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.     

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].     

C60的氧化反应研究

在C60的甲苯或二氯苯溶液中通入O3,通过改变O3的吸收量及反应时间可得到两种氧化产物,一种产物在有机溶剂及水中均不溶,但经性水解后得到水溶性产物,其红外光谱与C60羟基化合物相似,在长时间通O3条件下,得到水溶性的C60氧化产物,用变温红外光谱、XPS、元素分析、热谱和质谱研究了氧化产物的可能结构,发现生成的C60氧化产物对热不稳定,随着温度升高,有CO2,CO和H2O放出。     

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 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。     

Study on the non-isothermal kinetics of decomposition of 4Na<Subscript>2</Subscript>SO<Subscript>4</Subscript>·2H<Subscript>2</Subscript>O<Subscript>2</Subscript>·NaCl

The non-isothermal decomposition kinetics of 4Na₂SO₄·2H₂O₂·NaCl have been investigated by simultaneous TG-DSC in nitrogen atmosphere and in air. The decomposition processes undergo a single step reaction. The multivariate nonlinear regression technique is used to distinguish kinetic model of 4Na₂SO₄·2H₂O₂·NaCl. Results indicate that the reaction type Cn can well describe the decomposition process, the decomposition mechanism is n-dimensional autocatalysis. The kinetic parameters, n, A and E are obtained via multivariate nonlinear regression. The n ^th-order with autocatalysis model is used to simulate the thermal decomposition of 4Na₂SO₄·2H₂O₂·NaCl under isothermal conditions at various temperatures. The flow rate of gas has little effect on the decomposition of 4Na₂SO₄·2H₂O₂·NaCl.     

刺乌头碱氢溴酸盐的合成及晶体结构

报道了以双溴代烷烃和刺乌头碱合成刺乌头碱氢溴酸盐的方法. 用元素分析、红外光谱、高分辨质谱和核磁共振进行了表征. 并用X射线单晶衍射确定了标题化合物的绝对构型. 晶体结构表明, 该化合物通过分子间氢键形成了网状类似超分子结构. 晶体属于单斜晶系, P2₁空间群, 晶胞参数: a＝1.0619(2) nm, b＝1.2196(3) nm, c＝1.2282(2) nm, β＝90.87(1)°, V＝1.59037(54) nm³, Z＝2, D_m＝1.428 g/cm^－3, F(000)＝720.0, µ＝1.349 mm^－1. 环 A, B, C, D, E和F分别呈船式、椅式、信封式、船式、船式和信封式. 其绝对构型被确定为1S,4S,5S,7S,8S,9S,10S,11S,13R,14S,16S,17R.