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Understanding the metamagnetic transition and magnetic behavior of Ni48Co6Mn26Al20 polycrystalline ribbonsMay 27 2013Jul 05 2013In this work we demonstrate that the polycrystalline ribbons of (Ni48Co6)Mn26Al20 with B2 structure at room temperature show a magnetic behavior with competing magnetic exchange interactions leading to frozen disorders at low temperatures. It is established ... More

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

Energy filtering enhancement of thermoelectric performance of nanocrystalline Cr-Si compositesMar 02 2016Apr 13 2016We report on thermoelectric properties of nanocrystalline Cr$_{\rm 1-x}$Si$_{\rm x}$ composite films. As-deposited amorphous films were transformed into a nanocrystalline state with average grain size of 10--20~nm by annealing during in-situ thermopower ... More

Phase transitions in Ni2+xMn1-xGa with a high Ni excessNov 03 2005Mar 18 2006Ferromagnetic shape memory alloys Ni$_{2+x}$Mn$_{1-x}$Ga were studied in the range of compositions $0.16 \le x \le 0.36$. Experimental phase diagram, constructed from differential scanning calorimetry, transport and magnetic measurements, exhibits distinctive ... More

Universal Algorithm for Online Trading Based on the Method of CalibrationMay 16 2012Nov 04 2014We present a universal algorithm for online trading in Stock Market which performs asymptotically at least as good as any stationary trading strategy that computes the investment at each step using a fixed function of the side information that belongs ... More

Pele's hairs and exotic multiply twinned graphite closed-shell microcrystals in meteoritic dust of Chelyabinsk superbolideMay 20 2019When a space body enters Earth's atmosphere, its surface is exposed to high pressure and temperatures. The airflow tears off small droplets from the meteoroid forming a cloud of meteorite dust. Can new materials be synthesized in these unique conditions ... More

Analytic theory of the eight-vertex modelSep 22 2006Jan 12 2007We observe that the exactly solved eight-vertex solid-on-solid model contains an hitherto unnoticed arbitrary field parameter, similar to the horizontal field in the six-vertex model. The parameter is required to describe a continuous spectrum of the ... More

Eight-vertex model and non-stationary Lame equationNov 09 2004Nov 26 2004We study the ground state eigenvalues of Baxter's Q-operator for the eight-vertex model in a special case when it describes the off-critical deformation of the $\Delta=-1/2$ six-vertex model. We show that these eigenvalues satisfy a non-stationary Schrodinger ... More

Online Learning with Continuous Ranked Probability ScoreFeb 26 2019Probabilistic forecasts in the form of probability distributions over future events have become popular in several fields of statistical science. The dissimilarity between a probability forecast and an outcome is measured by a loss function (scoring rule). ... More

Online Aggregation of Unbounded Losses Using Shifting Experts with ConfidenceAug 02 2018Sep 30 2018We develop the setting of sequential prediction based on shifting experts and on a "smooth" version of the method of specialized experts. To aggregate experts predictions, we use the AdaHedge algorithm, which is a version of the Hedge algorithm with adaptive ... More

On Compatibility of Discrete RelationsApr 15 2005Jul 12 2005An approach to compatibility analysis of systems of discrete relations is proposed. Unlike the Groebner basis technique, the proposed scheme is not based on the polynomial ring structure. It uses more primitive set-theoretic and topological concepts and ... More

Connection between Different Function Theories in Clifford AnalysisJan 03 1995We describe an explicit connection between solutions to equations $Df=0$ (the Generalized Cauchy-Riemann equation) and $(D+M)f=0$, where operators $D$ and $M$ commute. The described connection allows to construct a ``function theory'' (the Cauchy theorem, ... More

No More Than Mechanics. IMay 02 1994Feb 05 2004One can introduce so-called {\em Plain Mechanics} having an {\bf operator realization}. Then the set of one-dimension representations of this operator realization may be identified with the Classical Mechanics. Different irreducible infinite-dimension ... More

An Example of Clifford Algebras Calculations with GiNaCOct 18 2004Dec 09 2005This example of Clifford algebras calculations uses GiNaC (http://www.ginac.de/) library, which includes a support for generic Clifford algebra starting from version~1.3.0. Both symbolic and numeric calculation are possible and can be blended with other ... More

