Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00079-5
Janusz Garecki
We show in a new way that the general relativity (GR) action (and Lagrangian) in recent Einstein-Palatini (EP) formulation is equivalent in four dimensions to the action (and Lagrangian) of a gauge field.
Firstly, we present EP action with cosmological constant Λ ≢ 0 and derive Einstein field equations from it. Then, we consider this action in terms of the corrected curvature Ωcor. We will see that in terms of Ωcor the EP action takes the typical form for action of a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ωcor.
{"title":"An Interesting Form of the Einstein-Palatini Action with Cosmological Constant Λ","authors":"Janusz Garecki","doi":"10.1016/S0034-4877(25)00079-5","DOIUrl":"10.1016/S0034-4877(25)00079-5","url":null,"abstract":"<div><div>We show in a new way that the general relativity (GR) action (and Lagrangian) in recent Einstein-Palatini (EP) formulation is equivalent in four dimensions to the action (and Lagrangian) of a gauge field.</div><div>Firstly, we present EP action with cosmological constant Λ ≢ 0 and derive Einstein field equations from it. Then, we consider this action in terms of the corrected curvature Ω<sub>cor</sub>. We will see that in terms of Ω<sub>cor</sub> the EP action takes the typical form for action of a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω<sub>cor</sub>.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 357-368"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871665","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}
Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00075-8
SeungJun Jeon, Chanju Kim, Yoonbai Kim
The BPS limit of the inhomogeneous abelian Higgs model is considered in (1 + 2)-dimensions. The second order Bogomolny equation is examined in the presence of an inhomogeneity expressed as a function of spatial coordinates. Assuming a physically reasonable upper bound on the norm of the inhomogeneity function, we prove the existence and uniqueness of nontrivial BPS vacuum solution of zero energy and topological BPS multi-vortex solutions of quantized positive energies.
{"title":"Existence and Uniqueness of BPS Vacuum and Multi-Vortices in Inhomogeneous Abelian Higgs Model","authors":"SeungJun Jeon, Chanju Kim, Yoonbai Kim","doi":"10.1016/S0034-4877(25)00075-8","DOIUrl":"10.1016/S0034-4877(25)00075-8","url":null,"abstract":"<div><div>The BPS limit of the inhomogeneous abelian Higgs model is considered in (1 + 2)-dimensions. The second order Bogomolny equation is examined in the presence of an inhomogeneity expressed as a function of spatial coordinates. Assuming a physically reasonable upper bound on the \u0000\t\t\t\t<span><math><msup><mi>L</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> norm of the inhomogeneity function, we prove the existence and uniqueness of nontrivial BPS vacuum solution of zero energy and topological BPS multi-vortex solutions of quantized positive energies.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 299-312"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871635","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}
Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00077-1
Mehdi Jafari , Amirhesam Zaeim, Yadollah AryaNejad, Adele Alemahdi
This research paper investigates the concepts of almost Riemann solitons and almost gradient Riemann solitons within the context of magneto-fluid spacetime in f(r)-gravity. Initially, the divergence of the almost Riemann soliton vector field is expressed in terms of scalar curvature specific to this magneto-fluid spacetime framework. Subsequently, by employing the Riemann soliton as our metric, we delineate the conditions necessary for the scalar curvature of the spacetime under consideration. Furthermore, by examining the gradient Riemann soliton, we elucidate certain properties related to particle density.
{"title":"Riemann Solitons on Magneto-Fluid Spacetime in f(r)-Gravity","authors":"Mehdi Jafari , Amirhesam Zaeim, Yadollah AryaNejad, Adele Alemahdi","doi":"10.1016/S0034-4877(25)00077-1","DOIUrl":"10.1016/S0034-4877(25)00077-1","url":null,"abstract":"<div><div>This research paper investigates the concepts of almost Riemann solitons and almost gradient Riemann solitons within the context of magneto-fluid spacetime in <em>f</em>(<em>r</em>)-gravity. Initially, the divergence of the almost Riemann soliton vector field is expressed in terms of scalar curvature specific to this magneto-fluid spacetime framework. Subsequently, by employing the Riemann soliton as our metric, we delineate the conditions necessary for the scalar curvature of the spacetime under consideration. Furthermore, by examining the gradient Riemann soliton, we elucidate certain properties related to particle density.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 327-342"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871637","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}
Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00076-X
Sameh Shenawy, Uday Chand De, Nasser Bin Turki
In this study, it is demonstrated that a space-time M is a mixed quasi-Einstein M(QE)n space-time if M is a pseudo-Ricci symmetric space-time and the Ricci tensor is a conformal Killing tensor. Additionally, it is proved that a Ricci symmetric M(QE)n space-time is either Einstein or a static space-time. As a result, it is established that a Ricci symmetric M(QE)n generalized Robertson-Walker space-time is either perfect fluid or a static space-time. A Ricci semi-symmetric M(QE)n space-time is proven to be an Einstein space-time, and its sectional curvature is given. Furthermore, a Ricci recurrent M(QE)n space-time is Einstein or the spacetime is a GRW space-time. A generalized Ricci recurrent M(QE)n space-time is also shown to be either an Einstein space-time or a GRW space-time.
