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Russian Journal of Mathematical Physics最新文献

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Uniform Spectral Asymptotics for a Schrödinger Operator on a Segment with Delta-Interaction 具有三角交互作用的段上薛定谔算子的均匀谱渐近线
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020018
D.I. Borisov, D.M. Polyakov
{"title":"Uniform Spectral Asymptotics for a Schrödinger Operator on a Segment with Delta-Interaction","authors":"D.I. Borisov,&nbsp;D.M. Polyakov","doi":"10.1134/S1061920824020018","DOIUrl":"10.1134/S1061920824020018","url":null,"abstract":"<p> We consider a Schrödinger operator on the segment <span>((0,1))</span> subject to the Dirichlet condition and perturb it by a delta-potential concentrated at the point <span>(x= varepsilon )</span>, where <span>( varepsilon )</span> is a small positive parameter. We show that the perturbed operator converges to the unperturbed one in the norm resolvent sense and this also implies the convergence of the spectrum. However, the latter convergence is true only inside each compact set on the complex plane and it does not characterize the behavior of the total ensemble of the eigenvalues under the perturbation. Our main result is the spectral asymptotics for the eigenvalues of the perturbed operator with an estimate for the error term uniform in the small parameter. This asymptotics involves an additional nonstandard term, which allows us to describe a global behavior of the total ensemble of the eigenvalues under the perturbation. </p><p> <b> DOI</b> 10.1134/S1061920824020018 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"149 - 161"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504355","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
Semiclassical Asymptotics on Stratified Manifolds 分层流形上的半经典渐近论
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020110
V.E. Nazaikinskii
{"title":"Semiclassical Asymptotics on Stratified Manifolds","authors":"V.E. Nazaikinskii","doi":"10.1134/S1061920824020110","DOIUrl":"10.1134/S1061920824020110","url":null,"abstract":"<p> We study the problem on semiclassical asymptotics for (pseudo)differential equations with singularities on a stratified manifold of a special form—the orbit space <span>(X)</span> of a smooth action of a compact Lie group <span>(G)</span> on a smooth manifold <span>(M)</span>. The operators under consideration are obtained as the restriction of <span>(G)</span>-invariant operators with smooth coefficients on <span>(M)</span> to the subspace of <span>(G)</span>-invariant functions, naturally identified with functions on <span>(X)</span>, and have singularities on strata of positive codimension. The asymptotics are associated with Lagrangian manifolds in the phase space defined by the Marsden–Weinstein symplectic reduction of the cotangent bundle <span>(T^*M)</span> under the action of the group <span>(G)</span>; rapidly oscillating integrals defining the Maslov canonical operator on such manifolds contain exponentials as well as special functions related to representations of the group <span>(G)</span>. For the simplest stratified manifold—a manifold with boundary obtained as the orbit space of a semi-free action of the group <span>( mathbb{S} ^1)</span> on a closed manifold—the corresponding construction of semiclassical asymptotics was realized earlier. Note that, in this case, the class of equations under consideration on manifolds with boundary includes the linearized shallow water equations in a basin with a sloping beach. The present paper deals with the general case. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"299 - 307"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523517","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 Upslope Propagation of an Adiabatic Normal Mode in a Wedge-Shaped Sea 论绝热正态模式在楔形海中的上坡传播
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020122
V.A. Sergeev
{"title":"On the Upslope Propagation of an Adiabatic Normal Mode in a Wedge-Shaped Sea","authors":"V.A. Sergeev","doi":"10.1134/S1061920824020122","DOIUrl":"10.1134/S1061920824020122","url":null,"abstract":"<p> We study a two-dimensional problem that models sound propagation in a narrow water wedge near a seashore. For the Helmholtz equation, an adiabatic normal mode propagating shoreward along the water wedge is discussed. We describe the phenomena arising when the mode reaches the <i>critical depth</i> and afterwards. Prior to this, the acoustic field is localized in the water wedge. When the critical depth is reached, the energy of the field radiates into the sea bottom. Thereafter, a surface wave propagates inside the bottom along the water-bottom interface, occasionally leaking back into the water wedge. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"308 - 314"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523518","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
