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Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: I. Discrete Spectrum 具有点相互作用的三个相同的一维量子粒子作为可解模型：1 .离散谱
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600850
M.A. Lyalinov
{"title":"Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: I. Discrete Spectrum","authors":"M.A. Lyalinov","doi":"10.1134/S1061920825600850","DOIUrl":"10.1134/S1061920825600850","url":null,"abstract":"<p> The paper deals with a Hamiltonian, namely, with a semi-bounded self-adjoint operator that is attributed to the problem of scattering of three one-dimensional particles with point interaction in pairs, in other words, with <span>( delta )</span>-functional singular potential of interaction. The support of the potential in the Hamiltonian coincides with a symmetric star-graph having six leads on the two-dimensional plane. Due to the symmetry, we find that such a model is exactly solvable, which means that the eigenfunctions of the discrete spectrum and the generalized eigenfunctions of the essential (absolutely continuous) spectrum are determined explicitly, i.e., by quadrature. In this (first part) of our work we describe the discrete spectrum and the eigenfunctions. </p><p> <b> DOI</b> 10.1134/S1061920825600850 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"537 - 553"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184078","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
Visually Smooth Non-Congruent Flat Simply Connected Domains That Are Numerically Dirichlet–Neumann Isospectral 数值上Dirichlet-Neumann等谱的视觉光滑非同余平面单连通域
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825601107
A.S. Demidov, A.S. Samokhin
{"title":"Visually Smooth Non-Congruent Flat Simply Connected Domains That Are Numerically Dirichlet–Neumann Isospectral","authors":"A.S. Demidov,&nbsp;A.S. Samokhin","doi":"10.1134/S1061920825601107","DOIUrl":"10.1134/S1061920825601107","url":null,"abstract":"<p> The paper presents two incongruent flat simply connected domains with a visually smooth boundary for which the eigenvalues of the Dirichlet–Neumann operator, obtained using the algorithm cited in the paper, are practically identical. </p><p> <b> DOI</b> 10.1134/S1061920825601107 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"451 - 457"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184040","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
Heterogeneous Stirling Numbers and Heterogeneous Bell Polynomials 非均匀斯特林数与非均匀贝尔多项式
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825601065
T. Kim, D. S. Kim
{"title":"Heterogeneous Stirling Numbers and Heterogeneous Bell Polynomials","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S1061920825601065","DOIUrl":"10.1134/S1061920825601065","url":null,"abstract":"<p> This paper introduces a novel generalization of Stirling and Lah numbers, termed “heterogeneous Stirling numbers,” which smoothly interpolate between these classical combinatorial sequences. Specifically, we define heterogeneous Stirling numbers of the second and first kinds, demonstrating their convergence to standard Stirling numbers as <span>(lambda rightarrow 0)</span> and to (signed) Lah numbers as <span>(lambda rightarrow 1)</span>. We derive fundamental properties, including generating functions, explicit formulas, and recurrence relations. Furthermore, we extend these concepts to heterogeneous Bell polynomials, obtaining analogous results such as generating function, combinatorial identity and Dobinski-like formula. Finally, we introduce and analyse heterogeneous <span>(r)</span>-Stirling numbers of the second kind and their associated <span>(r)</span>-Bell polynomials. </p><p> <b> DOI</b> 10.1134/S1061920825601065 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"498 - 509"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184081","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 Weakly Compact Sets in Normed Linear Spaces 赋范线性空间中弱紧集的凸性
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600539
I.G. Tsar’kov
