Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory with the fundamental group of arbitrary order. As a corollary we also obtain a calculation of the simple structure sets of the products of lens spaces and spheres of dimension grater or equal to $3$.
{"title":"Higher simple structure sets of lens spaces with the fundamental group of arbitrary order","authors":"L'udovít Balko, T. Macko, M. Niepel, T. Rusin","doi":"10.5817/am2019-5-267","DOIUrl":"https://doi.org/10.5817/am2019-5-267","url":null,"abstract":"Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory with the fundamental group of arbitrary order. As a corollary we also obtain a calculation of the simple structure sets of the products of lens spaces and spheres of dimension grater or equal to $3$.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77120028","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}
A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in C.R. Acad. Sci. Paris s'er. {bf I 333} (2001) 763-768. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.
黎曼-泊松李群是具有左不变黎曼度规和左不变泊松张量的李群，它们在C.R.中引入的意义上是相容的。巴黎 ' er。{bf I 333}(2001) 763-768。我们研究了这些李群，并给出了它们的李代数的一个表征。我们也给出了一种构造这些李代数的方法，并给出了5维李代数的列表。
{"title":"On Riemann-Poisson Lie groups","authors":"B. Alioune, M. Boucetta, Ahmed Sid’Ahmed Lessiad","doi":"10.5817/am2020-4-225","DOIUrl":"https://doi.org/10.5817/am2020-4-225","url":null,"abstract":"A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in C.R. Acad. Sci. Paris s'er. {bf I 333} (2001) 763-768. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"77 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79735189","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 that any semiartinian *-regular ring R is unit-regular; if, in addition, R is subdirectly irreducible then it admits a representation within some inner product space.
{"title":"Unit-regularity and representability for semiartinian $*$-regular rings","authors":"C. Herrmann","doi":"10.5817/am2020-1-43","DOIUrl":"https://doi.org/10.5817/am2020-1-43","url":null,"abstract":"We show that any semiartinian *-regular ring R is unit-regular; if, in addition, R is subdirectly irreducible then it admits a representation within some inner product space.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"36 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79368424","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":"Fixed points with respect to the L-slice homomorphism $sigma _{a} $","authors":"K. Sabna, N. R. Mangalambal","doi":"10.5817/am2019-1-43","DOIUrl":"https://doi.org/10.5817/am2019-1-43","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"35 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75681892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
(1.1) ∂tv + (u · ∇)v −∆v +∇π + 2∇|B| 2 = (B · ∇)B, ∂tB + (u · ∇)B − (B · ∇)v −∆B = 0, v = (1− α2∆)u, α > 0, div u = div v = divB = 0, (v,B)|t=0 = (v0, B0),div u0 = div v0 = divB0 = 0 in R3, where v : the fluid velocity field, u : “the filtered” fluid velocity, B : the magnetic field and π : the pressure, are the unknowns; α is the lengthscale parameter that represents the width of the filter. Note that the magnetic field is not regularized. It has lately received significant attention in mathematical fluid dynamics due to its connection to three-dimensional incompressible flows. When α→ 0, the model (1.1) reduce to the following MHD equations:
(1.1)∂电视+ v (u·∇)−∆v +∇π+ 2∇| | 2 = (B·∇)B,∂结核+ (u·∇)B−−(B·∇)v∆B = 0, v =(1−α2∆)u,α> 0,div div u = v = divB = 0, (v, B) | t = 0 = (v0, B0), div情况= div v0 = divB0 = 0 R3, v:流体速度场,u:“过滤”流体速度,B:磁场和π:压力,是未知的;α是表示滤波器宽度的长度尺度参数。注意磁场不是正则化的。由于它与三维不可压缩流动的联系，它最近在数学流体动力学中受到了极大的关注。当α→0时，模型(1.1)简化为如下MHD方程:
{"title":"Logarithmically improved blow-up criterion for smooth solutions to the Leray-$alpha $-magnetohydrodynamic equations","authors":"I. Omrane, S. Gala, Jae‐Myoung Kim, M. Ragusa","doi":"10.5817/AM2019-1-55","DOIUrl":"https://doi.org/10.5817/AM2019-1-55","url":null,"abstract":"(1.1) ∂tv + (u · ∇)v −∆v +∇π + 2∇|B| 2 = (B · ∇)B, ∂tB + (u · ∇)B − (B · ∇)v −∆B = 0, v = (1− α2∆)u, α > 0, div u = div v = divB = 0, (v,B)|t=0 = (v0, B0),div u0 = div v0 = divB0 = 0 in R3, where v : the fluid velocity field, u : “the filtered” fluid velocity, B : the magnetic field and π : the pressure, are the unknowns; α is the lengthscale parameter that represents the width of the filter. Note that the magnetic field is not regularized. It has lately received significant attention in mathematical fluid dynamics due to its connection to three-dimensional incompressible flows. When α→ 0, the model (1.1) reduce to the following MHD equations:","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"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":"72929652","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 existence of a homogeneous geodesic in homogeneous Finsler manifolds was investigated and positively answered in previous papers. It is conjectured that this result can be improved, namely that any homogeneous Finsler manifold admits at least two homogenous geodesics. Examples of homogeneous Randers manifolds admitting just two homogeneous geodesics are presented.
