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Diagnostics of turbulence properties through Velocity Gradient Amplitudes: Theory and ObservationsJan 31 2018Based on the properties of magneto-hydrodynamic (MHD) turbulence, the recent development of the Velocity Gradient Technique (VGT) allows observers to trace magnetic field directions using spectroscopic information. In this paper, we explore how the amplitudes ... More

Statistical tracing of magnetic fields: comparing and improving the techniquesApr 08 2018Aug 14 2018Magnetohydrodynamic(MHD) turbulence displays velocity anisotropies which reflect the direction of the magnetic field. This anisotropy has led to the development of a number of statistical techniques for studying magnetic fields in the interstellar medium. ... More

Distribution of velocity gradient orientations: Mapping magnetization with the Velocity Gradient TechniqueFeb 08 2018Aug 01 2018Recent developments of the Velocity Gradient Technique (VGT) show that the velocity gradients provide a reliable tracing of magnetic field direction in turbulent plasmas. In this paper, we explore the ability of velocity gradients to measure the magnetization ... More

Dispersion of velocity gradients: Mapping magnetization with the Velocity Gradient TechniqueFeb 08 2018Recent developments of the Velocity Gradient Technique (VGT) show that the velocity provides a robust measure of magnetic field direction. In this paper, we use velocity centroids as the measures of velocity and propose a new way of studying media magnetization. ... More

On the formation of density filaments in the turbulent interstellar mediumMay 15 2019This study is motivated by recent observations on ubiquitous interstellar density filaments and guided by modern theories of compressible magnetohydrodynamic (MHD) turbulence. The interstellar turbulence shapes the observed density structures. As the ... More

Parsing Images of Overlapping Organisms with Deep Singling-Out NetworksDec 19 2016This work is motivated by the mostly unsolved task of parsing biological images with multiple overlapping articulated model organisms (such as worms or larvae). We present a general approach that separates the two main challenges associated with such ... More

Instance Segmentation of Biological Images Using Harmonic EmbeddingsApr 10 2019We present a new instance segmentation approach tailored to biological images, where instances may correspond to individual cells, organisms or plant parts. Unlike instance segmentation for user photographs or road scenes, in biological data object instances ... More

Exact and approximate analytical solutions of Weiss equation of ferromagnetism and their experimental relevanceFeb 14 2017The recent progress in the theory of generalized Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical purposes. Precise approximate analytical solutions are ... More

Heat Transfer and Reconnection Diffusion in Turbulent Magnetized PlasmasAug 10 2011Feb 08 2012It is well known that magnetic fields constrain motions of charged particles, impeding the diffusion of charged particles perpendicular to magnetic field direction. This modification of transport processes is of vital importance for a wide variety of ... More

Obtaining Spectra of Turbulent Velocity from ObservationsNov 06 2008We discuss a long-standing problem of how turbulence can be studied using observations of Doppler broadened emission and absorption lines. The focus of the present review is on two new techniques, the Velocity-Channel Analysis (VCA), which makes use of ... More

Grain Alignment and CMB Polarization StudiesNov 06 2008Polarized microwave emission from dust is an important foreground that may contaminate polarized CMB studies unless carefully accounted for. Modeling of polarization from dust requires a quantitative understanding of grain alignment. I review the current ... More

Magnetic Fields via Polarimetry: Progress of Grain Alignment TheoryAug 28 2002Most astrophysical systems, e.g. stellar winds, the diffuse interstellar medium, molecular clouds, are magnetized with magnetic fields that influence almost all of their properties. One of the most informative techniques of magnetic field studies is based ... More

Physics and Chemistry of Purcell's AlignmentJan 17 1995Paramagnetic alignment of suprathermally rotating grains is discussed in view of recent progress in understanding subtle processes taking place over grain surface. It is shown that in typical ISM conditions, grains with surfaces of amorphous H$_{2}$O ... More

