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TOTALLY NONNEGATIVE PFAFFIAN FOR SOLITONS IN 5-TYPE KADOMTSEV–PETVIASHVILI EQUATION 5型kadomtsev-petviashvili方程孤子的完全非负普法性
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00027-8
Jen-Hsu Chang
{"title":"TOTALLY NONNEGATIVE PFAFFIAN FOR SOLITONS IN 5-TYPE KADOMTSEV–PETVIASHVILI EQUATION","authors":"Jen-Hsu Chang","doi":"10.1016/S0034-4877(25)00027-8","DOIUrl":"10.1016/S0034-4877(25)00027-8","url":null,"abstract":"<div><div>The <em>B</em>-type Kadomtsev–Petviashvili equation (BKP) is obtained from the reduction of Kadomtsev–Petviashvili (KP) hierarchy under the orthogonal type transformation group. The skew Schur's <em>Q</em> functions can be used to construct the t-functions of solitons in the BKP equation. Then the totally nonnegative Pfaffian can be defined via the skew Schur's <em>Q</em> functions to obtain nonsingular line-solitons solution in the BKP equation. The totally nonnegative Pfaffians are investigated. The line solitons interact to form web-like structure in the near field region and their resonances appearing in soliton graph could be investigated by the totally nonnegative Pfaffians.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 259-279"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107403","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
Riemann Solitons on ℍ2 × ℝ and Sol3 <s:1> 2 × l和Sol3上的Riemann孤子
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00022-9
Shahroud Azami
{"title":"Riemann Solitons on ℍ2 × ℝ and Sol3","authors":"Shahroud Azami","doi":"10.1016/S0034-4877(25)00022-9","DOIUrl":"10.1016/S0034-4877(25)00022-9","url":null,"abstract":"<div><div>In this paper, we consider the Lie groups <strong>&amp;</strong>Hopf;<sup>2</sup> × ℝ and Sol<sub>3</sub> with left-invariant Riemannian metrics and we study the Riemann solitons on them. We prove that the Lie group <strong>&amp;</strong>Hopf;<sup>2</sup> × ℝ admits the Riemann soliton and the Lie group Sol<sub>3</sub> does not admit the Riemann soliton. We classify all Riemann solitons on the Lie group <strong>&amp;</strong>Hopf;<sup>2</sup> × ℝ and we show which of the potential vector fields of Riemann solitons are Killing, Ricci collineation, and Ricci bi-conformal vector fields. Also, we classify all Ricci bi-conformal vector fields on the Lie group Sol<sub>3</sub> and we show which of them are Killing and Ricci collineation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 141-154"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107398","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 UMBRAL-ALGEBRAIC APPROACH TO STUDY THE SHEFFER-λ POLYNOMIALS 用本影代数方法研究sheffer -λ多项式
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00025-4
UMME ZAINAB
{"title":"THE UMBRAL-ALGEBRAIC APPROACH TO STUDY THE SHEFFER-λ POLYNOMIALS","authors":"UMME ZAINAB","doi":"10.1016/S0034-4877(25)00025-4","DOIUrl":"10.1016/S0034-4877(25)00025-4","url":null,"abstract":"<div><div>In this article, the family of Sheffer-associated λ polynomials is introduced, and their quasi-monomial properties are established. Additionally, certain properties of these polynomials are explored using umbral algebraic matrix algebra. This approach provides a powerful tool for investigating the properties of multi-variable special polynomials. The recursive formulae and differential equations for these polynomials are derived using the properties and relationships between the Pascal functional and Wronskian matrices. The corresponding results for the Appellassociated λ polynomials and Appell-λ polynomial families are also obtained. Furthermore, these findings are demonstrated for the Hermite-λ, exponential-λ, and Miller-Lee-λ polynomials.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 215-240"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107401","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
LIEB–THIRRING TYPE ESTIMATES FOR DIRICHLET LAPLACIANS ON SPIRAL-SHAPED DOMAINS 螺旋形区域上狄利克雷拉普拉斯算子的Lieb-thirring型估计
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00026-6
JUAN BORY-REYES , DIANA BARSEGHYAN, BARUCH SCHNEIDER
{"title":"LIEB–THIRRING TYPE ESTIMATES FOR DIRICHLET LAPLACIANS ON SPIRAL-SHAPED DOMAINS","authors":"JUAN BORY-REYES ,&nbsp;DIANA BARSEGHYAN,&nbsp;BARUCH SCHNEIDER","doi":"10.1016/S0034-4877(25)00026-6","DOIUrl":"10.1016/S0034-4877(25)00026-6","url":null,"abstract":"<div><div>In this present paper we consider the asymptotically Archimedean spiral-shaped regions for which the Dirichlet Laplacian spectrum consists of the essential part and the eigenvalues below the threshold of the essential spectrum. Our purpose here is to obtain the bounds on the moments of these eigenvalues in terms of the geometric properties of the region. As a consequence of the mentioned bound we describe the class of the asymptotically Archimedean spiral-shaped regions such that the Dirichlet Laplacian has only a finite number of eigenvalues below the threshold of the essential spectrum.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 241-257"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107402","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
