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Pseudo Z Symmetric Space-Times Admitting a Type of Semi-Symmetric Nonmetric Connection
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
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
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
Stability of a Generalized Linear Weingarten Spacelike Hypersurface in Robertson–Walker Spacetimes
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)00013-8
Hyelim Han
{"title":"Stability of a Generalized Linear Weingarten Spacelike Hypersurface in Robertson–Walker Spacetimes","authors":"Hyelim Han","doi":"10.1016/S0034-4877(25)00013-8","DOIUrl":"10.1016/S0034-4877(25)00013-8","url":null,"abstract":"<div><div>In this article, we study the variational problem of maximizing a certain linear combination of area functionals of a closed generalized linear Weingarten spacelike hypersurface <em>M<sup>n</sup></em> immersed in a foliated spacetime \u0000\t\t\t\t<span><math><mrow><msubsup><mover><mi>M</mi><mo>~</mo></mover><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></math></span>. Given a Robertson-Walker spacetime \u0000\t\t\t\t<span><math><mrow><msubsup><mover><mi>M</mi><mo>~</mo></mover><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>=</mo><mi>I</mi><msub><mo>×</mo><mi>ϕ</mi></msub><msup><mi>F</mi><mi>n</mi></msup></mrow></math></span>, we exhibit conditions on <em>M<sup>n</sup></em> which guarantee that (strong) stability is necessary and sufficient for <em>M<sup>n</sup></em> to be totally umbilic. Under a suitable restriction on <em>M<sup>n</sup></em>, we also prove that if a closed generalized linear Weingarten spacelike hypersurface in \u0000\t\t\t\t<span><math><mrow><msubsup><mi>S</mi><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></math></span> is (strongly) stable, then it must be a totally umbilic round sphere.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 111-128"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680616","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
Families of Differential Equations Associated with The Generalized 1-Parameter 3-Variable Hermite–Frobenius–Euler Polynomials
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)00010-2
Shahid Ahmad Wani, Mohra Zayed, Hassan Ali, Subuhi Khan
{"title":"Families of Differential Equations Associated with The Generalized 1-Parameter 3-Variable Hermite–Frobenius–Euler Polynomials","authors":"Shahid Ahmad Wani,&nbsp;Mohra Zayed,&nbsp;Hassan Ali,&nbsp;Subuhi Khan","doi":"10.1016/S0034-4877(25)00010-2","DOIUrl":"10.1016/S0034-4877(25)00010-2","url":null,"abstract":"<div><div>This paper presents a novel framework for introducing generalized 1-parameter 3-variable Hermite–Frobenius–Euler polynomials. These polynomials are characterized by generating functions, series definitions, and summation formulae, elucidating their fundamental properties. Moreover, the study establishes recurrence relations, shift operators, and various differential equations, including differential, integro-differential, and partial differential equations, utilizing a factorization method.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 53-70"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680613","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
A Geometric Application of Soliton Surfaces Associated with The Betchov–Da Rios Equation Using an Extended Darboux Frame Field in E4
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)00011-4
Ahmet Kazan, Mustafa Altin
{"title":"A Geometric Application of Soliton Surfaces Associated with The Betchov–Da Rios Equation Using an Extended Darboux Frame Field in E4","authors":"Ahmet Kazan,&nbsp;Mustafa Altin","doi":"10.1016/S0034-4877(25)00011-4","DOIUrl":"10.1016/S0034-4877(25)00011-4","url":null,"abstract":"<div><div>In this paper, for a soliton surface Ω = Ω(<em>u, v</em>) associated with the Betchov–Da Rios equation, we obtain the derivative formulae of an extended Darboux frame field of a unit speed <em>u</em>-parameter curve Ω = Ω(<em>u, v</em>) for all <em>v.</em> Also, we get the geometric invariants <em>k</em> and <em>h</em> of the soliton surface Ω = Ω(<em>u, v</em>) and we obtain the Gaussian curvature, mean curvature vector and Gaussian torsion of Ω. We give some important geometric characterizations such as flatness, minimality and semi-umbilicaly with the aid of these invariants. Additionally, we study the curvature ellipse of the Betchov–Da Rios soliton surface and Wintgen ideal (superconformal) Betchov–Da Rios soliton surface with respect to an extended Darboux frame field. Finally, we construct an application for the Betchov–Da Rios soliton surface with the aid of an extended Darboux frame field.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 71-92"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680614","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
Imaginarity Measures Induced by Relative Entropy
