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ROOT I/O compression algorithms and their performance impact within Run 3Jun 11 2019The LHCs Run3 will push the envelope on data-intensive workflows and, since at the lowest level this data is managed using the ROOT software framework, preparations for managing this data are starting already. At the beginning of LHC Run 1, all ROOT data ... More

Continuous Performance Benchmarking Framework for ROOTDec 07 2018Feb 21 2019Foundational software libraries such as ROOT are under intense pressure to avoid software regression, including performance regressions. Continuous performance benchmarking, as a part of continuous integration and other code quality testing, is an industry ... More

Migrating large codebases to C++ ModulesJun 12 2019ROOT has several features which interact with libraries and require implicit header inclusion. This can be triggered by reading or writing data on disk, or user actions at the prompt. Often, the headers are immutable, and reparsing is redundant. C++ Modules ... More

Evolution of ROOT package managementJun 11 2019ROOT is a large code base with a complex set of build-time dependencies; there is a significant difference in compilation time between the "core" of ROOT and the full-fledged deployment. We present results on a "delayed build" for internal ROOT packages ... More

Extending ROOT through ModulesDec 07 2018Dec 11 2018The ROOT software framework is foundational for the HEP ecosystem, providing capabilities such as IO, a C++ interpreter, GUI, and math libraries. It uses object-oriented concepts and build-time components to layer between them. We believe additional layering ... More

Optimizing Frameworks Performance Using C++ Modules Aware ROOTDec 10 2018ROOT is a core HEP framework which is used broadly in and outside HEP. As HEP software frameworks always strive for performance, ROOT was extended with experimental support for using C++ modules during runtime. C++ modules are designed in part to improve ... More

Optimizing Frameworks Performance Using C++ Modules Aware ROOTDec 10 2018May 17 2019ROOT is a data analysis framework broadly used in and outside of High Energy Physics (HEP). Since HEP software frameworks always strive for performance improvements, ROOT was extended with experimental support of runtime C++ Modules. C++ Modules are designed ... More

Some semi-direct products with free algebras of symmetric invariantsOct 05 2015Jan 18 2016Let $\mathfrak g$ be a complex reductive Lie algebra and $V$ the underling vector space of a finite-dimensional representation of $\mathfrak g$. Then one can consider a new Lie algebra $\mathfrak q=\mathfrak g{\ltimes} V$, which is a semi-direct product ... More

On the derived algebra of a centraliserMar 02 2010Let $\g$ be a classical Lie algebra, $e$ a nilpotent of $\g$ element and $\gt g_e$ the centraliser of $e$ in $\g$. We prove that $\g_e=[\g_e,\g_e]$ if and only if $e$ is rigid. It is also shown that if $e$ is contained in $[\g_e,\g_e]$, then the nilpotent ... More

Principal Gelfand pairsMar 24 2004Jul 02 2004Let X=G/K be a connected Riemannian homogeneous space of a real Lie group G. The homogeneous space X is called commutative if the algebra of G-invariant differential operators on X is commutative. We prove an effective commutativity criterion and classify ... More

New Properties of the Zeros of Classical and Nonclassical Orthogonal PolynomialsAug 12 2016We identify a new class of remarkable algebraic relations satisfied by the zeros of classical and nonclassical orthogonal polynomials. Given an orthogonal polynomial family $\{p_\nu(x)\}_{\nu=0}^\infty$, we relate the zeros of the polynomial $p_N$ with ... More

Asymptotics of correlation function of twist fields in two-dimensional lattice fermion modelJul 07 1999Nov 01 1999In two-dimensional lattice fermion model a determinant representation for the two-point correlation function of the twist field in the disorder phase is obtained. This field is defined by twisted boundary conditions for lattice fermion field. The large ... More

Surprising properties of centralisers in classical Lie algebrasMar 03 2008Nov 24 2008Let $g$ be a classical Lie algebra, i.e., either $gl_n$, $sp_n$, or $so_n$ and let $e\in g$ be a nilpotent element. We study various properties of centralisers $g_e$. The first four sections deal with rather elementary questions, like the centre of $g_e$, ... More

(Ir)Reducibility of some commuting varieties associated with involutionsApr 07 2005May 08 2005Here we prove that a commuting variety associated with a symmetric pair (g, g_0) is irreducible for (so_{n+m}, so_n + so_m) and reducible for (gl_{n+m}, {gl}_n + gl_m) with n>m, (so_{2n}, gl_n) with odd n, (E_6, {so}_{10} + k).