Partition Function for 1-Dimensional Kitaev Chain Model Engendering the Majorana Zero Mode 生成Majorana零模的一维Kitaev链模型的配分函数
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00021-7
Cheng Da , Hony-Yi Fan
{"title":"Partition Function for 1-Dimensional Kitaev Chain Model Engendering the Majorana Zero Mode","authors":"Cheng Da ,&nbsp;Hony-Yi Fan","doi":"10.1016/S0034-4877(25)00021-7","DOIUrl":"10.1016/S0034-4877(25)00021-7","url":null,"abstract":"<div><div>Partition function is an important physical quantity and is related to various thermodynamic functions, also is a key link that connects microscopic and macroscopic physical phenomena. In this article for the first time we calculate partition function Tr exp {-<em>iβt γ<sub>j,b</sub> γ<sub>j</sub></em>+1,<em><sub>a</sub></em>) for 1-dimensional Kitaev chain model which engenders the Majorana zero mode (MZM), where \u0000\t\t\t\t<span><math><mrow><msub><mi>y</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>a</mi></mrow></msub><mo>=</mo><msubsup><mi>c</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow><mo>†</mo></msubsup><mo>+</mo><msub><mi>c</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow><mi>j</mi><mo>,</mo><mi>b</mi></mrow></msub><mo>=</mo><mrow><mo>(</mo><mrow><msub><mi>c</mi><mi>j</mi></msub><mo>-</mo><msubsup><mi>c</mi><mi>j</mi><mo>†</mo></msubsup></mrow><mo>)</mo></mrow><mo>/</mo><mi>i</mi><mo>,</mo><mrow><mo>(</mo><mrow><msub><mi>c</mi><mrow><mi>j</mi><mo>,</mo></mrow></msub><msubsup><mi>c</mi><mi>j</mi><mo>†</mo></msubsup></mrow><mo>)</mo></mrow></mrow></math></span> are Dirac fermionic annihilation and creation operators. Following Fan's theorem we successfully disentangle exp {-<em>iβt γ<sub>j,b</sub> γ<sub>j</sub></em>+1,<em><sub>a</sub></em>) and derive the partition function by using the fermionic coherent state representation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 129-140"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107475","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
A NONAUTONOMOUS p-ADIC DIFFUSION EQUATION ON TIME CHANGING GRAPHS 时变图上的非自治p进扩散方程
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00023-0
PATRICK ERIK BRADLEY, ÁNGEL MORÁN LEDEZMA
{"title":"A NONAUTONOMOUS p-ADIC DIFFUSION EQUATION ON TIME CHANGING GRAPHS","authors":"PATRICK ERIK BRADLEY,&nbsp;ÁNGEL MORÁN LEDEZMA","doi":"10.1016/S0034-4877(25)00023-0","DOIUrl":"10.1016/S0034-4877(25)00023-0","url":null,"abstract":"<div><div>Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses), the very recent study of Turing patterns on locally ultrametric state spaces, and the study of Turing patterns in time changing networks, first nonautonomous diffusion operators on such systems, where finitely many compact <em>p</em>-adic spaces are joined by a graph structure, are studied, including their Dirichlet and von Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 155-180"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107399","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
Causality in the Maximally Extended Reissner-NordstrÖm Spacetime With Identifications 最大扩展Reissner-NordstrÖm时空中的因果关系
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00024-2
Andrzej Krasiński
{"title":"Causality in the Maximally Extended Reissner-NordstrÖm Spacetime With Identifications","authors":"Andrzej Krasiński","doi":"10.1016/S0034-4877(25)00024-2","DOIUrl":"10.1016/S0034-4877(25)00024-2","url":null,"abstract":"<div><div>The maximally extended Reissner-Nordström (RN) spacetime with <em>e</em><sup>2</sup> <em>m</em><sup>2</sup> can be interpreted either as an infinite chain of asymptotically flat regions connected by tunnels between timelike singularities or as a set of just one pair of asymptotically flat regions and one tunnel; the repetitions of this set in the infinite chain being identified. The second interpretation gives rise to the suspicion of acausality, i.e. the possibility of sending messages to one’s own past. A numerical investigation of this problem was carried out in this paper and gave the following result. Let E be the initial point of a radial timelike future-directed ingoing geodesic G, lying halfway between the outer horizon and the image of the null infinity in the maximally extended RN spacetime. Let E’ be the first future copy of E. It was verified whether the turning point of G lies outside or inside the past light cone (PLC) of E′. In the second case the breach of causality does occur. It turned out that the acausality is present when <em>V<sub>E</sub></em>, the timelike coordinate of E, is negative with a sufficiently large |<em>V<sub>E</sub></em>|, and is absent with a sufficiently large <em>V<sub>E</sub></em> &gt; 0. In between these values there exists a \u0000\t\t\t\t<span><math><mrow><msub><mover><mi>V</mi><mo>~</mo></mover><mi>E</mi></msub></mrow></math></span>, dependent on the initial data for the geodesic, for which the turning point lies on the PLC. So, the identification does lead to acausality. Nonradial timelike and null geodesics were also investigated, and a few hitherto unknown properties of the maximal extension were revealed. For example, the singularity arc at <em>r</em> = 0 may be convex or concave, depending on the values of <em>m</em> and <em>e</em>.