoretically analyze the depletion dynamics of an ensemble of cold atoms in a quasi one-dimensional optical lattice where atoms in one of the lattice sites are subject to decay. Unlike the previous studies of this problem in R. Labouvie, {\em et. ... More

Collective stimulated Brillouin scatterMay 11 2011We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS which has a much larger threshold than the ... More

Beyond the random phase approximation: Stimulated Brillouin backscatter for finite laser coherence timesNov 25 2013We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS (CBSBS) with intensity threshold controlled ... More

Elements of the Kopula (eventological copula) theoryFeb 17 2018New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known ... More

A focal subgroup theorem for outer commutator wordsAug 10 2011Dec 26 2011Let $G$ be a finite group of order $p^am$, where $p$ is a prime and $m$ is not divisible by $p$, and let $P$ be a Sylow $p$-subgroup of $G$. If $w$ is an outer commutator word, we prove that $P\cap w(G)$ is generated by the intersection of $P$ with the ... More

Gap solitons for the repulsive Gross-Pitaevskii equation with periodic potential: coding and method for computationSep 02 2016The paper is devoted to nonlinear localized modes ("gap solitons") for the spatially one-dimensional Gross-Pitaevskii equation (1D GPE) with a periodic potential and repulsive interparticle interactions. It has been recently shown (G. L. Alfimov, A. I. ... More

Free energy analysis of system comprising biased atomic force microscope tip, water meniscus and dielectric surfaceMay 18 2005We are concerned with free energy analysis of the system comprising an AFM tip, water meniscus, and polymer film. Under applied electrostatic potential, the minimum in free energy is at a distance greater than the initial tip--substrate separation in ... More

Wavelet decomposition of harmonic functions in growth spacesMar 23 2012Jan 30 2013Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of harmonic functions ... More

Procyclic coverings of commutators in profinite groupsMay 21 2014We consider profinite groups in which all commutators are contained in a union of finitely many procyclic subgroups. It is shown that if G is a profinite group in which all commutators are covered by m procyclic subgroups, then G possesses a finite characteristic ... More

Non-equilibrium current via geometric scatterersMay 17 2014We investigate non-equilibrium particle transport in the system consisting of a geometric scatterer and two leads coupled to heat baths with different chemical potentials. We derive expression for the corresponding current the carriers of which are fermions ... More

Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetriesDec 21 2017A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups due to the linear ... More

Continuous macroscopic limit of a discrete stochastic model for interaction of living cellsMar 02 2007In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit ... More

The logic of uncertainty as a logic of experience and chance and the co~event-based Bayes' theoremSep 28 2018The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called ... More

Postulating the theory of experience and chance as a theory of co~events (co~beings)Jan 17 2018The paper aim is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of probability theory ... More

Unconstrained SU(2) Yang-Mills Quantum Mechanics with Theta AngleNov 09 1998Oct 07 1999The unconstrained classical system equivalent to spatially homogeneous SU(2) Yang-Mills theory with theta angle is obtained and canonically quantized. The Schr\"odinger eigenvalue problem is solved approximately for the low lying states using variational ... More

The Everett axiom of parallelismApr 01 2013In this work we consider the meaningfulness of the concept parallel worlds. To that extent we propose the model of the infinite-dimensionaly multievent space, generating everettics altervers in each point of Minkowski space time. Our research reveals ... More

Finite BRST Mapping in Higher Derivative ModelsJun 12 2017We continue the study of finite field dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry ... More

Zeno product formula revisitedNov 09 2004Mar 15 2006We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive ... More

Enhancement of evanescent waves inside media with extreme optical anisotropyMay 14 2008Dec 02 2008Significant enhancement of evanescent spatial harmonics inside the slabs of media with extreme optical anisotropy is revealed. This phenomenon results from the pumping of standing waves and has the feature of being weakly sensitive to the material losses. ... More

Interpretation of interconnection of alternative macroscopic approaches associated with the Abraham-Minkowski con-troversy using microscopic descriptionMay 21 2019Interconnection of alternative equations of conservation of the momentum related with different interpretations of equations of the electromagnetic field is an essential aspect of the Abraham-Minkowski controversy, which is associated in the first place ... More

