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Russian Journal of Mathematical Physics最新文献

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On the Phase Spaces for a Class of Boundary-Degenerate Equations 一类边界退化方程的相空间
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040101
V.E. Nazaikinskii
{"title":"On the Phase Spaces for a Class of Boundary-Degenerate Equations","authors":"V.E. Nazaikinskii","doi":"10.1134/S1061920824040101","DOIUrl":"10.1134/S1061920824040101","url":null,"abstract":"<p> We study the relationship between the phase space recently introduced by Bolotin and Treschev in connection with the study of billiards with semirigid walls and the phase space arising in the construction of semiclassical asymptotics for a class of differential equations degenerating on the boundary of a domain. </p><p> <b> DOI</b> 10.1134/S1061920824040101 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"713 - 718"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373282","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 Existence and Asymptotic Stability of Two-Dimensional Periodic Solutions with an Internal Transition Layer in a Problem with a Finite Advection 有限平流问题中带内过渡层二维周期解的存在性及渐近稳定性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040113
N.N. Nefedov, E.I. Nikulin, L. Recke, K. Schneider
{"title":"On the Existence and Asymptotic Stability of Two-Dimensional Periodic Solutions with an Internal Transition Layer in a Problem with a Finite Advection","authors":"N.N. Nefedov,&nbsp;E.I. Nikulin,&nbsp;L. Recke,&nbsp;K. Schneider","doi":"10.1134/S1061920824040113","DOIUrl":"10.1134/S1061920824040113","url":null,"abstract":"<p> We consider a periodic boundary value problem for a singularly perturbed reaction-advection-diffusion equation in the case of a two-dimensional space variable. We construct a new interior layer-type formal asymptotics which includes an approximation of the location of the interior layer, investigate the order-preserving properties of the operators generating the asymptotics, and propose a modified procedure to obtain asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its asymptotics. We also prove the asymptotic Lyapunov stability of this solution. </p><p> <b> DOI</b> 10.1134/S1061920824040113 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"719 - 736"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373284","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
Local and Global Suns 本地太阳和全球太阳
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040150
I.G. Tsar’kov
{"title":"Local and Global Suns","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920824040150","DOIUrl":"10.1134/S1061920824040150","url":null,"abstract":"<p> Properties of local and global suns and protosuns are studied. In particular, we investigate properties of a space and a set under which the local solarity of the set implies its global solar properties. It is shown that, in CLUR-spaces, a segmented Chebyshev local sun is a sun. In particular, a Chebyshev local sun composed of an at most countable family of convex existence sets is a sun. </p><p> <b> DOI</b> 10.1134/S1061920824040150 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"765 - 773"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373314","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
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
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