Pub Date : 2025-02-01DOI: 10.1016/S0034-4877(25)00010-2
Shahid Ahmad Wani, Mohra Zayed, Hassan Ali, Subuhi Khan
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.
{"title":"Families of Differential Equations Associated with The Generalized 1-Parameter 3-Variable Hermite–Frobenius–Euler Polynomials","authors":"Shahid Ahmad Wani, Mohra Zayed, Hassan Ali, 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}
Pub Date : 2025-02-01DOI: 10.1016/S0034-4877(25)00011-4
Ahmet Kazan, Mustafa Altin
In this paper, for a soliton surface Ω = Ω(u, v) associated with the Betchov–Da Rios equation, we obtain the derivative formulae of an extended Darboux frame field of a unit speed u-parameter curve Ω = Ω(u, v) for all v. Also, we get the geometric invariants k and h of the soliton surface Ω = Ω(u, v) 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.
{"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, 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}
Pub Date : 2025-02-01DOI: 10.1016/S0034-4877(25)00003-5
Xiangyu Chen, Qiang Lei
In this paper, we introduce two measures for the resource theory of imaginarity. One is induced by α-z-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.
{"title":"Imaginarity Measures Induced by Relative Entropy","authors":"Xiangyu Chen, 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}
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