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Probabilistic Degenerate Bell Polynomials Associated with Random Variables 与随机变量相关的概率退化贝尔多项式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S106192082304009X
T. Kim, D. S. Kim
{"title":"Probabilistic Degenerate Bell Polynomials Associated with Random Variables","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S106192082304009X","DOIUrl":"10.1134/S106192082304009X","url":null,"abstract":"<p> The aim of this paper is to study probabilistic versions of the degenerate Stirling numbers of the second kind and the degenerate Bell polynomials, namely the probabilisitc degenerate Stirling numbers of the second kind associated with <span>(Y)</span> and the probabilistic degenerate Bell polynomials associated with <span>(Y)</span>, which are also degenerate versions of the probabilisitc Stirling numbers of the second and the probabilistic Bell polynomials considered earlier. Here <span>(Y)</span> is a random variable whose moment generating function exists in some neighborhood of the origin. We derive some properties, explicit expressions, certain identities and recurrence relations for those numbers and polynomials. In addition, we treat the special cases that <span>(Y)</span> is the Poisson random variable with parameter <span>(alpha (&gt;0))</span> and the Bernoulli random variable with probability of success <span>(p)</span>. </p><p> <b> DOI</b> 10.1134/S106192082304009X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"528 - 542"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flow Around a Curved Plate with Small Periodic Irregularities: a Double-Deck Boundary Layer 小周期不规则曲面板周围的流动：双层边界层
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040040
V. G. Danilov, A. M. Glazunova
{"title":"Flow Around a Curved Plate with Small Periodic Irregularities: a Double-Deck Boundary Layer","authors":"V. G. Danilov,&nbsp;A. M. Glazunova","doi":"10.1134/S1061920823040040","DOIUrl":"10.1134/S1061920823040040","url":null,"abstract":"<p> In this paper, equations describing a double-dimensional flow along a curved smooth plate with small periodic irregularities are derived. The parameters of the irregularities are chosen so that the flow has a double-deck structure. The equations describing the terms of the asymptotic solution are written in the original coordinate system, which required changes in the form of the usual ansatz. </p><p> <b> DOI</b> 10.1134/S1061920823040040 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"453 - 465"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Mean Square of the Pauli–Jordan–Dirac Anticommutator With Respect to Spatial Variables 相对于空间变量的保利-乔丹-狄拉克反调和器均方差
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040088
E.A. Karatsuba
{"title":"The Mean Square of the Pauli–Jordan–Dirac Anticommutator With Respect to Spatial Variables","authors":"E.A. Karatsuba","doi":"10.1134/S1061920823040088","DOIUrl":"10.1134/S1061920823040088","url":null,"abstract":"<p> The Pauli–Jordan–Dirac anticommutator mean-square formula is presented. </p><p> <b> DOI</b> 10.1134/S1061920823040088 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"522 - 527"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems 周期性双曲系统同质化的特洛特-卡托定理主题变奏曲
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S106192082304012X
Yu.M. Meshkova
{"title":"Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems","authors":"Yu.M. Meshkova","doi":"10.1134/S106192082304012X","DOIUrl":"10.1134/S106192082304012X","url":null,"abstract":"<p> In <span>(L_2(mathbb{R}^d;mathbb{C}^n))</span>, we consider a matrix elliptic second order differential operator <span>(B_varepsilon &gt;0)</span>. Coefficients of the operator <span>(B_varepsilon)</span> are periodic with respect to some lattice in <span>(mathbb{R}^d)</span> and depend on <span>(mathbf{x}/varepsilon)</span>. We study the quantitative homogenization for the solutions of the hyperbolic system <span>(partial _t^2mathbf{u}_varepsilon =-B_varepsilonmathbf{u}_varepsilon)</span>. In operator terms, we are interested in approximations of the operators <span>(cos (tB_varepsilon ^{1/2}))</span> and <span>(B_varepsilon ^{-1/2}sin (tB_varepsilon ^{1/2}))</span> in suitable operator norms. Approximations for the resolvent <span>(B_varepsilon ^{-1})</span> have been already obtained by T.A. Suslina. So, we rewrite hyperbolic equation as a system for the vector with components <span>(mathbf{u}_varepsilon )</span> and <span>(partial _tmathbf{u}_varepsilon)</span>, and consider the corresponding unitary group. For this group, we adapt the proof of the Trotter-Kato theorem by introduction of some correction term and derive hyperbolic results from elliptic ones. </p><p> <b> DOI</b> 10.1134/S106192082304012X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"561 - 598"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytic Solution of the System of Integro-Differential Equations for the Plasma Model in an External Field 外场等离子体模型积分微分方程系的解析解