A New Representation Formula for the Bernoulli Numbers 伯努利数的新表示公式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S106192082402016X
A. Petojević, H.M. Srivastava, D. Rastovac
{"title":"A New Representation Formula for the Bernoulli Numbers","authors":"A. Petojević,&nbsp;H.M. Srivastava,&nbsp;D. Rastovac","doi":"10.1134/S106192082402016X","DOIUrl":"10.1134/S106192082402016X","url":null,"abstract":"<p> In this paper, we present a presumably new representation of the Bernoulli numbers. We also give an elementary proof of the Akiyama-Tanigawa algorithm for calculating the Bernoulli numbers. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"335 - 338"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523522","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
Automatic Continuity of every Locally Bunded Homomorphism of a Perfect Connected Lie Group to a Connected Lie Group 完全连通李群到连通李群的每个局部束同构的自动连续性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020134
A.I. Shtern
{"title":"Automatic Continuity of every Locally Bunded Homomorphism of a Perfect Connected Lie Group to a Connected Lie Group","authors":"A.I. Shtern","doi":"10.1134/S1061920824020134","DOIUrl":"10.1134/S1061920824020134","url":null,"abstract":"<p> One of the simplest and most important results following directly from the commutativity of the discontinuity group of a locally bounded homomorphism between connected Lie groups is the automatic continuity of every locally bounded homomorphism of a perfect Lie group which is proved here. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"315 - 316"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523519","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
Convexity of (delta)-Suns and (gamma)-Suns in Asymmetric Spaces 非对称空间中 $$delta$$ -Suns 和 $$gamma$$ -Suns 的凸性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020158
I.G. Tsar’kov
{"title":"Convexity of (delta)-Suns and (gamma)-Suns in Asymmetric Spaces","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920824020158","DOIUrl":"10.1134/S1061920824020158","url":null,"abstract":"<p> Convexity of <span>(delta)</span>-suns and <span>(gamma)</span>-suns is studied in asymmetric spaces with due consideration of geometric properties of the spaces. Known results for usual normed spaces are carried over to the case of general asymmetric normed spaces. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"325 - 334"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523521","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
(mathbb{Z}_{2}-)Graded Lie Algebra of Quaternions and Superconformal Algebra in (D=4) Dimensions $$D=4$$ 维中的 $$mathbb{Z}_{2}-$$ 梯度四元数列代数和超共形代数
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S106192082402002X
B. C. S. Chauhan, P.K. Joshi, B.C. Chanyal
{"title":"(mathbb{Z}_{2}-)Graded Lie Algebra of Quaternions and Superconformal Algebra in (D=4) Dimensions","authors":"B. C. S. Chauhan,&nbsp;P.K. Joshi,&nbsp;B.C. Chanyal","doi":"10.1134/S106192082402002X","DOIUrl":"10.1134/S106192082402002X","url":null,"abstract":"<p> In the present discussion, we have studied the <span>(mathbb{Z}_{2}-)</span><span>(grading)</span> of the quaternion algebra <span>((mathbb{H}))</span>. We have made an attempt to extend the quaternion Lie algebra to the graded Lie algebra by using the matrix representations of quaternion units. The generalized Jacobi identities of <span>(mathbb{Z}_{2}-graded)</span> algebra then result in symmetric graded partners <span>((N_{1},N_{2},N_{3}))</span>. The graded partner algebra <span>((mathcal{F}))</span> of quaternions <span>((mathbb{H}))</span> thus has been constructed from this complete set of graded partner units <span>((N_{1},N_{2},N_{3}))</span>, and <span>(N_{0}=C)</span>. Keeping in view the algebraic properties of the graded partner algebra <span>((mathcal{F}))</span>, the <span>(mathbb{Z}_{2}-graded)</span> superspace <span>((S^{l,m}))</span> of quaternion algebra <span>((mathbb{H}))</span> has been constructed. It has been shown that the antiunitary quaternionic supergroup <span>(UU_{a}(l;m;mathbb{H}))</span> describes the isometries of <span>(mathbb{Z}_{2}-graded)</span> superspace <span>((S^{l,m}))</span>. The Superconformal algebra in <span>(D=4)</span> dimensions is then established, where the bosonic sector of the Superconformal algebra has been constructed from the quaternion algebra <span>((mathbb{H}))</span> and the fermionic sector from the graded partner algebra <span>((mathcal{F}))</span>: asymmetric space, convex set, <span>(delta)</span>-sun, <span>(gamma)</span>-sun. