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Russian Journal of Mathematical Physics最新文献

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On Some Degenerate Differential and Degenerate Difference Operators 关于一些退化微分算子和退化差分算子
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2022-03-23 DOI: 10.1134/S1061920822010046
T. Kim, D. S. Kim
{"title":"On Some Degenerate Differential and Degenerate Difference Operators","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S1061920822010046","DOIUrl":"10.1134/S1061920822010046","url":null,"abstract":"<p> The aim of this paper is to make use of certain degenerate differential and degenerate difference operators in order to study some identities involving the degenerate harmonic numbers, certain finite sums of general nature, the sums of the values of the generalized falling factorials at consecutive positive integers, and the degenerate Laguerre polynomials. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"29 1","pages":"37 - 46"},"PeriodicalIF":1.4,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4901666","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: 30
Structurally Stable Nondegenerate Singularities of Integrable Systems 可积系统的结构稳定非退化奇异性
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2022-03-23 DOI: 10.1134/S106192082201006X
E. A. Kudryavtseva, A. A. Oshemkov
{"title":"Structurally Stable Nondegenerate Singularities of Integrable Systems","authors":"E. A. Kudryavtseva,&nbsp;A. A. Oshemkov","doi":"10.1134/S106192082201006X","DOIUrl":"10.1134/S106192082201006X","url":null,"abstract":"<p> In this paper, we study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a nondegenerate singular fiber satisfying the so-called connectedness condition is structurally stable under (small enough) real-analytic integrable perturbations of the system. In other words, the topology of the fibration in a neighborhood of such a fiber is preserved after any such perturbation. As an illustration, we show that a simple saddle-saddle singularity of the Kovalevskaya top is structurally stable under real-analytic integrable perturbations and not structurally stable under <span>(C^infty)</span>-smooth integrable perturbations. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"29 1","pages":"57 - 75"},"PeriodicalIF":1.4,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4901806","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: 1
Integrable Hamiltonian Systems on the Symplectic Realizations of (textbf{e}(3)^*) 的辛实现上的可积哈密顿系统 (textbf{e}(3)^*)
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2022-03-23 DOI: 10.1134/S1061920822010095
A. Odzijewicz, E. Wawreniuk
{"title":"Integrable Hamiltonian Systems on the Symplectic Realizations of (textbf{e}(3)^*)","authors":"A. Odzijewicz,&nbsp;E. Wawreniuk","doi":"10.1134/S1061920822010095","DOIUrl":"10.1134/S1061920822010095","url":null,"abstract":"<p> The phase space of a gyrostat with a fixed point and a heavy top is the Lie–Poisson space <span>(textbf{e}(3)^*cong mathbb{R}^3times mathbb{R}^3)</span> dual to the Lie algebra <span>(textbf{e}(3))</span> of the Euclidean group <span>(E(3))</span>. One has three naturally distinguished Poisson submanifolds of <span>(textbf{e}(3)^*)</span>: (i) the dense open submanifold <span>(mathbb{R}^3times dot{mathbb{R}}^3subset textbf{e}(3)^*)</span> which consists of all <span>(4)</span>-dimensional symplectic leaves (<span>(vec{Gamma}^2&gt;0)</span>); (ii) the <span>(5)</span>-dimensional Poisson submanifold of <span>(mathbb{R}^3times dot{mathbb{R}}^3)</span> defined by <span>(vec{J}cdot vec{Gamma} = mu ||vec{Gamma}||)</span>; (iii) the <span>(5)</span>-dimensional Poisson submanifold of <span>(mathbb{R}^3times dot{mathbb{R}}^3)</span> defined by <span>(vec{Gamma}^2 = nu^2)</span>, where <span>(dot{mathbb{R}}^3:= mathbb{R}^3backslash {0})</span>, <span>((vec{J}, vec{Gamma})in mathbb{R}^3times mathbb{R}^3cong textbf{e}(3)^*)</span> and <span>(nu &lt; 0 )</span>, <span>(mu)</span> are some fixed real parameters. Using the <span>(U(2,2))</span>-invariant symplectic structure of Penrose twistor space we find full and complete <span>(E(3))</span>-equivariant symplectic realizations of these Poisson submanifolds which are <span>(8)</span>-dimensional for (i) and <span>(6)</span>-dimensional for (ii) and (iii). As a consequence of the above, Hamiltonian systems on <span>(textbf{e}(3)^*)</span> lift to Hamiltonian systems on the above symplectic realizations. In this way, after lifting the integrable cases of a gyrostat with a fixed point and of a heavy top, we obtain a large family of integrable Hamiltonian systems on the phase spaces defined by these symplectic realizations. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"29 1","pages":"91 - 114"},"PeriodicalIF":1.4,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4904429","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
