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Russian Journal of Mathematical Physics最新文献

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Reconstruction of Maslov’s Complex Germ in the Cauchy Problem for the Schrödinger Equation with a Delta Potential Localized on a Hypersurface 在超表面上定位三角势的薛定谔方程考希问题中重建马斯洛夫复 Germ
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030142
A.I. Shafarevich, O.A. Shchegortsova
{"title":"Reconstruction of Maslov’s Complex Germ in the Cauchy Problem for the Schrödinger Equation with a Delta Potential Localized on a Hypersurface","authors":"A.I. Shafarevich,&nbsp;O.A. Shchegortsova","doi":"10.1134/S1061920824030142","DOIUrl":"10.1134/S1061920824030142","url":null,"abstract":"<p> The semiclassical asymptotics of the solution of the Cauchy problem for the Schrödinger equation with a delta potential localized on a surface of codimension 1 is described. The Schrödinger operator with a delta potential is defined using extension theory and specified by boundary conditions on this surface. The initial conditions are chosen in the form of a narrow peak, which is a Gaussian packet, localized in a small neighborhood of a surface of arbitrary dimension, and oscillating rapidly along it. The Maslov complex germ method is used to construct the asymptotics. The reflection of an isotropic manifold with a complex germ interacting with the delta potential is described. </p><p> <b> DOI</b> 10.1134/S1061920824030142 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"526 - 543"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409598","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
Coincidence of the Dimensions of First Countable Spaces with a Countable Network 第一可数空间的维数与可数网络的巧合
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030178
I.M. Leibo
{"title":"Coincidence of the Dimensions of First Countable Spaces with a Countable Network","authors":"I.M. Leibo","doi":"10.1134/S1061920824030178","DOIUrl":"10.1134/S1061920824030178","url":null,"abstract":"<p> The coincidence of the <span>( operatorname{Ind} )</span> and <span>(dim)</span> dimensions for the first countable paracompact <span>(sigma)</span>-spaces is proved. This gives a positive answer to A.V. Arkhangel’skii’s question of whether the dimensions <span>( operatorname{ind} X)</span>, <span>( operatorname{Ind} X)</span>, and <span>(dim X)</span> are equal for the first countable spaces with a countable network. </p><p> <b> DOI</b> 10.1134/S1061920824030178 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"568 - 570"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409604","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
Explicit Formulas for Probabilistic Multi-Poly-Bernoulli Polynomials and Numbers 多伯努利概率多项式和数的明确公式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030087
T. Kim, D. S. Kim
{"title":"Explicit Formulas for Probabilistic Multi-Poly-Bernoulli Polynomials and Numbers","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S1061920824030087","DOIUrl":"10.1134/S1061920824030087","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 study probabilistic Bernoulli polynomials of order <span>(r)</span> associated with <span>(Y)</span> and probabilistic multi-poly-Bernoulli polynomials associated with <span>(Y)</span>. They are respectively probabilistic extensions of Bernoulli polynomials of order <span>(r)</span> and multi-poly-Bernoulli polynomials. We find explicit expressions, certain related identities and some properties for them. In addition, we treat the special cases of Poisson, gamma and Bernoulli random variables. </p><p> <b> DOI</b> 10.1134/S1061920824030087 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"450 - 460"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409639","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
Erratum to: “Solitary Wave Interactions in the Cubic Whitham Equation” [RJMP 31 (2), 199–208 (2024)] 勘误："立方惠森方程中的孤波相互作用》[RJMP 31 (2)，199-208 (2024)] 更正
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030208
M.V. Flamarion, E. Pelinovsky
{"title":"Erratum to: “Solitary Wave Interactions in the Cubic Whitham Equation” [RJMP 31 (2), 199–208 (2024)]","authors":"M.V. Flamarion,&nbsp;E. Pelinovsky","doi":"10.1134/S1061920824030208","DOIUrl":"10.1134/S1061920824030208","url":null,"abstract":"","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"575 - 575"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409645","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 the Uniqueness of Weak Solutions of the Incompressible Navier–Stokes Equations 关于不可压缩纳维-斯托克斯方程弱解唯一性的评论
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030154
K.N. Soltanov
{"title":"Remarks on the Uniqueness of Weak Solutions of the Incompressible Navier–Stokes Equations","authors":"K.N. Soltanov","doi":"10.1134/S1061920824030154","DOIUrl":"10.1134/S1061920824030154","url":null,"abstract":"<p> This paper studies the uniqueness of a weak solution of the incompressible Navier–Stokes Equations in the 3-dimensional case. Here the investigation is provided by using two different approaches. The first (the main) result is obtained for given functions possessing a certain smoothness, using a new approach. The other result works without additional conditions but is, in some sense, a “local” result, investigated by another approach. In addition, here the solvability and uniqueness of weak solutions to the auxiliary problems derived from the main problem are investigated. </p><p> <b> DOI</b> 10.1134/S1061920824030154 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"544 - 561"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409601","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
Exponential Localization for Eigensections of the Bochner–Schrödinger operator 波赫纳-薛定谔算子等差数列的指数定位
