Let (X, d) be a metric space and α > 0. We study homological properties and different types of amenability of Lipschitz algebras LipαX and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of X. Finally, some results concerning the character space and Arens regularity of Lipschitz algebras are provided.
{"title":"Some algebraic and homological properties of Lipschitz algebras and their second duals","authors":"F. Abtahi, E. Byabani, A. Rejali","doi":"10.5817/am2019-4-211","DOIUrl":"https://doi.org/10.5817/am2019-4-211","url":null,"abstract":"Let (X, d) be a metric space and α > 0. We study homological properties and different types of amenability of Lipschitz algebras LipαX and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of X. Finally, some results concerning the character space and Arens regularity of Lipschitz algebras are provided.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90162484","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 article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is $L^{1}_{alpha }$-caratheodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.
{"title":"Existence results for systems of conformable fractional differential equations","authors":"B. Bendouma, A. Cabada, A. Hammoudi","doi":"10.5817/AM2019-2-69","DOIUrl":"https://doi.org/10.5817/AM2019-2-69","url":null,"abstract":"In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is $L^{1}_{alpha }$-caratheodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89340885","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}
One of the important questions that remains after the classification of the finite simple groups is how to recognize a simple group via specific properties. For example, authors have been able to use graphs associated to element orders and to number of elements with specific orders to determine simple groups up to isomorphism. In this paper, we prove that Suzuki groups Sz(q), where q ± √ 2q + 1 is a prime number can be uniquely determined by the order of group and the number of elements with the same order.
{"title":"A new characterization of Suzuki groups","authors":"B. Ebrahimzadeh, R. Mohammadyari","doi":"10.5817/am2019-1-17","DOIUrl":"https://doi.org/10.5817/am2019-1-17","url":null,"abstract":"One of the important questions that remains after the classification of the finite simple groups is how to recognize a simple group via specific properties. For example, authors have been able to use graphs associated to element orders and to number of elements with specific orders to determine simple groups up to isomorphism. In this paper, we prove that Suzuki groups Sz(q), where q ± √ 2q + 1 is a prime number can be uniquely determined by the order of group and the number of elements with the same order.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"47 1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90054139","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}
{"title":"On the $gamma $-equivalence of semiholonomic jets","authors":"M. Doupovec, I. Kolář","doi":"10.5817/am2019-4-261","DOIUrl":"https://doi.org/10.5817/am2019-4-261","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91114109","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}
Groups of homeomorphisms related to locally trivial bundles are studied. It is shown that these groups are perfect. Moreover if the homeomorphism isotopy group of the base is bounded then the bundle homeomorphism group of the total space is uniformly perfect.
{"title":"On the uniform perfectness of groups of bundle homeomorphisms","authors":"T. Rybicki","doi":"10.5817/am2019-5-333","DOIUrl":"https://doi.org/10.5817/am2019-5-333","url":null,"abstract":"Groups of homeomorphisms related to locally trivial bundles are studied. It is shown that these groups are perfect. Moreover if the homeomorphism isotopy group of the base is bounded then the bundle homeomorphism group of the total space is uniformly perfect.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80610299","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 give some necessary and sufficient conditions such that each positive operator between two Banach lattices is weak almost Dunford-Pettis, and we derive some interesting results about the weak Dunford-Pettis property in Banach lattices.
{"title":"A complement of positive weak almost Dunford-Pettis operators on Banach lattices","authors":"A. Retbi","doi":"10.5817/AM2019-1-1","DOIUrl":"https://doi.org/10.5817/AM2019-1-1","url":null,"abstract":"In this paper, we give some necessary and sufficient conditions such that each positive operator between two Banach lattices is weak almost Dunford-Pettis, and we derive some interesting results about the weak Dunford-Pettis property in Banach lattices.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81674232","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}
One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the “main family” those given by [ Big ( frac{2}{lambda e^t+1} Big )^alpha e^{xt} = sum _{n=0}^{infty } mathcal{E}^{(alpha )}_{n}(x;lambda ) frac{t^n}{n!},, qquad lambda in mathbb{C}setminus lbrace -1rbrace ,, ] and as an “exceptional family” [ Big ( frac{t}{e^t-1} Big )^alpha e^{xt} = sum _{n=0}^{infty } mathcal{B}^{(alpha )}_{n}(x) frac{t^n}{n!},, ] both of these for $alpha in mathbb{C}$.
