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A New Triviality Theorem for Group Pseudorepresentations Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 A. I. Shtern
Abstract It is proved that if \(G\) is a group and \(\pi\) is a pseudorepresentation of \(G\) in a Banach space \(E\) with a sufficiently small defect and if \(\pi\) is a sufficiently small perturbation of the identity representation of \(G\) in \(E\), then \(\pi(g)=1_E\) for all \(g\in G\).
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A Hausdorff Operator with Commuting Family of Perturbation Matrices Is a Non-Riesz Operator Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 A. R. Mirotin
Abstract We consider a generalization of the notion of Hausdorff operator on Lebesgue spaces and, under natural conditions, prove that such an operator is not a Riesz operator provided it is non zero. In particular, it cannot be represented as a sum of a quasinilpotent and a compact operators.
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Local Asymptotics of Unfoldings of Edge and Corner Catastrophes Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 J. I. Bova, A. S. Kryukovskii, D. S. Lukin
Abstract Using symbolic calculations, a method of local asymptotics is developed, which describes the diffraction focusing of electromagnetic and acoustic fields for edge and corner catastrophes. Explicit expressions are found for the unfolding coefficients, the functional module, and the phase of the traveling wave, when the family of primary (geometrical-optical) and secondary (edge) rays form focuses
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Boundary Problems for Three-Dimensional Dirac Operators and Generalized MIT Bag Models for Unbounded Domains Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 V. S. Rabinovich
Abstract We consider the operators of the following boundary problems $$\mathbb{D}_{\boldsymbol{A,}\Phi,\mathfrak{B}}\boldsymbol{u}=\left\{ \begin{array} [c]{c} \mathfrak{D}_{\boldsymbol{A},\Phi}\boldsymbol{u}\text{ on }\Omega\\ \mathfrak{B}\boldsymbol{u}_{\partial\Omega}\text{ on }\partial\Omega \end{array} \right. $$(1) in unbounded domains \(\Omega\subset\mathbb{R}^{3}\), where \(\mathfrak{D} _{\boldsymbol{A}
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$$L_p-$$ Bounds for the Krein Spectral Shift Function: $$0 Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 M. Pliev, F. Sukochev, D. Zanin
Abstract We extend the inequalities originally obtained by D. Hundertmark and B. Simon for \(L_p-\)bounds, \(1\leq p\leq \infty\), for the Krein spectral shift function to the setting of general semifinite von Neumann algebras. We also complete these results by showing that in the quasi-normed setting, for example, for \(L^p\)-spaces with \(0
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Asymptotics of the Number of Restricted Partitions Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 V. L. Chernyshev, T. W. Hilberdink, V. E. Nazaikinskii
Abstract Let \(00\). For any \(T>0\) and \(k\in\overline{\mathbb{N}}=\mathbb{N}\cup\{\infty\}\), let \(N(k,T)\) be the number of solutions \(\{n_j\}_{j=1}^k\), \(n_j\in \mathbb{N}_0=\mathbb{N}\cup\{0\}\), of the inequality \(\sum_{j=1}^{k}n_jt_j\le T\). We are interested in the asymptotics of \(\log N(k,T)\) as \(T\to\infty\).
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Asymptotic Solutions of a System of Gas Dynamics with Low Viscosity that Describe Smoothed Discontinuities Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 A. I. Allilueva, A. I. Shafarevich
Abstract We construct formal asymptotic solutions describing shock waves and tangential and weak discontinuities for the nonlinear system of gas dynamics of a fluid with small viscosity.
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Motivation and Essence of the Term “Tropical Mathematics” Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 V. P. Maslov
Abstract In the present paper, we discuss the notion of “tropical mathematics” in view of the fact that, up to the present time, there is no generally accepted correct understanding of this notion. The paper presents, rather than mathematical proofs, humanitarian and social justification of the correct understanding of the term. The author proposes to describe the term “tropical mathematics” by means
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Linear Widths of Weighted Sobolev Classes with Conditions on the Highest Order and Zero Derivatives Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 A. A. Vasil’eva
Abstract In this paper, order estimates for the linear widths of some function classes are obtained; these classes are defined by restrictions on the weighted \(L_{p_1}\)-norm of the \(r\)th derivative and the weighted \(L_{p_0}\)-norm of zero derivatives.