{"title":"Mixed Quasi-Einstein M(QE)n Relativistic Spacetimes with Applications","authors":"Sameh Shenawy, Uday Chand De, Nasser Bin Turki","doi":"10.1016/S0034-4877(25)00076-X","DOIUrl":"10.1016/S0034-4877(25)00076-X","url":null,"abstract":"<div><div>In this study, it is demonstrated that a space-time <em>M</em> is a mixed quasi-Einstein M(QE)<sub>n</sub> space-time if <em>M</em> is a pseudo-Ricci symmetric space-time and the Ricci tensor is a conformal Killing tensor. Additionally, it is proved that a Ricci symmetric M(QE)<sub>n</sub> space-time is either Einstein or a static space-time. As a result, it is established that a Ricci symmetric M(QE)<sub>n</sub> generalized Robertson-Walker space-time is either perfect fluid or a static space-time. A Ricci semi-symmetric M(QE)<sub>n</sub> space-time is proven to be an Einstein space-time, and its sectional curvature is given. Furthermore, a Ricci recurrent M(QE)<sub>n</sub> space-time is Einstein or the spacetime is a GRW space-time. A generalized Ricci recurrent M(QE)<sub>n</sub> space-time is also shown to be either an Einstein space-time or a GRW space-time.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 313-326"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871636","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}
Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00080-1
Mona Khare, Ravi Singh Chauhan
In the present paper, we build up a theory of finite and countable product of quantum dynamical systems, and investigate the preservation of shadowing and ergodic shadowing properties under this product; examples are also given. The notion of ergodic shadowing property involves the concepts of asymptotic density and pseudo chain. It is shown that an ergodic pseudo chain need not be a pseudo chain. A sufficient condition for a quantum dynamical system to have shadowing property is constructed; it has been established that its converse need not be true. It is proved that a surjective morphism φ on such system that have the ergodic shadowing property implies that φ has finite shadowing property.
{"title":"Product of Quantum Measure Spaces and Shadowing","authors":"Mona Khare, Ravi Singh Chauhan","doi":"10.1016/S0034-4877(25)00080-1","DOIUrl":"10.1016/S0034-4877(25)00080-1","url":null,"abstract":"<div><div>In the present paper, we build up a theory of finite and countable product of quantum dynamical systems, and investigate the preservation of shadowing and ergodic shadowing properties under this product; examples are also given. The notion of ergodic shadowing property involves the concepts of asymptotic density and pseudo chain. It is shown that an ergodic pseudo chain need not be a pseudo chain. A sufficient condition for a quantum dynamical system to have shadowing property is constructed; it has been established that its converse need not be true. It is proved that a surjective morphism φ on such system that have the ergodic shadowing property implies that φ has finite shadowing property.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 369-384"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871632","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}
Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00078-3
Paolo Buttà, Guido Cavallaro, Carlo Marchioro
In the recent paper [11], the authors provided the first construction of classical solutions for Euler equations featuring leapfrogging motion for any time, by desingularizing via concentrated vortex patches a suitable four-point vortex dynamics in the plane. In this note, we show that the leapfrogging motion persists for very long times by replacing such patches with quite general initial data of concentrated vorticity.