Flux Sensitivity of VERITASMay 05 1999VERITAS is a new major ground-based gamma-ray observatory with an array of seven 10 m optical reflectors to be built at the Whipple Observatory in southern Arizona, USA. It will consist of an array of imaging Cherenkov telescopes designed to conduct critical ... More

Thermal emission from bare quark matter surfaces of hot strange starsMar 22 2001We consider the thermal emission of photons and electron-positron pairs from the bare quark surface of a hot strange star. The radiation of high-energy (> 20 MeV) equilibrium photons prevails at the surface temperature T_S > 5 x 10^{10} K, while below ... More

Glitches in the X-Ray Pulsar 1e 2259+586Dec 27 1993Starquakes are considered for fast-rotating magnetic white dwarfs. The X-ray pulsar 1E 2259 + 586 may be such a white dwarf. It is shown that in this case starquakes may be responsible for the decrease of the mean spin-down rate which was observed for ... More

Real-time data analysis at the LHC: present and futureSep 21 2015The Large Hadron Collider (LHC), which collides protons at an energy of 14 TeV, produces hundreds of exabytes of data per year, making it one of the largest sources of data in the world today. At present it is not possible to even transfer most of this ... More

On the Yang-Baxter equation for the six-vertex modelJan 25 2014Jun 10 2014In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of the corresponding ... More

Picard solution of Painlevé VI and related tau-functionsFeb 11 2010In this paper we obtain explicit expressions for tau-functions related to Picard type solutions of the Painlev\'e VI equation in terms of theta functions and their derivatives.

Ensembles of Cycles Programmed in GiNaCDec 09 2015This library manipulates ensembles of cycles (quadrics), which are interrelated through certain geometric relations (to be orthogonal, to be tangent, etc.). The code operates with numeric and symbolic data of cycles in spaces of arbitrary dimensionality ... More

An Algorithm to Decompose Permutation Representations of Finite Groups: Polynomial Algebra ApproachJan 29 2018Mar 03 2018We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in invariant subspaces ... More

The modelling of the automation schemes of technological processes in CAD-system of renovation of the enterprisesNov 27 2006According to the requirements of the Russian standards, the automation schemes are necessary practically in each project of renovation of industrial buildings and facilities, in which any technological processes are realized. The model representations ... More

The model of the tables in design documentation for operating with the electronic catalogs and for specifications making in a CAD systemMay 17 2004The hierarchic block model of the tables in design documentation as a part of a CAD system is described, intended for automatic specifications making of elements of the drawings, with usage of the electronic catalogs. The model is created for needs of ... More

Umbral Calculus and Cancellative Semigroup AlgebrasApr 01 1997Feb 08 2000We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of cancellative semigroup, ... More

Spectrum as the Support of Functional CalculusAug 30 2002We investigate the new definition of analytic functional calculus in the terms of representation theory of SL2(R). We avoid any usage of its algebraic homomorphism property and replace it by the demand to be an intertwining operator. The related notion ... More

On Instability of the Ergodic Limit Theorems with Respect to Small Violations of Algorithmic RandomnessMay 21 2011Jul 25 2012An instability property of the Birkhoff's ergodic theorem and related asymptotic laws with respect to small violations of algorithmic randomness is studied. The Shannon--McMillan--Breiman theorem and all universal compression schemes are also among them. ... More

Poincare Extension of Moebius TransformationsJul 08 2015Nov 17 2016Given sphere preserving (M\"obius) transformations in $n$-dimensional Euclidean space one can use the Poincar\'e extension to obtain sphere preserving transformations in a half space of $n+1$ dimensions. The Poincar\'e extension is usually provided either ... More

An Extension of Moebius--Lie Geometry with Conformal Ensembles of Cycles and Its Implementation in a GiNaC LibraryDec 09 2015Aug 19 2018We propose to consider ensembles of cycles (quadrics), which are interconnected through conformal-invariant geometric relations (e.g. "to be orthogonal", "to be tangent", etc.), as new objects in an extended Moebius--Lie geometry. It was recently demonstrated ... More

