Mathematical Physics, Analysis and Geometry最新文献

Essential Self-Adjointness of the Laplacian on Weighted Graphs: Harmonic Functions, Stability, Characterizations and Capacity 加权图上拉普拉斯算子的本质自伴随性：调和函数、稳定性、刻画和容量

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-26 DOI: 10.1007/s11040-025-09498-z

Atsushi Inoue, Sean Ku, Jun Masamune, Radosław K. Wojciechowski

引用次数: 0

The Ricci Curvature and the Normalized Ricci Flow on Generalized Wallach Spaces 广义Wallach空间上的Ricci曲率和归一化Ricci流

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-20 DOI: 10.1007/s11040-025-09509-z

Nurlan A. Abiev

{"title":"The Ricci Curvature and the Normalized Ricci Flow on Generalized Wallach Spaces","authors":"Nurlan A. Abiev","doi":"10.1007/s11040-025-09509-z","DOIUrl":"10.1007/s11040-025-09509-z","url":null,"abstract":"<div>We proved that the normalized Ricci flow does not preserve the positivity of the Ricci curvature of invariant Riemannian metrics on every generalized Wallach space with (a_1+a_2+a_3le 1/2), in particular, such a property takes place on the homogeneous spaces (operatorname {SU}(k+l+m)/operatorname {S}(operatorname {U}(k)times operatorname {U}(l) times operatorname {U}(m))) and (operatorname {Sp}(k+l+m)/operatorname {Sp}(k)times operatorname {Sp}(l) times operatorname {Sp}(m)) independently on their parameters k, l and m. We proved that the positivity of the Ricci curvature is preserved under the normalized Ricci flow on generalized Wallach spaces with (a_1+a_2+a_3> 1/2) if the conditions (4left( a_j+a_kright) ^2ge (1-2a_i)(1+2a_i)^{-1}) are satisfied for all ({i,j,k}={1,2,3}). We also established that the homogeneous spaces (operatorname {SO}(k+l+m)/operatorname {SO}(k)times operatorname {SO}(l)times operatorname {SO}(m)) satisfy the above conditions if (max {k,l,m}le 11), moreover, additional conditions were found to keep (operatorname {Ric}>0) in cases when (max {k,l,m}le 11) is violated. Answers have also been found to similar questions about maintaining or non-maintaining the positivity of the Ricci curvature on all other generalized Wallach spaces given in the classification of Yu. G. Nikonorov.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of Gibbs Measures and Stability of Dynamical System Linked to (1,1/2)-Mixed Ising Model on ((m,k))-Ary Trees ((m,k)) -Ary树上(1,1/2)-混合Ising模型动力学系统的Gibbs测度及稳定性分析

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-04 DOI: 10.1007/s11040-025-09504-4

Aminah Qawasmeh, Farrukh Mukhamedov, Hasan Akın

{"title":"Analysis of Gibbs Measures and Stability of Dynamical System Linked to (1,1/2)-Mixed Ising Model on ((m,k))-Ary Trees","authors":"Aminah Qawasmeh, Farrukh Mukhamedov, Hasan Akın","doi":"10.1007/s11040-025-09504-4","DOIUrl":"10.1007/s11040-025-09504-4","url":null,"abstract":"<div>This paper introduces a new (1,1/2) mixed spin Ising model (shortly, (1,1/2)-MSIM) having (J_1) and (J_2) competing interactions on (m, k)-ary trees. By constructing splitting Gibbs measures, we establish the presence of multiple Gibbs measures, which implies the occurrence of the phase transition for the (1, 1/2)-MSIM on the (m, k)-ary trees. Furthermore, the extremality of the two translation-invariant Gibbs measures is demonstrated for (1, k)-ary trees. Moreover, the extremality condition for the disordered phases is found and its non-extremality regimes are examined as well. It is well known that, to investigate lattice models on tree-like structures, conducting a stability analysis of the dynamical systems that represent the model and examining the behavior of the fixed points of these dynamical systems can provide significant insights into the model. We conducted a stability analysis around fixed points to investigate the behavior of the MSIM on the (m, k)-ary trees, also referred to as k-ary trees.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Gauge Transformations and Long-Time Asymptotics for the New Coupled Integrable Dispersionless Equations 新耦合可积无色散方程的规范变换和长渐近性

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-02 DOI: 10.1007/s11040-025-09507-1

Xumeng Zhou, Xianguo Geng, Minxin Jia, Yunyun Zhai

引用次数: 0

Classification of (1+0) Two-Dimensional Hamiltonian Operators (1+0)二维哈密顿算子的分类

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-04-29 DOI: 10.1007/s11040-025-09506-2

Alessandra Rizzo

引用次数: 0

Notions of Fermionic Entropies for Causal Fermion Systems 因果费米子系统的费米子熵概念

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-04-15 DOI: 10.1007/s11040-025-09505-3

Felix Finster, Robert H. Jonsson, Magdalena Lottner, Albert Much, Simone Murro

引用次数: 0

Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets 有限集上吉布斯测度的混沌传播与残差依赖

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-03-15 DOI: 10.1007/s11040-025-09503-5

Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe

引用次数: 0

Recurrence Relations for the Generalized Laguerre and Charlier Orthogonal Polynomials and Discrete Painlevé Equations on the (D_{6}^{(1)}) Sakai Surface (D_{6}^{(1)}) Sakai曲面上广义Laguerre和Charlier正交多项式及离散painlev<e:1>方程的递归关系

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-03-15 DOI: 10.1007/s11040-025-09502-6

Xing Li, Anton Dzhamay, Galina Filipuk, Da-jun Zhang

{"title":"Recurrence Relations for the Generalized Laguerre and Charlier Orthogonal Polynomials and Discrete Painlevé Equations on the (D_{6}^{(1)}) Sakai Surface","authors":"Xing Li, Anton Dzhamay, Galina Filipuk, Da-jun Zhang","doi":"10.1007/s11040-025-09502-6","DOIUrl":"10.1007/s11040-025-09502-6","url":null,"abstract":"<div>This paper concerns the discrete version of the Painlevé identification problem, i.e., how to recognize a certain recurrence relation as a discrete Painlevé equation. Often some clues can be seen from the setting of the problem, e.g., when the recurrence is connected with some differential Painlevé equation, or from the geometry of the configuration of indeterminate points of the equation. The main message of our paper is that, in fact, this only allows us to identify the configuration space of the dynamic system, but not the dynamics themselves. The refined version of the identification problem lies in determining, up to the conjugation, the translation direction of the dynamics, which in turn requires the full power of the geometric theory of Painlevé equations. To illustrate this point, in this paper we consider two examples of such recurrences that appear in the theory of orthogonal polynomials. We choose these examples because they get regularized on the same family of Sakai surfaces, but at the same time are not equivalent, since they result in non-equivalent translation directions. In addition, we show the effectiveness of a recently proposed identification procedure for discrete Painlevé equations using Sakai’s geometric approach for answering such questions. In particular, this approach requires no a priori knowledge of a possible type of the equation.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Matrix Solutions of the Cubic Szegő Equation on the Real Line 实线上三次塞格格方程的矩阵解

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-03-09 DOI: 10.1007/s11040-025-09500-8

Ruoci Sun

引用次数: 0

A Novel Discrete Integrable System Related to Hyper-Elliptic Curves of Genus Two 一类关于2属超椭圆曲线的新的离散可积系统

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-02-25 DOI: 10.1007/s11040-025-09501-7

Jing-Rui Wu, Xing-Biao Hu

引用次数: 0