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An Almost-Solvable Model of Complex Network Dynamics Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 Q. Guo, A. Sowa
Abstract We discuss a specific model, which we refer to as RandLOE, of a large multi-agent network whose dynamic is prescribed via a combination of deterministic local laws and random exogenous factors. The RandLOE approach lies outside the framework of Stochastic Differential Equations, but lends itself to analytic examination as well as to stable simulation even for relatively large networks. RandLOE
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Homogeneous Surfaces in $$\mathbb C^4$$ Associated with a 5-Dimensional Completely Nondegenerate Cubic Model Surface of CR-Type $$(1,3)$$ Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 V. K. Beloshapka, M. Sabzevari
Abstract The action on the space \(\mathbb C^4\) of the 7-dimensional Lie group of infinitesimal holomorphic automorphisms of a completely nondegenerate cubic model surface \(Q\) of CR-type \((1,3)\) is considered. All orbits of the given action are found and their biholomorphic classification is given. One of the orbits coincides with the surface \(Q\) (the 5-dimensional orbit), two orbits are 6-dimensional
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Dynamics of Multi-Link Uncontrolled Wheeled Vehicle Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 A. V. Borisov, E. A. Mikishanina, S. V. Sokolov
Abstract In the paper, the dynamics is investigated of an uncontrolled multi-link wheeled vehicle consisting of trolleys with one wheel pair that are attached to the previous link with metal frames and are capable of rotating around their anchor points. The mechanical system under consideration is nonholonomic, since it has additional nonholonmic kinamic connections. A system of differential equations
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Supersymmetrization: AKSZ and Beyond? Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-12-22 V. Salnikov
Abstract In this paper, we describe multigraded generalizations of certain constructions useful for the mathematical understanding of gauge theories: we perform a near-at-hand generalization of the Aleksandrov–Kontsevich–Schwarz–Zaboronsky procedure; we also extend the formalism of \(Q\)-bundles first introduced by A. Kotov and T. Strobl. We compare these approaches by studying certain supersymmetric
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Diophantine Tori and Pragmatic Calculation of Quasimodes for Operators with Integrable Principal Symbol Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-09-03 A. Yu. Anikin; S. Yu. Dobrokhotov
AbstractWe study an \(h\)-pseudodifferential operator (in particular, differential) acting on the \(n\)-D physical space with a principal symbol determining an integrable Hamiltonian system and with nontrivial subprincipal symbol which destroys the integrability. We propose a pragmatic method for calculating asymptotic eigenvalues and eigenfunctions (quasimodes) of such an operator. Unlike the approach
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Some Fixed Point Theorems for $$F(\psi,\varphi)$$ -Contractions and Their Application to Fractional Differential Equations Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-09-03 H. M. Srivastava; A. Shehata; S. I. Moustafa
AbstractThe main object of this paper is to establish some fixed point results for \(F(\psi,\varphi)\)-contractions in partially-ordered metric spaces. As an application of one of these fixed point theorems, we discuss the existence of a unique solution for a coupled system of higher-order fractional differential equations with multi-point boundary conditions. The results presented in this paper are
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Index of Elliptic Boundary Value Problems Associated with Isometric Group Actions Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-09-01 A. V. Boltachev; A. Yu. Savin
AbstractGiven a compact manifold with boundary, endowed with an isometric action of a discrete group of polynomial growth, we state an index theorem for elliptic elements in the algebra of nonlocal operators generated by the Boutet de Monvel algebra of pseudodifferential boundary value problems on the manifold and the shift operators associated with the group action.
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Note on the Degenerate Gamma Function Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-09-01 T. Kim; D. S. Kim
AbstractRecently, the degenerate gamma functions were introduced as a degenerate version of the usual gamma function. In this paper, we investigate several properties of these functions. Namely, we obtain an analytic continuation as a meromorphic function on the whole complex plane, the difference formula, the values at positive integers, some expressions following from the Weierstrass and Euler formulas
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Some Lemmata on the Perturbation of the Spectrum Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-08-26 A. I. Nazarov
AbstractWe give some sufficient conditions for the preservation of the second term in the spectral asymptotics of a compact operator under the perturbation of the metrics in the Hilbert space.
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Irreducible Locally Bounded Finite-Dimensional Pseudorepresentations of Connected Locally Compact Groups Revisited Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-08-26 A. I. Shtern
AbstractThe irreducible locally bounded finite-dimensional pure pseudorepresentations of connected locally compact groups are described.