Eventological H-theoremSep 19 2018We prove the eventological $H$-theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of thermodynamics) for what ... More

Frechet bounds of the 1-st kind for sets of half-rare eventsFeb 10 2018Frechet bounds of the 1-st kind for sets of events and its main properties are considered. The lemma on not more than two nonzero values of lower Frechet-bounds of the 1-st kind for a set of half-rare events is proved with the corollary on the analogous ... More

Theoretical Study of Atomic Structure and Elastic Properties of Branched Silicon NanowiresMay 16 2009The atomic structure and elastic properties of Y-silicon nanowire junctions of fork- and bough-types were theoretically studied and effective Young modulus were calculated using the Tersoff interatomic potential. In the final stages of bending, new bonds ... More

Enhanced Efficiency of Light-Trapping Nanoantenna Arrays for Thin Film Solar CellsJan 15 2013We suggest a novel concept of efficient light-trapping structures for thin-film solar cells based on arrays of planar nanoantennas operating far from plasmonic resonances. The operation principle of our structures relies on the excitation of chessboard-like ... More

Sample of Cataclysmic Variables from 400d X-ray SurveyJan 17 2017We present a sample of cataclysmic variables (CVs) identified among the X-ray sources from the 400 square degree X-ray survey based on ROSAT pointing data (400d). The procedure of the CV selection among the X-ray sources using additional optical and infrared ... More

Topological transition in coated wire mediumMay 13 2016We develop a theory of nonlocal homogenization for metamaterial consisting of parallel metallic wires with dielectric coating. It is demonstrated that manipulation of dielectric contrast between wire dielectric shell and host material results in switching ... More

Associative conformal algebras with finite faithful representationFeb 20 2004Aug 02 2005We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

Trion formation and unconventional superconductivity in a three-dimensional model with short-range attractionFeb 27 2019A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schroedinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane nearest-neighbor attraction. ... More

Systems of Oscillators Designed for a Specific Conscious PerceptMar 05 2019As put forward by neuroscientists, the mechanisms of consciousness can be elucidated by revealing correlations between neural dynamics and specific conscious percepts. Recently, I have elaborated on the mathematical formulation for a system of processes ... More

Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansionsJul 18 2018This paper summarizes the contents of a plenary talk at the Pan African Congress of Mathematics held in Rabat in July 2017. We provide a survey of recent results on spectral properties of Schr\"odinger operators with singular interactions supported by ... More

Distributed GNE seeking under partial-decision information over networks via a doubly-augmented operator splitting approachAug 13 2018We consider distributed computation of generalized Nash equilibrium (GNE) over networks, in games with shared coupling constraints. Existing methods require that each player has full access to opponents' decisions. In this paper, we assume that players ... More

Chern classes from Morava K-theories to $p^n$-typical oriented theoriesMay 23 2018Generalizing the definition of Cartier, we introduce $p^n$-typical formal group laws over $\mathbb{Z}_{(p)}$-algebras. An oriented cohomology theory in the sense of Levin-Morel is called $p^n$-typical if its corresponding formal group law is $p^n$-typical. ... More

On the Structure of Algebraic CobordismDec 11 2017May 31 2018In this paper we investigate the structure of algebraic cobordism of Levine-Morel as a module over the Lazard ring with the action of Landweber-Novikov and symmetric operations on it. We show that the associated graded groups of algebraic cobordism with ... More

Meridional circulation and reverse advection in hot thin accretion discsNov 01 2017In standard accretion discs, outward angular momentum transfer by viscous forces is compensated by the inward motion of the accreting matter. However, the vertical structure of real accretion discs leads to meridional circulation with comparable amplitudes ... More

Applications of Lie ring methods to group theoryJun 24 2017This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.

