Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

光学系统的等效变换

本文在普遍情况下使用矩阵方法详细讨论了光学系统的等效变换,证明光线变换矩阵为的光学系统当C≠0时可等效为一个薄透镜,当C=0时等效为一个薄透镜组。文中所得结果能用于分析光线或光束通过复杂光学系统的变换和多元件光腔的问题。     

STABLE DOUBLE LR ALGORITHM AND ITS ERROR ANALYSIS

In this paper, the normative matrices and their double LR transformation with origin shifts are defined, and the essential relationship between the double LR transformation of a normative matrix and the QR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable double LR algorithm for double LR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable double LR algorithm for normative matrices is only four sevenths of the rational QR algorithm for reed symmetric tridiagonal matrices.     

Study on Phase-Formation Mechanism and Intergrowth for Bi(Pb)-Sr-Ca-Cu-O System

In this paper, the phase-formation mechanism of Bi-based superconductors was systematically investigated by using high-temperature X-ray diffraction, differential thermal analysis (DTA) and crystallization of amorphous state. The transformations among Bi-based 2201, 2212 and 2223 phases were observed, and the intergrown phenomenon of the 2201, 2212 and 2223 phases was explained. It was proposed that there exist a composition equilibrium between 2212 phase and Ca2CuO3 and a competition of thermody-namic stability among Ca2CuO3, 2212 and 2223 phases. This is why it is difficult to prepare the 2223 phase. After Pb was doped in Bi-Sr-Ca-Cu-O system, Ca2CuO3 phase in the Bi-Sr-Ca-Cu-O system was replaced by Ca2PbO4, so that the composition equilibrium and competition of thermodynamic stability mentioned above were avoided.     

半群K(n,r)中的幂等生成元

设Singn是由一个n元集上的所有奇异变换所构成的奇异变换半群，I是由Singn中一些亏数为1的幂等元组成的集合，Howie利用有向图证明了：I是Singn的一个生成集当且仅当与其相应的有向图D（I）是强连通的完全图，本文利用多重有向图将这一结果推广到Singn的每个理想K（,r)上。     

带相变的铸坯热弹塑性应力分析基本方程

本文讨论了温度、相变、应力间的耦合关系，给出了铸坯在考虑相变时的热弹塑性蠕变的本构关系，以及计算铸坯内应力的有限元迭代公式。     

二阶椭圆型微分方程解的振动定理

考虑二阶非线性椭圆型微分方程∑^n_{i,j}∂/∂x_i{A_{i,j}(x,y)∂/∂x_j}+q(x)f(y)=0 (E)，其中q(x)在外区域 Ω∈R\+n上变号. 利用偏Riccati变换和积分平均技巧, 建立了方程(E)所有解振动的充分准则.     

The Möbius distribution on the disc

A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.     

Crystallization-induced asymmetric transformation. Application to conjugate addition of benzylamine to amides of benzoylacrylic acid

Adducts of the conjugate addition of benzylamine to enantiopure amides of aroylacrylic acid possess high enantiomeric and diastereomeric purity. A high degree of stereoselectivity has been achieved by means of crystallization-induced asymmetric transformation. A practical synthesis leading to dipeptides containing homophenylalanine is depicted.     

内源全息术的原理和数学描述

以往的全息术在对原子成像时,在相干光源、探测器空间分辨和信号强度三个方面遇到了难以克服的困难. 阐述了内源全息术克服这些困难的原理,研究了内源全息术的记录和再现全过程,推导出内源球面全息图的再现公式,并在散射因子球对称近似和能量无关近似下,推导出以δ函数表示原子全息再现像的解析表达式. 关键词： 内源全息术 同步辐射 晶体结构 傅里叶变换