{"title":"Convexity of Weakly Compact Sets in Normed Linear Spaces","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920825600539","DOIUrl":"10.1134/S1061920825600539","url":null,"abstract":"<p> We study weakly compact subsets of normed linear spaces admitting, for each <span>(varepsilon&gt;0)</span>, an <i>nw</i>-continuous <span>(varepsilon)</span>-selection and such that the closure of their convex hull is weakly compact in this space. Such sets are shown to be convex. An application of this result to the linear manifold of all analytic functions in <span>(L_1)</span> is given. </p><p> <b> DOI</b> 10.1134/S1061920825600539 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"585 - 589"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184073","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
Radial Compression with Controlled Unloading of a Layered-Stratified Elastoplastic Hollow Sphere 层状弹塑性空心球径向压缩控制卸载
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825030070
D.V. Georgievskii
{"title":"Radial Compression with Controlled Unloading of a Layered-Stratified Elastoplastic Hollow Sphere","authors":"D.V. Georgievskii","doi":"10.1134/S1061920825030070","DOIUrl":"10.1134/S1061920825030070","url":null,"abstract":"<p> The stress-strain state arising after a two-stage spherically symmetric process “radial loading– partial unloading” in a hollow sphere (thick-walled spherical layer) nonuniform in radius is investigated. The inner boundary is fixed, and a radial compressive stress is applied to the outer boundary. The material of the sphere agrees with Ilyushin’s theory of small elastoplastic deformations. Both discontinuous and continuously stratified nonuniformity are admitted, while the bulk modulus of compression at all points of the material is assumed to be constant. At the first (intermediate) step, an excessive compression (over-compression) occurs, as a result of which the radius of the outer boundary becomes less than the required one. At the second step, where partial unloading occurs, the system is transferred to the required final position. Such a two-stage nature enables one to control the stress-strain state in the hollow sphere both as a whole and concerning its individual parameters. </p><p> <b> DOI</b> 10.1134/S1061920825030070 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"480 - 484"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184077","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
Paraxial Diffraction on a Delta Potential Delta势上的近轴衍射
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600679
E.A. Zlobina, A.P. Kiselev
{"title":"Paraxial Diffraction on a Delta Potential","authors":"E.A. Zlobina,&nbsp;A.P. Kiselev","doi":"10.1134/S1061920825600679","DOIUrl":"10.1134/S1061920825600679","url":null,"abstract":"<p> A special Cauchy problem for the Schrödinger equation with a delta potential localized on a half-line is addressed. From the viewpoint of high-frequency parabolic-equation heuristics, the problem could be viewed as an approximation to a paraxial (i.e., nearly tangential) diffraction of a plane wave incident on a screen. Explicit solution of the problem, found with the help of integral transformations, is subjected to exhaustive asymptotic investigation for all values of the complex coefficient of the potential. The asymptotic findings are qualitatively interpreted using diffraction terminology and quantitatively compared with the results of diffraction theory. Some effects that have no analogs in the related diffraction problems are noted. The solution is shown to be, in a certain range of parameters, an asymptotic solution of the Helmholtz equation with a delta potential. </p><p> <b> DOI</b> 10.1134/S1061920825600679 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"597 - 613"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184082","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
Riemann Theta Function Solutions to a Hierarchy of Integrable Semi-Discrete Equations 一类可积半离散方程的Riemann Theta函数解
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600667
X.G. Geng, M.X. Jia, X. Zeng, J. Wei
{"title":"Riemann Theta Function Solutions to a Hierarchy of Integrable Semi-Discrete Equations","authors":"X.G. Geng,&nbsp;M.X. Jia,&nbsp;X. Zeng,&nbsp;J. Wei","doi":"10.1134/S1061920825600667","DOIUrl":"10.1134/S1061920825600667","url":null,"abstract":"<p> The theory of tetragonal curves is applied to the study of discrete integrable systems. Based on the discrete Lenard equation, we derive a hierarchy of Blaszak–Marciniak four-field lattice equations associated with the <span>(4times4)</span> matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the hierarchy of Blaszak–Marciniak four-field lattice equation, we introduce a tetragonal curve, a Baker-Akhiezer function, and three meromorphic functions on it. We study algebro-geometric properties of the tetragonal curve and asymptotic behaviors of the Baker-Akhiezer function and meromorphic functions near two infinite points. The straightening out of various flows is exactly given by means of the Abel map and the meromorphic differential. We finally obtain Riemann theta function solutions of the entire Blaszak–Marciniak four-field lattice hierarchy. </p><p> <b> DOI</b> 10.1134/S1061920825600667 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"464 - 479"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184041","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