Wavelets Beyond AdmissibilityNov 24 2009The purpose of this paper is to articulate an observation that many interesting type of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. This extends an applicability ... More

Classical/Quantum=Commutative/Noncommutative?Apr 09 2012Jun 18 2012In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires noncommutative ... More

Symmetry, Geometry, and Quantization with Hypercomplex NumbersNov 17 2016These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this framework. In particular, ... More

The Use of NMR for Solving the Problems of Quantum ComputersFeb 05 2001The analysis of papers on usage NMR in quantum computations is provided and the probable direction of the future investigations are considered.

Erlangen Programme at Large 3.2: Ladder Operators in Hypercomplex MechanicsMar 06 2011Jun 10 2011We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat the repulsive ... More

p-Mechanics and De Donder-Weyl TheoryJun 14 2003Jul 04 2003The orbit method of Kirillov is used to derive the p-mechanical brackets [quant-ph/0212101]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension ... More

The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant TransformSep 23 2012May 21 2014This note reviews complex and real techniques in harmonic analysis. We describe a common source of both approaches rooted in the covariant transform generated by the affine group. Keywords: wavelet, coherent state, covariant transform, reconstruction ... More

On the inverse braid monoidApr 23 2007Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to the inverse braid ... More

The eight-vertex model and Painleve VIFeb 13 2006In this letter we establish a connection of Picard-type elliptic solutions of Painleve VI equation with the special solutions of the non-stationary Lame equation. The latter appeared in the study of the ground state properties of Baxter's solvable eight-vertex ... More

Double-periodic maximal surfaces with singularitiesMar 07 2009We construct and study a family of double-periodic almost entire solutions of the maximal surface equation. The solutions are parameterized by a submanifold of $3\times 3$-matrices (the so-called generating matrices). We show that the constructed solutions ... More

A Paley-Wiener Theorem for Nilpotent Lie GroupsFeb 28 1996A version of Paley-Wiener like theorem for connected, simply connected nilpotent Lie groups is proven.

Poincare Extension of Moebius TransformationsJul 08 2015Aug 30 2016Given sphere preserving (M\"obius) transformations in $n$-dimensional Euclidean space one can use the Poincar\'e extension to obtain sphere preserving transformations in a half space of $n+1$ dimensions. The Poincar\'e extension is usually provided either ... More

Radiating Regions in Pulsar Magnetospheres: From Theory to Observations and BackNov 22 1999We discuss plausible locations of radiating regions in the magnetospheres of pulsars and argue that the mechanisms of pulsar radiation at different frequencies are closely connected with the locations of the radiating regions, especially in the radio ... More

Radiation from Relativistic Strongly Magnetized OutflowsSep 26 1999Relativistic strongly magnetized winds outflowing from fast-rotating compact objects like millisecond pulsars with surface magnetic fields of $\sim 10^{15}-10^{16}$ G are plausible sources of cosmological $\gamma$-ray bursts. In such winds, there are ... More

Low-mass normal-matter atmospheres of strange stars and their radiationMar 06 1997The quark surface of a strange star has a very low emissivity for X-ray photons. I find that a small amount of normal matter at the quark surface with temperature in the range $10^7\la T_{_S}} \ll mc^2/k\simeq 6\times 10^9$ K is enough to produce X-rays ... More

Physical processes in pulsar magnetospheres and non-thermal high-frequency emissionDec 09 1996The energy source of a pulsar's non-thermal emission is the rotational energy loss of the neutron star. The rotational energy of the neutron star is transformed into the pulsar radiation by a long sequence of processes. The processes of this sequence ... More

Combinatorial Approach to Modeling Quantum SystemsJul 30 2015Mar 23 2016Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers and unitarity ... More

Q-operators in the six-vertex modelJun 03 2014In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra $U_q(\widehat{sl(2)})$. Taking ... More

An Algorithm to Decompose Permutation Representations of Finite Groups: Polynomial Algebra ApproachJan 29 2018We describe an algorithm for splitting a permutation representation of a finite group into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in invariant subspaces are operators of projection ... More