On the Inverse Semigroup of Bimodules over a (C^*)-Algebra 关于(C^*) -代数上双模的逆半群
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2022-03-23 DOI: 10.1134/S1061920822010071
V. M. Manuilov
{"title":"On the Inverse Semigroup of Bimodules over a (C^*)-Algebra","authors":"V. M. Manuilov","doi":"10.1134/S1061920822010071","DOIUrl":"10.1134/S1061920822010071","url":null,"abstract":"<p> It was noticed recently that, given a metric space <span>((X,d_X))</span>, the equivalence classes of metrics on the disjoint union of the two copies of <span>(X)</span> coinciding with <span>(d_X)</span> on each copy form an inverse semigroup <span>(M(X))</span> with respect to concatenation of metrics. Now put this inverse semigroup construction in a more general context, namely, we define, for a <span>(C^*)</span>-algebra <span>(A)</span>, an inverse semigroup <span>(S(A))</span> of Hilbert <span>(C^*)</span>-<span>(A)</span>-<span>(A)</span>-bimodules. When <span>(A)</span> is the uniform Roe algebra <span>(C^*_u(X))</span> of a metric space <span>(X)</span>, we construct a mapping <span>(M(X)to S(C^*_u(X)))</span> and show that this mapping is injective, but not surjective in general. This allows to define an analog of the inverse semigroup <span>(M(X))</span> that does not depend on the choice of a metric on <span>(X)</span> within its coarse equivalence class. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"29 1","pages":"76 - 80"},"PeriodicalIF":1.4,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4901667","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
Bifurcations of Essential Spectra Generated by a Small Non-Hermitian Hole. I. Meromorphic Continuations 非厄米小洞产生的基本光谱的分岔。1 .亚纯延拓
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2021-12-06 DOI: 10.1134/S1061920821040026
D. I. Borisov, D. A. Zezyulin
{"title":"Bifurcations of Essential Spectra Generated by a Small Non-Hermitian Hole. I. Meromorphic Continuations","authors":"D. I. Borisov,&nbsp;D. A. Zezyulin","doi":"10.1134/S1061920821040026","DOIUrl":"10.1134/S1061920821040026","url":null,"abstract":"<p> This paper focuses on bifurcations that occur in the essential spectrum of certain non-Hermitian operators. We consider the eigenvalue problem for a self-adjoint elliptic differential operator in a multidimensional tube-like domain which is infinite along one dimension and can be bounded or unbounded in other dimensions. This self-adjoint eigenvalue problem is perturbed by a small hole cut out of the domain. The boundary of the hole is described by a non-Hermitian Robin-type boundary condition. The main result of the present paper states the existence and describes the properties of local meromorphic continuations of the resolvent of the operator in question through the essential spectrum. The continuations are constructed near the edge of the spectrum and in the vicinity of certain internal threshold points of the spectrum. Then we define the eigenvalues and resonances of the operator as the poles of these continuations and prove that both the edge and the internal thresholds bifurcate into eigenvalues and/or resonances. The total multiplicity of the eigenvalues and resonances bifurcating from internal thresholds can be up to twice larger than the multiplicity of the thresholds. In other words, the perturbation can increase the total multiplicity. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"28 4","pages":"416 - 433"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4245685","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: 2
Asymptotics of the Number of Endpoints of a Random Walk on a Certain Class of Directed Metric Graphs 一类有向度量图上随机游走端点数的渐近性
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2021-12-06 DOI: 10.1134/S1061920821040038
V. L. Chernyshev, A. A. Tolchennikov
{"title":"Asymptotics of the Number of Endpoints of a Random Walk on a Certain Class of Directed Metric Graphs","authors":"V. L. Chernyshev,&nbsp;A. A. Tolchennikov","doi":"10.1134/S1061920821040038","DOIUrl":"10.1134/S1061920821040038","url":null,"abstract":"<p> A certain class of directed metric graphs is considered. The asymptotics for a number of possible endpoints of a random walk at large times is found. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"28 4","pages":"434 - 438"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4245686","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: 2
