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A note on differential equations of logistic type 关于逻辑型微分方程的说明
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)00039-9
G. Dattoli, R. Garra
{"title":"A note on differential equations of logistic type","authors":"G. Dattoli,&nbsp;R. Garra","doi":"10.1016/S0034-4877(24)00039-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00039-9","url":null,"abstract":"<div><p>Logistic equations play a pivotal role in the study of any nonlinear evolution process exhibiting growth and saturation. The interest for the phenomenology they rule goes well beyond physical processes and covers many aspects of ecology, population growth, economy. . . According to such a broad range of applications, there are different forms of functions and distributions which are recognized as generalized logistics. Sometimes they are obtained by fitting procedures. Therefore, criteria might be needed to infer the associated nonlinear differential equations, useful to guess “hidden” evolution mechanisms. In this article we analyze different forms of logistic functions and use simple means to reconstruct the differential equation they satisfy. Our study includes also differential equations containing nonstandard forms of derivative operators, like those of the Laguerre type.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483877","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 nonintegrability of three-dimensional Ising model 论三维伊辛模型的不可控性
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)00037-5
Wojciech Niedziółka, Jacek Wojtkiewicz
{"title":"On nonintegrability of three-dimensional Ising model","authors":"Wojciech Niedziółka,&nbsp;Jacek Wojtkiewicz","doi":"10.1016/S0034-4877(24)00037-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00037-5","url":null,"abstract":"<div><p>It is well known that the partition function of two-dimensional Ising model can be expressed as a Grassmann integral over the action bilinear in Grassmann variables. The key aspect of the proof of this equivalence is to show that all polygons, appearing in Grassmann integration, enter with fixed sign. For three-dimensional model, the partition function can also be expressed by Grassmann integral. However, the action resulting from low-temperature (L-T) expansion contains quartic terms, which do not allow explicit computation of the integral. We wanted to check — apparently not explored — the possibility that using the high-temperature (H-T) expansion would result in action with only bilinear terms (in two dimensions, L-T and H-T expansions are equivalent, but in three dimensions, they differ from each other). It turned out, however, that polygons obtained by Grassmann integration are not of fixed sign for any ordering of Grassmann variables on sites. This way, it is not possible to express the partition function of three-dimensional Ising model as a Grassmann integral over bilinear action.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141487045","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
Nonabelianness of fundamental group of flat spacetime 平面时空基本群的非标注性
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)00036-3
Gunjan Agrawal, Deepanshi
{"title":"Nonabelianness of fundamental group of flat spacetime","authors":"Gunjan Agrawal,&nbsp;Deepanshi","doi":"10.1016/S0034-4877(24)00036-3","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00036-3","url":null,"abstract":"<div><p>In the present paper, it has been obtained that the fundamental group of <em>n</em>-dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for <em>n</em> = 2. Thereafter, it is extended to <em>n</em> &gt; 2 by proving that loops nonhomotopic in <em>M</em><sup>2</sup> continue to be nonhomotopic in <em>M<sup>n</sup></em> using embedding of <em>M</em><sup>2</sup> in <em>M<sup>n</sup></em> as a retract through the projection map.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483875","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
Complete solvability of the time dependent self-dual equations Of Chern—Simons—Higgs model 时间相关自偶方程的完全可解性 Of Chern-Simons-Higgs model
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)00042-9
Hyungjin Huh
{"title":"Complete solvability of the time dependent self-dual equations Of Chern—Simons—Higgs model","authors":"Hyungjin Huh","doi":"10.1016/S0034-4877(24)00042-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00042-9","url":null,"abstract":"<div><p>We find an explicit solution formula of the time dependent self-dual equations of Chern—Simons—Higgs model. The solution is expressed completely in terms of initial data.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141487044","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
Conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld—Rowlands equation 广义因费尔德-罗兰兹方程的守恒定律和局部哈密顿结构的不存在性
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)00038-7
Jakub Vašíček
{"title":"Conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld—Rowlands equation","authors":"Jakub Vašíček","doi":"10.1016/S0034-4877(24)00038-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00038-7","url":null,"abstract":"<div><p>For a certain natural generalization of the Infeld—Rowlands equation we prove nonexistence of nontrivial local Hamiltonian structures and nontrivial local symplectic structures of any order, as well as of nontrivial local Noether and nontrivial local inverse Noether operators of any order, and exhaustively characterize all cases when the equation in question admits nontrivial local conservation laws of any order; the method of establishing the above nonexistence results can be readily applied to many other PDEs.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483876","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 nonisospectral super integrable hierarchies associated with Lie superalgebraSL (1, 2) 与李超代数SL (1, 2) 相关的非等谱超可积分层次结构
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)00041-7
Si-Yu Gao, Bai-Ying He
{"title":"The nonisospectral super integrable hierarchies associated with Lie superalgebra\u0000S\u0000L (1, 2)","authors":"Si-Yu Gao,&nbsp;Bai-Ying He","doi":"10.1016/S0034-4877(24)00041-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00041-7","url":null,"abstract":"<div><p>Based on Lie superalgebra sI(1, 2) and the TAH scheme, we derive (1+1)-dimensional and (2+1)-dimensional nonisospectral integrable hierarchies and the corresponding super Hamiltonian structures. At the same time, we construct a generalized Lie superalgebra sI(1, 2), and apply it to (1+1)-dimensional and (2+1)-dimensional integrable systems. Finally, we discuss the super Hamiltonian structures of (1+1)-dimensional and (2+1)-dimensional integrable hierarchies associated with Lie superalgebra\u0000<span><math><mi>G</mi></math></span>sI(1, 2).</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483879","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
Index 索引
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)00045-4
{"title":"Index","authors":"","doi":"10.1016/S0034-4877(24)00045-4","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00045-4","url":null,"abstract":"","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000454/pdfft?md5=d2d49aef699b64b4b48f473b989fa096&pid=1-s2.0-S0034487724000454-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483874","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
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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