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Monotone Path-Connected Boundedly Weakly Compact Set is a Sun 单调路径连通有界弱紧集是一个Sun
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600200
I.G. Tsar’kov
{"title":"Monotone Path-Connected Boundedly Weakly Compact Set is a Sun","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920826600200","DOIUrl":"10.1134/S1061920826600200","url":null,"abstract":"<p> We study solar properties of monotone path-connected and Menger-connected boundedly weakly compact sets in normed linear spaces. We show that any Menger-connected boundedly weakly compact subset of a separable normed space is a sun. We also prove that any nonempty monotone path-connected weakly compact subset of normed linear space is a sun. For boundedly weakly compact subsets of the space <span>(C(Q,mathbb{R}))</span>, we obtain a criterion of monotone path-connectedness in terms of solarity. Namely, if <span>(M)</span> is a nonempty boundedly weakly compact set in <span>( C(Q))</span>, then <span>(M)</span> is a sun if and only if <span>(M)</span> is monotone path-connected. We show that, given a monotone path-connected subset <span>(M)</span> of a rotund space <span>(X)</span>, if <span>(xnotin M)</span> has a unique nearest point in <span>(M)</span>, then <span>(x)</span> is a solar point for <span>(M)</span>. As a corollary, we prove that in a rotund space every proximinal monotonously path-connected set is a Chebyshev sun. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"434 - 439"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458753","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
Degenerate r-Bell Numbers and Coherent States 简并r-贝尔数与相干态
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S106192082602010X
T. Kim, D. S. Kim
{"title":"Degenerate r-Bell Numbers and Coherent States","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S106192082602010X","DOIUrl":"10.1134/S106192082602010X","url":null,"abstract":"<p> This paper derives the normal ordering expansion for the operator <span>((a^{dagger}a+r)_{n,lambda})</span>, using two methods: the action of the generalized displacement operator on number states and the determination of a recurrence relation for expansion coefficients. Here <span>(a^{dagger})</span> and <span>(a)</span> are respectively the boson creation and annihilation operators. We also deduce the inverse relation for this expansion. Applying coherent state techniques, we establish identities for the diagonal matrix elements <span>(langle z| (a^{dagger} a+r)_{k,lambda}|zrangle)</span>, which directly yield a Dobinski-like formula for the degenerate <span>(r)</span>-Bell numbers. Furthermore, we present a new recurrence relation for these combinatorial numbers. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"332 - 339"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458761","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
Relaxation Oscillations in a System with Compactly Supported Nonlinearity Containing a Delay 含时滞紧支持非线性系统的松弛振荡
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S106192082560151X
A.A. Kashchenko
{"title":"Relaxation Oscillations in a System with Compactly Supported Nonlinearity Containing a Delay","authors":"A.A. Kashchenko","doi":"10.1134/S106192082560151X","DOIUrl":"10.1134/S106192082560151X","url":null,"abstract":"<p> A system of two differential equations with nonlinear delayed feedback containing a large parameter is considered. The nonlinearity is assumed to be compactly supported, i.e., it takes the zero value outside a certain domain of variation of the argument. The construction of asymptotics of solutions for sufficiently large values of the parameter appearing in the original system is investigated. Conditions for the existence of various types of relaxation oscillations with asymptotically large amplitude are identified. An asymptotics of the corresponding solutions is constructed, and it is shown that their dynamical properties can be complicated. The research methodology is based on the application of a special large parameter method using the reduction of the study of the original system to the analysis of constructed finite-dimensional mappings. The possibility of obtaining asymptotic formulas for solutions of the original system is due to the fact that the significant influence of nonlinearity occurs only on relatively small time intervals while, on the “main” time interval, the behavior of the solutions is determined by a linear system of differential equations. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"317 - 331"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458760","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
Points of Monotone Connectedness and Solar Properties of Sets 单调连通性点与集合的太阳性质
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600303
A.R. Alimov, N.A. Ilyasov