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"162 - 176"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504356","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
Asymptotics of the Solution of the Initial Boundary Value Problem for the One-Dimensional Klein–Gordon Equation with Variable Coefficients 具有可变系数的一维克莱因-戈登方程初始边界值问题解的渐近性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020043
S.Yu. Dobrokhotov, E.S. Smirnova
{"title":"Asymptotics of the Solution of the Initial Boundary Value Problem for the One-Dimensional Klein–Gordon Equation with Variable Coefficients","authors":"S.Yu. Dobrokhotov,&nbsp;E.S. Smirnova","doi":"10.1134/S1061920824020043","DOIUrl":"10.1134/S1061920824020043","url":null,"abstract":"<p> In the paper, formal asymptotic solutions of the initial-boundary value problem for the one-dimensional Klein–Gordon equation with variable coefficients on the semi-axis are constructed. Such a problem can be used, in particular, to simulate the propagation of plane acoustic waves in atmospheric gas initiated by a source at the lower boundary of the domain. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"187 - 198"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523511","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
Natural Volume Forms on Pseudo-Finslerian Manifolds with (m)th Root Metrics 具有 $$m$$ th 根度量的伪芬斯勒方程上的自然体积形式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020146
A.V. Solov’yov
{"title":"Natural Volume Forms on Pseudo-Finslerian Manifolds with (m)th Root Metrics","authors":"A.V. Solov’yov","doi":"10.1134/S1061920824020146","DOIUrl":"10.1134/S1061920824020146","url":null,"abstract":"<p> We define natural volume forms on <span>(n)</span>-dimensional oriented pseudo-Finslerian manifolds with nondegenerate <span>(m)</span>-th root metrics. Our definitions of the natural volume forms depend on the parity of the positive integer <span>(m&gt;1)</span>. The advantage of the stated definitions is their algebraic structure. The natural volume forms are expressed in terms of Cayley hyperdeterminants. In particular, the computation of the natural volume form does not require the difficult integration over the domain within the indicatrix in the tangent space <span>(T_x M^n)</span> of the pseudo-Finslerian manifold at a point <span>(x)</span>. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"317 - 324"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523520","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
Probabilistic Bernoulli and Euler Polynomials 概率伯努利和欧拉多项式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010072
T. Kim, D. S. Kim
{"title":"Probabilistic Bernoulli and Euler Polynomials","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S106192084010072","DOIUrl":"10.1134/S106192084010072","url":null,"abstract":"<p> Let <span>(Y)</span> be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to introduce and study the probabilistic extension of Bernoulli polynomials and Euler polynomials, namely the probabilistic Bernoulli polynomials associated <span>(Y)</span> and the probabilistic Euler polynomials associated with <span>(Y)</span>. Also, we introduce the probabilistic <span>(r)</span>-Stirling numbers of the second associated <span>(Y)</span>, the probabilistic two variable Fubini polynomials associated <span>(Y)</span>, and the probabilistic poly-Bernoulli polynomials associated with <span>(Y)</span>. We obtain some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of <span>(Y)</span>, we treat the gamma random variable with parameters <span>(alpha,beta &gt; 0)</span>, 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/S106192084010072 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 1","pages":"94 - 105"},"PeriodicalIF":1.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171670","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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