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Russian Journal of Mathematical Physics最新文献

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Inverse Semigroups of Metrics on Doubles Related to Certain Subsets 与某些子集相关的双精度上的度量逆半群
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020097
V. Manuilov
{"title":"Inverse Semigroups of Metrics on Doubles Related to Certain Subsets","authors":"V. Manuilov","doi":"10.1134/S1061920823020097","DOIUrl":"10.1134/S1061920823020097","url":null,"abstract":"<p> Recently we have shown that the equivalence classes of metrics on the double of a metric space <span>(X)</span> form an inverse semigroup. Here we define an inverse subsemigroup related to a family of isometric subspaces of <span>(X)</span>, which is more computable. As a special case, we study this subsemigroup related to the family of geodesic rays starting from the basepoint, for Euclidean spaces and for trees. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"239 - 245"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4724187","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
Smoothness of Solutions of the Eikonal Equation and Regular Points of Their Level Surfaces Eikonal方程解的光滑性及其水平面的正则点
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020127
I. G. Tsar’kov
{"title":"Smoothness of Solutions of the Eikonal Equation and Regular Points of Their Level Surfaces","authors":"I. G. Tsar’kov","doi":"10.1134/S1061920823020127","DOIUrl":"10.1134/S1061920823020127","url":null,"abstract":"<p> Properties of local solarity and regularity in essentially asymmetric locally uniformly rotund spaces are studied. The results obtained are applied to the study of smooth solutions of the eikonal equation <span>(|nabla u|equiv 1)</span>. For this purpose, sets of regular points are investigated. Examples of the influence of caustics on the evolution of elliptical galaxies into spiral ones are given. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"259 - 269"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4723319","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
Solitary Wave Solutions to a Generalization of the mKdV Equation mKdV方程推广的孤立波解
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020103
G. Omel’yanov, J. Noyola Rodriguez
{"title":"Solitary Wave Solutions to a Generalization of the mKdV Equation","authors":"G. Omel’yanov,&nbsp;J. Noyola Rodriguez","doi":"10.1134/S1061920823020103","DOIUrl":"10.1134/S1061920823020103","url":null,"abstract":"<p> We consider a generalization of the mKdV equation which contains dissipation terms similar to those contained in both the Benjamin–Bona–Mahoney equation and the famous Camassa–Holm and Degasperis–Procesi equations. Our objective is the construction of classical (solitons) and non-classical (peakons and cuspons) solitary wave solutions of this equation. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"246 - 256"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4727269","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: 1
Quantization of Nonsmooth Curves and the Semiclassical Spectrum of the One-Dimensional Schrödinger Operator with a Localized Perturbation of the Potential 位能局域扰动下非光滑曲线的量化和一维Schrödinger算子的半经典谱
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020073
I. A. Lavrinenko, A. I. Shafarevich
{"title":"Quantization of Nonsmooth Curves and the Semiclassical Spectrum of the One-Dimensional Schrödinger Operator with a Localized Perturbation of the Potential","authors":"I. A. Lavrinenko,&nbsp;A. I. Shafarevich","doi":"10.1134/S1061920823020073","DOIUrl":"10.1134/S1061920823020073","url":null,"abstract":"<p> A semiclassical asymptotics of eigenfunctions and eigenvalues is constructed for the one-dimensional Schrödinger operator in which the potential rapidly changes around a certain point. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"209 - 218"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5019440","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
Trajectory Symbols and the Fredholm Property of Boundary Value Problems for Differential Operators with Shifts 带移位微分算子边值问题的轨迹符号与Fredholm性质
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020012
A. V. Boltachev, A. Yu. Savin
{"title":"Trajectory Symbols and the Fredholm Property of Boundary Value Problems for Differential Operators with Shifts","authors":"A. V. Boltachev,&nbsp;A. Yu. Savin","doi":"10.1134/S1061920823020012","DOIUrl":"10.1134/S1061920823020012","url":null,"abstract":"<p> Boundary value problems are considered in which the main operator and the operators of boundary conditions include differential and shift operators corresponding to the action of a discrete group. The manifold on which the boundary value problem is considered is not assumed to be group invariant. A definition of trajectory symbols for this class of boundary value problems is given. It is shown that elliptic problems define Fredholm operators in the corresponding Sobolev spaces. An application to problems with extensions and contractions is given. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"135 - 151"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4724188","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
Conclusive Discrimination by (N) Sequential Receivers between (rgeq2) Arbitrary Quantum States (N)顺序接收器在(rgeq2)任意量子态之间的结论性判别
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020085
E. R. Loubenets, M. Namkung
{"title":"Conclusive Discrimination by (N) Sequential Receivers between (rgeq2) Arbitrary Quantum States","authors":"E. R. Loubenets,&nbsp;M. Namkung","doi":"10.1134/S1061920823020085","DOIUrl":"10.1134/S1061920823020085","url":null,"abstract":"<p> In the present paper, we develop a general mathematical framework for discrimination between <span>(rgeq2)</span> quantum states by <span>(Ngeq1)</span> sequential receivers for the case in which every receiver obtains a conclusive result. This type of discrimination constitutes an <span>(N)</span>-sequential extension of the minimum-error discrimination by one receiver. The developed general framework, which is valid for a conclusive discrimination between any number <span>(rgeq2)</span> of quantum states, pure or mixed, of an arbitrary dimension and any number <span>(Ngeq1)</span> of sequential receivers, is based on the notion of a quantum state instrument, and this allows us to derive new important general results. In particular, we find a general condition on <span>(rgeq2)</span> quantum states under which, within the strategy in which all types of receivers’ quantum measurements are allowed, the optimal success probability of the <span>(N)</span>-sequential conclusive discrimination between these <span>(rgeq2)</span> states is equal to that of the first receiver for any number <span>(Ngeq2)</span> of further sequential receivers and specify the corresponding optimal protocol. Furthermore, we extend our general framework to include an <span>(N)</span>-sequential conclusive discrimination between <span>(rgeq2)</span> arbitrary quantum states under a noisy communication. As an example, we analyze analytically and numerically a two-sequential conclusive discrimination between two qubit states via depolarizing quantum channels. The derived new general results are important both from the theoretical point of view and for the development of a successful multipartite quantum communication via noisy quantum channels. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"219 - 238"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4727565","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
Lattice Equations and Semiclassical Asymptotics 格方程与半经典渐近
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020024
V. L. Chernyshev, V. E. Nazaikinskii, A. V. Tsvetkova
{"title":"Lattice Equations and Semiclassical Asymptotics","authors":"V. L. Chernyshev,&nbsp;V. E. Nazaikinskii,&nbsp;A. V. Tsvetkova","doi":"10.1134/S1061920823020024","DOIUrl":"10.1134/S1061920823020024","url":null,"abstract":"<p> We consider linear equations with shifts of the arguments on the rectangular lattice with small step <span>(h)</span> in <span>(mathbb{R}^n)</span> and construct a version of the canonical operator providing semiclassical asymptotics for such equations. Examples include the Feynman checkers model arising in quantum theory and a problem on the wave packet propagation on a homogeneous tree. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"152 - 164"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4725853","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
Semiclassical Asymptotic Expansions for Functions of the Bochner–Schrödinger Operator Bochner-Schrödinger算子函数的半经典渐近展开式
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020061
Y. A. Kordyukov
{"title":"Semiclassical Asymptotic Expansions for Functions of the Bochner–Schrödinger Operator","authors":"Y. A. Kordyukov","doi":"10.1134/S1061920823020061","DOIUrl":"10.1134/S1061920823020061","url":null,"abstract":"<p> The Bochner–Schrödinger operator <span>(H_{p}=frac 1pDelta^{L^potimes E}+V)</span> on tensor powers <span>(L^p)</span> of a Hermitian line bundle <span>(L)</span> twisted by a Hermitian vector bundle <span>(E)</span> on a Riemannian manifold of bounded geometry is studied. For any function <span>(varphiin mathcal S(mathbb R))</span>, we consider the bounded linear operator <span>(varphi(H_p))</span> in <span>(L^2(X,L^potimes E))</span> defined by the spectral theorem and describe an asymptotic expansion of its smooth Schwartz kernel in a fixed neighborhood of the diagonal in the semiclassical limit <span>(pto infty)</span>. In particular, we prove that the trace of the operator <span>(varphi(H_p))</span> admits a complete asymptotic expansion in powers of <span>(p^{-1/2})</span> as <span>(pto infty)</span>. We also prove a result on the asymptotic localization of the Schwartz kernel of the spectral projection on the diagonal in the case when the curvature is of full rank. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"192 - 208"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4727254","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: 2
Ice-Water Phase Transition on a Substrate 衬底上的冰-水相变
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020036
V. G. Danilov, R. K. Gaydukov
{"title":"Ice-Water Phase Transition on a Substrate","authors":"V. G. Danilov,&nbsp;R. K. Gaydukov","doi":"10.1134/S1061920823020036","DOIUrl":"10.1134/S1061920823020036","url":null,"abstract":"<p> In this paper, we construct and study a model of phase transition in a system of two phases (liquid and ice) and three media, namely, water, a piece of ice, and a nonmelting solid substrate. Namely, the melting-crystallization process is considered in the problem of water flow along a small ice irregularity (such as a frozen drop) on a flat substrate for large Reynolds numbers. The results of numerical simulation are presented. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"165 - 175"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4723318","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 Homogenization for Piecewise Locally Periodic Operators 关于分段局部周期算子的均匀化问题
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI: 10.1134/S1061920823020139
N. N. Senik
{"title":"On Homogenization for Piecewise Locally Periodic Operators","authors":"N. N. Senik","doi":"10.1134/S1061920823020139","DOIUrl":"10.1134/S1061920823020139","url":null,"abstract":"<p> We discuss homogenization of a strongly elliptic operator <span>(mathcal A^varepsilon=-operatorname{div}A(x,x/varepsilon_#)nabla)</span> on a bounded <span>(C^{1,1})</span> domain in <span>(mathbb R^d)</span> with either Dirichlet or Neumann boundary condition. The function <span>(A)</span> is piecewise Lipschitz in the first variable and periodic in the second one, and the function <span>(varepsilon_#)</span> is identically equal to <span>(varepsilon_i(varepsilon))</span> on each piece <span>(Omega_i)</span>, with <span>(varepsilon_i(varepsilon)to0)</span> as <span>(varepsilonto0)</span>. For <span>(mu)</span> in a resolvent set, we show that the resolvent <span>((mathcal A^varepsilon-mu)^{-1})</span> converges, as <span>(varepsilonto0)</span>, in the operator norm on <span>(L_2(Omega)^n)</span> to the resolvent <span>((mathcal A^0-mu)^{-1})</span> of the effective operator at the rate <span>(varepsilon_ {vee} )</span>, where <span>(varepsilon_ {vee} )</span> stands for the largest of <span>(varepsilon_i(varepsilon))</span>. We also obtain an approximation for the resolvent in the operator norm from <span>(L_2(Omega)^n)</span> to <span>(H^1(Omega)^n)</span> with error of order <span>(varepsilon_ {vee} ^{1/2})</span>. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"270 - 274"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4725849","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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