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A nonlocal finite-dimensional integrable system related to the nonlocal mKdV equation 与非局部 mKdV 方程相关的非局部有限维可积分系统
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030024
Xue Wang, Dianlou Du, Hui Wang
{"title":"A nonlocal finite-dimensional integrable system related to the nonlocal mKdV equation","authors":"Xue Wang,&nbsp;Dianlou Du,&nbsp;Hui Wang","doi":"10.1134/S0040577924030024","DOIUrl":"10.1134/S0040577924030024","url":null,"abstract":"<p> We propose a hierarchy of the nonlocal mKdV (NmKdV) equation. Based on a constraint, we obtain nonlocal finite-dimensional integrable systems in a Lie–Poisson structure. By a coordinate transformation, the nonlocal Lie–Poisson Hamiltonian systems are reduced to nonlocal canonical Hamiltonian systems in the standard symplectic structure. Moreover, using the nonlocal finite-dimensional integrable systems, we give parametric solutions of the NmKdV equation and the generalized nonlocal nonlinear Schrödinger (NNLS) equation. According to the Hamilton–Jacobi theory, we obtain the action–angle-type coordinates and the inversion problems related to Lie–Poisson Hamiltonian systems. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalizing the holographic fishchain 推广全息鱼链
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030048
R. M. Iakhibbaev, D. M. Tolkachev
{"title":"Generalizing the holographic fishchain","authors":"R. M. Iakhibbaev,&nbsp;D. M. Tolkachev","doi":"10.1134/S0040577924030048","DOIUrl":"10.1134/S0040577924030048","url":null,"abstract":"<p> We attempt to generalize the integrable Gromov–Sever models, the so-called fishchain models, which are dual to biscalar fishnets. We show that they can be derived in any dimension, at least for some integer deformation parameter of the fishnet lattice. In particular, we focus on the study of fishchain models in AdS<span>(_7)</span> that are dual to the six-dimensional fishnet models. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Stabilization of the statistical solutions for large times for a harmonic lattice coupled to a Klein–Gordon field 与克莱因-戈登场耦合的谐波晶格的大时间统计解的稳定性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020053
T. V. Dudnikova
{"title":"Stabilization of the statistical solutions for large times for a harmonic lattice coupled to a Klein–Gordon field","authors":"T. V. Dudnikova","doi":"10.1134/S0040577924020053","DOIUrl":"10.1134/S0040577924020053","url":null,"abstract":"<p> We consider the Cauchy problem for the Hamiltonian system consisting of the Klein–Gordon field and an infinite harmonic crystal. The dynamics of the coupled system is translation-invariant with respect to the discrete subgroup <span>(mathbb{Z}^d)</span> of <span>(mathbb{R}^d)</span>. The initial date is assumed to be a random function that is close to two spatially homogeneous (with respect to the subgroup <span>(mathbb{Z}^d)</span>) processes when <span>(pm x_1&gt;a)</span> with some <span>(a&gt;0)</span>. We study the distribution <span>(mu_t)</span> of the solution at time <span>(tinmathbb{R})</span> and prove the weak convergence of <span>(mu_t)</span> to a Gaussian measure <span>(mu_infty)</span> as <span>(ttoinfty)</span>. Moreover, we prove the convergence of the correlation functions to a limit and derive the explicit formulas for the covariance of the limit measure <span>(mu_infty)</span>. We give an application to Gibbs measures. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Solution of the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives in statistical mechanics 利用统计力学中的黎曼-利乌维尔和卡普托导数求解分数利乌维尔方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020107
Z. Korichi, A. Souigat, R. Bekhouche, M. T. Meftah
