Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

三氮宾分子的磁性设计

采用量子化学ＧＡＵＳＳＩＡＮ９４ａｂｉｎｉｔｉｏＵＨＦ方法和ＳＴＯ－３Ｇ基组设计一系列三氮宾分子，讨论分子的几何结构和取代基对其磁性的影响，计算结果表明，这些分子都具有铁磁性并有高自旋基态，有效交换积分值随代基的变化而变化，其中一种具有较代的总能量和高的有效交换积分值的分子，可期望被合成。     

Monolayer adsorption isotherms and a disordered medium model

A model of disordered medium is proposed to describe the monolayer adsorption isotherm on heterogeneous surfaces. The model is based on the premise that adsorption medium consists of separate regions in each of which there is a permanent local equilibrium constant, the character of the changes of which is determined by the disorder parameter of the medium. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 3, pp. 189–193, May–June, 2006.     

The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

A Note on Calculation of Phase Space Path Integral by Means of Invariants

In this note we use the method of invariant to calculate the phase space path integral appearing in our previous article.     

上海深紫外自由电子激光装置波荡器磁场调整

 在对上海深紫外项目的波荡器建造过程中,应用亥姆霍兹线圈系统测量了全部单磁块,并使用模拟退火法对磁块进行组合排序优化,使反映磁场的成本函数下降了3个数量级。对一段波荡器进行了多次测量、调整,使积分场、峰峰值误差、位相误差等各项指标达到设计要求。     

局部对称伪黎曼流形中的伪脐类空子流形

研究局部对称伪黎曼流形中的紧致伪脐类空子流形,得到了这类空子流形的一个积分不等式,将局部对称空间的相关结果推广到伪黎曼流形．     

振荡型积分对极大函数的估计

首先将2维KaKeya型的极大函数通过Fourier变换转化成振荡型积分的形式,对此振荡型积分作相应的估计。通过Littlewood—Paley方法将此振荡型积分分解成不同的算子,在估计极大算子时,通过Newton—Leibnig公式,将其转化为相应的积分形式,最后通过经典的振荡型积分的估计,得到最后的结果,本方法强调振荡型积分的方法和以前几何测度论的方法不同。     

氦同位素原子与钠分子碰撞转动激发积分散射截面的理论计算

多体刚性椭球模型是一种比较精确的描述氦原子与钠分子碰撞的理论模型.本文用多体刚性椭球模型计算了不同能量下He的同位素原子3He,4He,7He,10He与Na2分子碰撞的转动激发积分散射截面,表明增加椭球等势面个数可以得到更准确的转动激发积分散射截面;总结出3He,4He,7He,10He-Na2碰撞体系转动激发积分散射截面随相对入射能量和体系约化质量变化的规律;讨论了相对入射能量为100meV时,相互作用势的不同区域对4He-Na2碰撞体系转动激发积分散射截面的影响情况.