Parametric representations and boundary fixed points of univalent self-maps of the unit diskFeb 01 2017A classical result in the theory of Loewner's parametric representation states that the semigroup $\mathfrak U_*$ of all conformal self-maps $\phi$ of the unit disk $\mathbb{D}$ normalized by $\phi(0) = 0$ and $\phi'(0) > 0$ can be obtained as the reachable ... More

Tverberg type theorems for matroidsFeb 27 2017In this paper we show a variant of colorful Tverberg's theorem which is valid in any matroid: Let $S$ be a sequence of non-loops in a matroid $M$ of finite rank $m$ with closure operator cl. Suppose that $S$ is colored in such a way that the first color ... More

The heat kernel for two Aharonov-Bohm solenoids in a uniform magnetic fieldNov 21 2016A non-relativistic quantum model is considered with a point particle carrying a charge $e$ and moving on the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of magnitude $B$. Relying ... More

On Artin L-functions and Gassmann Equivalence for Global Function FieldsOct 18 2016Nov 16 2016In this paper we present an approach to study arithmetical properties of global function fields by working with Artin L-functions. In particular we recall and then extend a criteria of two function fields to be arithmetically equivalent in terms of Artin ... More

On the distribution of runners on a circleJun 06 2019Consider $n$ runners running on a circular track of unit length with constant speeds such that $k$ of the speeds are distinct. We show that, at some time, there will exist a sector $S$ which contains at least $|S|n+ \Omega(\sqrt{k})$ runners. The result ... More

Momentum operators on graphsMay 27 2012Sep 07 2012We discuss ways in which momentum operators can be introduced on an oriented metric graph. A necessary condition appears to the balanced property, or a matching between the numbers of incoming and outgoing edges; we show that a graph without an orientation, ... More

Gradient Method With Inexact Oracle for Composite Non-Convex OptimizationMar 27 2017In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"' convex part. Informally ... More

Synthesis of fast multiplication algorithms for arbitrary tensorsFeb 23 2016A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast tensor - vector ... More

Virtual surfaces, director domains and the Freedericksz transition in polymer stabilized nematic liquid crystalsMay 28 2002The critical field of the Freedericksz transition and switching dynamics are investigated for polymer stabilized nematic liquid crystals as a function of polymer concentration. A simple phenomenological model is proposed to describe the observed critical ... More

Room temperature coherent spin alignment of silicon vacancies in 4H- and 6H-SiCFeb 27 2012Jun 08 2012We report the realization of the optically induced inverse population of the ground-state spin sublevels of the silicon vacancies ($V_{\mathrm{Si}}$) in silicon carbide (SiC) at room temperature. The data show that the probed silicon vacancy spin ensemble ... More

Multilinear commutators in residually finite groupsDec 13 2010Let w be a multilinear commutator and n a positive integer. Suppose that G is a residually finite group in which every product of at most 896 w-values has order dividing n. Then the verbal subgroup w(G) is locally finite.

Nonlocal elliptic problems with nonlinear argument transformations near the points of conjugationApr 18 2014We consider elliptic equations of order $2m$ in a domain $G\subset\mathbb R^n$ with nonlocal conditions that connect the values of the unknown function and its derivatives on $(n-1)$-dimensional submanifolds $\Upsilon_i$ (where $\bigcup_i\Upsilon_i=\partial ... More

The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spacesJan 29 2006We study a variant of the Whitney extension problem for the space $C^{k,\omega}(R^n)$. We identify this space with a space of Lipschitz mappings from $R^n$ into the space $P_k \times R^n$ of polynomial fields on $R^n$ equipped with a certain metric. This ... More

On infinite Jacobi matrices with a trace class resolventApr 30 2019Let $\{\hat{P}_{n}(x)\}$ be an orthonormal polynomial sequence and denote by $\{w_{n}(x)\}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for $\{\hat{P}_{n}(x)\}$ is determinate and denote by $J$ the corresponding ... More

Spanning Forests and the Golden RatioDec 27 2006Sep 09 2007For a graph G, let f_{ij} be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path, the f_{ij}'s can be expressed as the products of Fibonacci numbers; for a cycle, they are products ... More

