Differentiability of Convex Functions in Locally Convex Spaces（Ⅰ）──Continuous Convex Functions and Gateaux Differentiability

The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces.

ON THE PRODUCT OF GTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.

SOME BEST APPROXIMATION RESULTS IN LOCALLY CONVEX SPACES

In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.

Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.

CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY CONVEX H-SPACES

A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.

ON FULLY CONVEX AND LOCALLY FULLY CONVEX BANACH SPACE*

In this paper, we introduce the concept of locally fully convexity. We study the properties of fully convex and locally fully convex Banach spaces and the relations between them. We also give some applications of the fully convex and locally fully convex Banach spaces.

Equicontinuous Seton Locally Convex Spaces

Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can find a f 0∈E′ and extract subsequences {f n i } and {x n j } such that {f n i } converges to f 0 on {x n j } uniformly. If (E,γ) is metrizable,then we can show that the converse is also valid.

Differentiability of Convex Functions in Locally Convex Spaces(Ⅱ)──Frechet

ＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙｏｆＣｏｎｖｅｘＦｕｎｃｔｉｏｎｓｉｎＬｏｃａｌｌｙＣｏｎｖｅｘＳｐａｃｅｓ（ＩＩ）──ＦｒｅｃｈｅｔＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙＷＵＣｏｎｇｘｉｎＷＡＮＧＸｉａｏｍｉｎＣＨＥＮＧＬｉｘｉｎ吴从ａａａｙ，王晓敏...

Generalized Bi quasi variational Inequalities in Locally Convex Topological Vector Spaces

In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].

The Theory of Vector-Valued Function in Locally Convex Space

In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.

A NEW CLASS OF LOCALLY CONVEX SPACES AND THE GENERALIZATION OF KALTON'S CLOSED GRAPH THEOREM

By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.

THE SIMULTANEOUS APPROXIMATION IN THE LOCALLY CONVEX SPACES

In this paper, we study the characterization of f-Chebyshev radius and f-Chebyshev centers and the existence of f-Chebyshev centers in locally convex spaces.

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMSIN LOCALLY G-CONVEX SPACES

Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

POTENTIAL SPACE ESTIMATES IN LOCAL HARDY SPACES FOR GREEN POTENTIALS IN CONVEX DOMAINS

Let Ω be a bounded convex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△on Ω Let hPT(Ω) = {f∈D'(Ω) : (?)F ∈ hP(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f Ω(?)2(Gf) for every f ∈hPr(Ω) is obtained, where n/(n + 1) <p≤1.

Simulation of bacterial flagellar phase transition by non-convex and non-local continuum modeling

Bacterial flagellar filament can undergo a stress-induced polymorphic phase transition in both vitro and vivo environments.The filament has 12 different helical forms(phases) characterized by different pitch lengths and helix radii.When subjected to the frictional force of flowing fluid,the filament changes between a left-handed normal phase and a right-handed semi-coiled phase via phase nucleation and growth.This paper develops non-local finite element method(FEM) to simulate the phase transition under a displacement-controlled loading condition(controlled helix-twist).The FEM formulation is based on the Ginzburg-Landau theory using a one-dimensional non-convex and non-local continuum model.To describe the processes of the phase nucleation and growth,viscosity-type kinetics is also used.The non-local FEM simulation captures the main features of the phase transition:two-phase coexistence with an interface of finite thickness,phase nucleation and phase growth with interface propagation.The non-local FEM model provides a tool to study the effects of the interfacial energy/thickness and loading conditions on the phase transition.

无线传感器网络基于凸规划的改进定位算法:Convex-PIT

定位技术是无线传感器网络的关键技术之一,为了提高无线传感器网络的定位精度,在Convex算法基础上提出了Convex-PIT算法.Convex-PIT算法通过引入锚节点构成的三角形进一步滤掉节点不可能存在的区域,缩小节点可能存在范围,提高定位精度.Convex-PIT算法增加了判断未知节点是否在锚节点组成的三角形内的计算量,但不需要增加节点的硬件条件和额外的功能.仿真结果表明,和Convex算法相比,Convex-PIT可以明显的提高定位精度,在锚节点的比例从10%增加到30%的过程中,定位精度提高幅度平均约15%.

基于SOCP理论的船舶导航雷达海杂波抑制算法研究

为了有效降低海杂波对船舶导航雷达工作的影响,提出了一种基于二阶锥规划(SOCP)理论的杂波抑制算法。针对传统的实系数有限冲激响应(FIR)数字滤波器组无法保证通带群延时(小数)精度的问题,通过将初始优化问题转化为对偶问题进行求解,利用SOCP理论的分布式计算优势,稳定有效地求取其局部最优点,同时用重构的海杂波样本反复训练理论模型。通过仿真实验证明SOCP理论可以更好地重构信号检测模型,大幅抑制海杂波的影响,提高船舶导航雷达的目标检测能力。

How to Select the Best Sensors for TDOA and TDOA/AOA Localization?

This paper focuses on the sensor subset optimization problem in time difference of arrival(TDOA) passive localization scenario. We seek for the best sensor combination by formulating a non-convex optimization problem, which is to minimize the trace of covariance matrix of localization error under the condition that the number of selected sensors is given. The accuracy metric is described by the localization error covariance matrix of classical closed-form solution, which is introduced to convert the TDOA nonlinear equations into pseudo linear equations. The non-convex optimization problem is relaxed to a standard semi-definite program(SDP) and efficiently solved in a short time. In addition, we extend the sensor selection method to a mixed TDOA and angle of arrival(AOA) localization scenario with the presence of sensor position errors. Simulation results validate that the performance of the proposed sensor selection method is very close to the exhaustive search method.

QUASI_EQUILIBRIUM PROBLEMS IN NONCOMPACT GENERALIZED CONVEX SPACES

By applying a new fixed point theorem due to the author, some new equilibrium existence theorems of quasi-equilibrium problems are proved in noncompact generalized convex spaces. These theorems improve and generalize a number of important known results in recent literature.