The interaction of relativistic spacecrafts with the interstellar mediumAug 18 2016Dec 27 2016The Breakthrough Starshot initiative aims to launch a gram-scale spacecraft to a speed of $v\sim 0.2$c, capable of reaching the nearest star system, $\alpha$ Centauri, in about 20 years. However, a critical challenge for the initiative is the damage to ... More

Grain Alignment, Polarization and Magnetic FieldsAug 02 2006Aligned non-spherical dust particles polarize starlight passing through the dust cloud. They also emit polarized far infrared and sub-mm radiation. Substantial progress in understanding of grain alignment theory makes the interpretation of the polarized ... More

Paramagnetic alignment of thermally rotating dustFeb 16 1997Paramagnetic alignment of thermally rotating oblate dust grains is studied analytically for finite ratios of grain to gas temperatures. For such ratios, the alignment of angular momentum J in respect to the grain axis of maximal inertia is only partial. ... More

Davis-Greenstein alignment of non-spherical grainsMay 07 1995Paramagnetic alignment of non-spherical dust grains rotating at thermal velocities is studied. The analytical solution is found for the alignment measure of oblate grains. Perturbative approach is used for solving the problem. It is shown that even the ... More

Observational Diagnostics for Two-Fluid Turbulence in Molecular Clouds As Suggested by SimulationsJul 12 2013Jul 18 2013We present high resolution simulations of two-fluid (ion-neutral) MHD turbulence with resolutions as large as 512^3. The simulations are supersonic and mildly sub-Alfvenic, in keeping with the conditions present in molecular clouds. Such turbulence is ... More

Comment on Clark et al. (2019) "The Physical Nature of Neutral Hydrogen Intensity Structure"Apr 05 2019A recent publication by Clark et.al (2019, CX19) uses both GALFA-HI observational data and numerical simulations to address the nature of intensity fluctuations in Position-Position-Velocity (PPV) space. The study questions the validity and applicability ... More

Power of Turbulent Reconnection: Star Formation, Acceleration of Cosmic Rays, Heat Transfer, Flares and Gamma Ray BurstsDec 14 2011Turbulence is ubiquitous in astrophysical fluids. Therefore it is necessary to study magnetic reconnection in turbulent environments. The model of fast turbulent reconnection proposed in Lazarian & Vishniac 1999 has been successfully tested numerically ... More

Quantitative Theory of Grain Alignment: Probing Grain Environment and Grain CompositionMar 05 2009While the problem of grain alignment was posed more than 60 years ago the quantitative model of grain alignment that can account for the observed polarization arising from aligned grains has been formulated only recently. The quantitative predictions ... More

Grain Alignment by Radiative TorquesDec 03 2008Grain alignment is a notoriously difficult problem, that is extremely rich in underlying physics. The long history of attempts theoretical handling of the problem resulted in rather sceptical approach to the theory on the part of some polarimetry practitioners. ... More

Tracing Magnetic Fields with Aligned GrainsJul 05 2007Jul 05 2007Magnetic fields play a crucial role in various astrophysical processes, including star formation, accretion of matter, transport processes (e.g., transport of heat), and cosmic rays. One of the easiest ways to determine the magnetic field direction is ... More

Astrophysical Implications of Turbulent Reconnection: from cosmic rays to star formationMay 28 2005Turbulent reconnection allows fast magnetic reconnection of astrophysical magnetic fields. This entails numerous astrophysical implications and opens new ways to approach long standing problems. I briefly discuss a model of turbulent reconnection within ... More

Diffusion Processes in Turbulent Magnetic FieldsJul 04 2007Jul 05 2007We study of the effect of turbulence on diffusion processes within magnetized medium. While we exemplify our treatment with heat transfer processes, our results are quite general and are applicable to different processes, e.g. diffusion of heavy elements. ... More