Time-dependent polynomials with one multiple root and new solvable dynamical systemsAug 01 2018A time-dependent monic polynomial in the z variable with N distinct roots such that exactly one root has multiplicity m>=2 is considered. For k=1,2, the k-th derivatives of the N roots are expressed in terms of the derivatives of order j<= k of the first ... More

Covariant Differential and Integral Calculi for Lattice (l,q)-deformed FieldsJan 09 1995Using the Hecke $\hat R$-matrix, we give a definition of the lattice $(l,q)$-deformed $n$-component boson and Grassmann fields. Here $l$ is a deformation parameter for the commutation relations of "values" of these fields in two arbitrary lattice sites ... More

One-parameter contractions of Lie-Poisson bracketsFeb 14 2012We consider contractions of Lie and Poisson algebras and the behaviour of their centres under contractions. A polynomial Poisson algebra A=K[W] is said to be of Kostant type, if its centre Z(A) is freely generated by homogeneous polynomials F_1,...,F_r ... More

New Properties of the Zeros of Krall PolynomialsAug 12 2016Jan 19 2017We identify a class of remarkable algebraic relations satisfied by the zeros of the Krall orthogonal polynomials that are eigenfunctions of linear differential operators of order higher than two. Given an orthogonal polynomial family {p_n(x)}, we relate ... More

On Duality of Two-dimensional Ising Model on Finite LatticeJan 20 1996It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with corresponding boundary ... More

Duality of the 2D Nonhomogeneous Ising Model on the TorusMar 05 1997Duality relations for the 2D nonhomogeneous Ising model on the finite square lattice wrapped on the torus are obtained. The partition function of the model on the dual lattice with arbitrary combinations of the periodical and antiperiodical boundary conditions ... More

Boundary conditions at the interface of finite thickness between ferromagnetic and antiferromagnetic materialsJan 31 2019Systematic approach has been applied to obtain the boundary conditions for magnetization at an interface between ferromagnetic (FM) and antiferromagnetic (AFM) materials in the continuous medium approximation. Three order parameters are considered inside ... More

Propagation of Spin Waves Through an Interface Between Ferromagnetic and Antiferromagnetic MaterialsJan 30 2019Boundary conditions for order parameters at an interface between ferromagnetic (FM) and two-sublattice antiferromagnetic (AFM) materials were obtained in the continuous medium approximation similarly to the approach which allows one to take into account ... More

Factorized finite-size Ising model spin matrix elements from Separation of VariablesApr 15 2009Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted to the cyclic Baxter--Bazhanov--Stroganov or $\tau^{(2)}$-model, we derive factorized formulae for general finite-size Ising model spin matrix elements, proving a recent conjecture ... More

Nilpotent subspaces and nilpotent orbitsJan 13 2016Let $G$ be a semisimple algebraic group with Lie algebra $\mathfrak g$. For a nilpotent $G$-orbit $\mathcal O\subset\mathfrak g$, let $d_\mathcal O$ denote the maximal dimension of a subspace $V\subset \mathfrak g$ that is contained in the closure of ... More

Effect of mesoscopic fluctuations on equation of state in cluster-forming systemsJan 02 2012Jul 12 2012Equation of state for systems with particles self-assembling into aggregates is derived within a mesoscopic theory combining density functional and field-theoretic approaches. We focus on the effect of mesoscopic fluctuations in the disordered phase. ... More

Monomial bases and branching rulesDec 10 2018Following a question of Vinberg, a general method to construct monomial bases for finite-dimensional irreducible representations of a reductive Lie algebra was developed in a series of papers by Feigin, Fourier, and Littelmann. Relying on this method, ... More

Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed CurvesJan 31 2007Jan 23 2008The problem of minimal distortion bending of smooth compact embedded connected Riemannian $n$-manifolds $M$ and $N$ without boundary is made precise by defining a deformation energy functional $\Phi$ on the set of diffeomorphisms $\diff(M,N)$. We derive ... More

Distortion Minimal Morphing I: The Theory For StretchingMay 25 2006Aug 23 2007We consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion (with respect ... More

Order-preserving Renaming in Synchronous Message Passing Systems with Byzantine FaultsMay 02 2012Mar 03 2013Renaming is a fundamental problem in distributed computing, which consists of a set of processes picking distinct names from a given namespace. The paper presents algorithms that solve order-preserving renaming in synchronous message passing systems with ... More

Random Walk on Directed Dynamic GraphsJan 31 2011Feb 01 2011Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the undirected dynamic ... More

The Chazy XII Equation and Schwarz Triangle FunctionsDec 25 2017Dubrovin [Lecture Notes in Math., Vol. 1620, Springer, Berlin, 1996, 120-348] showed that the Chazy XII equation $y'''- 2yy''+3y'^2 = K(6y'-y^2)^2$, $K \in \mathbb{C}$, is equivalent to a projective-invariant equation for an affine connection on a one-dimensional ... More

Symmetric pairs and associated commuting varietiesJan 22 2006We obtain a series of new results on the problem of irreducibility of commuting varieties associated with symmetric pairs or, in other words, $Z_2$-graded simple Lie algebras. In particular, we present many examples of reducible commuting varieties and ... More

Consistent estimation in Cox proportional hazards model with measurement errors and unbounded parameter setMar 31 2017Cox proportional hazards model with measurement error is investigated. In Kukush et al. (2011) [Journal of Statistical Research 45, 77-94] and Chimisov and Kukush (2014) [Modern Stochastics: Theory and Applications 1, 13-32] asymptotic properties of simultaneous ... More

Solvable and/or integrable many-body models on a circleJul 08 2014Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants of motion ... More

Generations of monic polynomials such that the coefficients of the polynomials of the next generation coincide with the zeros of the polynomials of the current generation, and new solvable many-body problemsOct 16 2015The notion of generations of monic polynomials such that the coefficients of the polynomials of the next generation coincide with the zeros of the polynomials of the current generation is introduced, and its relevance to the identification of endless ... More

Takiff algebras with polynomial rings of symmetric invariantsOct 09 2017Extending results of Rais-Tauvel, Macedo-Savage, and Arakawa-Premet, we prove that under mild restrictions on the Lie algebra $\mathfrak q$ having the polynomial ring of symmetric invariants, the m-th Takiff algebra of $\mathfrak q$, $\mathfrak q\langle ... More

On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebrasDec 06 2013For any involution $\sigma$ of a semisimple Lie algebra $\mathfrak g$, one constructs a non-reductive Lie algebra $\mathfrak k$, which is called a $\mathbb Z_2$-contraction of $\mathfrak g$. In this paper, we attack the problem of describing maximal commutative ... More

Diophantine properties of the zeros of (monic) polynomials the coefficients of which are the zeros of Hermite polynomialsJul 14 2015We introduce a monic polynomial p_N(z) of degree N whose coefficients are the zeros of the N-th degree Hermite polynomial. Note that there are N! such different polynomials p_N(z), depending on the ordering assignment of the N zeros of the Hermite polynomial ... More

Discrete Laplacian Growth: Linear Stability vs Fractal FormationMay 07 2008We introduce stochastic Discrete Laplacian Growth and consider its deterministic continuous version. These are reminiscent respectively to well-known Diffusion Limited Aggregation and Hele-Shaw free boundary problem for the interface propagation. We study ... More

Ambiguous representations of semilattices and imperfect informationApr 26 2019Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their ambiguous representations, ... More

Time-dependent polynomials with one double root, and related new solvable systems of nonlinear evolution equationsJun 19 2018Recently new solvable systems of nonlinear evolution equations -- including ODEs, PDEs and systems with discrete time -- have been introduced. These findings are based on certain convenient formulas expressing the $k$-th time-derivative of a root of a ... More