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030099
Yu.A. Kordyukov
{"title":"Exponential Localization for Eigensections of the Bochner–Schrödinger operator","authors":"Yu.A. Kordyukov","doi":"10.1134/S1061920824030099","DOIUrl":"10.1134/S1061920824030099","url":null,"abstract":"<p> We study asymptotic spectral properties of the Bochner–Schrödinger operator <span>(H_{p}=frac 1pDelta^{L^potimes E}+V)</span> on high tensor powers of a Hermitian line bundle <span>(L)</span> twisted by a Hermitian vector bundle <span>(E)</span> on a Riemannian manifold <span>(X)</span> of bounded geometry under the assumption that the curvature form of <span>(L)</span> is nondegenerate. At an arbitrary point <span>(x_0)</span> of <span>(X)</span>, the operator <span>(H_p)</span> can be approximated by a model operator <span>(mathcal H^{(x_0)})</span>, which is a Schrödinger operator with constant magnetic field. For large <span>(p)</span>, the spectrum of <span>(H_p)</span> asymptotically coincides, up to order <span>(p^{-1/4})</span>, with the union of the spectra of the model operators <span>(mathcal H^{(x_0)})</span> over <span>(X)</span>. We show that, if the union of the spectra of <span>(mathcal H^{(x_0)})</span> over the complement of a compact subset of <span>(X)</span> has a gap, then the spectrum of <span>(H_{p})</span> in the gap is discrete, and the corresponding eigensections decay exponentially away from a compact subset. </p><p> <b> DOI</b> 10.1134/S1061920824030099 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"461 - 476"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409602","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
The Uniform Structure of (mathfrak{g}^{otimes 4}) 的统一结构
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030038
M. Avetisyan, A.P. Isaev, S.O. Krivonos, R. Mkrtchyan
{"title":"The Uniform Structure of (mathfrak{g}^{otimes 4})","authors":"M. Avetisyan,&nbsp;A.P. Isaev,&nbsp;S.O. Krivonos,&nbsp;R. Mkrtchyan","doi":"10.1134/S1061920824030038","DOIUrl":"10.1134/S1061920824030038","url":null,"abstract":"<p> We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the fourth power of the adjoint representation <span>(mathfrak{g}^{otimes 4})</span> for all simple Lie algebras. We present universal, in Vogel’s sense, formulas for the dimensions and split Casimir operator’s eigenvalues of all terms in this decomposition. We assume that a similar uniform decomposition into Casimir eigenspaces with universal dimension formulas exists for an arbitrary power of the adjoint representations. </p><p> <b> DOI</b> 10.1134/S1061920824030038 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"379 - 388"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409620","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 Condition for the Strong Continuity of Representations of Topological Groups in Reflexive Fréchet Spaces 反身弗雷谢特空间中拓扑群表征的强连续性条件
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S106192082403018X
A.I. Shtern
{"title":"A Condition for the Strong Continuity of Representations of Topological Groups in Reflexive Fréchet Spaces","authors":"A.I. Shtern","doi":"10.1134/S106192082403018X","DOIUrl":"10.1134/S106192082403018X","url":null,"abstract":"<p> Some necessary and sufficient conditions for the strong continuity of representations of topological groups in reflexive Fréchet spaces are obtained. </p><p> <b> DOI</b> 10.1134/S106192082403018X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"571 - 573"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409610","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
Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities 具有 KPZ 非线性的季霍诺夫型反应-扩散-平流系统中周期抛物问题的解的存在性和渐近稳定性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030129
E.I. Nikulin, N.N. Nefedov, A.O. Orlov
{"title":"Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities","authors":"E.I. Nikulin,&nbsp;N.N. Nefedov,&nbsp;A.O. Orlov","doi":"10.1134/S1061920824030129","DOIUrl":"10.1134/S1061920824030129","url":null,"abstract":"<p> This paper studies time-periodic solutions of singularly perturbed Tikhonov systems of reaction–diffusion–advection equations with nonlinearities that include the square of the gradient of the unknown function (KPZ nonlinearities). The boundary layer asymptotics of solutions are constructed for Neumann and Dirichlet boundary conditions. The study considers both the case of quasimonotone sources and systems without the quasimonotonicity condition. The asymptotic method of differential inequalities is used to prove theorems on the existence of solutions and their Lyapunov asymptotic stability. </p><p> <b> DOI</b> 10.1134/S1061920824030129 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"504 - 516"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409641","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
Explicit Solution to the Birman Problem for the 2D-Laplace Operator 二维拉普拉斯算子的比尔曼问题的显式求解
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030117
M. Malamud
{"title":"Explicit Solution to the Birman Problem for the 2D-Laplace Operator","authors":"M. Malamud","doi":"10.1134/S1061920824030117","DOIUrl":"10.1134/S1061920824030117","url":null,"abstract":"<p> We construct an appropriate restriction of the 2-dimensional Laplace operator that has compact preresolvent though the resolvent of its Friedrichs extension is not compact and, moreover, its spectrum is absolutely continuous. This result solves the Birman problem. </p><p> <b> DOI</b> 10.1134/S1061920824030117 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"495 - 503"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409599","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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