Intermittency of Magnetohydrodynamic Turbulence: Astrophysical PerspectiveAug 02 2006Intermittency is an essential property of astrophysical fluids, which demonstrate an extended inertial range. As intermittency violates self-similarity of motions, it gets impossible to naively extrapolate the properties of fluid obtained computationally ... More

Turbulence Statistics from Spectral Line ObservationsMay 28 2005Turbulence is a crucial component of dynamics of astrophysical fluids dynamics, including those of ISM, clusters of galaxies and circumstellar regions. Doppler shifted spectral lines provide a unique source of information on turbulent velocities. We discuss ... More

Grain Alignment in Molecular CloudsNov 17 2003One of the most informative techniques of studying magnetic fields in molecular clouds is based on the use of starlight polarization and polarized emission arising from aligned dust. How reliable the interpretation of the polarization maps in terms of ... More

Turbulence in Atomic HydrogenApr 02 1998Understanding the properties of interstellar turbulence is a great intellectual challenge and the urge to solve this problem is partially motivated by a necessity to explain the star formation mystery. This review deals with a recently suggested inversion ... More

Alignment of suprathermally rotating grainsAug 15 1995It is shown, that mechanical alignment can be efficient for suprathermally rotating grains, provided that they drift with supersonic velocities. Such a drift should be widely spread due to both Alfv\'{e}nic waves and ambipolar diffusion. Moreover, if ... More

Mechanical alignment of suprathermally rotating grainsMay 01 1995It is shown that mechanical alignment of grains can be efficient for grains rotating suprathermally, i.e. with kinetic energy substantially exceeding $k$ (the Boltzmann constant) over any temperature in the system. The paper studies suprathermal rotation ... More

Theoretical approaches to particle propagation and acceleration in turbulent intergalactic mediumAug 02 2006Intercluster medium is expected to be turbulent with turbulence being superAlfvenic at large scales. Magnetic fields substantially modify the turbulent cascade when the turbulence reaches the scales at which the fluctuation velocity gets less than the ... More

SINS of Viscosity Damped TurbulenceAug 02 2006Oct 26 2006The problems with explaining the Small Ionized and Neutral Structures (SINS) appealing to turbulence stem from inefficiency of the Kolmogorov cascade in creating large fluctuations at sufficiently small scales. However, other types of cascades are possible. ... More

Obtaining Statistics of Turbulent Velocity from Astrophysical Spectral Line DataAug 10 2004Turbulence is a crucial component of dynamics of astrophysical fluids dynamics, including those of ISM, clusters of galaxies and circumstellar regions. Doppler shifted spectral lines provide a unique source of information on turbulent velocities. We discuss ... More

Enhancement and suppression of heat transfer by MHD turbulenceAug 02 2006Aug 03 2006We study of the effect of turbulence on heat transfer within magnetized plasmas for energy injection velocities both larger and smaller that the Alfven speed. We find that in the latter regime the heat transfer is partially suppressed, while in the former ... More

Polarized Microwave Radiation from DustDec 30 2000Observations of cosmic microwave background in the range 10-90 GHz have revealed an anomalous foreground component well correlated with 12 \mum, 60 \mum and 100 \mum emission from interstellar dust. As the recent cross-correlation analysis of WHAM H\alpha ... More

Instance Segmentation by Deep ColoringJul 26 2018We propose a new and, arguably, a very simple reduction of instance segmentation to semantic segmentation. This reduction allows to train feed-forward non-recurrent deep instance segmentation systems in an end-to-end fashion using architectures that have ... More

Damping of Alfven waves by Turbulence and its Consequences: from Cosmic-Rays Streaming to Launching WindsJul 06 2016This paper considers turbulent damping of Alfven waves in magnetized plasmas. We identify two cases of damping, one related to damping of cosmic rays streaming instability, the other related to damping of Alfven waves emitted by a macroscopic wave source, ... More

Reconnection Diffusion, Star Formation and Numerical SimulationsApr 10 2013We consider fast magnetic reconnection that takes place within turbulent magnetic flux and show that the process results in diffusion of magnetic fields and matter, which we term reconnection diffusion. The process of reconnection diffusion is based on ... More