Rank of Projection-Algebraic Representations of Some Differential OperatorsNov 16 2010The Lie-algebraic method approximates differential operators that are formal polynomials of {1,x,d/dx} by linear operators acting on a finite dimensional space of polynomials. In this paper we prove that the rank of the n-dimensional representation of ... More

Generalized Pseudospectral Method and Zeros of Orthogonal PolynomialsJan 19 2017Jun 18 2018Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on ... More

Properties of the zeros of the polynomials belonging to the q-Askey schemeOct 02 2014Oct 16 2014In this paper we provide properties -- which are, to the best of our knowledge, new -- of the zeros of the polynomials belonging to the q-Askey scheme. These findings include Diophantine relations satisfied by these zeros when the parameters characterizing ... More

On seaweed subalgebras and meander graphs in type CJan 03 2016Jul 29 2016In 2000, Dergachev and Kirillov introduced subalgebras of "seaweed type" in $\mathfrak{gl}(n)$ and computed their index using certain graphs. In this article, those graphs are called type-A meander graphs. Then the subalgebras of seaweed type, or just ... More

Nonreciprocal Scattering by PT-symmetric stack of the layersMay 11 2015The nonreciprocal wave propagation in PT-symmetric periodic stack of binary dielectric layers characterised by balances loss and gain is analysed. The main mechanisms and resonant properties of the scattered plane waves are illustrated by the simulation ... More

Scattering properties of PT-symmetric layered periodic structuresMay 11 2015Oct 18 2015The optical properties of PT-symmetric periodic stack of the layers with balanced loss and gain are examined. We demonstrate that tunnelling phenomenon in periodic structures is connected with excitation of surface waves at the boundaries separating gain ... More

Coadjoint orbits of reductive type of seaweed Lie algebrasJan 05 2011Nov 22 2011A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of its dual of reductive type, that is such that the quotient of its stabiliser by the centre of Q is a reductive subgroup of GL(q), where ... More

Stochastic Loewner Evolutions, Fuchsian Systems and Orthogonal PolynomialsApr 02 2019We find a wide class of Levy-Loewner evolutions for which the value of integral means beta-spectrum $\beta(q)$ at $q=2$ is the maximal real eigenvalue of a three-diagonal matrix. The second moments of derivatives of corresponding conformal mappings are ... More

Properties of the zeros of generalized basic hypergeometric polynomialsApr 07 2015We define the generalized basic hypergeometric polynomial of degree $N \geq 1$ in terms of the generalized basic hypergeometric function, which depends on (arbitrary, generic, possibly complex) parameters $q \neq 1$, the $r \geq 0$ parameters $\alpha ... More

A remarkable contraction of semisimple Lie algebrasJul 04 2011Recently, E.Feigin introduced a very interesting contraction $\mathfrak q$ of a semisimple Lie algebra $\mathfrak g$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of ... More

Orthogonal sequences constructed from quasi-orthogonal ultraspherical polynomialsMay 10 2019Let $\displaystyle \{x_{k,n-1}\} _{k=1}^{n-1}$ and $\displaystyle \{x_{k,n}\} _{k=1}^{n},$ $n \in \mathbb{N}$, be two sets of real, distinct points satisfying the interlacing property $ x_{i,n}<x_{i,n-1}< x_{i+1,n}, \, \, \, i = 1,2,\dots,n-1.$ Wendroff ... More

Properties of the zeros of the polynomials belonging to the Askey schemeJul 12 2014In this paper we provide properties---which are, to the best of our knowledge, new---of the zeros of the polynomials belonging to the Askey scheme. These findings include Diophantine relations satisfied by these zeros when the parameters characterizing ... More

Nilpotent subspaces and nilpotent orbitsJan 13 2016Feb 26 2018Let $G$ be a semisimple algebraic group with Lie algebra $\mathfrak g$. For a nilpotent $G$-orbit $\mathcal O\subset\mathfrak g$, let $d_\mathcal O$ denote the maximal dimension of a subspace $V\subset \mathfrak g$ that is contained in the closure of ... More

