The multiple-scale wave equation

An analytic and numerical study of the behavior of the linear nonhomogeneous wave equation of the form ε²u_tt = Δu + tf with high wave speed (ε 1) is carried out. This study was initially motivated by meteorological observations which have indicated the presence of large spatial scale gravity waves in the neighborhood of a number of summer and winter storms, mainly from visible images of ripples in clouds in satellite photos. There is a question as to whether the presence of these waves is caused by the nearby storms. Since the linear wave equation is an approximation to the full system describing pressure waves in the atmosphere, yet is considerably more tractable, we have chosen to analyze the behavior of the linear nonhomogeneous wave equation with high wave speed. The analysis is shown to be valid in one, two, and three space dimensions. Partly because of the high wave speed, the solution is known to consist of behavior which changes on two different time scales, one rapid and one slow. Additionally, because of the presence of the nonhomogeneous forcing term tf, we show that there is a component of the solution which will vary only on a very large spatial scale. Since even the linearized wave equation can give rise to persistent large spatial scale waves under the right conditions, the implication is that certain storms could be responsible for the generation of large-scale waves. Numerical simulations in one and two dimensions confirm analytic results.     

Max—min神经网络的一种有效学习算法

本文在Ａ．Ｂｌａｎｃｏ等人的算法的基础上，提出了ｍａｘ－ｍｉｎ神经网络的一种改进了的反馈学习算法，严格证明了该算法的迭代收敛性，理论分析及实例计算结果均表明，本文算法具有算法简单，收敛速度快，输出误差小等显著特点。     

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.     

Selective quenching of tryptophanyl fluorescence in bovine serum albumin by the iodide ion

Modified Stern-Volmer equation is obeyed by bovine serum albumin (BSA)-iodide system showing selective quenching of tryptophanyl fluorescence of BSA. The fraction of accessible protein fluorescence is 0.56 and the effective Stern-Volmer constant is 290 M^-1 at pH 7.4 in 0.005 M phosphate buffer at 25°C. Collisional quenching is operative both in the BSA -I⁻¹ system and the model system, tryptophan-I⁻¹. It is supported by the observed relationship between the ratio of quenching rate constants (k _q ) and diffusion coefficients and alsok _q with bulk viscosity.     

On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator

A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.     

处理原子-辐射场相互作用系统的变分方法

用Heisenberg-Weyl(简H-W)群直积SU(2)群上的相干态表述了原子-辐射场相互作用系统的非平衡态统计力学.引入一个新定义的含时分布函数,将非平衡态下密度矩阵所满足的von Neumann方程转化成可分离变量的偏微分方程,给出了方程的形式解,算符的平均值表示.本文还就便于作微扰展开的相互作用绘景作了讨论.     

关于多正解问题的某些研究

本文以ｆｐ 同伦方法为工具，借助于一些适当的变换，研究有序的（Ｂ）空间中的集值映象方程的多正解问题；在文中的有关工作中，还使用了集值映象的拟导数的某些性质．     

谐振子薛定谔方程的简单解法

物质的许多物理与化学性质都可以用线性谐振子模型解释，本文用简单的数学运算求解线性谐振子的薛定谔方程，避免了特殊函数等复杂的数学运算，得出了量子力学教材完全相同的结果。     

拟线性常微分方程在半无限区间的边值问题

Existence of positive solution is established for boundary value problems of non-singular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method.     

具连续分布滞量的非线性中立型抛物偏泛函微分方程的振动性

考虑一类具连续分布滞量的非线性中立型抛物偏泛函微分方程解的振动性,借助Green定理和时滞微分不等式获得了这类方程在Robin,Dirichlet边值条件下所有解振动的若干充分条件.