Iterative Algorithms for Nonlinear Operators

Iterative algorithms for nonexpansive mappings and maximal monotoneoperators are investigated. Strong convergence theorems areproved for nonexpansive mappings, including an improvement ofa result of Lions. A modification of Rockafellar’s proximalpoint algorithm is obtained and proved to be always stronglyconvergent. The ideas of these algorithms are applied to solvea quadratic minimization problem.     

过氧多酸盐[NBu4]3[M(O2)W5O18]的合成及表征

过渡金属过氧化合物是一类性能良好的催化剂,在有机合成中得到广泛的应用[1,2].过氧多酸催化过氧化氢氧化有机物的反应,近年来倍受重视[3～5].     

Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities

We investigate a wide class of two-dimensional hyperbolic systems with singularities, and prove the almost sure invariance principle (ASIP) for the random process generated by sequences of dynamically Hölder observables. The observables could be unbounded, and the process may be non-stationary and need not have linearly growing variances. Our results apply to Anosov diffeomorphisms, Sinai dispersing billiards and their perturbations. The random processes under consideration are related to the fluctuation of Lyapunov exponents, the shrinking target problem, etc.     

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P _h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that (P _h ? I)/h converges for small h to a second order elliptic differential operator ${\mathcal{L}}$ L on compactly supported functions and that the Markov chain process associated to P _h converges to a diffusion with infinitesimal generator ${\mathcal{L}}$ L . Both P _h and ${\mathcal{L}}$ L are self-adjoint (densely) defined on the space ${L^2(\mathbb{H},\eta)}$ L 2 ( H , η ) of square-integrable functions over the (lower) half-space ${\mathbb{H}}$ H in ${\mathbb{R}^m}$ R m , where η is a stationary measure. This measure’s density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator ${\mathcal{L}}$ L respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.     

A compactness result for differentiable functions with an application to boundary value problems

We characterize the relative compactness of subsets of the space ${\mathcal{BC}^m([0,+\infty [;E)}$ of bounded and m-differentiable functions defined on [0, +∞[ with values in a Banach space E. Moreover, we apply this characterization to prove the existence of solutions of a boundary value problem in Banach spaces.     

金纳米粒子比色探针检测牛奶及鸡蛋中的三聚氰胺

三聚氰胺能诱导金纳米粒子(AuNPs)团聚,溶液颜色由酒红色变为紫色或蓝灰色.以AuNPs作为比色探针,建立了快速检测牛奶和鸡蛋中三聚氰胺的方法.实验优化得最佳反应条件为:AuNPs粒径13 min、pH=7、反应时间10 min和温度为室温.对样品中常见物质进行了干扰实验.样品经10％三氯乙酸和氯仿提取、离心分离后可...     

Spectral Gap for a Class of Random Billiards

A random billiard is a random dynamical system similar to an ordinary billiard system except that the standard specular reflection law is replaced with a more general stochastic operator specifying the post-collision distribution of velocities for any given pre-collision velocity. We consider such collision operators for certain random billiards that we call billiards with microstructure. Collisions modeled by these operators can still be thought of as elastic and time reversible. The operators are canonically determined by a second (deterministic) billiard system that models “microscopic roughness” on the billiard table boundary. Our main purpose here is to develop some general tools for the analysis of the collision operator of such random billiards. Among the main results, we give geometric conditions for these operators to be Hilbert-Schmidt and relate their spectrum and speed of convergence to stationary Markov chains with geometric features of the microscopic billiard structure. The relationship between spectral gap and the shape of the microstructure is illustrated with several simple examples.     

A Regularization Method for the Proximal Point Algorithm

A regularization method for the proximal point algorithm of finding a zero for a maximal monotone operator in a Hilbert space is proposed. Strong convergence of this algorithm is proved.Hong-Kun Xu: Supported in part by NRF     

4-(1,2,4-三唑-1-基)苯酚铜(Ⅱ)/镍(Ⅱ)配合物的晶体结构及荧光性质

合成并通过单晶和粉末X射线衍射、元素分析、红外光谱、热失重以及荧光光谱技术表征了含有4-（1,2,4-三唑-1-基）苯酚（hptrz）配体的2个过渡金属配合物{[Ni（H₂O）₂（hptrz）₂（tp）]·2DMF}_n（1）和[Cu（hptrz）₂（SCN）₂]·2H₂O（2）（H₂tp为对苯二甲酸）。配合物1中八面体的Ni（Ⅱ）离子由tp^2-阴离子拓展形成线性的一维链状结构;而配合物2则呈现中心对称的单核结构。配合物中,中性的hptrz配体呈现端基配位模式,并通过形成O-H…O氢键相互作用将低维结构拓展为高维超分子网络。此外,配体内的电荷转移使这2个配合物均在紫外区发射出强的荧光发射峰。     

Strong convergence of the CQ method for fixed point iteration processes

Strong convergence theorems are obtained for the CQ method for an Ishikawa iteration process, a contractive-type iteration process for nonexpansive mappings, and the proximal point algorithm for maximal monotone operators in Hilbert spaces.