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Dynamics of Self-Excited Generators with Diverse Nonlinear Delayed Feedbacks Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-08-26 S. A. Kashchenko
AbstractA special asymptotic large parameter analysis is used to study the attractors of self-excited generators with different nonlinear delay elements. Asymptotic formulas for stable relaxation cycles and more complex attractors are derived.
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On a Time-Dependent Nonholonomic Oscillator Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-08-26 A. V. Tsiganov
AbstractIn this note, we compare the first integrals and exact solutions of equations of motion for scleronomic and rheonomic, and holonomic and nonholonomic oscillators.
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Group Classification of the System of Equations of Two-Dimensional Shallow Water over Uneven Bottom Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-08-26 A. V. Aksenov; K. P. Druzhkov
AbstractA system of equations of two-dimensional shallow water over an uneven bottom is considered. An overdetermined system of equations for finding the corresponding symmetries is obtained. The compatibility of this overdetermined system of equations is investigated. A general form of the solution of the overdetermined system is found. The kernel of the symmetry operators is found. The cases of kernel
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Asymptotic Approximations for Solutions of Sturm–Liouville Differential Equations with a Large Complex Parameter and Nonsmooth Coefficients Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-08-26 P. Malits
AbstractThis article deals with fundamental solutions of the Sturm–Liouville differential equations \(\left( P\left( x\right) y^{\prime }\right) ^{\prime }+\left( R\left( x\right) -\xi ^{2}Q\left( x\right) \right) y=0\) with a complex parameter \(\xi \), \(\left\vert \xi \right\vert \gg 1\), whose coefficients \(P\left( x\right) \) and \(Q\left( x\right) \) are positive piecewise continuous functions
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On Simple Solutions of Some Equations of Mathematical Physics Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-08-26 V. K. Beloshapka
AbstractAll solutions to the Burgers, Hopf, Helmholtz, Klein–Gordon, sine-Gordon, Schrödinger, and Monge–Ampere equations having analytical complexity one (simple solutions) are described. It turns out that all simple solutions of the Burgers and Hopf equation are represented by elementary functions. An example of a family of solutions of complexity two to the Burgers equation is presented. Simple
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On the Mixed Neumann–Robin Problem for the Elasticity System in Exterior Domains Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 H. A. Matevossian
We study the properties of generalized solutions of the mixed Neumann–Robin problem for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of this problem at infinity under the assumption that the energy integral with weight |x|a is finite for such solutions. We use the variation principle and, depending on the value of the parameter a,
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Continuous Finite-Dimensional Pseudorepresentations of SL (2,ℚ p ) with Small Defect are Trivial: a Quantitative Approach Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 A. I. Shtern
It is proved that an arbitrary continuous finite-dimensional pseudorepresentation of the group SL(2,ℚp) with sufficiently small defect is a multiple of the identity representation.
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A Note on a New Type of Degenerate Bernoulli Numbers Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 D. S. Kim; T. Kim
Studying degenerate versions of various special polynomials has became an active area of research and has yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of the polylogarithm function, the so-called degenerate polylogarithm function. Then we construct a new type of degenerate Bernoulli polynomial and number, the so-called degenerate poly-Bernoulli
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Knots in Mathematics and Medicine Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 V. P. Maslov
The analogy between knots in mathematical knot theory and “knots” in medicine is studied for the example of a certain invariant of Legendrian knots. The connection between the “Chern class” and the “Maslov class” is analyzed. A conjecture on the connection between the “Connes-Chern character” and the “Maslov class” is proposed.