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 181-214"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107400","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
Pseudo Z Symmetric Space-Times Admitting a Type of Semi-Symmetric Nonmetric Connection 伪Z对称时空允许一类半对称非度量连接
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00009-6
Hülya Bağdatli Yilmaz, Uday Chand De
{"title":"Pseudo Z Symmetric Space-Times Admitting a Type of Semi-Symmetric Nonmetric Connection","authors":"Hülya Bağdatli Yilmaz,&nbsp;Uday Chand De","doi":"10.1016/S0034-4877(25)00009-6","DOIUrl":"10.1016/S0034-4877(25)00009-6","url":null,"abstract":"<div><div>This paper aims at investigating pseudo Z symmetric space-times (PZS)<sub>4</sub> admitting a type of semi-symmetric nonmetric connection (ssnmc). At first, we scrutinize the impact of a ssnmc on Lorentzian manifolds and establish a nontrivial example. Then, we examine the general properties of (PZS)<sub>4</sub> space-times and express the physical consequences of this space-time. Among others, it is demonstrated that a (PZS)<sub>4</sub> space-time admitting a ssnmc whose Ricci tensor vanishes becomes a GRW space-time as well as a perfect fluid space-time and a purely electric space-time under a certain condition.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 39-52"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topology behind Topological Insulators 拓扑绝缘体背后的拓扑
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00008-4
Koushik Ray, Siddhartha Sen
{"title":"Topology behind Topological Insulators","authors":"Koushik Ray,&nbsp;Siddhartha Sen","doi":"10.1016/S0034-4877(25)00008-4","DOIUrl":"10.1016/S0034-4877(25)00008-4","url":null,"abstract":"<div><div>In this paper topological <em>K</em>-group calculations for fiber bundles with structure group SO(3) over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is shown that these special points are gapless and conducting for topological reasons and follow from the <em>K</em>-group calculations. The existence of gapless surface points is established with the help of an additional topological property of the <em>K</em>-groups which relates them to the index theorem of an operator. The index theorem relates zeros of operators to topology. For the topological insulator the relevant operator is a Dirac operator, that emerges in the problem because the system has strong spin-orbit interactions and time reversal invariance. Calculating <em>K</em>-groups over tori require some special topological tools that are not widely known. These are explained. We then show that the actual calculation of <em>K</em>-groups over tori becomes straightforward once a few topological results are in place. Since condensed matter systems with periodic lattices are always bundles over tori the procedures described is of general interest.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 11-37"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On HA-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree Cayley树上带外域的p进Ising模型的ha -弱周期p进广义Gibbs测度
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00012-6
Muzaffar M. Rahmatullaev, Zulxumor T. Abdukaxorova
{"title":"On HA-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree","authors":"Muzaffar M. Rahmatullaev,&nbsp;Zulxumor T. Abdukaxorova","doi":"10.1016/S0034-4877(25)00012-6","DOIUrl":"10.1016/S0034-4877(25)00012-6","url":null,"abstract":"<div><div>In the present paper, we investigate weakly periodic <em>p</em>-adic generalized Gibbs measures for <em>p</em>-adic Ising model with an external field on the Cayley tree of order two. For a normal subgroup of the group representation of the Cayley tree we prove that there exists at least one unbounded weakly periodic (in particular, nonperiodic) <em>p</em>-adic generalized Gibbs measures for this model. Moreover, we show that if <em>p</em> is any odd prime then a phase transition occurs, if <em>p</em> = 2 then a quasi phase transition occurs for <em>p</em>-adic Ising model with an external field.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 93-109"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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