{"title":"Solution of the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives in statistical mechanics","authors":"Z. Korichi,&nbsp;A. Souigat,&nbsp;R. Bekhouche,&nbsp;M. T. Meftah","doi":"10.1134/S0040577924020107","DOIUrl":"10.1134/S0040577924020107","url":null,"abstract":"<p> We solve the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives for systems exhibiting noninteger power laws in their Hamiltonians. Based on the fractional Liouville equation, we calculate the density function (DF) of a classical ideal gas. If the Riemann–Liouville derivative is used, the DF is a function depending on both the momentum <span>(p)</span> and the coordinate <span>(q)</span>, but if the derivative in the Caputo sense is used, the DF is a constant independent of <span>(p)</span> and <span>(q)</span>. We also study a gas consisting of <span>(N)</span> fractional oscillators in one-dimensional space and obtain that the DF of the system depends on the type of the derivative. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Infinitely many rotating periodic solutions for damped vibration systems 阻尼振动系统的无限多旋转周期解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020089
K. Khachnaoui
{"title":"Infinitely many rotating periodic solutions for damped vibration systems","authors":"K. Khachnaoui","doi":"10.1134/S0040577924020089","DOIUrl":"10.1134/S0040577924020089","url":null,"abstract":"<p> We investigate a particular type of damped vibration systems that incorporate impulsive effects. The objective is to establish the existence and multiplicity of <span>(Q)</span>-rotating periodic solutions. To achieve this, the variational method and the fountain theorem, as presented by Bartsch, are used. The research builds upon recent findings and extends them by introducing notable enhancements. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions 二维和三维大地线汉密尔顿-雅可比方程中的变量分离
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020065
M. O. Katanaev
{"title":"Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions","authors":"M. O. Katanaev","doi":"10.1134/S0040577924020065","DOIUrl":"10.1134/S0040577924020065","url":null,"abstract":"<p> On (pseudo)Riemannian manifolds of two and three dimensions, we list all metrics that admit a complete separation of variables in the Hamilton–Jacobi equation for geodesics. There are three different classes of separable metrics on two-dimensional surfaces. Three-dimensional manifolds admit six classes of separable metrics. Within each class, metrics are related by canonical transformations and a nondegenerate transformation of parameters that does not depend on coordinates. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139988020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 structure of shift-invariant subspaces of Sobolev spaces 索波列夫空间的移变量子空间结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020016
A. Aksentijević, S. Aleksić, S. Pilipović
{"title":"The structure of shift-invariant subspaces of Sobolev spaces","authors":"A. Aksentijević,&nbsp;S. Aleksić,&nbsp;S. Pilipović","doi":"10.1134/S0040577924020016","DOIUrl":"10.1134/S0040577924020016","url":null,"abstract":"<p> We analyze shift-invariant spaces <span>(V_s)</span>, subspaces of Sobolev spaces <span>(H^s(mathbb{R}^n))</span>, <span>(sinmathbb{R})</span>, generated by a set of generators <span>(varphi_i)</span>, <span>(iin I)</span>, with <span>(I)</span> at most countable, by the use of range functions and characterize Bessel sequences, frames, and the Riesz basis of such spaces. We also describe <span>(V_s)</span> in terms of Gramians and their direct sum decompositions. We show that <span>(finmathcal D_{L^2}'(mathbb{R}^n))</span> belongs to <span>(V_s)</span> if and only if its Fourier transform has the form <span>(hat f=sum_{iin I}f_ig_i)</span>, <span>(f_i=hatvarphi_iin L_s^2(mathbb{R}^n))</span>, <span>({varphi_i(,cdot+k)colon kinmathbb Z^n,,iin I})</span> is a frame, and <span>(g_i=sum_{kinmathbb{Z}^n}a_k^ie^{-2pisqrt{-1},langle,{cdot},,krangle})</span>, with <span>((a^i_k)_{kinmathbb{Z}^n}inell^2(mathbb{Z}^n))</span>. Moreover, connecting two different approaches to shift-invariant spaces <span>(V_s)</span> and <span>(mathcal V^2_s)</span>, <span>(s&gt;0)</span>, under the assumption that a finite number of generators belongs to <span>(H^scap L^2_s)</span>, we give the characterization of elements in <span>(V_s)</span> through the expansions with coefficients in <span>(ell_s^2(mathbb{Z}^n))</span>. The corresponding assertion holds for the intersections of such spaces and their duals in the case where the generators are elements of <span>(mathcal S(mathbb R^n))</span>. We then show that <span>(bigcap_{s&gt;0}V_s)</span> is the space consisting of functions whose Fourier transforms equal products of functions in <span>(mathcal S(mathbb R^n))</span> and periodic smooth functions. The appropriate assertion is obtained for <span>(bigcup_{s&gt;0}V_{-s})</span>. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Bose gas modeling of the Schwarzschild black hole thermodynamics 施瓦兹柴尔德黑洞热力学的玻色气体模型
