Some Characterizations of Spaces with Weak Form of $cs$-Networks

In this paper, we introduce the concept of statistically sequentially quotient map:A mapping f : X → Y is statistically sequentially quotient map if whenever a convergent sequence S in Y, there is a convergent sequence L in X such that f(L) is statistically dense in S. Also, we discuss the relation between statistically sequentially quotient map and covering maps by characterizing statistically sequentially quotient map and we prove that every closed and statistically sequentially quotient image of a g-metrizable space is g-metrizable. Moreover,we discuss about the preservation of generalization of metric space in terms of weakbases and sn-networks by closed and statistically sequentially quotient map.     

A Characterization of Generalized Monotone Normed Cones

Let C be a cone and consider a quasi-norm p defined on it. We study the structure of the couple （C, p） as a topological space in the case where the function p is also monotone. We characterize when the topology of a quasi-normed cone can be defined by means of a monotone norm. We also define and study the dual cone of a monotone normed cone and the monotone quotient of a general cone. We provide a decomposition theorem which allows us to write a cone as a direct sum of a monotone subcone that is isomorphic to the monotone quotient and other particular subcone.     

Essentially normal Hilbert modules and K-homology Ⅲ:Homogenous quotient modules of Hardy modules on the bidisk

In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk.     

On the Structure of the Augmentation Quotient Group for Some Non-abelian p-groups

In this paper,we study the basis of augmentation ideals and the quotient groups of finite non-abelian p-group which has a cyclic subgroup of index p,where p is an odd prime,and k is greater than or equal to 3.A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.     

THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM

51. Introduction and PreliminaryThe multiplier bimodule of imprimitive bimodule and its application to coaction systemwere introduced in [if, but it is generally not an imprimitive bimodule as noted in [II by anexample. In this paper, the same concept is introduced for Hilbert bimodules which properlycontain imprimitive bimodules (for example, the same example as above), and we obtainthe realization of multiplier bimodule on a quotient of bidual space and Tietze extensiontheorem similar to t…     

A VIEWPOINT TO MEASURE OF NON-COMPACTNESS OF OPERATORS IN BANACH SPACES

This article is committed to deal with measure of non-compactness of operators in Banach spaces. Firstly, the collection C(X)(consisting of all nonempty closed bounded convex sets of a Banach space X endowed with the uaual set addition and scaler multiplication) is a normed semigroup, and the mapping J from C(X) onto F(?) is a fully order-preserving positively linear surjective isometry, where ? is the closed unit ball of X*and F(?) the collection of all continuous and w*-lower semicontinuous sublinear functions on X*but restricted to ?. Furthermore, both ■ and ■ are Banach lattices and EK is a lattice ideal of EC. The quotient space EC/EK is an abstract M space, hence,order isometric to a sublattice of C(K) for some compact Haudorspace K, and(FQJ)C which is a closed cone is contained in the positive cone of C(K), where Q : E_C → E_C/E_K is the quotient mapping and F : E_C/E_K → C(K) is a corresponding order isometry. Finally, the representation of the measure of non-compactness of operators is given: Let B_X be the closed unit ball of a Banach space X, then■     

商不可分解Banach空间上线性算子的谱

This paper discusses the special properties of the spectrum of linear operators (in particular, bounded linear operators) on quotient indecomposable Banach spaces; shows that in such spaces generators of Co-groups are always bounded linear operators, and that generators of Co-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of Co-semigroups in quotient indecomposable spaces are not necessarily bounded.     

INEQUALITY OF KORN‘S TYPE ON COMPACT SURFACES WITHOUT BOUNDARY

Inequalities of Korn's type on a surface with boundary have been proved in many papers using different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn's type on a compact surface without boundary. The idea is to use a finite number of maps for defining the surface and the inequality of Korn's type without boundary conditions for every map and to recast these in a general functional analysis setting about quotient spaces.     

ON THE RAYLEIGH QUOTIENT FOR SINGULAR VALUES

In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, some results of the Rayleigh quotient （matrix） of Hermitian matrices are extended to those for arbitrary matrix on one hand. On the other hand, some unitarily invariant norm bounds for singular values are presented for Rayleigh quotient matrices. Our results improve the existing bounds.     

On Subgroups and Quotient Groups of L-fuzzy Topological Groups

In paper [1], it gave the concept and basic properties of L-fuzzy topological groups. This paper will enter the concept of quotient groups of L-fuzzy topological groups and will prove some properties of subgroups and quotient groups. The persent work is the continuation of [1] and hence all the conventions in [1] still hold good in the present paper.     

Prequantale同余及其性质

本文给出了Prequantale同余的概念，讨论了它与Prequantale商和核映射之问的关系，得到了Prequantale上的全体商、全体核映射和全体同余作为完备格是同构的结论．找到了与同余相对应的商的具体结构．证明了Prequantale范畴有余等子．     

格序代数的商及其代数性质

研究了格序代数的商及其一些重要的代数性质.给出了格序代数的商的概念,定义了商f-代数、商几乎f-代数和商d-代数,并给出其等价刻画.讨论了这三类格序代数的商的半素性和交换性质,得到了这些性质的若干刻画.     

关于Quotient Context of Morita Context的讨论

本文讨论了ＱｕｏｔｉｅｎｔＣｏｎｔｅｘｔｏｆ Ｍｏｒｉｔａ Ｃｏｎｔｅｘｔ的一些性质,并在此基础上证明：如果ＤＲ是一个完备Ｇａｂｒｉｅｌ拓扑,则一个（Ｐ,Ｑ）的商（Ｐ,Ｑ）作为Ｒ与Ｓ之间ＭＣ,它的商同构于（Ｐ,Ｑ）的一个商。     

Essentially normal Hilbert modules and Khomology Ⅲ: Homogenous quotient modules of Hardy modules on the bidisk

In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk.     

Fuzzy HX环的推广

为改进Fuzzy HX环的结果,使之包含Fuzzy商环,提出了弱Fuzzy HX环的概念,研究了它的性质与结构,并重新讨论了拟Fuzzy商环,证明了在正则条件下拟Fuzzy商环与弱Fuzzy HX环的统一性：同时也得到了一致弱Fuzzy HX环与普通Fuzzy商环的关系。     

超格的商结构

通过引入超格的强闭集、上半补超格、数量上界单位元等概念,引出超格上的等价关系.构造数量上界单位集,在此基础上进一步研究超格的一些性质.商代数结构定理的建立对于完善超格的商结构具有实际意义.     

QR algorithm with two-sided Rayleigh quotient shifts

We introduce the two-sided Rayleigh quotient shift to the QR algorithm for non-Hermitian matrices to achieve a cubic local convergence rate. For the singly shifted case, the two-sided Rayleigh quotient iteration is incorporated into the QR iteration. A modified version of the method and its truncated version are developed to improve the efficiency. Based on the observation that the Francis double-shift QR iteration is related to a 2D Grassmann–Rayleigh quotient iteration, A doubly shifted QR algorithm with the two-sided 2D Grassmann–Rayleigh quotient double-shift is proposed. A modified version of the method and its truncated version are also developed. Numerical examples are presented to show the convergence behavior of the proposed algorithms. Numerical examples also show that the truncated versions of the modified methods outperform their counterparts including the standard Rayleigh quotient single-shift and the Francis double-shift.