Semisimple Algebraic Nijenhuis Operators and Three-Dimensional Lie Groups as Nijenhuis Manifolds 半简单代数Nijenhuis算子和作为Nijenhuis流形的三维李群
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600758
E. Zhikhareva
{"title":"Semisimple Algebraic Nijenhuis Operators and Three-Dimensional Lie Groups as Nijenhuis Manifolds","authors":"E. Zhikhareva","doi":"10.1134/S1061920825600758","DOIUrl":"10.1134/S1061920825600758","url":null,"abstract":"<p> The aim of this paper is to disprove the conjecture that the only Lie algebras admitting semisimple algebraic Nijenhuis operators are Abelian ones. We do not only provide examples in arbitrary dimension but also classify three-dimensional Lie algebras which admit such an operator in both complex and real cases. As a byproduct, we obtain a list of three-dimensional Lie groups which are left-invariant Nijenhuis manifolds. </p><p> <b> DOI</b> 10.1134/S1061920825600758 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"590 - 596"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184080","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
Radius Constants for Cesàro Operator of Analytic and Harmonic Functions in the Unit Disk 单位圆盘上解析函数和调和函数算子Cesàro的半径常数
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920824601484
Z.Y. Hu, H.M. Srivastava, X.Y. Wang
{"title":"Radius Constants for Cesàro Operator of Analytic and Harmonic Functions in the Unit Disk","authors":"Z.Y. Hu,&nbsp;H.M. Srivastava,&nbsp;X.Y. Wang","doi":"10.1134/S1061920824601484","DOIUrl":"10.1134/S1061920824601484","url":null,"abstract":"<p> Given coefficient conditions of analytic in unit disk <span>(mathbf{D})</span>, we obtain the radius of starlike of order <span>(alpha)</span> and convex of order <span>(alpha)</span> for Cesàro operator of analytic functions <span>(f)</span> in <span>(mathbf{D})</span>. Furthermore, we consider the Cesàro operator of harmonic functions and give the radius of starlike of order <span>(alpha)</span> and convex of order <span>(alpha)</span> for Cesàro operator of harmonic functions <span>(f)</span> in <span>(mathbf{D})</span>. All results are sharp. </p><p> <b> DOI</b> 10.1134/S1061920824601484 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"485 - 497"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184038","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
Remarks on an Integral Equation of Landau–Lifschitz Type 关于Landau-Lifschitz型积分方程的注释
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600576
Yutian Lei
{"title":"Remarks on an Integral Equation of Landau–Lifschitz Type","authors":"Yutian Lei","doi":"10.1134/S1061920825600576","DOIUrl":"10.1134/S1061920825600576","url":null,"abstract":"<p> In this paper, we are concerned with the asymptotic behavior and the Liouville theorem for the nonlinear integral equation </p><p> where <span>(u in C^{infty}(mathbb{R}^{n},mathbb{S}^{k-1}))</span> with <span>(n geq 3)</span>, <span>(k geq 2)</span>, <span>(alpha in (0,n/2))</span>, <span>(mathbb{S}^{k-1}={u=(u_1,u_2,cdots,u_k) in mathbb{R}^{k}; |u|=1})</span>, <span>(e_k=(0,cdots,0,1))</span>, <span>(C_*)</span> is a positive constant, and <span>(ell in mathbb{R}^{k})</span> is a constant vector. We prove that, if <span>(u_k in L^2(mathbb{R}^n))</span> and <span>(nabla u in L^2(mathbb{R}^n) cap L^infty(mathbb{R}^n))</span>, then <span>(u to ell)</span> as <span>(|x| to infty)</span> with <span>(ell_k=0)</span>. Moreover, if <span>(alpha in (1,n/2))</span>, then <span>(u equiv ell)</span> on <span>(mathbb{R}^n)</span>. </p><p> <b> DOI</b> 10.1134/S1061920825600576 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"530 - 536"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184039","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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