Parabolic contractions of semisimple Lie algebras and their invariantsJan 02 2013Let $G$ be a connected semisimple algebraic group with Lie algebra $g$ and $P$ a parabolic subgroup of $G$ with $Lie(P)=p$. The parabolic contraction of $g$ is the semi-direct product of $p$ and a $p$-module $g/p$ regarded as an abelian ideal. We are ... More

Baxter-Bazhanov-Stroganov model: Separation of Variables and Baxter EquationMar 12 2006The Baxter-Bazhanov-Stroganov model (also known as the \tau^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using ... More

On Harmonic Measure of the Whole Plane Levy-Loewner EvolutionJan 28 2013Jan 22 2014Levy-Loewner evolution (LLE) is a generalization of the Schramm-Loewner evolution (SLE) where the branching is possible in a course of growth process. We consider a class of radial Levy-Loewner evolutions for which sets of points of the average means ... More

On Exact Multi-fractal Spectrum of the Whole-Plane SLEMar 13 2012Oct 23 2012We consider the whole-plane Shramm-Loewner evolution. Using exact solutions of fundamental equations for moments of derivative of conformal mappings we determine its average integral means beta-spectrum.

Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body ForcesOct 09 2013The class of solvable many-body problems "of goldfish type" is extended by including (the additional presence of) three-body forces. The solvable $N$-body problems thereby identified are characterized by Newtonian equations of motion featuring 19 arbitrary ... More

The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase SpacesApr 17 2010The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a ... More

On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian GrowthFeb 06 2019We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory ... More

Polynomials Whose Coefficients Coincide with Their ZerosMay 05 2017Jun 18 2018In this paper we consider monic polynomials such that their coefficients coincide with their zeros. These polynomials were first introduced by S. Ulam. We combine methods of algebraic geometry and dynamical systems to prove several results. We obtain ... More

On seaweed subalgebras and meander graphs in type DFeb 25 2017In 2000, Dergachev and Kirillov introduced subalgebras of "seaweed type" in $\mathfrak{gl}_n$ and computed their index using certain graphs, which we call type-${\sf A}$ meander graphs. Then the subalgebras of seaweed type, or just "seaweeds", have been ... More

Semi-direct products of Lie algebras and covariantsMay 07 2017The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\mathfrak q$ (= $\mathfrak q$-invariants in the symmetric algebra $S(\mathfrak q)$) can be considered ... More

Topological stability of continuous functions with respect to averaging by measures with locally constant densitiesJan 02 2016Let $\mu$ be a measure on $[-1,1]$. Then for every continuous function $f:\mathbb{R}\to\mathbb{R}$ and $\alpha>0$ one can define its averaging $f_{\alpha}:\mathbb{R}\to\mathbb{R}$ by the formula: \[ f_{\alpha}(x) = \int_{-1}^{1} f(x+t\alpha)d\mu. \] In ... More

Topological stability of continuous functions with respect to averagingsSep 20 2015We present sufficient conditions for topological stability of continuous functions $f:\mathbb{R}\to\mathbb{R}$ having finitely many local extrema with respect to averagings by discrete measures with finite supports.

Wave scattering by PT-symmetric epsilon-near-zero periodic structuresMay 11 2015The optical properties of PT-symmetric epsilonnear-zero (ENZ) periodic stack of the layers with balanced loss and gain have been examined. The effect of periodicity on the unidirectional tunneling phenomenon and symmetry breaking is determined. The performed ... More

Lax Integrable Supersymmetric Hierarchies on Extented Phase SpacesJan 04 2006We obtain via B\"acklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended by evolutions ... More

Generations of solvable discrete-time dynamical systemsJun 23 2016A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving N time-dependent ... More

Minimal Distortion Bending and Morphing of Compact ManifoldsAug 30 2007Let $M$ and $N$ be compact smooth oriented Riemannian $n$-manifolds without boundary embedded in $\mathbb{R}^{n+1}$. Several problems about minimal distortion bending and morphing of $M$ to $N$ are posed. Cost functionals that measure distortion due to ... More

Poisson-commutative subalgebras of $S(\mathfrak g)$ associated with involutionsSep 02 2018The symmetric algebra $S(\mathfrak g)$ of a reductive Lie algebra $\mathfrak g$ is equipped with the standard Poisson structure, i.e., the Lie-Poisson bracket. Poisson-commutative subalgebras of $S(\mathfrak g)$ attract a great deal of attention, because ... More

Novel solvable many-body problemsJan 19 2016Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These models are ... More

A new solvable many-body problem of goldfish typeJul 14 2015A new solvable many-body problem of goldfish type is introduced and the behavior of its solutions is tersely discussed.