Asymptotics of Multiple Orthogonal Hermite Polynomials (H_{n_1,n_2}(z,alpha)) Determined by a Third-Order Differential Equation 由三阶微分方程确定的多个正交埃尔米特多项式(H_{n_1,n_2}(z,alpha))的渐近性
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2021-12-06 DOI: 10.1134/S106192082104004X
S. Yu. Dobrokhotov, A. V. Tsvetkova
{"title":"Asymptotics of Multiple Orthogonal Hermite Polynomials (H_{n_1,n_2}(z,alpha)) Determined by a Third-Order Differential Equation","authors":"S. Yu. Dobrokhotov,&nbsp;A. V. Tsvetkova","doi":"10.1134/S106192082104004X","DOIUrl":"10.1134/S106192082104004X","url":null,"abstract":"<p> In the paper, we study the asymptotics of multiple orthogonal Hermite polynomials <span>(H_{n_1,n_2}(z,alpha))</span> that are determined by orthogonality relations with respect to two weights that are Gaussian exponents with shifted maxima. These polynomials can be defined using recurrence relations, and also, as shown by A. I. Aptekarev, A. Branquinho, and W. Van Assche, as certain solutions to a third-order differential equation. Starting from this differential equation, we obtain asymptotics of such polynomials as <span>(|n|=sqrt{n_1^2+n_2^2} rightarrow infty)</span> in the form of the Airy function <span>({rm Ai})</span> and its derivative <span>({rm Ai}')</span> of a compound argument. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"28 4","pages":"439 - 454"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4244902","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
Two-Dimensional Dirac Operators with Interactions on Unbounded Smooth Curves 无界光滑曲线上具有相互作用的二维Dirac算子
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2021-12-06 DOI: 10.1134/S1061920821040105
V. Rabinovich
{"title":"Two-Dimensional Dirac Operators with Interactions on Unbounded Smooth Curves","authors":"V. Rabinovich","doi":"10.1134/S1061920821040105","DOIUrl":"10.1134/S1061920821040105","url":null,"abstract":"<p> We consider the 2D Dirac operator with singular potentials </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"28 4","pages":"524 - 542"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4245687","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: 6
Spectral Analysis for Some Multifractional Gaussian Processes 一些多分数高斯过程的谱分析
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2021-12-06 DOI: 10.1134/S1061920821040075
A. I. Karol, A. I. Nazarov
{"title":"Spectral Analysis for Some Multifractional Gaussian Processes","authors":"A. I. Karol,&nbsp;A. I. Nazarov","doi":"10.1134/S1061920821040075","DOIUrl":"10.1134/S1061920821040075","url":null,"abstract":"<p> We study the small ball asymptotics problem in <span>(L_2)</span> for two generalizations of the fractional Brownian motion with variable Hurst parameter. To this end, we perform a careful analysis of the singular value asymptotics for associated integral operators. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"28 4","pages":"488 - 500"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4244903","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: 1
Analytic Solutions of the Cylindrical Heat Equation with a Heat Source 带热源圆柱热方程的解析解
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2021-12-06 DOI: 10.1134/S1061920821040129
H. M. Srivastava, K.-Y. Kung, S.-F. Lee, S.-D. Lin
{"title":"Analytic Solutions of the Cylindrical Heat Equation with a Heat Source","authors":"H. M. Srivastava,&nbsp;K.-Y. Kung,&nbsp;S.-F. Lee,&nbsp;S.-D. Lin","doi":"10.1134/S1061920821040129","DOIUrl":"10.1134/S1061920821040129","url":null,"abstract":"<p> In this article, the superposition and the separation of variables methods are applied in order to investigate the analytical solutions of a heat conduction equation in cylindrical coordinates. The structures of the transient temperature and the heat transfer distributions are summed up for a direct mix of the results of the Fourier–Bessel series of the exponential type for the partial differential equation which we investigate here. Relevant connections of the results, which we have presented in this article, with those in some other closely-related earlier works are also indicated. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"28 4","pages":"545 - 552"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4243987","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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