Fast Reconnection and Reconnection Diffusion: Implications for Star FormationNov 03 2011Feb 05 2012Fast reconnection of magnetic field in turbulent fluids allows magnetic field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. The diffusion of plasmas ... More

Turbulence Spectra from Doppler-shifted Spectral LinesOct 26 2006Turbulence is a key element of the dynamics of astrophysical fluids, including those of interstellar medium, clusters of galaxies and circumstellar regions. Turbulent motions induce Doppler shifts of observable emission and absorption lines. In the review ... More

Statistics of Turbulence from Spectral-Line Data CubesJan 01 2000Emission in spectral lines can provide unique information on interstellar turbulence. Doppler shifts due to supersonic motions contain information on turbulent velocity field which is otherwise difficult to measure. However, the problem of separation ... More

Gold alignment & internal dissipationFeb 16 1997The measures of mechanical alignment were obtained for both prolate and oblate grains when their temperature is comparable with grain kinetic energy devided by k, the Boltzmann constant. For such grains, the alignment of angular momentum, J, with the ... More

Paramagnetic alignment of fractal grainsAug 23 1994Paramagnetic alignment of fractal suprathermally rotating grains is discussed. It is shown that if the concentration of H$_{2}$formation sites is low and resurfacing is active, fractal structure of grains enhances their alignment. Studying the influence ... More

Perfectly matched layers for the stationary Schrodinger equation in a periodic structureJun 12 2008We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show ... More

Corrections to the book ``Vertex algebras for beginners'', second edition, by Victor KacJan 18 1999These are corrections to the second edition of the book ``Vertex algebras for beginners'', University Lecture Series, 10, American Mathematical Society, Providence, RI, 1998.

The meaning of concurrent programsOct 07 2008The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on event sequences ... More

Hori--Vafa mirror models for complete intersections in weighted projective spaces and weak Landau--Ginzburg modelsMar 26 2010Jul 12 2011We prove that Hori--Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials.

Astrophysical Data and Conformal Unified TheoryOct 31 2002Astrophysical data reformulated in the units of the relative Paris meter and running Planck mass are used for restoration of a conformal version of the unified theory where the absolute Planck mass belongs to ordinary initial data (like the absolute Ptolemaeus ... More

Non stationary nucleation: the model with averaged velocityFeb 01 2013A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. The key characteristic which arises in frames of this theory is the mean ... More

Late periods of the condensation processNov 15 2010The full evolution during the late periods of the condensation process is described in the analytical form. The process is split into several periods and for every period the simple approximate solution is given.

Different approaches to describe depletion regions in first order phase transition kineticsJul 31 2002The theory of nucleation with depletion zones is discussed. The approach of stochastic effects of solitary droplet is analyzed. The negative features of a solution with fixed boundary are outlined. A new solution with effective fixed boundary is proposed. ... More

Non stationary nucleation: the model with minimal environmentJan 06 2013A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. As the result the free energy has to be recalculated which brings a new ... More

Variations of parameters in nucleation process under different external conditionsAug 21 2008The nucleation process under different external conditions is considered. It is shown that the duration of this process can be connected with the microscopic corrections to the free energy of the critical embryo. Connection between variations in the value ... More

Some properties of evolution equation for homogeneous nucleation period under the smooth behavior of initial conditionsMar 10 2005The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated ... More

Multicomponent nonisothermal nucleation. 1. Kinetic equationSep 03 1999The first part of the theory for the multicomponent nonisothermal nucleation is presented. On the base of analysis of the elementary acts of interation between an embryo and environment the kinetic equation is derived. This equation will be solved later ... More

Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebrasAug 16 2000We give a detailed calculation of the Hochschild and cyclic homology of the algebra $\CIc(G)$ of locally constant, compactly supported functions on a reductive p-adic group G. We use these calculations to extend to arbitrary elements the definition the ... More