{"title":"Remarks on the Leapfrogging Motion for Planar Euler Equations","authors":"Paolo Buttà, Guido Cavallaro, Carlo Marchioro","doi":"10.1016/S0034-4877(25)00078-3","DOIUrl":"10.1016/S0034-4877(25)00078-3","url":null,"abstract":"<div><div>In the recent paper [<span><span>11</span></span>], the authors provided the first construction of classical solutions for Euler equations featuring leapfrogging motion for any time, by desingularizing via concentrated vortex patches a suitable four-point vortex dynamics in the plane. In this note, we show that the leapfrogging motion persists for very long times by replacing such patches with quite general initial data of concentrated vorticity.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 343-355"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871664","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}
Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00074-6
Jan Dereziński , Christian Gaß , Joonas Mikael Vättö
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well known, these integrals are convergent only for a limited range of parameters. However, when one uses the generalized integral they can be computed essentially without restricting the parameters. This gives the (generalized) Gram matrix of Laguerre polynomials. If the parameters are not negative integers, then Laguerre polynomials are orthogonal, or at least pseudo-orthogonal in the case of generalized integrals. For negative integer parameters, the orthogonality relations are more complicated.
{"title":"Confluent Functions, Laguerre Polynomials and Their (Generalized) Bilinear Integrals","authors":"Jan Dereziński , Christian Gaß , Joonas Mikael Vättö","doi":"10.1016/S0034-4877(25)00074-6","DOIUrl":"10.1016/S0034-4877(25)00074-6","url":null,"abstract":"<div><div>We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well known, these integrals are convergent only for a limited range of parameters. However, when one uses <em>the generalized integral</em> they can be computed essentially without restricting the parameters. This gives the (generalized) Gram matrix of Laguerre polynomials. If the parameters are not negative integers, then Laguerre polynomials are orthogonal, or at least pseudo-orthogonal in the case of generalized integrals. For negative integer parameters, the orthogonality relations are more complicated.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 275-297"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871634","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}
Pub Date : 2025-12-01DOI: 10.1016/S0034-4877(25)00081-3
Pece Trajanovski, Irina Petreska, Katarzyna Górska, Ljupco Kocarev, Trifce Sandev
A space-fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the nonlocality in space. A specific example of the nonlocal term is considered in combination with three different forms of the memory kernel. To analyse the probability density function, we utilize the subordination approach. Subsequently, the corresponding continuous time random walk model is presented. Furthermore, we investigate the effects of the stochastic resetting on the dynamics of the process and we showed that in the long time limit the system approaches a nonequilibrium stationary state.
{"title":"Generalized Diffusion Process with Nonlocal Interactions: Continuous Time Random Walk Model and Stochastic Resetting","authors":"Pece Trajanovski, Irina Petreska, Katarzyna Górska, Ljupco Kocarev, Trifce Sandev","doi":"10.1016/S0034-4877(25)00081-3","DOIUrl":"10.1016/S0034-4877(25)00081-3","url":null,"abstract":"<div><div>A space-fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the nonlocality in space. A specific example of the nonlocal term is considered in combination with three different forms of the memory kernel. To analyse the probability density function, we utilize the subordination approach. Subsequently, the corresponding continuous time random walk model is presented. Furthermore, we investigate the effects of the stochastic resetting on the dynamics of the process and we showed that in the long time limit the system approaches a nonequilibrium stationary state.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 3","pages":"Pages 385-405"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145871633","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}
Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00061-8
Günther Hörmann, Ljubica Oparnica, Christian Spreitzer
We discuss spectral properties of a regularization approach to a Schrödinger equation setup for the diffraction of a quantum particle at almost planar patterns. Physically meaningful initial values and potentials are modeled in terms of regularizing families and the solutions can be interpreted as generalized functions. We establish spectral and scattering theoretical properties of the regularizing solution families and provide some comparison with the more direct approximations and simplifications used in physics.
{"title":"Modeling Schrödinger Equation Diffraction With Generalized Function Potentials And Initial Values","authors":"Günther Hörmann, Ljubica Oparnica, Christian Spreitzer","doi":"10.1016/S0034-4877(25)00061-8","DOIUrl":"10.1016/S0034-4877(25)00061-8","url":null,"abstract":"<div><div>We discuss spectral properties of a regularization approach to a Schrödinger equation setup for the diffraction of a quantum particle at almost planar patterns. Physically meaningful initial values and potentials are modeled in terms of regularizing families and the solutions can be interpreted as generalized functions. We establish spectral and scattering theoretical properties of the regularizing solution families and provide some comparison with the more direct approximations and simplifications used in physics.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 159-187"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584164","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}
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