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Correlation between the Hochschild Cohomology and the Eilenberg–MacLane Cohomology of Group Algebras from a Geometric Point of View Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 A. S. Mishchenko
There are two approaches to the study of the cohomology of group algebras ℝ[G]: the Eilenberg-MacLane cohomology and the Hochschild cohomology. In the case of Eilenberg-MacLane cohomology, one has the classical cohomology of the classifying space BG. The Hochschild cohomology represents a more general construction, in which the so-called two-sided bimodules are considered. The Hochschild cohomology
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Evolution of Perturbations Imposed on 1D Unsteady Shear in a Viscous Half-Plane with Oscillating Boundary Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 D. V. Georgievskii; V. G. Putkaradze
We study unsteady shear flows realized in a half-plane with viscous incompressible fluid, where the law of motion of the boundary oscillating along itself is given. Either the longitudinal velocity of the boundary or the shear stress on it can be specified. The statement of the linearized problem with respect to small initial perturbations imposed on the kinematics in the entire half-plane is presented
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How to Estimate Past Quantum Measurement Interventions After Continuous Monitoring Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 J. Gough
We analyze the problem of estimating past quantum states of a monitored system from a mathematical perspective in order to ensure self-consistency with the principle of quantum nondemolition. Despite several claims of “measuring noncommuting observables” in the physics literature, we show that we are always measuring commuting processes. Our main interest is in the notion of quantum smoothing, or retrodiction
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Uniform Formulas for the Asymptotic Solution of a Linear Pseudodifferential Equation Describing Water Waves Generated by a Localized Source Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 S. Yu. Dobrokhotov; V. E. Nazaikinskii; A. A. Tolchennikov
We consider the Cauchy problem with localized initial data for a linear pseudodifferential equation describing water waves with dispersion taken into account and obtain a uniform asymptotic solution in a neighborhood of regular points of the wave front, the size of the neighborhood being independent of the small parameters occurring in the problem.
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Dynamic Response Analysis of Fractionally-Damped Generalized Bagley–Torvik Equation Subject to External Loads Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 H. M. Srivastava; Rajarama Mohan Jena; Snehashish Chakraverty; Subrat Kumar Jena
This article deals with the solution of a fractionally-damped generalized Bagley–Torvik (BT) equation whose damping characteristics are well-defined by means of the fractional derivative (FD) of the Riemann–Liouville and the Liouville–Caputo types. The Ho-motopy Analysis Method (HAM) is implemented for computing the dynamic response (DR) analysis. Two external forces or loads (namely, the unit step
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The Variational Factors Problem for Systems of Equations Written in an Extended Kovalevskaya Form Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 K. P. Druzhkov
In the paper, a solution to the variational factors problem for systems of equations written in an extended Kovalevskaya form is given. The solution is presented locally in a coordinate form.
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Short-Wave Asymptotic Solutions of the Wave Equation with Localized Perturbations of the Velocity Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 A. I. Allilueva; A. I. Shafarevich
To describe the propagation of waves in media containing localized rapidly changing inhomogeneities (e.g., narrow underwater ridges or pycnoclines in the ocean, layers with sharply changing optical or acoustic density, etc.), it is natural to use the wave equation with a small parameter characterizing the ratio of the scales of the localized inhomogeneity and of the general change of velocity (e.g
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Arithmetic Properties of Generalized Hypergeometric F -Series Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 V. G. Chirskii
In the paper, using a generalization of the Siegel-Shidlovskii method in the theory of transcendental numbers, we prove the infinite algebraic independence of elements, generated by generalized hypergeometric series, of direct products of the fields of \(\mathbb{K}_v\)-completions of an algebraic number field\(\mathbb{K}\) of finite degree over the field of rational numbers with respect to a valuation
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New Zeta Functions of Reidemeister Type and the Twisted Burnside–Frobenius Theory Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 A. Fel’shtyn; E. Troitsky; M. Ziętek
We introduce new zeta functions related to an endomorphism ϕ of a discrete group Γ. They are of two types: counting numbers of fixed (ρ ~ ρ o ϕn) irreducible representations for iterations of ϕ from an appropriate dual space of Γ and counting Reidemeister numbers R(φn) of different compactifications. Many properties of these functions and their coefficients are obtained. In many cases, it is proved
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CR -Manifolds of Finite Bloom–Graham Type: the Model Surface Method Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-05-31 V. K. Beloshapka
In the paper, the model surface method is applied to arbitrary CR-manifolds of finite Bloom–Graham type. A family of basic assertions is proved. It is proved also that, for a model surface, the condition that the Bloom–Graham type is constant is a criterion for holomorphic homogeneity. Distinctions from the case of rigid models treated earlier are clarifies. A series of questions and conjectures is
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Almost Connected DMAP Groups Are FIR Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 A. I. Shtern
Let DMAP be the class of locally compact groups that admit a (not necessarily continuous) embedding in a compact topological group, and let FIR be the class of locally compact groups all of whose continuous irreducible unitary representations are finite-dimensional. We prove that every almost connected DMAP group is an FIR group.