{"title":"Homogeneous Randers spaces admitting just two homogeneous geodesics","authors":"Z. Dušek","doi":"10.5817/am2019-5-281","DOIUrl":"https://doi.org/10.5817/am2019-5-281","url":null,"abstract":"The existence of a homogeneous geodesic in homogeneous Finsler manifolds was investigated and positively answered in previous papers. It is conjectured that this result can be improved, namely that any homogeneous Finsler manifold admits at least two homogenous geodesics. Examples of homogeneous Randers manifolds admitting just two homogeneous geodesics are presented.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"82 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73059291","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 aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved. As an application, a fixed point theorem in the given context is presented.
{"title":"Topological degree theory in fuzzy metric spaces","authors":"M. Rashid","doi":"10.5817/AM2019-2-83","DOIUrl":"https://doi.org/10.5817/AM2019-2-83","url":null,"abstract":". The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved. As an application, a fixed point theorem in the given context is presented.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84316820","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}
Kevin Esmeral, O. Ferrer, Jorge Jalk, Boris Lora Castro
. In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators T for which there exists a fundamental decomposition K = K + ⊕ K − of the Krein space K with K + and K − invariant under T .
． 本文介绍了Krein空间上的次正规算子。我们给出了有界算子次正则性的条件，重点讨论了在T下K +和K−不变量的Krein空间K存在基本分解K = K +⊕K−的算子T。
{"title":"On hyponormal operators in Krein spaces","authors":"Kevin Esmeral, O. Ferrer, Jorge Jalk, Boris Lora Castro","doi":"10.5817/am2019-4-249","DOIUrl":"https://doi.org/10.5817/am2019-4-249","url":null,"abstract":". In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators T for which there exists a fundamental decomposition K = K + ⊕ K − of the Krein space K with K + and K − invariant under T .","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":"90435976","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 prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.
{"title":"On the adjoint map of homotopy abelian DG-Lie algebras","authors":"Donatella Iacono, M. Manetti","doi":"10.5817/AM2019-1-7","DOIUrl":"https://doi.org/10.5817/AM2019-1-7","url":null,"abstract":". We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"15 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81834766","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 a completely contractive Banach algebra B, we find conditions under which the completely bounded multiplier algebra Mcb(B) is a dual Banach algebra and the operator amenability of B is equivalent to the operator Connes-amenability of Mcb(B). We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.
{"title":"Operator Connes-amenability of completely bounded multiplier Banach algebras","authors":"B. Hayati, A. Bodaghi, M. Amini","doi":"10.5817/AM2019-1-31","DOIUrl":"https://doi.org/10.5817/AM2019-1-31","url":null,"abstract":"For a completely contractive Banach algebra B, we find conditions under which the completely bounded multiplier algebra Mcb(B) is a dual Banach algebra and the operator amenability of B is equivalent to the operator Connes-amenability of Mcb(B). We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"17 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84371552","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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