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A generalization of certain associated Bessel functions in connection with a group of shifts 与一组移位有关的某些贝塞尔函数的推广
Communications in Mathematics Pub Date : 2022-04-02 DOI: 10.46298/cm.9305
J. Choi, I. Shilin
{"title":"A generalization of certain associated Bessel functions in connection\u0000 with a group of shifts","authors":"J. Choi, I. Shilin","doi":"10.46298/cm.9305","DOIUrl":"https://doi.org/10.46298/cm.9305","url":null,"abstract":"Considering the kernel of an integral operator intertwining two realizations\u0000of the group of motions of the pseudo-Euclidian space, we derive two formulas\u0000for series containing Whittaker's functions or Weber's parabolic cylinder\u0000functions. We can consider this kernel as a special function. Some particular\u0000values of parameters involved in this special function are found to coincide\u0000with certain variants of Bessel functions. Using these connections, we also\u0000establish some analogues of orthogonality relations for Macdonald and Hankel\u0000functions.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49051684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the Generalised Ricci Solitons and Sasakian Manifolds 关于广义Ricci孤立子和Sasakian流形
Communications in Mathematics Pub Date : 2022-03-31 DOI: 10.46298/cm.9311
A. Cherif, Kaddour Zegga, G. Beldjilali
{"title":"On the Generalised Ricci Solitons and Sasakian Manifolds","authors":"A. Cherif, Kaddour Zegga, G. Beldjilali","doi":"10.46298/cm.9311","DOIUrl":"https://doi.org/10.46298/cm.9311","url":null,"abstract":"In this note, we find a necessary condition on odd-dimensional Riemannian\u0000manifolds under which both of Sasakian structure and the generalised Ricci\u0000soliton equation are satisfied, and we give some examples.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46349134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Transitions between root subsets associated with Carter diagrams 与Carter图相关联的根子集之间的转换
Communications in Mathematics Pub Date : 2022-03-15 DOI: 10.46298/cm.11568
Rafael Stekolshchik
{"title":"Transitions between root subsets associated with Carter diagrams","authors":"Rafael Stekolshchik","doi":"10.46298/cm.11568","DOIUrl":"https://doi.org/10.46298/cm.11568","url":null,"abstract":"For any two root subsets associated with two Carter diagrams that have the\u0000same $ADE$ type and the same size, we construct the transition matrix that maps\u0000one subset to the other. The transition between these two subsets is carried\u0000out in some canonical way affecting exactly one root, so that this root is\u0000mapped to the minimal element in some root subsystem. The constructed\u0000transitions are involutions. It is shown that all root subsets associated with\u0000the given Carter diagram are conjugate under the action of the Weyl group. A\u0000numerical relationship is observed between enhanced Dynkin diagrams\u0000$Delta(E_6)$, $Delta(E_7)$ and $Delta(E_8)$ (introduced by Dynkin-Minchenko)\u0000and Carter diagrams. This relationship echoes the $2-4-8$ assertions obtained\u0000by Ringel, Rosenfeld and Baez in completely different contexts regarding the\u0000Dynkin diagrams $E_6$, $E_7$, $E_8$.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48994442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Arkady Onishchik: on his life and work on supersymmetry Arkady Onishchik：论他的超对称生活和工作
Communications in Mathematics Pub Date : 2022-03-13 DOI: 10.46298/cm.9337
D. Leites
{"title":"Arkady Onishchik: on his life and work on supersymmetry","authors":"D. Leites","doi":"10.46298/cm.9337","DOIUrl":"https://doi.org/10.46298/cm.9337","url":null,"abstract":"Selected stories about the life of A. L. Onishchik, and a review of his\u0000contribution to the classification of non-split supermanifolds, in particular,\u0000supercurves a.k.a. superstrings; his editorial and educational work. A brief\u0000overview of his and his students' results in supersymmetry, and their impact on\u0000other researchers.\u0000 Several open problems growing out of Onishchik's research are presented, some\u0000of them are related with odd parameters of deformations and non-holonomic\u0000structures of supermanifolds important in physical models, such as Minkowski\u0000superspaces and certain superstrings.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41819972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Local derivations of semisimple Leibniz algebras 半单Leibniz代数的局部导子
Communications in Mathematics Pub Date : 2022-02-01 DOI: 10.46298/cm.9274
I. Kaygorodov, K. Kudaybergenov, Inomjon Yuldashev
{"title":"Local derivations of semisimple Leibniz algebras","authors":"I. Kaygorodov, K. Kudaybergenov, Inomjon Yuldashev","doi":"10.46298/cm.9274","DOIUrl":"https://doi.org/10.46298/cm.9274","url":null,"abstract":"We prove that every local derivation on a complex semisimple\u0000finite-dimensional Leibniz algebra is a derivation.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49534153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On the degree of approximation of continuous functions by a linear transformation of their Fourier series 关于连续函数的傅立叶级数线性变换的逼近度
Communications in Mathematics Pub Date : 2022-01-31 DOI: 10.46298/cm.9273