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A Family of Theta-Function Identities Related to Jacobi’s Triple-Product Identity Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 H. M. Srivastava; M. P. Chaudhary; S. Chaudhary
The main object of this paper is to present a family of q-series identities which involve some of the theta functions of Jacobi and Ramanujan. Each of these (presumably new) q-series identities reveals interesting relationships among three of the theta-type functions which stem from the celebrated Jacobi’s triple-product identity in a remarkably simple way. The q-results presented in this paper are
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Reduced Dynamics of the Wigner Function Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 M. O. Burkatskii
In the paper, we derive a formula expressing the reduced dynamics of the Wigner function using the dynamics of the Wigner function of a larger system. Here the latter system is assumed to be isolated and generating the dynamics of its subsystem.
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A Note on Central Bell Numbers and Polynomials Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 T. Kim; D. S. Kim
The central factorial numbers of the second kind appear in the expansion of powers of x in terms of the central factorial sequence. In this paper, we introduce the central Bell numbers and polynomials associated with those central factorial numbers of the second kind and investigate some identities and properties of them.
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Schrödinger Equation with Signed Hamiltonian Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 A. A. Loboda
A functional integral with respect to the Wiener measure that represents a solution of the Schrödinger equation with signed Hamiltonian is obtained. In turn, this integral is derived, using the analytic continuation with respect to the argument, from a similar integral for the corresponding heat equation.
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Semi-Classical Limit and Least Action Principle Revisited with (min,+) Path Integral and Action-Particle Duality Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 A. Kenoufi; M. Gondran; A. Gondran
One shows that the Feynman’s Path Integral designed for quantum mechanics has an analogous in classical mechanics, the so-called (min, +) Path Integral. This former is build on (min, +)-algebra and (min, +)-analysis which permit to handle in a linear way non-linear problems occurring in mathematical physics. The Hamilton-Jacobi equations and their solutions within this mathematical framework, are introduced
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Maslov’s Model of Stationary Cooling, Overheating, and Energy Localization in an Accident Reactor Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 I. A. Molotkov
We study a nonlinear problem of gas filtration in a porous and weakly conducting medium that is used to model the overheating process in reactors. We obtain explicit estimates for the critical values of the similarity parameter of the problem which determine a condition for the existence of a steady-state cooling regime for a system open to atmosphere and a condition for global overheating. The bifurcation
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Mathematical Quantum Yang—Mills Theory Revisited II: Mass without Mass Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 A. Dynin
Massless Dirac equation for spinor multiplets is minimally coupled with a unitary representation of an arbitrary compact semisimple gauge group. The spectrum of the quantized coupled Dirac Hamiltonian has a positive mass gap running along the classical energy scale.
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Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. II Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 A. V. Borisov; E. V. Vetchanin; I. S. Mamaev
This paper considers the plane-parallel motion of an elliptic foil in a fluid with a nonzero constant circulation under the action of external periodic forces and torque. The existence of the first integral is shown for the case in which there is no external torque and an external force acts along one of the principal axes of the foil. It is shown that, in the general case, in the absence of friction
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Creation, Annihilation, and Interaction of Delta-Waves in Nonlinear Models: a Distributional Product Approach Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 C. O. R. Sarrico; A. Paiva
Using a solution concept defined in the setting of a product of distributions, we consider the nonlinear equation f(t)ut + (u2)x = 0, where f is a continuous function. This equation can be regarded a generalization of Burgers inviscid equation and allows to study several kinds of interaction of δ-waves. If f(t) ≠ 0 for all t, collisions of δ-waves cannot exist. If f(t) = 0 for certain values of t,
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Trace Formulas for Schrödinger Operators with Complex Potentials Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 E. Korotyaev
We consider 3-dimensonal Schrödinger operators with complex potential. We obtain new trace formulas with new terms, associated with singular measure. In order to prove these results, we study analytic properties of a modified Fredholm determinant as a function from Hardy spaces in the upper half-plane. In fact, we reformulate spectral theory problems as problems of analytic functions from Hardy spaces
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Asymptotics of the Propagation Problem for Linear Waves on a Two-Dimensional Lattice and Modified Maslov’s Canonical Operator Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 V. V. Grushin; S. A. Sergeev