Super-connections and non-commutative geometryJun 14 1996Aug 21 1996We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in the spectrum. ... More

An index theorem for families invariant with respect to a bundle of Lie groupsJun 28 1999Aug 16 2000We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle $\GR$ of Lie groups. If the fibers of $\GR \to B$ are simply-connected solvable, we then compute the Chern character of the ... More

Two-point free energy distribution function in (1+1) directed polymersApr 24 2013May 07 2013In this brief technical communication it is demonstrated how using Bethe ansatz technique the explicit expression for the two-point free energy distribution function in (1+1) directed polymers can be derived in rather simple way. Obtained result is equivalent ... More

Two-time free energy distribution function in (1+1) directed polymersApr 02 2013Aug 09 2013The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the $N$-particle quantum ... More

Context-free manifold calculus and the Fulton-MacPherson OperadApr 02 2012The paper gives an explicit description of the Weiss embedding tower in terms of spaces of maps of truncated modules over the framed Fulton-MacPherson operad.

On H.Weyl and H.Minkowski PolynomialsFeb 06 2007Feb 14 2007We introduce certain polynomials, so-called H.Weyl and H.Minkowski polynomials, which have a geometric origin. The location of roots of these polynomials is studied.

Stellar scintillation in short exposure regime and atmospheric coherence time evaluationMar 31 2011Accurately measuring the atmospheric coherence time is still an important problem despite a variety of applicable methods. The Multi-aperture scintillation sensor (MASS) designed for the vertical profiling of optical turbulence, also provides a measurements ... More

Non-perturbative microscopic theory of superconducting fluctuations near a quantum critical pointOct 10 2007We consider an inhomogeneous anisotropic gap superconductor in the vicinity of the quantum critical point, where the transition temperature is suppressed to zero by disorder. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action for ... More

Linear Datalog and Bounded Path Duality of Relational StructuresApr 07 2005Jun 28 2005In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems, all these concepts ... More

Generalized Majority-Minority Operations are TractableSep 19 2006Sep 27 2006Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where all constraint ... More

Calabi-Yau algebrasDec 06 2006Jan 09 2007We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution. In dimension ... More

A remark on a theorem of M. HaimanJul 04 2005We deduce a special case of a theorem of M. Haiman concerning alternating polynomials in 2n variables from our results about almost commuting variety, obtained earlier in a joint work with W.-L. Gan.

Lectures on Noncommutative GeometryJun 29 2005These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild cohomology, Serre ... More

Isospectral commuting variety, the Harish-Chandra D-module, and principal nilpotent pairsAug 26 2011Sep 07 2011Let g be a complex reductive Lie algebra with Cartan algebra h. Hotta and Kashiwara defined a holonomic D-module M, on g x h, called Harish-Chandra module. We relate gr(M), an associated graded module with respect to a canonical Hodge filtration on M, ... More

Perverse sheaves on a Loop group and Langlands' dualityNov 13 1995Nov 20 2000An intrinsic construction of the tensor category of finite dimensional representations of the Langlands dual group of G in terms of a tensor category of perverse sheaves on the loop group, LG, is given. The construction is applied to the study of the ... More

Quarkonium suppression as a probe of a saturated gluon plasma ?Jun 21 2001A dense parton system is expected to be formed in the early stage of relativistic heavy-ion collisions at RHIC energies and above. The probability of a quark gluon plasma production and the resulting strength of its signatures depends strongly on the ... More

Multiple Volume Reflection from Different Planes Inside One Bent CrystalMay 29 2007It is shown that multiple volume reflections from different planes of one bent crystal becomes possible when particles move at a small angle with respect to a crystal axis. Such a Multiple Volume Reflection makes it possible to increase the particle deflection ... More

Has the E791 experiment measured the pion wave function profile ?Mar 28 2001Jun 13 2001The cross section of hard diffractive dissociation of the pion into two jets is calculated. It is obtained that the distribution of longitudinal momenta for jets is not simply proportional to the profile of the pion wave function, but depends on it in ... More

Estimates of flavoured scalar production in B - decaysFeb 17 2001Mar 04 2001Estimates are presented for the branching ratios of several two-particle B-meson decays into flavoured scalar mesons.

