发布求助
文献互助 智能选刊 最新文献

Russian Journal of Mathematical Physics最新文献

筛选
英文 中文
Homogenization of Fourth-Order Elliptic Operators with Periodic Coefficients in the Energy Norm 能量范数中具有周期系数的四阶椭圆算子的均匀化
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1134/S1061920826601060
I. Safronov
{"title":"Homogenization of Fourth-Order Elliptic Operators with Periodic Coefficients in the Energy Norm","authors":"I. Safronov","doi":"10.1134/S1061920826601060","DOIUrl":"10.1134/S1061920826601060","url":null,"abstract":"<p> A fourth-order matrix periodic elliptic differential operator <span>( mathcal{A}_varepsilon )</span> in <span>( mathbb{R}^d )</span> with rapidly oscillating coefficients (depending on <span>( mathbf{x} / varepsilon )</span>) is studied. The principal part of the operator is given in a factorized form <span>( b(mathbf{D})^* g(mathbf{x} / varepsilon) b(mathbf{D}) )</span>, where <span>( g )</span> is a periodic bounded and positive definite matrix-valued function; <span>( b(mathbf{D}) )</span> is a second-order matrix operator whose symbol is a matrix of maximal rank. The operator also includes lower-order terms with unbounded coefficients. It is shown that, in the small period limit, the inverse operator converges in the operator norm on <span>( L_2(mathbb{R}^d; mathbb{C}^n) )</span> to the inverse of the effective operator. The effective operator is a fourth-order elliptic operator with constant coefficients. A sharp-order error estimate is obtained. Also, an approximation for the resolvent in the norm of operators acting from <span>( L_{2}(mathbb{R}^d; mathbb{C}^n) )</span> to <span>( H^{2}(mathbb{R}^d; mathbb{C}^n) )</span> with the corrector taken into account is obtained. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 3","pages":"609 - 615"},"PeriodicalIF":1.9,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965350","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 a Graph with Small Edges and the Weakly Nonlinear Robin Condition 小边图和弱非线性Robin条件
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1134/S1061920826030015
D.I. Borisov
{"title":"On a Graph with Small Edges and the Weakly Nonlinear Robin Condition","authors":"D.I. Borisov","doi":"10.1134/S1061920826030015","DOIUrl":"10.1134/S1061920826030015","url":null,"abstract":"<p> We consider a second-order linear elliptic equation on a general graph having both finite and small edges; the lengths of latter are proportional to a small parameter <span>(varepsilon.)</span> The small edges form an arbitrary graph, and we only suppose that small edges and finite edges are connected by a single vertex, with one finite incident edge and one small incident edge. At this single vertex, a weakly nonlinear Robin condition is imposed, while other vertices are subject to general linear boundary conditions. We make several additional assumptions on the coefficients in the considered problem, which allow us to establish its unique solvability. Then we show that, on finite edges, the solution of the perturbed problem converges to the solution of some limit problem with a special nonlinear Robin condition at <span>(M_0.)</span> The nonlinearity in this condition depends essentially on the behavior of the coefficients in the perturbed problem on small edges. We establish appropriate operator estimates. We find the leading term in the asymptotics for the perturbed solution on small edges and estimate the error term uniformly in the right-hand side in the equation. We also prove that the nonlinear mapping which sends the right-hand expression in the perturbed problem into its solutions is infinitely differentiable in <span>( varepsilon )</span> in an appropriate sense. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 3","pages":"445 - 464"},"PeriodicalIF":1.9,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965522","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
Wave Fields Coupled to a Finite Chain of Harmonic Oscillators: Convergence to Equilibrium 耦合到谐振子有限链的波场：收敛到平衡
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1134/S1061920826600686
T.V. Dudnikova
{"title":"Wave Fields Coupled to a Finite Chain of Harmonic Oscillators: Convergence to Equilibrium","authors":"T.V. Dudnikova","doi":"10.1134/S1061920826600686","DOIUrl":"10.1134/S1061920826600686","url":null,"abstract":"<p> We consider the Hamiltonian system consisting of a finite chain of harmonic oscillators and several fields described by Klein–Gordon or wave equations. The initial date of the system is a random function with a finite mean density of energy which also satisfies a Rosenblatt- or Ibragimov-type mixing condition. We study the distribution <span>(mu_t)</span> of the solution at time <span>(tinmathbb{R})</span>. The main result is the convergence of <span>(mu_t)</span> to a Gaussian measure as <span>(ttoinfty)</span>, what gives a Central Limit Theorem for a model under consideration. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 3","pages":"523 - 542"},"PeriodicalIF":1.9,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965349","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
Operator-Valued Generalization of Bell Polynomials Arising from Generalized Heisenberg Algebra 由广义海森堡代数引起的贝尔多项式的算子值推广
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-09-16 DOI: 10.1134/S1061920826601151
T. Kim, D. S. Kim
{"title":"Operator-Valued Generalization of Bell Polynomials Arising from Generalized Heisenberg Algebra","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S1061920826601151","DOIUrl":"10.1134/S1061920826601151","url":null,"abstract":"<p> This paper introduces a unified operational framework that bridges combinatorial mathematics and nonlinear quantum mechanics by systematically developing the theory of generalized, degenerate, and <span>(r)</span>-extended operator-valued Stirling numbers and Bell polynomials. Constructed within the framework of the Generalized Heisenberg Algebra <span>(text{GHA}_f)</span>, where the standard commutation relation is modulated by an analytic function of the Hamiltonian <span>(f(H))</span>, these novel algebraic objects capture the intrinsic nonlinearity of deformed quantum systems. By implementing operational methods and evaluating operator actions on coherent and number states, we establish explicit representations, structural recurrence relations, and robust generating functions. We demonstrate that in the special case of <span>(f(H) = H + 1)</span>, our operator-valued formulations gracefully reduce to their classical combinatorial counterparts, successfully recovering foundational milestones such as Dobinski’s formula. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 3","pages":"543 - 559"},"PeriodicalIF":1.9,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965530","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
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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书