In the paper, the problem of propagation of waves generated by localized source on a two-dimensional lattice is studied. The discrete problem is reduced to a continuous Cauchy problem, and the answer for this problem is constructed using the modified Maslov’s canonical operator, including a neighborhood of the leading wave front. The strong and weak dispersion effects depending on the relationship
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Asymptotic Series for a Feynman Integral in the One-Dimensional Case Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 T. Yu. Semenova
In the one-dimensional case, an asymptotic expansion with respect to the parameter for the Feynman integral in the Lee—Pomeransky representation, is obtained. The previously stated conjecture on how to obtain asymptotic series is proved, and the form of the terms of the series and the relationship of the series with Newton’s polyhedron of the polynomial participating in the integrand are determined
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On Operators with Closed Range and Semi-Fredholm Operators Over W *-Algebras Russ. J. Math. Phys. (IF 1.292) Pub Date : 2020-03-20 S. Ivković
In this paper, we consider \({\mathcal A}\)-Fredholm and semi-\({\mathcal A}\)-Fredholm operators on Hilbert C*-modules over a W*-algebra \({\mathcal A}\) defined in [3] and [9]. Using the assumption that \({\mathcal A}\) is a W*-algebra (rather than an arbitrary C*-algebra), we obtain a generalization of Schechter—Lebow characterization of semi-Fredholm operators and a generalization of the “punctured
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Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. I Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 A. V. Borisov; E. V. Vetchanin; I. S. Mamaev
A plane-parallel motion of a circular foil is considered in a fluid with a nonzero constant circulation under the action of external periodic force and torque. Various integrable cases are treated. Conditions for the existence of resonances of two types are found. In the case of resonances of the first type, the phase trajectory of the system and the trajectory of the foil are unbounded. In the case
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On the Transfer of the Wiener Measure to the Set of Continuous Trajectories in the Heisenberg Group Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 S. V. Mamon
In the paper, problems related to the theory of stochastic processes on nilpotent Lie groups are studied. In particular, a stochastic process on the Heisenberg group H3(ℝ) is considered such that the trajectories of this process, in the stochastic sense, satisfy the horizontality conditions with respect to the standard contact structure on H3(ℝ). The main result claims that the measure defined on the
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Roe Bimodules as Morphisms of Discrete Metric Spaces Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 V. M. Manuilov
For two discrete metric spaces X and Y, we consider metrics on X ⊔ Y compatible with the metrics on X and Y. As morphisms from X to Y, we consider Roe bimodules, i.e., the norm closures of bounded finite propagation operators from l2(X) to l2(Y). We study the corresponding category \(\mathcal{M}\), which is also a 2-category. We show that almost isometries determine morphisms in \(\mathcal{M}\). We
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Stationary-Phase Method for Hankel Transform of Order Zero Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 S. A. Stepin; A. G. Tarasov
The stationary phase method is applied to investigate the asymptotic behavior at infinity of the Hankel transform of order zero.
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Connected Lie Groups Admitting an Embedding in a Connected Amenable Lie Group Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 A. I. Shtern
The main result is that a Lie group admitting a (not necessarily continuous) embedding in an amenable Lie group is amenable.
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On the Notions of Hole and Vacuum in Mathematics and in the Humanities Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 V. P. Maslov
The notions of “hole” and “vacuum” in various branches of science are considered. A philosophical generalization of these notions on the basis of examples from physics, history, and linguistics is presented. Some aspects of the further development of these notions in mathematical logic, thermodynamics of nuclear matter, and other branches of science are sketched.
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Remarks on Asymptotic Solutions of Linearized Equations of Relativistic Hydrodynamics Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 A. I. Allilueva; A. I. Shafarevich
In the present note, we show that, for some special classes of external flows, the short-wave asymptotic behavior of the solution of linearized equations of relativistic gas dynamics can be described rather explicitly.
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Sobolev Problems with Spherical Mean Conditions and Traces of Quantized Canonical Transformations Russ. J. Math. Phys. (IF 1.292) Pub Date : 2019-12-10 V. E. Nazaikinskii; A. Yu. Savin; P. A. Sipailo
We consider Sobolev problems (problems for an elliptic operator on a closed manifold with conditions on a closed submanifold) for the case in which these conditions are of nonlocal nature and include weighted spherical means of the unknown function over spheres of a given radius. For such problems, we establish a criterion for the Fredholm property and, in some special cases, obtain index formulas
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