Properties of the zeros of generalized hypergeometric polynomialsJul 28 2015We define the generalized hypergeometric polynomial of degree N in terms of the generalized hypergeometric function that depends on p parameters a_1, ..., a_p and q parameters b_1, ..., b_q. The parameters are "generic", possibly complex, numbers. In ... More

Non-Laplacian growth, algebraic domains and finite reflection groupsJan 31 2006Feb 26 2006Dynamics of planar domains with moving boundaries driven by the gradient of a scalar field that satisfies an elliptic PDE is studied. We consider the question: For which kind of PDEs the domains are algebraic, provided the field has singularities at a ... More

An Exactly Conservative Integrator for the n-Body ProblemDec 23 2001Aug 03 2002The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value ... More

Symmetries and solutions of field equations of axion electrodynamicsJan 24 2012Jul 04 2012The group classification of models of axion electrodynamics with arbitrary self interaction of axionic field is carried out. It is shown that extensions of the basic Poincar\'e invariance of these models appear only for constant and exponential interactions. ... More

Form-factors in the Baxter-Bazhanov-Stroganov model II: Ising model on the finite latticeNov 03 2007Apr 14 2008We continue our investigation of the Baxter-Bazhanov-Stroganov or \tau^{(2)}-model using the method of separation of variables [nlin/0603028,arXiv:0708.4342]. In this paper we derive for the first time the factorized formula for form-factors of the Ising ... More

Invariant solutions for equations of axion electrodynamicsJan 30 2010Aug 16 2012Using the three-dimensional subalgebras of the Lie algebra of Poincar\'e group an extended class of exact solutions for the field equations of the axion electrodynamics is obtained. These solutions include arbitrary parameters and arbitrary functions ... More

Spin operator matrix elements in the superintegrable chiral Potts quantum chainDec 28 2009We derive spin operator matrix elements between general eigenstates of the superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by R.Baxter. For each pair of spaces ... More

Resonant Combinatorial Frequency Generation Induced by a PT-symmetric Periodic Layered StackOct 18 2015The nonlinear interaction of waves in PT-symmetric periodic stacks with an embedded nonlinear anisotropic dielectric layer illuminated by plane waves of two tones is examined. The three-wave interaction technique is applied to study the nonlinear processes. ... More

Statistical field theory for a multicomponent fluid: The collective variables approachJul 02 2007Using the collective variables (CV) method the basic relations of statistical field theory of a multicomponent non-homogeneous fluids are reconsidered. The corresponding CV action depends on two sets of scalar fields - fields $\rho_{\alpha}$ connected ... More

The argument shift method and maximal commutative subalgebras of Poisson algebrasFeb 20 2007Let $S$ be the symmetric algebra of an algebraic Lie algebra. We provide a sufficient condition for the maximality of Poisson commutative subalgebras of $S$ obtained by the argument shift method.

A Complete Set of Grad's Thirteen Regularized Moment EquationsSep 30 2010Oct 07 2010This paper derives transport equations for medium rarefied gases from the Bhatnagar-Gross-Krook (BGK) model kinetic equation using a Hermite polynomial approximation for the monoatomic gas distribution function. We apply the Chapman-Enskog regularization ... More

Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear SystemsApr 28 2006The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and $\phi^4$-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher dispersion, and ... More

Ionic fluids: charge and density correlations near gas-liquid criticalityMay 17 2005Jun 12 2005The correlation functions of an ionic fluid with charge and size asymmetry are studied within the framework of the random phase approximation. The results obtained for the charge-charge correlation function demonstrate that the second-moment Stillinger-Lovett ... More