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040039
S.I. Bezrodnykh, N.M. Gordeeva
{"title":"Analytic Solution of the System of Integro-Differential Equations for the Plasma Model in an External Field","authors":"S.I. Bezrodnykh,&nbsp;N.M. Gordeeva","doi":"10.1134/S1061920823040039","DOIUrl":"10.1134/S1061920823040039","url":null,"abstract":"<p> We study a system of two integro-differential equations that arises as the result of linearization of Boltzmann–Maxwell’s kinetic equations, where the collision integral is chosen in the Bhatnagar–Gross–Krook approximation, and the unperturbed state of the plasma is characterized by the Fermi–Dirac distribution. The unknown functions are the linear parts of the perturbations of the distribution function of the charged particles and the electric field strength in plasma. In the paper, an analytical representation for the general solution of this system is found. When deriving this representation, some new results were applied to Fourier transforms of distributions (generalized functions). </p><p> <b> DOI</b> 10.1134/S1061920823040039 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"443 - 452"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rectilinear Vortex Thread in a Radially Nonhomogeneous Bingham Solid 径向非均匀Bingham固体中的直线涡旋螺纹
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030019
V. A. Banko, D. V. Georgievskii
{"title":"Rectilinear Vortex Thread in a Radially Nonhomogeneous Bingham Solid","authors":"V. A. Banko,&nbsp;D. V. Georgievskii","doi":"10.1134/S1061920823030019","DOIUrl":"10.1134/S1061920823030019","url":null,"abstract":"<p> We study an initial boundary value problem of axially symmetric one-dimensional unsteady shear in the viscoplastic space (a Bingham solid) initiated by a rectilinear vortex thread located along the symmetry axis. The force intensity of the thread is represented by a given monotone piecewise continuous function of time. The density and the dynamical viscosity of the medium are constant, and the yield point is a given piecewise continuous function of radius. We find similar and quasisimilar expressions for the tangent stress and for the rotating component of the velocity both in viscoplastic shear domains and in rigid zones. We show that the vortex thread with time-bounded force intensity may generate a viscoplastic shear only inside a cylinder of certain radius. If the thread intensity growth linearly with time, then the radius of the shear domain grows proportionally to <span>(sqrt t)</span>. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"275 - 279"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4230924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Monodromization and a ( mathcal{P} mathcal{T} )-Symmetric Nonself-Adjoint Quasi-Periodic Operator 一元化与( mathcal{P} mathcal{T} ) -对称非自伴随拟周期算子
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030032
D. I. Borisov, A. A. Fedotov
{"title":"Monodromization and a ( mathcal{P} mathcal{T} )-Symmetric Nonself-Adjoint Quasi-Periodic Operator","authors":"D. I. Borisov,&nbsp;A. A. Fedotov","doi":"10.1134/S1061920823030032","DOIUrl":"10.1134/S1061920823030032","url":null,"abstract":"<p> We study the operator acting in <span>(L_2(mathbb{R}))</span> by the formula <span>(( mathcal{A} psi)(x)=psi(x+omega)+psi(x-omega)+ lambda e^{-2pi i x} psi(x))</span>, where <span>(xinmathbb R)</span> is a variable, and <span>(lambda&gt;0)</span> and <span>(omegain(0,1))</span> are parameters. It is related to the simplest quasi-periodic operator introduced by P. Sarnak in 1982. We investigate <span>( mathcal{A} )</span> using the monodromization method, the Buslaev–Fedotov renormalization approach, which arose when trying to extend the Bloch–Floquet theory to difference equations on <span>( mathbb{R} )</span>. Within this approach, the analysis of <span>( mathcal{A} )</span> turns out to be very natural and transparent. We describe the geometry of the spectrum and calculate the Lyapunov exponent. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"294 - 309"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4232890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Real Submanifolds of (mathbf{C}^2) With Singularities 具有奇点的(mathbf{C}^2)的实子流形
