Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions. We can consider this kernel as a special function. Some particular values of parameters involved in this special function are found to coincide with certain variants of Bessel functions. Using these connections, we also establish some analogues of orthogonality relations for Macdonald and Hankel functions.
{"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}
In this note, we find a necessary condition on odd-dimensional Riemannian manifolds under which both of Sasakian structure and the generalised Ricci soliton equation are satisfied, and we give some examples.
{"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}
For any two root subsets associated with two Carter diagrams that have the same $ADE$ type and the same size, we construct the transition matrix that maps one subset to the other. The transition between these two subsets is carried out in some canonical way affecting exactly one root, so that this root is mapped to the minimal element in some root subsystem. The constructed transitions are involutions. It is shown that all root subsets associated with the given Carter diagram are conjugate under the action of the Weyl group. A numerical relationship is observed between enhanced Dynkin diagrams $Delta(E_6)$, $Delta(E_7)$ and $Delta(E_8)$ (introduced by Dynkin-Minchenko) and Carter diagrams. This relationship echoes the $2-4-8$ assertions obtained by Ringel, Rosenfeld and Baez in completely different contexts regarding the Dynkin diagrams $E_6$, $E_7$, $E_8$.
{"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}
Selected stories about the life of A. L. Onishchik, and a review of his contribution to the classification of non-split supermanifolds, in particular, supercurves a.k.a. superstrings; his editorial and educational work. A brief overview of his and his students' results in supersymmetry, and their impact on other researchers. Several open problems growing out of Onishchik's research are presented, some of them are related with odd parameters of deformations and non-holonomic structures of supermanifolds important in physical models, such as Minkowski superspaces and certain superstrings.
{"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}
I. Kaygorodov, K. Kudaybergenov, Inomjon Yuldashev
We prove that every local derivation on a complex semisimple finite-dimensional Leibniz algebra is a derivation.
我们证明了复半单维莱布尼兹代数上的每一个局部导数都是一个导数。
{"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}
In this paper, we have proved four theorems on the degree of approximation of continuous functions by matrix means of their Fourier series which is expressed in terms of the modulus of continuity and a non-negative mediate function.
本文利用连续函数的傅立叶级数和一个非负中介函数，用矩阵方法证明了连续函数逼近度的四个定理。
{"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}
The Lie algebra of infinitesimal isometries of a Riemannian manifold contains at most two commutative ideals. One coming from the horizontal nullity space of the Nijenhuis tensor of the canonical connection, the other coming from the constant vectors fields independent of the Riemannian metric.
{"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}
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.
{"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}
Abstract In this paper we investigate Ramanujan’s inequality concerning the prime counting function, asserting that π(x2)
摘要在本文中，我们研究了关于素数计数函数的Ramanujan不等式，断言对于足够大的x，π（x2）
{"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}
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.
{"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：