在数学文献中，我们可以找到许多研究广义apostoll - bernoulli多项式、apostoll - euler多项式和apostoll - genocchi多项式的最新论文，它们是用生成函数来定义的。在本文中，我们澄清了这些定义有效的参数范围，以及当它们提供本质上不同的多项式族时。特别是，我们表明，直到乘法常数，它足以作为“主要族”的那些由[ Big ( frac{2}{lambda e^t+1} Big )^alpha e^{xt} = sum _{n=0}^{infty } mathcal{E}^{(alpha )}_{n}(x;lambda ) frac{t^n}{n!},, qquad lambda in mathbb{C}setminus lbrace -1rbrace ,, ]和作为一个“例外族”[ Big ( frac{t}{e^t-1} Big )^alpha e^{xt} = sum _{n=0}^{infty } mathcal{B}^{(alpha )}_{n}(x) frac{t^n}{n!},, ]这两个为$alpha in mathbb{C}$。
{"title":"Existence and reduction of generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials","authors":"L. M. Navas, F. Ruiz, J. Varona","doi":"10.5817/am2019-3-157","DOIUrl":"https://doi.org/10.5817/am2019-3-157","url":null,"abstract":"One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the “main family” those given by [ Big ( frac{2}{lambda e^t+1} Big )^alpha e^{xt} = sum _{n=0}^{infty } mathcal{E}^{(alpha )}_{n}(x;lambda ) frac{t^n}{n!},, qquad lambda in mathbb{C}setminus lbrace -1rbrace ,, ] and as an “exceptional family” [ Big ( frac{t}{e^t-1} Big )^alpha e^{xt} = sum _{n=0}^{infty } mathcal{B}^{(alpha )}_{n}(x) frac{t^n}{n!},, ] both of these for $alpha in mathbb{C}$.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"55 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76070543","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}
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we call current Lie groupoids. We then study basic differential geometry and Lie theory for these Lie groupoids of mappings. In particular, we show that certain Lie groupoid properties, like being a proper 'etale Lie groupoid, are inherited by the current groupoid. Furthermore, we identify the Lie algebroid of a current Lie groupoid as a current Lie algebroid (analogous to the current Lie algebra associated to a current Lie group). To establish these results, we study superposition operators given by postcomposition with a fixed function, between manifolds of $C^ell$-functions. Under natural hypotheses, these operators turn out to be a submersion (an immersion, an embedding, proper, resp., a local diffeomorphism) if so is the underlying map. These results are new in their generality and of independent interest.
{"title":"Lie groupoids of mappings taking values in a Lie groupoid","authors":"H. Amiri, Helge Glockner, Alexander Schmeding","doi":"10.5817/am2020-5-307","DOIUrl":"https://doi.org/10.5817/am2020-5-307","url":null,"abstract":"Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we call current Lie groupoids. We then study basic differential geometry and Lie theory for these Lie groupoids of mappings. In particular, we show that certain Lie groupoid properties, like being a proper 'etale Lie groupoid, are inherited by the current groupoid. Furthermore, we identify the Lie algebroid of a current Lie groupoid as a current Lie algebroid (analogous to the current Lie algebra associated to a current Lie group). \u0000To establish these results, we study superposition operators given by postcomposition with a fixed function, between manifolds of $C^ell$-functions. Under natural hypotheses, these operators turn out to be a submersion (an immersion, an embedding, proper, resp., a local diffeomorphism) if so is the underlying map. These results are new in their generality and of independent interest.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"181 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77104627","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}
We show how the theory of $mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.
{"title":"The graded differential geometry of mixed symmetry tensors","authors":"A. Bruce, Eduardo Ibarguengoytia","doi":"10.5817/AM2019-2-123","DOIUrl":"https://doi.org/10.5817/AM2019-2-123","url":null,"abstract":"We show how the theory of $mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"2013 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82694394","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 introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid.
{"title":"On F-algebroids and Dubrovin’s duality","authors":"John Alexander Cruz Morales, A. Torres-Gomez","doi":"10.5817/am2019-2-109","DOIUrl":"https://doi.org/10.5817/am2019-2-109","url":null,"abstract":"In this note we introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90516574","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}
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