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
Identification of the Potential Coefficient in the Schrödinger Equation with Incomplete Initial Conditions from a Boundary Observation 不完全初始条件下Schrödinger方程位系数的边界观测辨识
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/S1061920823020048
B. Elhamza, A. Hafdallah
{"title":"Identification of the Potential Coefficient in the Schrödinger Equation with Incomplete Initial Conditions from a Boundary Observation","authors":"B. Elhamza,&nbsp;A. Hafdallah","doi":"10.1134/S1061920823020048","DOIUrl":"10.1134/S1061920823020048","url":null,"abstract":"<p> This paper deals with an inverse problem of the Schrödinger equation, a fundamental equation in quantum mechanics. Specifically, we focus on incomplete data, where there are missing terms in the potential term and the initial condition. The potential term is a critical part of the equation, representing the potential energy of the system under investigation. Our objective is to obtain valuable information about this potential term without the need to determine the unknown initial condition. To achieve this, we employ the sentinel method, which is a functional that is sensitive to only one unknown and insensitive to others. Our research shows that the existence of this functional is connected to solving an optimal control problem, which we accomplish using the Hilbert Uniqueness Method. By using this approach, we are able to gain insights into the potential coefficient, which can provide significant benefits in a wide range of applications. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"176 - 183"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5019432","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 Version of the Weyl Complete Reducibility Theorem for Not Necessarily Continuous Representations of Connected Lie Groups 连通李群不一定连续表示的Weyl完全可约定理的一个版本
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/S1061920823020115
A. I. Shtern
{"title":"A Version of the Weyl Complete Reducibility Theorem for Not Necessarily Continuous Representations of Connected Lie Groups","authors":"A. I. Shtern","doi":"10.1134/S1061920823020115","DOIUrl":"10.1134/S1061920823020115","url":null,"abstract":"<p> A version of the Weyl complete reducibility theorem for finite-dimensional quasirepresentations of general connected Lie groups is proved. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"257 - 258"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4725917","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
Thick Elements and States in (C^*)-Algebras in View of Frame Theory 基于框架理论的(C^*) -代数中的厚元与厚态
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/S106192082302005X
D. V. Fufaev
{"title":"Thick Elements and States in (C^*)-Algebras in View of Frame Theory","authors":"D. V. Fufaev","doi":"10.1134/S106192082302005X","DOIUrl":"10.1134/S106192082302005X","url":null,"abstract":"<p> We study some classes of noncommutative <span>(C^*)</span>-algebras and generalize some results which were originally obtained for commutative algebras in topological terms. In particular, we are interested in results obtained for topological spaces with properties close to separability and <span>( sigma )</span>-compactness. To obtain the algebraic, noncommutative versions of corresponding properties, we define and use the notions of thick elements and states. In particular, an element is thick if the only element orthogonal to it is zero. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"184 - 191"},"PeriodicalIF":1.4,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4727253","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
Extension of the Generalized Lebesgue–Feynman–Smolyanov Measure on a Hilbert Space Hilbert空间上广义Lebesgue-Feynman-Smolyanov测度的推广
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI: 10.1134/S1061920823010089
M. G. Shelakov
{"title":"Extension of the Generalized Lebesgue–Feynman–Smolyanov Measure on a Hilbert Space","authors":"M. G. Shelakov","doi":"10.1134/S1061920823010089","DOIUrl":"10.1134/S1061920823010089","url":null,"abstract":"<p> As is well known, on an infinite-dimensional Hilbert space, there is no countably additive sigma-finite locally finite nonzero translation-invariant nonnegative Borel measure (Andre Weil’s theorem, [1]). For this reason, to formalize the Feynman path integrals [2], one has to introduce a generalized translation-invariant measure (Lebesgue–Feynman in the sense of the definition in [2]) as a linear functional on some space of functions. The present paper proposes a natural extension of one of these functionals that were introduced in [3] and called there the generalized Lebesgue measure (henceforth, we call this (generalized) measure the Lebesgue–Feynman–Smolyanov). The extension makes it possible to give a precise mathematical meaning to the Schrödinger quantization of noncylindrical Hamiltonians for Hamiltonian systems with infinitely many degrees of freedom [3]: in particular, to give a correct mathematical solution to the problem of infinite vacuum energy at the bosonic quantization of the “free” electromagnetic field (N. N. Bogoliubov, D. V. Shirkov, Introduction to the Theory of Quantized Fields, John Wiley &amp; Sons, New York–Chichester–Brisbane, 1980); invariant measures themselves have recently been used for the mathematical description of the phenomena of quantum anomalies [4, 5, 6]. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"114 - 125"},"PeriodicalIF":1.4,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4690851","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 Domain of Constancy of the Sign of a Harmonic Function in the Unit Disk with Additional Conditions on the Boundary 边界上有附加条件的单位圆盘上调和函数符号的恒常性定域
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI: 10.1134/S1061920823010077
T. Yu. Semenova
{"title":"On the Domain of Constancy of the Sign of a Harmonic Function in the Unit Disk with Additional Conditions on the Boundary","authors":"T. Yu. Semenova","doi":"10.1134/S1061920823010077","DOIUrl":"10.1134/S1061920823010077","url":null,"abstract":"<p> An estimate for the domain of constant sign for a function harmonic in the unit disk is obtained under the condition that the function is represented on the boundary of the circle as a sine series with monotonic coefficients. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"111 - 113"},"PeriodicalIF":1.4,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4690168","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
