In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topo...In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.展开更多
As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the ...As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.展开更多
文章以1996-2015年Web of Science数据库收录的大数据领域文献为研究样本,从总体态势、空间格局演变特征和当前研究力量布局三个角度进行了分析。结果显示,大数据领域研究正处于中前期加速发展期,学科交叉性强;研究中心正在向中、美、...文章以1996-2015年Web of Science数据库收录的大数据领域文献为研究样本,从总体态势、空间格局演变特征和当前研究力量布局三个角度进行了分析。结果显示,大数据领域研究正处于中前期加速发展期,学科交叉性强;研究中心正在向中、美、英、德等多个核心区演变,呈现"核心-边缘"结构,并且各国研发实力相差悬殊,核心区主要发达国家研究力量和影响力稳步增长,而中国及亚洲地区的研究成果产出量增长较快,但研究成果学术质量亟待提升。展开更多
文摘In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.
文摘As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.
文摘文章以1996-2015年Web of Science数据库收录的大数据领域文献为研究样本,从总体态势、空间格局演变特征和当前研究力量布局三个角度进行了分析。结果显示,大数据领域研究正处于中前期加速发展期,学科交叉性强;研究中心正在向中、美、英、德等多个核心区演变,呈现"核心-边缘"结构,并且各国研发实力相差悬殊,核心区主要发达国家研究力量和影响力稳步增长,而中国及亚洲地区的研究成果产出量增长较快,但研究成果学术质量亟待提升。