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)00003-5
Xiangyu Chen, Qiang Lei
{"title":"Imaginarity Measures Induced by Relative Entropy","authors":"Xiangyu Chen,&nbsp;Qiang Lei","doi":"10.1016/S0034-4877(25)00003-5","DOIUrl":"10.1016/S0034-4877(25)00003-5","url":null,"abstract":"<div><div>In this paper, we introduce two measures for the resource theory of imaginarity. One is induced by α-<em>z</em>-Rényi relative entropy and the other, defined for positive-definite density matrices, is induced by Tsallis relative operator entropy. The relationships between different imaginarity measures and their properties are also discussed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 1-10"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680672","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
Ground states for the potts model with an external field
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00082-X
Muhayyo A. Rasulova
{"title":"Ground states for the potts model with an external field","authors":"Muhayyo A. Rasulova","doi":"10.1016/S0034-4877(24)00082-X","DOIUrl":"10.1016/S0034-4877(24)00082-X","url":null,"abstract":"<div><div>We consider a <em>(q +</em> 1)-state Potts model with nonzero external field on the Cayley tree. We describe all ground states for this model with a translation-invariant external field and all two-periodic ground states with a periodic external field.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 325-334"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317063","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 mixed integrable lattice hierarchy associated with the relativistic toda lattice: conservation laws, N-fold Darboux transformation and soliton solutions
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00080-6
Guang-Hao Zhang, Fang-Cheng Fan
{"title":"A mixed integrable lattice hierarchy associated with the relativistic toda lattice: conservation laws, N-fold Darboux transformation and soliton solutions","authors":"Guang-Hao Zhang,&nbsp;Fang-Cheng Fan","doi":"10.1016/S0034-4877(24)00080-6","DOIUrl":"10.1016/S0034-4877(24)00080-6","url":null,"abstract":"<div><div>Beginning with a more generalized discrete 2 × 2 matrix spectral problem and applying the Tu scheme, a mixed integrable lattice hierarchy based on the negative and positive lattice hierarchies is constructed, it includes the well-known relativistic Toda lattice hierarchy and can reduce to other new integrable lattice hierarchies. For the first nontrivial lattice equation in the mixed hierarchy, the corresponding infinite number of conservation laws and <em>N</em>-fold Darboux transformation are established on the base of its Lax pair. As an application of the obtained Darboux transformation, we obtain the discrete <em>N</em>-fold explicit solutions in determinant form, from which we get one-and two-soliton solutions with proper parameters and their dynamical properties and evolutions are illustrated graphically. Some interesting soliton structures are presented, such as kink and bell-shaped two-soliton, bell and anti-bell shaped two-soliton and anti-bell shaped two-soliton and so on. What is more, we observe that these solitary waves pass through without change of shapes, amplitudes, wave-lengths and directions, which means they are much stable during the propagation. These results and properties given in this paper may help us better understand nonlinear lattice dynamics.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 279-304"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317283","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 existence, asymptotic behaviour and blow-up of solution of a plate equation with nonlinear averaged damping
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00081-8
Hongwei Zhang, Ling Liu, Hongyun Yue, Donghao Li, Khaled Zennir
{"title":"The existence, asymptotic behaviour and blow-up of solution of a plate equation with nonlinear averaged damping","authors":"Hongwei Zhang,&nbsp;Ling Liu,&nbsp;Hongyun Yue,&nbsp;Donghao Li,&nbsp;Khaled Zennir","doi":"10.1016/S0034-4877(24)00081-8","DOIUrl":"10.1016/S0034-4877(24)00081-8","url":null,"abstract":"<div><div>The initial boundary-value problem for a plate equation with nonlocal damping is considered. The local existence of solution is proved by the monotone operator theory with locally Lipschitz perturbation. By using the potential well theory, we get the global existence of solution. By Nakao's inequality, the decay estimate of polynomial type is obtained. We provide also the sufficient conditions of finite time blow-up of weak solutions with suitable conditions on the initial data by an ordinary differential inequality for an appropriately chosen functional.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 305-323"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317066","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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