ON SOME RESULTS RELATED TO SOBER SPACES

This paper investigates sober spaces and their related structures from different perspectives.First,we extend the descriptive set theory of second countable sober spaces to first countable sober spaces.We prove that a first countable T_(0) space is sober if and only if it does not contain a∏_(2)^(0)-subspace homeomorphic either to S_(D),the natural number set equipped with the Scott topology,or to S_(1),the natural number set equipped with the cofinite topology,and it does not contain any directed closed subset without maximal elements either.Second,we show that if Y is sober,the function space TOP(X,Y)equipped with the Isbell topology(respectively,Scott topology)may be a non-sober space.Furthermore,we provide a uniform construction to d-spaces and well-filtered spaces via irreducible subset systems introduced in[9];we called this an H-well-filtered space.We obtain that,for a T_(0) space X and an H-well-filtered space Y,the function space TOP(X,Y)equipped with the Isbell topology is H-well-filtered.Going beyond the aforementioned work,we solve several open problems concerning strong d-spaces posed by Xu and Zhao in[11].

A Monotonicity Condition for Strong Convergence of the Mann Iterative Sequence for Demicontractive Maps in Hilbert Spaces

Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= (1 - an) xn +?anT xn, where an ∈?(0, 1) n?≥?0, converges strongly to an element of F (T):= {x?∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed.

SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES

We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points,related to the so-called Rolewicz’s property(α).We give a characterization of those points in terms of continuity properties of the identity mapping.The connection between these two geometric properties is established,and finally an application to approximative compactness is given.

SOME PROPERTIES OF STRONGLY MONOTONICALLY T2 SPACES

This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

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(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) 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∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

CHEBYSHEV CENTERS PROXIMINALITY AND FARTHEST POINTS IN STRONG NORMED ALMOST LINEAR SPACES

Some results from the theory of best (or best simultaneous) approximation in a narmed linear space have been extended to a normed almost linear space [strong normed almost linear space].

Iterative Approximation of Fixed Points for Uniformly Continuous and Strongly Pseudocontractive Mappings in Smooth Banach Spaces

With an inequality and some analysis techniques,iterative approximation of fixed points for uniformly continuous and strongly pseudocontractive mappings in smooth Banach spaces is studied,and the recent corresponding results of Chidume are improved.

Stable Perturbed Algorithms for a New Class of Generalized Nonlinear Implicit Quasi Variational Inclusions in Banach Spaces

In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.

GENERAL SPLIT FEASIBILITY PROBLEMS FOR TWO FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES

The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

SINGLE PROJECTION ALGORITHM FOR VARIATIONAL INEQUALITIES IN BANACH SPACES WITH APPLICATION TO CONTACT PROBLEM

We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach space.The underline cost function of the variational inequality is assumed to be monotone and Lipschitz continuous.A weak convergence result is obtained under reasonable assumptions on the variable step-sizes.We also give the strong convergence result for when the underline cost function is strongly monotone and Lipchitz continuous.For this strong convergence case,the proposed method does not require prior knowledge of the modulus of strong monotonicity and the Lipschitz constant of the cost function as input parameters,rather,the variable step-sizes are diminishing and non-summable.The asymptotic estimate of the convergence rate for the strong convergence case is also given.For completeness,we give another strong convergence result using the idea of Halpern iteration when the cost function is monotone and Lipschitz continuous and the variable step-sizes are bounded by the inverse of the Lipschitz constant of the cost function.Finally,we give an example of a contact problem where our proposed method can be applied.

Some Topological Properties of Charming Spaces

In this paper, we mainly discuss the class of charming spaces. First, we show that there exists a charming space such that the Tychonoff product is not a charming space. Then we discuss some properties of charming spaces and give some characterizations of some class of charming spaces. Finally, we show that the Suslin number of an arbitrary charming rectifiable space is countable.

Far-field analysis of effects of unilateral rupturing fault on the space correlation of strong ground motion

On the assumption that seismic source is simplified as linear rupture fault with finite length, this paper qualitatively studies the seismic source effects on space correlation of strong ground motion. Based on expanding expression of Fourier spectrum of strong ground motion with space coordinate variables, this paper also gives a expression of describing correlation of strong ground motion field. According to far-field condition, the theoretical formula of the expression can be obtained. Furthermore, this paper presents a theoretical formula of estimation the radius of strong ground motion field, which depends on expansion condition of Fourier spectrum of strong ground motion, with space variables. At last, taking one earthquake as an example, this paper gives three-dimension patterns of radius of the field with epicenter distance and azimuth as well as frequency.

Common Fixed Point Iterations of Generalized Asymptotically Quasi-Nonexpansive Mappings in Hyperbolic Spaces

We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.

A system of general nonlinear variational inclusions in Banach spaces

A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces.

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.

Study of Nonlinear Earthquake Flow Functions and Their Application to the Space Increased Probability of Strong Earthquake (SIP)

The definition and abnormality discriminatory criteria of earthquake flow function are introduced in this paper based on the algorithm of Space Increased Probability (SIP). Nine earthquake flow functions were defined by the method. The retrospect test that applied the SIP algorithm with the nonlinear earthquake flow function to 7 earthquakes, which occurred from 1975 to 1989 in Eastern China, with a magnitude of 6 or greater depicted that 6 of the 7 strong earthquakes (86%) were located in the SIP areas, and the SIP covers about 32% of the total research time-space domain. These suggest that the R-value, an effective scale for earthquake forecast, is 54% and may imply that the nonlinear earthquake flow function introduced in this paper can be applied to the intermediate-term earthquake forecast research.

Curvature Estimates for Strongly Stable Domains on Surfaces with Constant Mean Curvature in Space Forms

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能量选择电磁防护方法理论与应用

随着信息技术的发展,电磁空间逐渐成为国家重大公共基础设施及信息网络的基石。近年来,强电磁源生成技术加速发展,对电磁空间安全形成严重威胁,开展强电磁防护技术研究具有迫切的现实需求。能量选择防护方法是一种新型自适应强电磁防护方法,突破了电子设备前门防护“能防”和“兼容”的难题,为强电磁防护提供了新的技术思路。本文对能量选择防护方法进行了系统综述,首先详细介绍了能量选择防护的内涵和相关概念;其次以能量选择表面为例阐述了其工作原理与实现方式,在此基础上对能量选择防护方法的研究现状和最新成果进行介绍,梳理了能量选择防护方法的发展脉络;最后,对能量选择防护方法的未来研究方向进行了展望。

FT-粗糙集模型的一些性质

T-粗糙集是Pawlak粗糙集理论发展过程中的一个重要模型,已成功应用于数据挖掘等诸多领域.FT-粗糙集模型能够在保持数据的完整性下处理连续型数据,是对仅能处理离散型数据的T-粗糙集模型上的发展.文章引入模糊近似空间(X,Y,T)一对模糊集的弱逆和强逆定义,用量化方法研究FT-粗糙集的一些性质,得到模糊技能映射在析取模型、合取模型下分别生成的知识结构;用量化方法与矩阵表示探究FT-粗糙集模糊集值映射在并、交运算下的性质.