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020028
I. Ya. Aref’eva, I. V. Volovich
{"title":"Bose gas modeling of the Schwarzschild black hole thermodynamics","authors":"I. Ya. Aref’eva,&nbsp;I. V. Volovich","doi":"10.1134/S0040577924020028","DOIUrl":"10.1134/S0040577924020028","url":null,"abstract":"<p> Black holes violate the third law of thermodynamics, and this gives rise to difficulties with the microscopic description of their entropy. Recently, it has been shown that the microscopic description of the Schwarzschild black hole thermodynamics in <span>(D = 4)</span> space–time dimensions is provided by the analytic continuation of the entropy of Bose gas with a nonrelativistic one-particle energy to <span>(d =-4)</span> negative spatial dimensions. In this paper, we show that the <span>(D=5)</span> and <span>(D=6)</span> Schwarzschild black holes thermodynamics can be modeled by the <span>(d)</span>-dimensional Bose gas, <span>(d=1,2,3,dots,)</span>, with the one-particle energy <span>(varepsilon(k)=k^alpha)</span> under the respective conditions <span>(alpha=-d/3)</span> and <span>(alpha=-d/4)</span>. In these cases, the free energy of the Bose gas has divergences, and we introduce a cut-off and perform the minimal renormalizations. We also perform renormalizations using analytic regularization and prove that the minimal cut-off renormalization gives the same answer as the analytic regularization by the Riemann zeta-function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Lotka–Volterra model with mutations and generative adversarial networks 带有突变和生成式对抗网络的洛特卡-沃尔特拉模型
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020077
S. V. Kozyrev
{"title":"Lotka–Volterra model with mutations and generative adversarial networks","authors":"S. V. Kozyrev","doi":"10.1134/S0040577924020077","DOIUrl":"10.1134/S0040577924020077","url":null,"abstract":"<p> A model of population genetics of the Lotka–Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace–Beltrami operator with a Fisher–Rao metric, that is, the model combines population genetics and information geometry. This model describes a generalization of the model of machine learning theory, the model of generative adversarial network (GAN), to the case of populations of generative adversarial networks. The introduced model describes the control of overfitting for generating adversarial networks. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139988010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems 弗拉索夫-麦克斯韦-爱因斯坦型方程及其后果。天体物理问题的应用
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI: 10.1134/S0040577924020041
V. V. Vedenyapin, N. N. Fimin, M. Chechetkin
{"title":"Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems","authors":"V. V. Vedenyapin,&nbsp;N. N. Fimin,&nbsp;M. Chechetkin","doi":"10.1134/S0040577924020041","DOIUrl":"10.1134/S0040577924020041","url":null,"abstract":"<p> We consider a method for obtaining equations of the Hamiltonian dynamics for system of interacting massive charged particles using the general relativistic Einstein–Hilbert action. In the general relativistic case, Vlasov-type equations are derived in the nonrelativistic and weakly relativistic limits. Expressions are proposed for corrections to the Poisson equation, which can contribute to the effective action of dark matter and dark energy. In this case, an efficient approach to synchronizing the proper times of different particles of a many-particle system is proposed. Based on the obtained expressions for the action, we analyze the possibility of a composite structure of the cosmological term in the Einstein equations. Reduced Euler equations leading to the Milne–McCrea cosmological model are derived using a hydrodynamic substitution and are solved in the self-similar class. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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