Global Asymptotics for Functions of Parabolic Cylinder and Solutions of the Schrödinger Equation with a Potential in the Form of a Nonsmooth Double Well 抛物柱面函数的全局渐近性及具有非光滑双井形式势的Schrödinger方程的解
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI: 10.1134/S106192082301003X
S. Yu. Dobrokhotov, A. V. Tsvetkova
{"title":"Global Asymptotics for Functions of Parabolic Cylinder and Solutions of the Schrödinger Equation with a Potential in the Form of a Nonsmooth Double Well","authors":"S. Yu. Dobrokhotov,&nbsp;A. V. Tsvetkova","doi":"10.1134/S106192082301003X","DOIUrl":"10.1134/S106192082301003X","url":null,"abstract":"<p> In the paper, an approach is discussed that makes it possible to obtain global formulas in terms of Airy functions <span>({rm Ai})</span> and <span>({rm Bi})</span> of compound argument for the asymptotics of the functions of parabolic cylinder <span>(D_{nu}(z))</span> for real <span>(z)</span> and large <span>(nu)</span>. The parabolic cylinder functions are determined from the Schrödinger equation, with potential in the form of a quadratic parabola, whose asymptotic solution can be constructed using the semiclassical approximation. In this case, the Bohr–Sommerfeld condition singles out the functions with an integer index whose asymptotics is determined only by the function <span>({rm Ai})</span>. For noninteger indices, the function <span>({rm Bi})</span> also contributes into the asymptotics. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"46 - 61"},"PeriodicalIF":1.4,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4690838","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
On Relationships between the Spectral Potential of Transfer Operators, (boldsymbol t)-Entropy, Entropy and Topological Pressure 论传递算子的谱势，(boldsymbol t) -熵，熵与拓扑压力的关系
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI: 10.1134/S1061920823010016
V. I. Bakhtin, A. V. Lebedev
{"title":"On Relationships between the Spectral Potential of Transfer Operators, (boldsymbol t)-Entropy, Entropy and Topological Pressure","authors":"V. I. Bakhtin,&nbsp;A. V. Lebedev","doi":"10.1134/S1061920823010016","DOIUrl":"10.1134/S1061920823010016","url":null,"abstract":"<p> The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism (entropy and topological pressure). We present explicit formulas linking these objects with the <span>(t)</span>-entropy and spectral potential. Herewith we uncover the role of inverse rami-rate, the forward entropy along with an essential set, and the property of noncontractibility of a dynamical system. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"1 - 24"},"PeriodicalIF":1.4,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4690843","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
Classification of Singularities of Smooth Functions with a Finite Cyclic Symmetry Group 有限循环对称群光滑函数奇异性的分类
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI: 10.1134/S1061920823010053
E. A. Kudryavtseva, M. V. Onufrienko
{"title":"Classification of Singularities of Smooth Functions with a Finite Cyclic Symmetry Group","authors":"E. A. Kudryavtseva,&nbsp;M. V. Onufrienko","doi":"10.1134/S1061920823010053","DOIUrl":"10.1134/S1061920823010053","url":null,"abstract":"<p> In the paper, we study the singularities of smooth functions of two variables that are invariant under the action of a finite group <span>(G)</span> acting by rotations. A classification is obtained for critical points arising in typical parametric families of <span>(G)</span>-invariant smooth functions with at most two parameters, when <span>(|G|ne4)</span>. A criterion is obtained for the reducibility of a smooth <span>(G)</span>-invariant function to a normal form (by means of a <span>(G)</span>-equivariant change of variables) when the Taylor polynomial of degree <span>(|G|)</span> of the function is not a polynomial in <span>(x^2+y^2)</span> and the Milnor <span>(G)</span>-multiplicity (the <span>(G)</span>-codimension, respectively) of the singularity is less than <span>(|G|)</span> (than <span>(|G|/2)</span>, respectively). A criterion is obtained for the reducibility of a smooth parametric family of <span>(G)</span>-invariant functions to a normal form near the critical point of the type in question. The criteria are given in terms of partial derivatives of the function at the critical point. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"76 - 95"},"PeriodicalIF":1.4,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4694851","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
Model (CR) Surfaces: Weighted Approach 模型(CR)曲面:加权方法
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI: 10.1134/S1061920823010028
V. K. Beloshapka
{"title":"Model (CR) Surfaces: Weighted Approach","authors":"V. K. Beloshapka","doi":"10.1134/S1061920823010028","DOIUrl":"10.1134/S1061920823010028","url":null,"abstract":"<p> In the paper, a systematic construction of the theory of “weighted” model surfaces using the Bloom–Graham–Stepanova concept of the type of a <i> CR</i>-manifold is given. The construction is based on the Poincaré construction. It is shown how the use of weighted model surfaces expands the abilities of the method. New questions are being posed. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"25 - 45"},"PeriodicalIF":1.4,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4690206","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
Some Identities Involving Degenerate Stirling Numbers Associated with Several Degenerate Polynomials and Numbers 与若干退化多项式和数相关的退化斯特林数的一些恒等式
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI: 10.1134/S1061920823010041
T. K. Kim, D. S. Kim
{"title":"Some Identities Involving Degenerate Stirling Numbers Associated with Several Degenerate Polynomials and Numbers","authors":"T. K. Kim,&nbsp;D. S. Kim","doi":"10.1134/S1061920823010041","DOIUrl":"10.1134/S1061920823010041","url":null,"abstract":"<p> The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate Stirling numbers of both kinds associated with degenerate hyperharmonic numbers and also with degenerate Bernoulli, degenerate Euler, degenerate Bell, and degenerate Fubini polynomials. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"62 - 75"},"PeriodicalIF":1.4,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4694853","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: 11
首页 上一页
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：481959085
Book学术官方微信