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030020
V. K. Beloshapka
{"title":"Real Submanifolds of (mathbf{C}^2) With Singularities","authors":"V. K. Beloshapka","doi":"10.1134/S1061920823030020","DOIUrl":"10.1134/S1061920823030020","url":null,"abstract":"<p> We consider real submanifolds of <span>(mathbf{C}^2)</span> with singularities of three types: <span>(RC)</span>-singular 2 - dimensional surfaces, real quadratic cones, and hypersurfaces with degeneration of the Levi form. The holomorphic automorphisms of singular germs are evaluated. We also discuss resolution of singularities in the context of <span>(mathit{CR})</span> geometry. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"280 - 293"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localized Waves Propagating Along an Angular Junction of Two Thin Semi-Infinite Elastic Membranes Terminating an Acoustic Medium 沿两个半无限薄弹性膜的角交界处传播的局域波终止于声介质
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030068
M. A. Lyalinov
{"title":"Localized Waves Propagating Along an Angular Junction of Two Thin Semi-Infinite Elastic Membranes Terminating an Acoustic Medium","authors":"M. A. Lyalinov","doi":"10.1134/S1061920823030068","DOIUrl":"10.1134/S1061920823030068","url":null,"abstract":"<p> We study the existence of localized waves that can propagate in an acoustic medium bounded by two thin semi-infinite elastic membranes along their common edge. The membranes terminate an infinite wedge that is filled by the medium, and are rigidly connected at the points of their common edge. The acoustic pressure of the medium in the wedge satisfies the Helmholtz equation and the third-order boundary conditions on the bounding membranes as well as the other appropriate conditions like contact conditions at the edge. The existence of such localized waves is equivalent to existence of the discrete spectrum of a semi-bounded self-adjoint operator attributed to this problem. In order to compute the eigenvalues and eigenfunctions, we make use of an integral representation (of the Sommerfeld type) for the solutions and reduce the problem to functional equations. Their nontrivial solutions from a relevant class of functions exist only for some values of the spectral parameter. The asymptotics of the solutions (eigenfunctions) is also addressed. The far-zone asymptotics contains exponentially vanishing terms. The corresponding solutions exist only for some specific range of physical and geometrical parameters of the problem at hand. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"345 - 359"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Whitney–Sullivan Constructions for Transitive Lie Algebroids–Smooth Case 传递李代数群的Whitney-Sullivan构造-光滑情况
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S106192082303007X
A. S. Mishchenko, J. R. Oliveira
{"title":"Whitney–Sullivan Constructions for Transitive Lie Algebroids–Smooth Case","authors":"A. S. Mishchenko,&nbsp;J. R. Oliveira","doi":"10.1134/S106192082303007X","DOIUrl":"10.1134/S106192082303007X","url":null,"abstract":"<p> Let <span>(M)</span> be a smooth manifold, smoothly triangulated by a simplicial complex <span>(K)</span>, and <span>( {cal A} )</span> a transitive Lie algebroid on <span>(M)</span>. A piecewise smooth form on <span>( {cal A} )</span> is a family <span>(omega=(omega_{Delta})_{Deltain K})</span> such that <span>(omega_{Delta})</span> is a smooth form on the Lie algebroid restriction of <span>( {cal A} )</span> to <span>(Delta)</span>, satisfying the compatibility condition concerning the restrictions of <span>(omega_{Delta})</span> to the faces of <span>(Delta)</span>, that is, if <span>(Delta')</span> is a face of <span>(Delta)</span>, the restriction of the form <span>(omega_{Delta})</span> to the simplex <span>(Delta')</span> coincides with the form <span>(omega_{Delta'})</span>. The set <span>(Omega^{ast}( {cal A} ;K))</span> of all piecewise smooth forms on <span>( {cal A} )</span> is a cochain algebra. There exists a natural morphism </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"360 - 374"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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