J/Psi theory review, or from J to PsiJun 16 1999Jul 16 19991) Hard exclusive processes in QCD: main characteristic properties; 2) Experimental and theoretical status of the J/Psi and Psi^\prime decays.

Properties of the SU(N_c) Yang-Mills vacuum stateAug 16 1998Mar 18 1999The asymptotic behaviour of the vacuum energy density, ${\bar E}(\theta)$, at $\theta \ra \pm i \infty$ is found out. A new interpretation and a qualitative discussion of the ${\bar E}(\theta)$ behaviour are presented. It is emphasized that the vacuum ... More

The Infrared Boundary of Perturbative QCDSep 14 2001Evidence is reviewed suggesting that QCD remains a perturbative theory with a (relatively) small coupling constant down to a distinct infrared boundary on perturbative physics, a boundary corresponding to the momentum scale associated with a beta-function ... More

A nonclassical symbolic theory of working memory, mental computations, and mental setJan 08 2009The paper tackles four basic questions associated with human brain as a learning system. How can the brain learn to (1) mentally simulate different external memory aids, (2) perform, in principle, any mental computations using imaginary memory aids, (3) ... More

A rational construction of Lie algebras of type E_7Sep 27 2013Jul 03 2015We give an explicit construction of Lie algebras of type $E_7$ out of a Lie algebra of type $D_6$ with some restrictions. Up to odd degree extensions, every Lie algebra of type $E_7$ arises this way. For Lie algebras that admit a $56$-dimensional representation ... More

Scaling Exponents of Strong Turbulence in the Eddy Viscosity ApproximationJul 20 1996A dynamic equation for velocity structure functions $S_{n}(r) = <(u(x)-u(x'))^{n}>$ in strong turbulence is derived in the one-loop (eddy viscosity) approximation. This homogemeous differential equation yields scaling exponents $\xi_{n}$ in the relations ... More

On a puzzle posed by the Kurien-Sreenivasan boundary layer experimentJun 24 2002The Kolmogorov inertial range ratio of the mixed- to- longitudinal third-order structure functions of isotropic and homogeneous turbulence is $\frac{S_{1,2}}{S_{3,0}}=1/3$. Recent measurements by Kurien and Sreenivasan (Phys. Rev. E {\bf 64}, 056302 (2001)), ... More

Two-time free energy distribution function in the KPZ problemJul 22 2015The explicit expression for the two time free energy distribution function in one-dimensional random directed polymers is derived in terms of the Bethe ansatz replica technique. It is show that such type of the distribution function can be represented ... More

100 years of Weyl's lawAug 13 2016We discuss the asymptotics of the eigenvalue counting function for partial differential operators and related expressions paying the most attention to the sharp asymptotics. We consider Weyl asymptotics, asymptotics with Weyl principal parts and correction ... More

Minimax theorem for the spectral radius of the product of non-negative matricesMar 17 2016Sep 29 2016We prove the minimax equality for the spectral radius $\rho(AB)$ of the product of matrices $A\in\mathcal{A}$ and $B\in\mathcal{B}$, where $\mathcal{A}$ and $\mathcal{B}$ are compact sets of non-negative matrices of dimensions $N\times M$ and $M\times ... More

Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Viéte--Euler identity to Anderson localizationApr 28 2016It is shown that in a large class of disordered systems with non-degenerate disorder, in presence of non-local interactions, the Integrated Density of States (IDS) is at least H\"older continuous in one dimension and universally infinitely differentiable ... More

