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Differential geometry of the quantum supergroup GLH,H′ (1|1) 量子超群 GLH,H′ (1|1) 的微分几何学
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00044-2
Salih Celik, Ilknur Temli
{"title":"Differential geometry of the quantum supergroup GLH,H′ (1|1)","authors":"Salih Celik,&nbsp;Ilknur Temli","doi":"10.1016/S0034-4877(24)00044-2","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00044-2","url":null,"abstract":"<div><p>In this paper, we construct a bi-covariant (<em>h,h′</em>)-deformed differential calculus on the Hopf superalgebra of functions on the quantum supergroup GL<sub><em>h.h</em>′</sub> (1|1) and obtain an extended differential calculus (Cartan calculus) by including inner derivations and Lie derivatives. In doing so, we use left-Cartan-Maurer 1-forms and left-vector fields.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 371-391"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141482854","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
IDENTIFYING DIFFUSION CONCENTRATION AND SOURCE TERM FOR ANOMALOUS DIFFUSION EQUATION 确定异常扩散方程的扩散浓度和源项
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00023-5
Asim Ilyas, Salman A. Malik, Kamran Suhaib
{"title":"IDENTIFYING DIFFUSION CONCENTRATION AND SOURCE TERM FOR ANOMALOUS DIFFUSION EQUATION","authors":"Asim Ilyas,&nbsp;Salman A. Malik,&nbsp;Kamran Suhaib","doi":"10.1016/S0034-4877(24)00023-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00023-5","url":null,"abstract":"<div><p>We consider an inverse problem for diffusion equation involving fractional Laplacian operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary conditions. The inverse problem is to recover time-dependent source term and diffusion concentration with an integral type over-determination condition. We discuss the analytical solution of the inverse problem and prove the existence and uniqueness of the analytical solution. Some special cases and examples for the considered inverse problem are provided.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 145-163"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880224","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
ON THE SOLITON-LIKE SOLUTIONS OF THE REFINED MODEL OF ELASTIC MEDIA CONTAINING INCLUSIONS 关于含有夹杂物的弹性介质细化模型的孤子类解法
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00024-7
Lucjan Sapa, Sergii Skurativskyi, Vsevolod Vladimirov
{"title":"ON THE SOLITON-LIKE SOLUTIONS OF THE REFINED MODEL OF ELASTIC MEDIA CONTAINING INCLUSIONS","authors":"Lucjan Sapa,&nbsp;Sergii Skurativskyi,&nbsp;Vsevolod Vladimirov","doi":"10.1016/S0034-4877(24)00024-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00024-7","url":null,"abstract":"<div><p>A model of nonlinear elastic media containing cavities, microcracks, or soft inclusions is considered. We propose a modification of the well-known model to such media. The modification consists in taking into account those terms in the approximate equation of state that were discarded in the previously considered models. The main goal of the ongoing research is to show the persistence of the soliton-like solutions in the modified model, and to study their dynamical properties.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 165-177"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880225","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
QUANTUM REVIVALS AND FRACTALITY FOR THE SCHRÖDINGER EQUATION 薛定谔方程的量子复兴与分形
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00022-3
Gunwoo Cho, Jimyeong Kim, Ihyeok Seo, Seongyeon Kim, Yehyun Kwon
{"title":"QUANTUM REVIVALS AND FRACTALITY FOR THE SCHRÖDINGER EQUATION","authors":"Gunwoo Cho,&nbsp;Jimyeong Kim,&nbsp;Ihyeok Seo,&nbsp;Seongyeon Kim,&nbsp;Yehyun Kwon","doi":"10.1016/S0034-4877(24)00022-3","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00022-3","url":null,"abstract":"<div><p>We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov [<span>16</span>] and Rodnianski [<span>18</span>] on the free Schrödinger evolution to the general case regarding potentials.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 129-143"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880213","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
CHAIN TRANSITIVITY AND SHADOWING PROPERTY IN QUANTUM DYNAMICAL SYSTEMS 量子动力学系统中的链传递性和阴影特性
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00026-0
Mona Khare, Ravi Singh Chauhan
{"title":"CHAIN TRANSITIVITY AND SHADOWING PROPERTY IN QUANTUM DYNAMICAL SYSTEMS","authors":"Mona Khare,&nbsp;Ravi Singh Chauhan","doi":"10.1016/S0034-4877(24)00026-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00026-0","url":null,"abstract":"<div><p>In the present paper we investigate the notions of chain transitivity, ε-shadowing and expansiveness in the dynamics of quantum measure spaces (<em>P</em>, μ). Besides of several results proved for a chain transitive quantum dynamical system, it is shown that if a measure preserving morphism φ on (<em>P</em>, μ) is chain mixing, then φ<sup><em>n</em></sup> is chain transitive for each <em>n</em> ∊ ℕ. The present study also elucidates interrelationship between ε-shadowing and expansiveness of a quantum dynamical system (<em>P</em>, μ, φ) under suitable conditions. Examples are given to support the theory.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 195-211"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880208","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
SINGULAR REDUCTION OF CONTACT HAMILTONIAN SYSTEMS 接触哈密顿系统的奇异还原
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00029-6
Qianqian Xia