The methods of support of the requirements of the Russian standards at development of a CAD of industrial objectsDec 08 2004The methods of support of the requirements of the Russian standards in a CAD of industrial objects are explained, which were implemented in the CAD system TechnoCAD GlassX with an own graphics core and own structures of data storage. It is rotined, that ... More

The Features of the Complex CAD system of Reconstruction of the Industrial PlantsDec 08 2004The features of designing of reconstruction of the acting plant by its design department are considered: the results of work are drawings corresponding with the national standards; large number of the small projects for different acting objects; variety ... More

Modular technology of developing of the problem-oriented extensions of a CAD system of reconstruction of the plantMay 14 2004The modular technology of creation of the problem-oriented extensions of a CAD system is described, which was realised in a system TechnoCAD GlassX for designing of reconstruction of the plants. The modularity of the technology is expressed in storage ... More

The modulus in the CAD system drawings as a base of developing of the problem-oriented extensionsMay 12 2004The concept of the "modulus" in the CAD system drawings is characterized, being a base of developing of the problem-oriented extensions. The modulus consists of visible geometric elements of the drawing and invisible parametric representation of the modelling ... More

Quantum and Classic BracketsJul 25 2000Mar 22 2001We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \emph{do not} use any kind of semiclassic ... More

Polynomial Sequences of Binomial Type and Path IntegralsAug 09 1998Oct 22 2001Polynomial sequences $p_n(x)$ of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express $p_n(x)$ as a \emph{path integral} in the ``phase space'' $\Space{N}{} \times {[-\pi,\pi]}$. The Hamiltonian is $h(\phi)=\sum_{n=0}^\infty ... More

Classification problems for system of forms and linear mappingsJan 05 2008We devise a method that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. Canonical matrices of (i) bilinear or sesquilinear forms, (ii) pairs of symmetric, skew-symmetric, ... More

Harmonic Analysis and Localization TechniqueFeb 02 1999We study relationships between different formulations of the local principle. Also we establish a connection among the local principle and the non-commutative Fourier transform approach to the investigation of convolution operator algebras. Keywords: ... More

On Properties of Polynomials in Random ElementsMay 17 2016The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean value theorem, characterization problem, bounds for probabilities to hit ... More

True self energy function and reducibility in effective scalar theories. (Revised)Oct 12 2017Oct 15 2017This is the revised version of Sect. I - IV of the paper https://doi.org/10.1103/PhysRevD.89.125022 originally published in 2014. The thing is that in https://doi.org/10.1103/PhysRevD.89.125022 the text was insufficiently clear and, in addition, it contained ... More

Covariant TransformNov 17 2010Jan 26 2011The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors ... More

Multielement order separability in free products of groupsMay 26 2010Jul 20 2010We introduce the notion of multielement order separability and study this property for free groups and free products.

About presentations of braid groups and their generalizationsApr 27 2013In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard Artin presentation ... More

Unitary representability of free abelian topological groupsApr 11 2006For every Tikhonov space $X$ the free abelian topological group $A(X)$ and the free locally convex vector space $L(X)$ admit a topologically faithful unitary representation. For compact spaces $X$ this is due to Jorge Galindo.

Spaces of Analytical Functions and Wavelets--Lecture NotesApr 01 2002This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a classification ... More

Projectively universal countable metrizable groupsSep 14 2014Oct 27 2015We prove that there exists a countable metrizable topological group $G$ such that every countable metrizable group is isomorphic to a quotient of $G$. The completion $H$ of $G$ is a Polish group such that every Polish group is isomorphic to a quotient ... More

Representations of residually finite groups by isometries of the Urysohn spaceJan 28 2006May 30 2006As a consequence of Kirchberg's work, Connes' Embedding Conjecture is equivalent to the property that every homomorphism of the group $F_\infty\times F_\infty$ into the unitary group $U(\ell^2)$ with the strong topology is pointwise approximated by homomorphisms ... More

Canonical matrices of isometric operators on indefinite inner product spacesOct 04 2007We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases: (i) F is an algebraically closed field of characteristic different from ... More