Bricklayer: An Authentic Introduction to the Functional Programming Language SMLDec 16 2014Functional programming languages are seen by many as instrumental to effectively utilizing the computational power of multi-core platforms. As a result, there is growing interest to introduce functional programming and functional thinking as early as ... More

Toric Landau-Ginzburg modelsSep 24 2018This is a review of the theory of toric Landau-Ginzburg models - the effective approach to mirror symmetry for Fano varieties. We mainly focus on the cases of dimensions 2 and 3, as well as on the case of complete intersections in weighted projective ... More

An efficient algorithm to decide periodicity of b-recognisable sets using LSDF conventionAug 21 2017Dec 19 2018Let b be an integer strictly greater than 1. Each set of nonnegative integers is represented in base b by a language over {0,1,...,b-1}. The set is said to be b-recognisable if it is represented by a regular language. It is known that ultimately periodic ... More

Using boundaries to find smooth normsNov 06 2013Apr 28 2014The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with $C^k$ smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of $B_{X^*}$, namely boundaries. Of interest ... More

Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?Jul 26 2017Nov 25 2017We choose some special unit vectors $\boldsymbol{n}_1,\dots,\boldsymbol{n}_5$ in $\mathbb{R}^3$ and denote by $\mathscr{L}\subset\mathbb{R}^5$ the set of all points $(L_1,\dots,L_5)\in\mathbb{R}^5$ with the following property: there exists a compact convex ... More

On a theorem of V. Bernik in the metrical theory of Diophantine approximationFeb 13 2008This paper goes back to a famous problem of Mahler in metrical Diophantine approximation. The problem has been settled by Sprindzuk and subsequently improved by Alan Baker and Vasili Bernik. In particular, Bernik's result establishes a convergence Khintchine ... More

The function $(\cosh\sqrt{at^2+b})$ is exponentially convexFeb 14 2015May 20 2016Given positive numbers $a$ and $b$, the function $\sqrt{at^2+b}$ is exponentially convex function of $t$ on the whole real axis. Three proofs of this result are presented.

Converting of algebraic Diophantine equations to a diagonal form with the help of an integer non-orthogonal transformation, maintaining the asymptotic behavior of the number of its integer solutionsAug 04 2017The author showed that any homogeneous algebraic Diophantine equation of the second order can be converted to a diagonal form using an integer non-orthogonal transformation maintaining asymptotic behavior of the number of its integer solutions. In this ... More

Estimations of the number of solutions of algebraic Diophantine equations with natural coefficients using the circle method of Hardy-LittlewoodDec 22 2015This article discusses the question - how to estimate the number of solutions of algebraic Diophantine equations with natural coefficients using Circular method developed by Hardy and Littlewood. This paper considers the estimate of the number of solutions ... More

Asymptotics of the ground state energy of heavy molecules in self-generated magnetic fieldMar 19 2013Dec 31 2013We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\cdot\boldsymbol{\sigma})^2-V $$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a corresponding ... More

Global trace asymptotics in the self-generated magnetic field in the case of Coulomb-like singularitiesDec 12 2011Dec 23 2011We consider a semiclassical asymptotics of local trace for the 3D-Schroedinger operator with self-generated magnetic field in the case when electric potential has one or several Coulomb-like singularities; it is given by Weyl expression plus (magnetic) ... More

Operators with Periodic Hamiltonian Flows in Domains with the BoundaryMay 06 2010We consider operators in the domains with the boundaries and derive sharp spectral asymptotics (containing non-Weyl correction) in the case when Hamiltonian flow is periodic. Even if operator is scalar but not second order (or even second-order but there ... More

Schroedinger Operator with Strong Magnetic Field near BoundaryMay 03 2010May 04 2010We consider 2-dimensional Schroedinger operator with the non-degenerating magnetic field in the domain with the boundary and under certain non-degeneracy assumptions we derive spectral asymptotics with the remainder estimate better than $O(h^{-1})$, up ... More