In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup...In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.展开更多
Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control ...Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control of the norm and of the support of the extension.展开更多
Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenabilit...Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55（2）, 359-377 （1987）） is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.展开更多
In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are con...In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^＊-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.展开更多
For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A =...For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.展开更多
Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contractin...Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contracting iff for any [μ]εT(X), where is the Poincare series operator. Furthermore the inclusion is not a uniform contraction on T(X).展开更多
Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenabilit...Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.展开更多
We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,we define the relative entropy dimensions and the dimen...We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity.we also investigate the relations among these.Second,we introduce the notion of a relative dimension set.Moreover,using the method,we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions,which says that if the relative dimension sets of two extensions are different,then the extensions are disjoint.展开更多
Amenity trees are an essential element of most urban communities,contributing significantly to human well-being and improving environmental quality.Good knowledge of the diversity and abundance of trees in our environ...Amenity trees are an essential element of most urban communities,contributing significantly to human well-being and improving environmental quality.Good knowledge of the diversity and abundance of trees in our environment and their importance can help promote conservation,which is essential for sustainability.This study aimed at assessing the diversity and abundance of amenity trees on the premises of the International Institute of Tropical Agriculture(IITA),Ibadan Nigeria.The institute was divided into working and residential areas.The trees in the study area were identified using a walking and windshield survey.A total population of 2626 trees from 126 species and 42 families were identified on the premises of IITA.The highest tree population of 523 trees was recorded in the Tropical Crescent residential area with 321 trees of Lagerstroemia speciosa being the most frequent species.Across working and residential areas,Elaeis guineensis was the most frequent species accounting for 19.92%of the total tree population.A Shannon-Wiener Diversity Index(H’)of 3.383 and species evenness of 0.43 was obtained from the study area.The high values of diversity indices obtained indicate that IITA premises are rich in diverse tree species both indigenous and exotic hence should be referenced as a good urban landscape.The current management practices can be recommended for other institutions.展开更多
Based on road characters in Jiangnan New District in Mudanjiang Municipality,four typical roads were selected to carry out road afforestation design with consideration of local building features and local vegetations,...Based on road characters in Jiangnan New District in Mudanjiang Municipality,four typical roads were selected to carry out road afforestation design with consideration of local building features and local vegetations,in order to integrate both of landscape effects,in terms of improving and beautifying city environment,and of ecological effects,such as filtering air,reducing temperature,increasing humidity,and reducing noise.展开更多
文摘In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.
文摘Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control of the norm and of the support of the extension.
基金UGC for UGC-SAP-DRS-Ⅱ(Grant No.F.510/3/DRS/2009)provided to the Department of Mathematics,Sardar Patel University,Vallabh Vidyanagar-388120,India
文摘Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55（2）, 359-377 （1987）） is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.
基金supported by National Natural Science Foundation of China (Grant No. 11226125)
文摘In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^＊-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.
文摘For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.
文摘Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contracting iff for any [μ]εT(X), where is the Poincare series operator. Furthermore the inclusion is not a uniform contraction on T(X).
文摘Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.
基金supported by the NNSF of China (12201120,12171233)the Educational Research Project for Young and Middle-aged Teachers of Fujian Province (JAT200045).
文摘We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity.we also investigate the relations among these.Second,we introduce the notion of a relative dimension set.Moreover,using the method,we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions,which says that if the relative dimension sets of two extensions are different,then the extensions are disjoint.
文摘Amenity trees are an essential element of most urban communities,contributing significantly to human well-being and improving environmental quality.Good knowledge of the diversity and abundance of trees in our environment and their importance can help promote conservation,which is essential for sustainability.This study aimed at assessing the diversity and abundance of amenity trees on the premises of the International Institute of Tropical Agriculture(IITA),Ibadan Nigeria.The institute was divided into working and residential areas.The trees in the study area were identified using a walking and windshield survey.A total population of 2626 trees from 126 species and 42 families were identified on the premises of IITA.The highest tree population of 523 trees was recorded in the Tropical Crescent residential area with 321 trees of Lagerstroemia speciosa being the most frequent species.Across working and residential areas,Elaeis guineensis was the most frequent species accounting for 19.92%of the total tree population.A Shannon-Wiener Diversity Index(H’)of 3.383 and species evenness of 0.43 was obtained from the study area.The high values of diversity indices obtained indicate that IITA premises are rich in diverse tree species both indigenous and exotic hence should be referenced as a good urban landscape.The current management practices can be recommended for other institutions.
基金Supported by Special Project for Teaching Reform of Mudanjiang Normal University(2013JGZX0072)Project for Teaching Reform of Mudanjiang Normal University(2013ALZX019)+1 种基金Training Program of Mudanjiang Normal UniversityHorizontal Topic of Mudanjiang Normal University(KH0472)~~
文摘Based on road characters in Jiangnan New District in Mudanjiang Municipality,four typical roads were selected to carry out road afforestation design with consideration of local building features and local vegetations,in order to integrate both of landscape effects,in terms of improving and beautifying city environment,and of ecological effects,such as filtering air,reducing temperature,increasing humidity,and reducing noise.
