Reports on Mathematical Physics最新文献

{"title":"Index","authors":"","doi":"10.1016/S0034-4877(25)00038-2","DOIUrl":"10.1016/S0034-4877(25)00038-2","url":null,"abstract":"","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 3","pages":"Pages 411-412"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523260","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}

{"title":"A Moving Curve Description of The Hunter–Saxton Equation","authors":"Tuna Bayrakdar,&nbsp;Z. Ok Bayrakdar","doi":"10.1016/S0034-4877(25)00036-9","DOIUrl":"10.1016/S0034-4877(25)00036-9","url":null,"abstract":"<div><div>In this work we show that the Hunter–Saxton equation appears as the identity for the curvature of a two-dimensional Riemannian manifold. As being motivated by this result we show that the time evolution of a curve along a geodesic curve on the Riemannian manifold is governed by the Hunter–Saxton equation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 3","pages":"Pages 381-391"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523226","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}

{"title":"Lightlike Statistical Submersions from A Mixed 3-Sasakian Statistical Manifold","authors":"Mohammad Bagher Kazemi Balgeshir,&nbsp;Sara Miri","doi":"10.1016/S0034-4877(25)00037-0","DOIUrl":"10.1016/S0034-4877(25)00037-0","url":null,"abstract":"<div><div>In the present paper, we study invariant and screen real lightlike statistical submersions <em>h</em> from a mixed 3-Sasakian statistical manifold. We prove that the fibers of an invariant lightlike statistical submersion are totally geodesic. We obtain some properties of screen real lightlike statistical submersions from a mixed 3-Sasakian statistical manifold. Some examples related to these notions are also constructed. Finally, we investigate warped product manifolds of the type <em>M</em> = Δ ×_ϑ <em>s</em> (Ker <em>h</em>_*).</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 3","pages":"Pages 393-409"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523259","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}

{"title":"On Yang-Mills Stability Bounds and Plaquette Field Generating Function","authors":"Paulo A. Faria da Veiga,&nbsp;Michael O'Carroll","doi":"10.1016/S0034-4877(25)00035-7","DOIUrl":"10.1016/S0034-4877(25)00035-7","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider the local gauge-invariant Yang-Mills quantum field theory on the finite hyper-cubic lattice Λ ⊂ &lt;em&gt;aℤ&lt;sup&gt;d&lt;/sup&gt;&lt;/em&gt; ⊂ &lt;em&gt;ℝ&lt;sup&gt;d&lt;/sup&gt;&lt;/em&gt;, &lt;em&gt;d&lt;/em&gt; = 2, 3, 4, &lt;em&gt;a&lt;/em&gt; ∊ (0, 1], with &lt;em&gt;L&lt;/em&gt; (even) sites on a side and with the gauge Lie groups \u0000\t\t\t\t&lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; = U(&lt;em&gt;N&lt;/em&gt;), &lt;em&gt;SU&lt;/em&gt;(&lt;em&gt;N&lt;/em&gt;). To each Λ bond &lt;em&gt;b&lt;/em&gt;, there is a unitary matrix gauge variable &lt;em&gt;U&lt;sub&gt;b&lt;/sub&gt;&lt;/em&gt; from an irrep of \u0000\t\t\t\t&lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The vector gauge potentials (gluon fields) are parameters in the Lie algebra of \u0000\t\t\t\t&lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The Wilson finite lattice partition function Z&lt;sub&gt;Λ&lt;/sub&gt; (&lt;em&gt;a&lt;/em&gt;) is used. The action A&lt;sub&gt;Λ&lt;/sub&gt; (&lt;em&gt;a&lt;/em&gt;) is a sum of gauge-invariant plaquette actions times \u0000\t\t\t\t&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, \u0000\t\t\t\t&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msubsup&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, \u0000\t\t\t\t&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Each plaquette action has the product of four bond variables; the partition function is the integral over the Boltzmann factor with a product over bonds of \u0000\t\t\t\t&lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; Haar measures. Formally, in the continuum, ultraviolet (UV) limit &lt;em&gt;a &amp;&lt;/em&gt;drarr; 0, the action gives the YM classical continuum action. For free and periodic boundary conditions (b.c.), and using scaled fields, defined with an &lt;em&gt;a-&lt;/em&gt;dependent noncanonical scaling, we show thermodynamic and UV stable (TUV) stability bounds for a scaled partition function, with constants independent of &lt;em&gt;L, a&lt;/em&gt; and &lt;em&gt;g.&lt;/em&gt; Passing to scaled fields does not alter the model energy-momentum spectrum and can be interpreted as an a priori field strength renormalization, making the action more regular. With scaled fields, we can isolate the UV singularity of the finite lattice physical, unscaled free energy &lt;em&gt;f&lt;/em&gt;Λ(&lt;em&gt;a&lt;/em&gt;) = [ln ZΛ ]/Λ&lt;em&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt;, where Λ&lt;sub&gt;s&lt;/sub&gt; = &lt;em&gt;L&lt;sup&gt;d&lt;/sup&gt;&lt;/em&gt; is the total number of lattice sites. With this, we show the existence of, at least, the subsequential thermodynamic (Λ &amp;nearr; &lt;em&gt;dℤ&lt;sup&gt;d&lt;/sup&gt;&lt;/em&gt;) and UV limits of a scaled free energy. To obtain the TUV bounds, the Weyl integration formula is used in the gauge integral and the random matrix probability distributions of the CUE and GUE appear naturally. Using periodic b.c. and the multireflection method, the generating function of &lt;em&gt;r&lt;/em&gt; scaled plaquette field correlations is bounded uniformly in &lt;em&gt;L, a, g&lt;/em&gt; and the location/orientation of the &lt;em&gt;r&lt;/em&gt; plaquette fields. Consequently, &lt;em&gt;r&lt;/em&gt;-scaled plaquette field correlati","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 3","pages":"Pages 303-380"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523169","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}

{"title":"A Rellich Type Theorem for The Generalized Oscillator","authors":"Tomoya Tagawa","doi":"10.1016/S0034-4877(25)00029-1","DOIUrl":"10.1016/S0034-4877(25)00029-1","url":null,"abstract":"<div><div>For the Schrödinger operator generalized from the harmonic oscillator, we prove a Rellich type theorem, which characterizes the order of growth of eigenfunctions at infinity. The proofs are given by an extensive use of commutator arguments invented recently by Ito and Skibsted. These arguments are simple and elementary and do not employ energy cut-offs or microlocal analysis.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 3","pages":"Pages 281-302"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523168","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}

{"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}

{"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;² × ℝ and Sol₃ with left-invariant Riemannian metrics and we study the Riemann solitons on them. We prove that the Lie group <strong>&amp;</strong>Hopf;² × ℝ admits the Riemann soliton and the Lie group Sol₃ does not admit the Riemann soliton. We classify all Riemann solitons on the Lie group <strong>&amp;</strong>Hopf;² × 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 Sol₃ 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}

{"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}

{"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}

{"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_j,b γ_j</em>+1,<em>_a</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_j,b γ_j</em>+1,<em>_a</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}