Quasiperiodicity, bistability and chaos in the Landau-Lifshitz equationMay 04 1999The dynamics of an individual magnetic moment is studied through the Landau-Lifshitz equation with a periodic driving in the direction perpendicular to the applied field. For fields lower than the anisotropy field and small values of the perturbation ... More

Influence of tilted magnetic field on excited states of the two-dimensional hydrogen atomFeb 21 2017Apr 26 2017The aim of the current work is the research of the influence of the \textbf{tilted} magnetic field direction on statistical properties of energy levels of a two-dimensional (2D) hydrogen atom and of an exciton in GaAs/Al$_{0.33}$Ga$_{0.67}$As quantum ... More

RKappa: Software for Analyzing Rule-Based ModelsSep 21 2018RKappa is a framework for the development, simulation and analysis of rule-base models within the mature statistically empowered R environment. It is designed for model editing, parameter identification, simulation, sensitivity analysis and visualisation. ... More

Enhanced group classification of Gardner equations with time-dependent coefficientsJul 31 2014Mar 03 2015We classify the Lie symmetries of variable coefficient Gardner equations (called also the combined KdV-mKdV equations). In contrast to the particular results presented in Molati and Ramollo (2012) we perform the exhaustive group classification. It is ... More

Group analysis of variable coefficient generalized fifth-order KdV equationsJan 28 2014We carry out group analysis of a class of generalized fifth-order Korteweg-de Vries equations with time dependent coefficients. Admissible transformations, Lie symmetries and similarity reductions of equations from the class are classified exhaustively. ... More

Form-factors in the Baxter-Bazhanov-Stroganov model I: Norms and matrix elementsAug 31 2007Sep 02 2007We continue our investigation of the Z_N-Baxter-Bazhanov-Stroganov model using the method of separation of variables [nlin/0603028]. In this paper we calculate the norms and matrix elements of a local Z_N-spin operator between eigenvectors of the auxiliary ... More

Numerical recovering a density by BC-methodJun 04 2009In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.

Anisotropic Features of the Two-dimensional Hydrogen Atom in a Magnetic FieldJan 22 2017Feb 06 2017The aim of the current work is the numerical research of the anisotropic characteristics of the two-dimensional hydrogen atom induced by a magnetic field. The ground state energy (GSE) of the two-dimensional hydrogen atom and the corresponding wave function ... More

Asynchrony and Collusion in the N-party BAR Transfer ProblemApr 18 2012The problem of reliably transferring data from a set of $N_P$ producers to a set of $N_C$ consumers in the BAR model, named N-party BAR Transfer (NBART), is an important building block for volunteer computing systems. An algorithm to solve this problem ... More

RKappa: Statistical sampling suite for Kappa modelsDec 13 2014We present RKappa, a framework for the development and analysis of rule-based models within a mature, statistically empowered R environment. The infrastructure allows model editing, modification, parameter sampling, simulation, statistical analysis and ... More

Group classification of variable coefficient generalized Kawahara equationsSep 27 2013Jan 05 2014An exhaustive group classification of variable coefficient generalized Kawahara equations is carried out. As a result, we derive new variable coefficient nonlinear models admitting Lie symmetry extensions. All inequivalent Lie reductions of these equations ... More

CoCalc as a Learning Tool for Neural Network Simulation in the Special Course "Foundations of Mathematic Informatics"Jul 02 2018The role of neural network modeling in the learning content of the special course "Foundations of Mathematical Informatics" was discussed. The course was developed for the students of technical universities - future IT-specialists and directed to breaking ... More

Symmetric invariants related to representations of exceptional simple groupsSep 07 2016We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with $\mathfrak g={\sf Lie}(G)$ such that the symmetric invariants of the semi-direct product $\mathfrak g\ltimes V$, where $V$ is an Abelian ideal, ... More

SPS-Sintered NaTaO3-Fe2O3 Composite exhibits Large Seebeck Coefficient and Electric CurrentSep 24 2013Sep 25 2013NaTaO3-50wt% Fe2O3 composite ceramics showed a large Seebeck voltage of -300 mV at a temperature gradient of 650 K yielding a constant Seebeck coefficient of more than -500 microV/K over a wide temperature range. We report for the first time that SPS ... More