Geometric representation of binary codes and computation of weight enumeratorsMay 12 2008Jul 10 2009For every linear binary code $C$, we construct a geometric triangular configuration $\Delta$ so that the weight enumerator of $C$ is obtained by a simple formula from the weight enumerator of the cycle space of $\Delta$. The triangular configuration $\Delta$ ... More

Geometric representations of binary codes embeddable in three dimensionsDec 05 2012We say that a binary linear code C has a geometric representation if there exists a two dimensional simplicial complex D such that C is a punctured code of the kernel ker D of the incidence matrix of D and dim C = dim ker D. We show that every binary ... More

Adaptive Domain Model: Dealing With Multiple Attributes of Self-Managing Distributed Object SystemsJul 13 2003Self-managing software has emerged as modern systems have become more complex. Some of the distributed object systems may contain thousands of objects deployed on tens or even hundreds hosts. Development and support of such systems often costs a lot. ... More

On Artin L-functions and Gassmann Equivalence for Global Function FieldsOct 18 2016In this paper we present an approach to study arithmetical properties of global function fields by working with Artin L-functions. In particular we recall and then extend a criteria of two function fields to be arithmetically equivalent in terms of Artin ... More

Enhanced stability of bound pairs at nonzero lattice momentaNov 10 2003A two-body problem on the square lattice is analyzed. The interaction potential consists of strong on-site repulsion and nearest-neighbor attraction. Exact pairing conditions are derived for s-, p-, and d-symmetric bound states. The pairing conditions ... More

Star cluster formation and some implications for GAIANov 23 2011Nov 29 2011Stars form in spatially and temporarily correlated star formation events (CSFEs) and the dynamical processes within these "embedded clusters" leave imprints in the stellar populations in galactic fields. Such imprints are correlations in phase space (e.g. ... More

Thickening of galactic disks through clustered star formationNov 08 2001(Abridged) The building blocks of galaxies are star clusters. These form with low-star formation efficiencies and, consequently, loose a large part of their stars that expand outwards once the residual gas is expelled by the action of the massive stars. ... More

ARE THE NEARBY AND PHOTOMETRIC STELLAR LUMINOSITY FUNCTIONS DIFFERENT?May 27 1995The stellar luminosity function derived from the sample of stars within 5.2--20~pc is the nearby luminosity function. The luminosity function obtained from deep low spatial resolution surveys to distances of typically 100--200~pc is the photometric luminosity ... More

Magnetoresonances on a lasso graphJan 06 1997We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection amplitude ... More

Weakly coupled states on branching graphsDec 11 1995We consider a Schr\"odinger particle on a graph consisting of $\,N\,$ links joined at a single point. Each link supports a real locally integrable potential $\,V_j\,$; the self--adjointness is ensured by the $\,\delta\,$ type boundary condition at the ... More

An isoperimetric problem for point interactionsJun 10 2004We consider Hamiltonian with $N$ point interactions in $\R^d, d=2,3,$ all with the same coupling constant, placed at vertices of an equilateral polygon $\PP_N$. It is shown that the ground state energy is locally maximized by a regular polygon. The question ... More

Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagonJun 14 2004Jul 24 2004The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the thermodynamic limit, ... More

Lecture notes on torsionsJun 14 2014These are the lecture notes for the introductory course on Whitehead, Reidemeister and Ray-Singer torsions, given by the author at the University of Zurich in Spring semester 2014.

On the Wedderburn principal theorem in conformal algebrasAug 05 2005Apr 04 2006We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal semisimple factor ... More

Caratheodory convergence of immediate basins of attraction to a Siegel diskAug 25 2006Aug 31 2007Let f_n be a sequence of analytic functions in a domain U with a common attracting fixed point z_0. Suppose that f_n converges to f_0 uniformly on each compact subset of U and that z_0 is a Siegel point of f_0. We establish a sufficient condition for ... More

Critical phenomena in the Dyson hierarchical model and renormalization groupOct 28 2010We review some results on the critical phenomena in the Dyson hierarchical model and renormalization group.