WEAK CONVERGENCE FOR NON-UNIFORM φ-MIXING RANDOM FIELDS

Let $\{\xi_{\bold t}, {\bold t} \in {\bold Z}^d\}$ be a nonuniform $\varphi$-mixing strictly stationary real random field with $E\xi_{\bold 0}=0, E|\xi_{\bold 0}|^{2+\delta}<\infty$ for some $0<\delta<1$. A sufficient condition is given for the sequence of partial sum set-indexed process $\{Z_n(A),\ A\in \Cal A\}$ to converge to Brownian motion. By a direct calculation, the author shows that the result holds for a more general class of set index ${\Cal A}$, where ${\Cal A}$ is assumed only to have the metric entropy exponent $r, 0相似文献   

一种可能的简并谱NNS分布

利用随机矩阵理论,通过对一特殊情形的简并谱展开研究,得到了简并谱一种可能的最小相邻间距NNS分布函数．研究表明,由于简并的存在,简并谱不仅可分解成随机谱和规则谱两个子谱,同时还影响其规则谱,使规则谱的能级斥力减少．     

On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes

It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Θ(n²). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyzing what occurs if the points are chosen from a 2-dimensional region in 3-dimensional space. As an example, we examine the situation when the points are drawn from a Poisson distribution with rate n on the surface of a convex polytope. We prove that, in this case, the expected complexity of the resulting Voronoi diagram is O(n).     

Zero Dissipative, Explicit Numerov-Type Methods for Second Order IVPs with Oscillating Solutions

New explicit, zero dissipative, hybrid Numerov type methods are presented in this paper. We derive these methods using an alternative which avoids the use of costly high accuracy interpolatory nodes. We only need the Taylor expansion at some internal points then. The method is of sixth algebraic order at a cost of seven stages per step while their phase lag order is fourteen. The zero dissipation condition is satisfied, so the methods possess an non empty interval of periodicity. Numerical results over some well known problems in physics and mechanics indicate the superiority of the new method.     

Synthesis of molecular imprinted organic-inorganic hybrid polymer binding caffeine

Random copolymers of poly{(methacrylamide)-co-(vinyl trimethoxysilane)} and poly{(methacrylic acid)-co-(vinyl trimethoxysilane)} were synthesized via a free radical polymerization reaction. Acid catalyzed sol-gel process of tetraethylorthosilicate (TEOS) with aforementioned polymers in the presence of methyl xanthine class of alkaloid like caffeine resulted in the formation of highly transparent monoliths. Solvent extraction of the template leaves behind the recognition sites intact with high selectivity towards the print molecule. The ionic and non-specific adsorptions, which are considered to be the main disadvantages of the molecularly imprinted polymers (MIP), are prevented to a considerable extent by the end capping of surface silanol groups. The template binding efficiencies of MIP were determined by HPLC analysis.     

一类具有非局部反应扩散方程的奇摄动问题

本文讨论一类具非局部反应扩散方程的奇摄动初始边值问题，利用迭代法及微分不等式，研究了初始边值问题的存在唯一及其渐近性态。     

Global Smooth Solutions of the Equations of a Viscous,Heat - Conducting,One - Dimensional Gas with Density - Dependent Viscosity

We consider initial boundary value problems for the equations of the one-dimensional motion of a viscous, heat-conducting gas with density-dependent viscosity that decreases (to zero) with decreasing density. We prove that if the viscosity does not decrease to zero too rapidly, then smooth solutions exist globally in time.     

Field optimized initial state based control of photodissociation

A new scheme for controlling photodissociation through preparation of a variationally optimized linear superposition of field free vibrational eigenstates is applied for selective control of IBr and HI dissociation. The dependence of photodissociation on various field parameters and initial conditions is examined to investigate the mechanistic basis of selective control. The parametric equations of motion approach for determining vibrational dynamics as a function of field parameters without having to solve the time dependent Schrödinger equation explicitly for each field parameter separately is outlined and its use to identify field characteristics which will provide the requisite population mix represented by the optimal linear superposition of vibrational states is advocated.