{"title":"SINGULAR REDUCTION OF CONTACT HAMILTONIAN SYSTEMS","authors":"Qianqian Xia","doi":"10.1016/S0034-4877(24)00029-6","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00029-6","url":null,"abstract":"<div><p>We study singular reduction of contact Hamiltonian systems acted upon properly by a Lie group. The tools we use are the category of differential space.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 241-260"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880211","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
INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION 具有广义阻抗边界条件的亚扩散方程的反源问题
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00025-9
Mansur I. Ismailov, Muhammed Çiçek
{"title":"INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION","authors":"Mansur I. Ismailov,&nbsp;Muhammed Çiçek","doi":"10.1016/S0034-4877(24)00025-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00025-9","url":null,"abstract":"<div><p>The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 179-194"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880226","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
NEW QUANTUM CODES DERIVED FROM THE DIRECT PRODUCT OF RINGS, USING CYCLIC CODES OVER THE RING 利用环上的循环码，从环的直接乘积推导出新的量子密码
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00027-2
Pooja Soni, Manju Pruthi, Arun Kumar Yadav
{"title":"NEW QUANTUM CODES DERIVED FROM THE DIRECT PRODUCT OF RINGS, USING CYCLIC CODES OVER THE RING","authors":"Pooja Soni,&nbsp;Manju Pruthi,&nbsp;Arun Kumar Yadav","doi":"10.1016/S0034-4877(24)00027-2","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00027-2","url":null,"abstract":"<div><p>This research paper discusses the construction of novel and better quantum codes from the direct product of <em>t</em>-copies of ring <em>R</em> (discussed in Section 2), using cyclic codes over <em>R</em> by employing the CSS construction technique. Here, we present an overview of the structure and essential properties of a ring <em>R</em>. Furthermore, we analyze the distance-preserving nature of the Gray map in Subsection 2.1. Here, we also investigate maximum distance separable (MDS) codes by using the concept of quantum singleton defect (QSD), which indicates the overall quality of codes. To demonstrate the practicality of our findings, we provide illustrative examples implemented using the Magma software.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 213-229"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880209","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
RICCI SOLITONS AND RICCI BI-CONFORMAL VECTOR FIELDS ON THE LIE GROUP ℍ2 × ℝ 里奇孤子和里奇双共形矢量场上的谎群ℍ2 × ℝ
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00028-4
Shahroud Azami, Mehdi Jafari
{"title":"RICCI SOLITONS AND RICCI BI-CONFORMAL VECTOR FIELDS ON THE LIE GROUP ℍ2 × ℝ","authors":"Shahroud Azami,&nbsp;Mehdi Jafari","doi":"10.1016/S0034-4877(24)00028-4","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00028-4","url":null,"abstract":"<div><p>In the present paper, we investigate the 3-dimensional Lie group (ℍ<sup>2</sup> × ℝ, <em>g</em>) where <em>g</em> is a left-invariant Riemannian metric and we determine the Ricci solitons and Ricci bi-conformal vector fields on it.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 231-239"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880210","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
New regularity criteria for an MHD Darcy-Forchheimer fluid 多流体力学达西-福克海默流体的新规则性标准
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00008-9
Saeed ur Rahman, José Luis Díaz Palencia
{"title":"New regularity criteria for an MHD Darcy-Forchheimer fluid","authors":"Saeed ur Rahman,&nbsp;José Luis Díaz Palencia","doi":"10.1016/S0034-4877(24)00008-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00008-9","url":null,"abstract":"<div><p>The purpose of the presented article is to develop some new global regularity criteria for a magnetohydrodynamic (MHD) fluid flowing in a saturated porous medium. The effect of the porous medium, over the fluid flow, is characterized by a Darcy–Forchheimer law. The fluid, under study, is considered as one-dimensional and flowing in the <em>x–</em>direction with velocity component <em>u.</em> In addition, such a component is assumed to vary with the <em>y–</em>direction, i.e. <em>u</em>(<em>y</em>). Then, given the vorticity function\u0000<span><math><mrow><mi>w</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>y</mi></mrow></mfrac></mrow></math></span>, such that\u0000<span><math><mrow><msubsup><mrow><mrow><mo>‖</mo><mi>w</mi><mo>‖</mo></mrow></mrow><mrow><mtext>BMO</mtext></mrow><mn>2</mn></msubsup></mrow></math></span> is sufficiently small, we develop the regularity criteria under the scope of the <em>L</em><sup>2</sup> space. We extend our results to the spaces <em>L<sup>s</sup></em>, where <em>s</em> &gt; 2. Afterward, we prove the Liouville-type theorem for the MHD Darcy–Forchheimer flow equation. Eventually, we obtain some characterization about the asymptotic behaviour of solutions, particularly, the nonuniform convergence in <em>L</em><sup>2</sup> for\u0000<span><math><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></math></span>.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 21-36"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000089/pdfft?md5=0d1891c76d0aee709cdeee928726e3d4&pid=1-s2.0-S0034487724000089-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975999","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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