{"title":"Points of Monotone Connectedness and Solar Properties of Sets","authors":"A.R. Alimov,&nbsp;N.A. Ilyasov","doi":"10.1134/S1061920826600303","DOIUrl":"10.1134/S1061920826600303","url":null,"abstract":"<p> Luminosity points of sets are studied; these are the points for which the Kolmogorov (solar) condition for a best approximant holds. We obtain sufficient conditions for a given point of a set to be a luminosity point of this set. The results are formulated in terms of points of monotone connectedness of the set. We consider the characteristics of luminosity points which involve individual characteristics of both the space and the set (points of monotone connectedness of a set and rotund points of the unit sphere of the space). Prox-monotone path-connected sets are introduced; for such a set <span>(M)</span>, if a point <span>(y)</span> is a nearest point from this set for some point <span>(xnotin M)</span>, then <span>(y)</span> is a point of monotone connectedness of <span>(M)</span>. We also show that each boundedly compact prox-monotone path-connected set (prox-Menger connected set) is a sun. Applications to the space <span>(c_0)</span> are also given. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"195 - 201"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458976","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
Decomposition of the Wiener Measure with Respect to the Orbits of the Action of the Diffeomorphism Group 关于微分同胚群作用轨道的维纳测度分解
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600546
V.V. Belokurov, E.T. Shavgulidze, N.E. Shavgulidze
{"title":"Decomposition of the Wiener Measure with Respect to the Orbits of the Action of the Diffeomorphism Group","authors":"V.V. Belokurov,&nbsp;E.T. Shavgulidze,&nbsp;N.E. Shavgulidze","doi":"10.1134/S1061920826600546","DOIUrl":"10.1134/S1061920826600546","url":null,"abstract":"<p> In the paper, theorems on the decomposition of the Wiener measure with respect to the orbits of the action of the diffeomorphism group are proved. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"202 - 224"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458980","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
Billiard with Coulomb Potential Inside an Elliptic Ring 椭圆环内具有库仑势的台球
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600315
G.V. Belozerov, S.A. Galkin
{"title":"Billiard with Coulomb Potential Inside an Elliptic Ring","authors":"G.V. Belozerov,&nbsp;S.A. Galkin","doi":"10.1134/S1061920826600315","DOIUrl":"10.1134/S1061920826600315","url":null,"abstract":"<p> We consider a billiard system inside a ring formed by two ellipses with common foci <span>(F_1)</span> and <span>(F_2)</span> affected by Coulomb forces, condensed in <span>(F_1)</span> and <span>(F_2)</span> with charges <span>(gamma_1)</span> and <span>(gamma_2)</span>, respectively. The reflection from the boundary of the domain is supposed to be essentially elastic. This billiard is Liouville integrable in terms of piecewise smoothness. An explicit formula of the additional first integral was found. We study the topology of the Liouville foliation of this system in several cases: <span>(gamma_1&lt;0,gamma_2=0)</span> (Kepler case); <span>(gamma_1&gt;0,gamma_2=0)</span>; <span>(gamma_1=gamma_2)</span>. For each of these cases, Fomenko and Fomenko–Zieschang invariants are calculated. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"225 - 240"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458751","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
Atiyah–Bott–Lefschetz Formula on Manifolds with Periodic Ends 具有周期末端流形的atiyah - bot - lefschetz公式
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826020184
V.E. Nazaikinskii, A.Yu. Savin
{"title":"Atiyah–Bott–Lefschetz Formula on Manifolds with Periodic Ends","authors":"V.E. Nazaikinskii,&nbsp;A.Yu. Savin","doi":"10.1134/S1061920826020184","DOIUrl":"10.1134/S1061920826020184","url":null,"abstract":"<p> The classical Atiyah–Bott formula (1967) expresses the Lefschetz number of a geometric endomorphism of an elliptic complex of (pseudo)differential operators on a closed smooth manifold as the sum of contributions of fixed points of the corresponding diffeomorphism, assuming that all fixed points are nondegenerate. These contributions explicitly depend only on the endomorphism itself but not on the operators forming the complex. In 1999, one of the authors, together with B.-W. Schulze, B. Yu. Sternin, and V. E. Shatalov, generalized this formula to the case of manifolds with conical singularities (or, equivalently, with cylindrical ends), where the contributions of interior fixed points are supplemented by those of fixed cylindrical ends (which already depend on the operators of the complex themselves). In recent decades, a number of papers have appeared in the literature devoted to elliptic theory on manifolds with periodic ends. The present paper gives a Lefschetz formula on such manifolds; in the special case of manifolds with cylindrical ends, it strengthens previously obtained results. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"440 - 444"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458754","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
Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: III. Positive Essential Spectrum 具有点相互作用的三个相同的一维量子粒子的可解模型正本质谱
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600236
M.A. Lyalinov
{"title":"Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: III. Positive Essential Spectrum","authors":"M.A. Lyalinov","doi":"10.1134/S1061920826600236","DOIUrl":"10.1134/S1061920826600236","url":null,"abstract":"<p> This is the third part of our work dealing with spectral analysis for the Hamiltonian of three identical one-dimensional quantum particles. It deals with positive energies and the corresponding generalized eigenfunctions. The asymptotic behavior of the generalized eigenfunctions is studied and interpreted in terms of the diffraction theory. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"392 - 406"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458758","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
Exploring Algebraic and Probabilistic Properties for Degenerate Bivariate Appell Polynomials 探讨退化二元阿佩尔多项式的代数和概率性质
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920824600867
M. Riyasat, S. Khan
{"title":"Exploring Algebraic and Probabilistic Properties for Degenerate Bivariate Appell Polynomials","authors":"M. Riyasat,&nbsp;S. Khan","doi":"10.1134/S1061920824600867","DOIUrl":"10.1134/S1061920824600867","url":null,"abstract":"<p> The purpose of this paper is to carry out a comprehensive analysis of the properties of degenerate bivariate Appell polynomials by making extensive use of algebraic and probabilistic techniques. The determinant expressions for the degenerate cosine-Appell and sine-Appell polynomials and for their conjugate forms are established by employing several recursive formulas. Further, we focus on exploring probabilistic properties, in which there associated a family of degenerate bivariate Appell polynomials to every random variable <span>(chi)</span> with some exponential moments <span>(e^{chi u})</span>, which provides some powerful tools for a deeper understanding of the behavior and properties of degenerate bivariate Appell polynomials. Examples are framed which introduces a random variable whose mass function is given in terms of degenerate bivariate Bernoulli polynomials. Some expressions for the expectation <span>(E[chi])</span> of the random variable associated with the degenerate bivariate Bernoulli polynomials are derived. It is demonstrated that the probabilistic approach offers interesting new results and developments for these polynomials. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"417 - 430"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458755","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 Homogenization of a Parabolic Equation with a Nonlocal Convolution Type Operator 一类具有非局部卷积型算子的抛物方程的齐化问题
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826020147
A. Piatnitski, V. Sloushch, T. Suslina, E. Zhizhina
{"title":"On the Homogenization of a Parabolic Equation with a Nonlocal Convolution Type Operator","authors":"A. Piatnitski,&nbsp;V. Sloushch,&nbsp;T. Suslina,&nbsp;E. Zhizhina","doi":"10.1134/S1061920826020147","DOIUrl":"10.1134/S1061920826020147","url":null,"abstract":"<p> In <span>(L_2(mathbb{R}^d))</span>, we consider a self-adjoint bounded operator <span>({mathbb A}_varepsilon(t))</span>, <span>(tge 0)</span>, <span>(varepsilon &gt;0)</span>, of the form </p><p> It is assumed that <span>(a(cdot)in L_1(mathbb R^d))</span> is a nonnegative function such that <span>(int_{mathbb{R}^d} | mathbf{x} |^3 a(mathbf{x}),dmathbf{x}&lt;infty)</span> and <span>(a(-mathbf{x}) = a(mathbf{x}))</span>; the function <span>(mu(mathbf{x},mathbf{y},t))</span> is measurable and periodic in all variables, moreover, <span>(mu(mathbf{x},mathbf{y},t) = mu(mathbf{y},mathbf{x},t))</span> and <span>(0&lt; mu_- leqslant mu(mathbf{x},mathbf{y},t) leqslant mu_+&lt; infty)</span>. Let <span>(u_varepsilon(mathbf{x},t))</span>, <span>(mathbf{x} in {mathbb R}^d)</span>, <span>(t ge 0)</span>, be the solution of the Cauchy problem </p><p> where <span>(varphi in L_2({mathbb R}^d))</span>. We show that, for a chosen <span>(t&gt;0)</span>, the solution <span>(u_varepsilon(cdot,t))</span> converges in <span>(L_2({mathbb R}^d))</span>, as <span>(varepsilon to 0)</span>, to the solution <span>(u_0(cdot,t))</span> of the homogenized problem </p><p> where <span>({mathbb A}^0= - operatorname{div} g^0 nabla)</span> and <span>(g^0)</span> is a positive definite effective matrix. The following error estimate holds: </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"407 - 416"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458752","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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