Response of bare strange stars to energy input onto their surfacesJul 02 2001We study numerically the thermal emission of $e^+e^-$ pairs from a bare strange star heated by energy input onto its surface; heating starts at some moment, and is steady afterwards. The thermal luminosity in $e^+e^-$ pairs increases to some constant ... More

A new algorithm for irreducible decomposition of representations of finite groupsDec 23 2018An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a complete set of ... More

Uniqueness theorem for the non-local ionization source in glow discharge and hollow cathodeMar 31 2012The paper is devoted to the proof of the uniqueness theorem for solution of the equation for the non-local ionization source in a glow discharge and a hollow cathode in general 3D geometry. The theorem is applied to wide class of electric field configurations, ... More

Integral equation for source of ionization in hollow cathodeFeb 16 2009Feb 19 2009To simulate the influence of pendulum effect in hollow cathode configuration on a current-voltage characteristic it is proposed to consider a plane glow discharge in one-dimensional space configuration with two plane parallel cathodes and one plane anode ... More

Non-local model of hollow cathode and glow discharge - theory calculations and experiment comparisonNov 09 2009General form of the non-local equation for an ionization source in glow discharge and hollow cathode 3D-simulation is formulated. It is a fundamental equation in a hollow cathode theory, which allows to make up a complete set of field equations for a ... More

Environment of development of the programs of parametric creating of the drawings in CAD-system of renovation of the enterprisesNov 17 2006The main ideas, data structures, structure and realization of operations with them in environment of development of the programs of parametric creating of the drawings are considered for the needs of the automated design engineering system of renovation ... More

The modelling of the build constructions in a CAD of the renovation of the enterprises by means of units in the drawingsDec 08 2004The parametric model of build constructions and features of design operations are described for making drawings, which are the common component of the different parts of the projects of renovation of enterprises. The key moment of the deep design automation ... More

Tokens: An Algebraic Construction Common in Combinatorics, Analysis, and PhysicsJan 02 2002We give a brief account of a construction called tokens here, which is significant in algebra, analysis, combinatorics, and physics. Tokens allow to express a semigroup on one set via a semigroup convolution on another set. Therefore tokens are similar ... More

Erlangen Program at Large-0: Starting with the group SL(2,R)Jul 17 2006Nov 10 2008This is an easy-reading which describes few geometric invariants which can be obtained from the group SL(2,R) within the Erlangen program of F.Klein.

Canonical matrices of forms and pairs of forms over finite and p-adic fieldsNov 13 2010Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over finite fields of characteristic not 2 and over finite extensions of the ... More

Erlangen Programme at Large 3.1: Hypercomplex Representations of the Heisenberg Group and MechanicsMay 27 2010Jul 04 2011In the spirit of geometric quantisation we consider representations of the Heisenberg(--Weyl) group induced by hypercomplex characters of its centre. This allows to gather under the same framework, called p-mechanics, the three principal cases: quantum ... More

Order separability of HNN-extensions and free products with commutative subgroupsJul 19 2010Jul 20 2010This paper is devoted to the investigation of the property of order separability for HNN extensions and free products with commutative subgroups. Particularly it was proven that HNN extension of a free group with maximal connected cyclic subgroups is ... More

Generalization of order separability for free groupsJun 17 2010Jul 20 2010In this work the author studies the property close to property of order separability.

Quasipotency and $g$-potency in free constructionsJun 09 2010Oct 23 2010In this paper we investigate the properties of quasipotency and $g$-potency for free products with amalgamation.

Towards to Analysis in $\mathbb{R}^{pq}$Nov 30 2018We are looking for a possible development of analysis in indefinite space $\mathbb{R}^{pq}$ from their group of Moebius automorphisms. [This is historic submission of the paper published in 1996]

An Algorithm for Computing Invariant Projectors in Representations of Wreath ProductsMay 29 2019We describe an algorithm for computing the complete set of primitive orthogonal idempotents in the centralizer ring of the permutation representation of a wreath product. This set of idempotents determines the decomposition of the representation into ... More

Arnold-type invariants of wave fronts on surfacesJan 28 1999Aug 11 1999Recently Arnold's $\St$ and $J^{\pm}$ invariants of generic planar curves have been generalized to the case of generic planar wave fronts. We generalize these invariants to the case of wave fronts on an arbitrary surface $F$. All invariants satisfying ... More