X. Krasniqi
{"title":"On the degree of approximation of continuous functions by a linear\u0000 transformation of their Fourier series","authors":"X. Krasniqi","doi":"10.46298/cm.9273","DOIUrl":"https://doi.org/10.46298/cm.9273","url":null,"abstract":"In this paper, we have proved four theorems on the degree of approximation of\u0000continuous functions by matrix means of their Fourier series which is expressed\u0000in terms of the modulus of continuity and a non-negative mediate function.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42699527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On Lie algebras associated with a spray 关于与喷相关的李代数
Communications in Mathematics Pub Date : 2022-01-26 DOI: 10.46298/cm.9007
Manelo Anona, H. Ratovoarimanana
{"title":"On Lie algebras associated with a spray","authors":"Manelo Anona, H. Ratovoarimanana","doi":"10.46298/cm.9007","DOIUrl":"https://doi.org/10.46298/cm.9007","url":null,"abstract":"The Lie algebra of infinitesimal isometries of a Riemannian manifold contains\u0000at most two commutative ideals. One coming from the horizontal nullity space of\u0000the Nijenhuis tensor of the canonical connection, the other coming from the\u0000constant vectors fields independent of the Riemannian metric.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48542951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
(ϕ, φ)-derivations on semiprime rings and Banach algebras 半素环和Banach代数上的（ξ，φ）-导子
Communications in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/cm-2021-0013
B. Wani
{"title":"(ϕ, φ)-derivations on semiprime rings and Banach algebras","authors":"B. Wani","doi":"10.2478/cm-2021-0013","DOIUrl":"https://doi.org/10.2478/cm-2021-0013","url":null,"abstract":"Abstract Let ℛ be a semiprime ring with unity e and ϕ, φ be automorphisms of ℛ. In this paper it is shown that if ℛ satisfies 2𝒟(xn)=𝒟(xn-1)φ(x)+ϕ(xn-1)𝒟(x)+𝒟(x)φ(xn-1)+ϕ(x)𝒟(xn-1)2mathcal{D}left( {{x^n}} right) = mathcal{D}left( {{x^{n - 1}}} right)phi left( x right) + varphi left( {{x^{n - 1}}} right)mathcal{D}left( x right) + mathcal{D}left( x right)phi left( {{x^{n - 1}}} right) + varphi left( x right)mathcal{D}left( {{x^{n - 1}}} right) for all x ∈ ℛ and some fixed integer n ≥ 2, then 𝒟 is an (ϕ, φ)-derivation. Moreover, this result makes it possible to prove that if ℛ admits an additive mappings 𝒟, 𝒢 : ℛ → ℛ satisfying the relations 2𝒟(xn)=𝒟(xn-1)φ(x)+ϕ(xn-1)𝒟(x)+𝒟(x)φ(xn-1)+ϕ(x)𝒟(xn-1)2mathcal{D}left( {{x^n}} right) = mathcal{D}left( {{x^{n - 1}}} right)phi left( x right) + varphi left( {{x^{n - 1}}} right)mathcal{D}left( x right) + mathcal{D}left( x right)phi left( {{x^{n - 1}}} right) + varphi left( x right)mathcal{D}left( {{x^{n - 1}}} right)2𝒢(xn)=𝒢(xn-1)φ(x)+ϕ(xn-1)D(x)+𝒟(x)φ(xn-1)+ϕ(x)𝒟(xn-1),2mathcal{G}left( {{x^n}} right) = mathcal{G}left( {{x^{n - 1}}} right)phi left( x right) + varphi left( {{x^{n - 1}}} right)mathcal{D}left( x right) + mathcal{D}left( x right)phi left( {{x^{n - 1}}} right) + varphi left( x right)mathcal{D}left( {{x^{n - 1}}} right), for all x ∈ ℛ and some fixed integer n ≥ 2, then 𝒟 and 𝒢 are (ϕ, φ)--derivations under some torsion restriction. Finally, we apply these purely ring theoretic results to semi-simple Banach algebras.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":"29 1","pages":"371 - 383"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41720680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remarks on Ramanujan’s inequality concerning the prime counting function 关于素数计数函数的拉马努金不等式的注解
Communications in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/cm-2021-0014
M. Hassani
{"title":"Remarks on Ramanujan’s inequality concerning the prime counting function","authors":"M. Hassani","doi":"10.2478/cm-2021-0014","DOIUrl":"https://doi.org/10.2478/cm-2021-0014","url":null,"abstract":"Abstract In this paper we investigate Ramanujan’s inequality concerning the prime counting function, asserting that π(x2)<exlogxπ(xe)pi left( {{x^2}} right) < {{ex} over {log x}}pi left( {{x over e}} right) for x sufficiently large. First, we study its sharpness by giving full asymptotic expansions of its left and right hand sides expressions. Then, we discuss the structure of Ramanujan’s inequality, by replacing the factor xlogx{x over {log x}} on its right hand side by the factor xlogx-h{x over {log x - h}} for a given h, and by replacing the numerical factor e by a given positive α. Finally, we introduce and study inequalities analogous to Ramanujan’s inequality.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":"29 1","pages":"473 - 482"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46942518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On the completeness of total spaces of horizontally conformal submersions 关于水平共形淹没总空间的完备性
Communications in Mathematics Pub Date : 2021-10-01 DOI: 10.2478/cm-2021-0031
M. Abbassi, Ibrahim Lakrini
{"title":"On the completeness of total spaces of horizontally conformal submersions","authors":"M. Abbassi, Ibrahim Lakrini","doi":"10.2478/cm-2021-0031","DOIUrl":"https://doi.org/10.2478/cm-2021-0031","url":null,"abstract":"Abstract In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45514461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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