A new iterative algorithm for the variational inequality problem over the fixed point set of a firmly nonexpansive mapping

Many problems to appear in signal processing have been formulated as the variational inequality problem over the fixed point set of a nonexpansive mapping. In particular, convex optimization problems over the fixed point set are discussed, and operators which are considered to the problems satisfy the monotonicity. Hence, the uniqueness of the solution of the problem is not always guaranteed. In this article, we present the variational inequality problem for a monotone, hemicontinuous operator over the fixed point set of a firmly nonexpansive mapping. The main aim of the article is to solve the proposed problem by using an iterative algorithm. To this goal, we present a new iterative algorithm for the proposed problem and its convergence analysis. Numerical examples for the proposed algorithm for convex optimization problems over the fixed point set are provided in the final section.     

在Pbkc（c[0,1]）与Pbkc（Lp[0,1]）取值的集值随机变量（1）

对拟连续测度空间(G,β,u)的一致有界等度连续函数族,通过包含关系,取凸包和闭包,构造了在Pbkc(c[0,1])与Pbkc(Lp[0,1])取值的集值随机变量及连续的集值映射,深化了集值随机过程理论研究.     

A new method for solving a system of generalized nonlinear variational inequalities in Banach spaces

The purpose of this paper is by using the generalized projection approach to introduce an iterative scheme for finding a solution to a system of generalized nonlinear variational inequality problem. Under suitable conditions, some existence and strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces. The results presented in the paper improve and extend some recent results.     

Doping level and environment dependence of structural stability and magnetic properties in Mn-doped WS2 bilayer in first principles

We carried out first-principles electronic structure calculation to study the structural stability and magnetic properties of Mn-doped WS₂ ultra-thin films within the density functional theory. Adopting various configurations of Mn doping into WS₂ bilayer, we find that the magnetic phase can be manipulated among the ferromagnetic, antiferromagnetic, or ferrimagnetic phases by altering doping level and growth environment. Magnetic phase and strength are determined by magnetic coupling of Mn dopants 3d electrons which can be attributed crucially to the exchange interaction mediated by neighboring S atoms 3p electrons. Accompanying to the magnetic phase transition, the electronic structure reveals that transport properties switch from semiconducting with various bandgap to half-metallic states. This result implicates possible way to develop magnetic semiconductors based on Mn doped 2D WS₂ ultra-thin films for spintronics applications.     

Hierarchic Natures and Dynamics of Photoinduced Structural Phase Transition in Non-Degenerate Charge Density Wave States Via Successive Photoexcitations

We investigate the adiabatic and dynamical natures of the lattice relaxation of excitons in strongly coupled electron-phonon (e-ph) systems using the extended Peierls-Hubbard model, so as to clarify the possible mechanisms of the photoinduced structural phase transition (PISPT) via multi-photon. Focusing on the growth process of relaxed domains that is induced by multi-photoexcitation, we calculate the adiabatic potential energy surfaces relevant to the nonlinear lattice relaxations of excitons in this process. Calculated potentials lead to an essential model of a multi-stepwise potential-crossing (MSPC) system that is composed of many displaced harmonic oscillators as an elementary process of the domain growth in the strongly coupled e-ph systems. We also investigate the dynamical natures in such MSPC systems calculating the time-developments the excited wave packet in this system using the density operator. It is concluded from calculated results that the system possibly develops from the lowest-energy potential state to the higher ones by the effect of the photoexcitations followed by the lattice relaxations.     

主被动光学图像融合技术研究

本文应用扫描式激光成像雷达获取试验数据并实现对激光数据的三维成像处理,给出了基于目标特征的激光雷达图像与被动光学图像的数据融合方法,实现了激光图像和光学图像间的三维融合。试验结果表明,本文所提出的基于目标特征的两种不同质图像间的融合方法是可行的,融合后的图像具有丰富的光谱信息和三维立体信息。     

逼近严格伪压缩映象不动点的Ishikawa迭代程序

Let(X,‖·‖ ) be a Banach space.Let K be a nonempty closed,convex subset of Xand T∶K→K.Assume that T is Lipschitzian,i.e.there exists L>0 such that‖ T(x) -T(y)‖≤ L‖ x -y‖for all x,y∈K.Withoutloss of generality,assume that L≥ 1 .Assume also that T is strictly pseudocontractive.According to[1 ] this may be statedas:there exists k∈ (0 ,1 ) such that‖ x -y‖≤‖ x -y + r[(I -T -k I) x -(I -T -k I) y]‖for all r>0 and all x,y∈ K.Throughout,let N denote the set of positive in…     

Extending the Balas-Yu bounds on the number of maximal independent sets in graphs to hypergraphs and lattices

A result of Balas and Yu (1989) states that the number of maximal independent sets of a graph G is at most ^p+1, where is the number of pairs of vertices in G at distance 2, and p is the cardinality of a maximum induced matching in G. In this paper, we give an analogue of this result for hypergraphs and, more generally, for subsets of vectors in the product of n lattices =₁××_n, where the notion of an induced matching in G is replaced by a certain binary tree each internal node of which is mapped into . We show that our bounds may be nearly sharp for arbitrarily large hypergraphs and lattices. As an application, we prove that the number of maximal infeasible vectors x=₁××_n for a system of polymatroid inequalities does not exceed max{Q,^logt/c(2Q,)}, where is the number of minimal feasible vectors for the system, , , and c(,) is the unique positive root of the equation 2^c(^c/log–1)=1. This bound is nearly sharp for the Boolean case ={0,1}ⁿ, and it allows for the efficient generation of all minimal feasible sets to a given system of polymatroid inequalities with quasi-polynomially bounded right-hand sides . This research was supported by the National Science Foundation (Grant IIS-0118635), and by the Office of Naval Research (Grant N00014-92-J-1375). The second and third authors are also grateful for the partial support by DIMACS, the National Science Foundation's Center for Discrete Mathematics and Theoretical Computer Science.Mathematics Subject Classification (2000):20E28, 20G40, 20C20     

On the Ulam stability of Jensen and Jensen type mappings on restricted domains

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.     

空间遥感测绘光学系统研究综述

将遥感技术应用到测绘当中是现代地质测绘技术的发展趋势,随着光学载荷分辨率的不断提高,遥感测绘已经成为社会发展和国民经济发展的重要保障。光学载荷决定了测绘空间遥感器的分辨率、测绘精度、卫星平台体积与重量,是遥感器的核心部分。本文对高成像质量透射光学系统、同轴三反光学系统、离轴三反系统等常用的空间遥感测绘光学系统的结构形式和光学性能分别进行了介绍,并对处于研发阶段的新型空间反射光学系统的结构形式和光学性能进行了展望。分析认为,根据不同的应用环境和技术指标,合理选用不同种类的遥感测绘光学系统,可以最大程度利用平台资源,满足遥感测绘需求。