Riemann boundary value problem with piecewise constant matrixApr 13 2019The vector-matrix Riemann boundary value problem for the unit disk with piecewise constant matrix is constructively solved by a method of functional equations. By functional equations we mean iterative functional equations with shifts involving compositions ... More

Two-Dimensional Conformal Models of Space-Time and Their CompactificationNov 21 2006Apr 13 2007We study geometry of two-dimensional models of conformal space-time based on the group of Moebius transformation. The natural geometric invariants, called cycles, are used to linearise Moebius action. Conformal completion of the space-time is achieved ... More

Erlangen Program at Large-1: Geometry of InvariantsDec 17 2005Jul 15 2013This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL(2,R) group. We describe here geometries of corresponding ... More

Erlangen Programme at Large: An OverviewJun 08 2011Nov 13 2011This is an overview of Erlangen Programme at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the group SL(2,R). ... More

Relative Convolutions. I. Properties and ApplicationsOct 03 1994Feb 05 2004To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already studied (operators ... More

Log-Optimal Portfolio Selection Using the Blackwell Approachability TheoremOct 22 2014Jun 28 2015We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a ... More

The observational appearance of strange starsNov 22 2001Strange quark matter with the density of ~ 5\times 10^{14} g cm^{-3} might exist up to the surface of a strange star. This differs qualitatively from the case of a neutron star and opens observational possibilities to distinguish strange stars from neutron ... More

On the Nature of Nonthermal Radiation from Cosmological Gamma-Ray BurstersDec 13 1993Relativistic electron-positron winds with strong magnetic fields are considered as a source of radiation for cosmological $\gamma$-ray bursters. Such a wind is generated by a millisecond pulsar with a very strong magnetic field. An electron-positron plasma ... More

Analysis in $R^{1,1}$ or the Principal Function TheoryDec 09 1997Dec 14 1997We explore a function theory connected with the principal series representation of SL(2,R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann ... More

Erlangen Program at Large-2.5: Induced Representations and Hypercomplex NumbersSep 24 2009Feb 04 2013In the search for hypercomplex analytic functions on the half-plane, we review the construction of induced representations of the group G=SL(2,R). Firstly we note that G-action on the homogeneous space G/H, where H is any one-dimensional subgroup of SL(2,R), ... More

Schwerdtfeger-Fillmore-Springer-Cnops Construction Implemented in GiNaCDec 17 2005Dec 10 2015This paper presents an implementation of the Schwerdtfeger-Fillmore-Springer-Cnops construction (SFSCc) along with illustrations of its usage. SFSCc linearises the linear-fraction action of the Moebius group in R^n. This has clear advantages in several ... More

Order separabilityMar 04 2010Jul 20 2010This paper is devoted to the investigation of the property of order separability for free products of groups.

Order separability of free product of free groups with cyclic amalgamationJul 01 2010Jul 08 2010This paper is devoted to the proof of the property of order separability for free product of free groups with maximal cyclic amalgamated subgroups.

Uncertainty and AnalyticityDec 16 2013Jan 10 2014We describe a connection between minimal uncertainty states and holomorphy-type conditions on the images of the respective wavelet transform. The most familiar example is the Fock-Segal-Bargmann transform generated by the Gaussian, however, this also ... More

Nilpotent Lie Groups in Clifford Analysis: Five Directions for ResearchSep 10 2000The aim of the paper is to popularise nilpotent Lie groups (notably the Heisenberg group and alike) in the context of Clifford analysis and related models of mathematical physics. It is argued that these groups are underinvestigated in comparison with ... More

Wavelets in Banach SpacesJul 25 1998Jul 27 1999We describe a construction of wavelets (coherent states) in Banach spaces generated by ``admissible'' group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example we ... More

Canonical matrices for linear matrix problemsSep 16 2007We consider a large class of matrix problems, which includes the problem of classifying arbitrary systems of linear mappings. For every matrix problem from this class, we construct Belitskii's algorithm for reducing a matrix to a canonical form, which ... More