Congruence criteria for finite subsets of complex projective and complex hyperbolic spaces

We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP ⁿ . For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP ⁿ and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by congruence classes or if distances π/2 are allowed. Finally we do the same kind of investigation also for the complex hyperbolic space ℂH ⁿ . Most of the results are completely analogous, however, there are also some interesting differences. Received: 15 January 1996     

A dual graph-norm refinement indicator for finite volume approximations of the Euler equations

Summary. We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Süli and Warnecke in [15] and [16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement indicator into the DLR--Code which is based on a finite volume method of box type on an unstructured grid and present numerical results. Received May 15, 1995 / Revised version received April 17, 1996     

Numerical methods for finding multiple eigenvalues of matrices depending on parameters

Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods. Received December 19, 1994 / Revised version received January 18, 1996     

Diastereoselective Alkylation of (Diene-Aldehyde)Fe(CO)3 Complexes with Functionalized Zinc-Copper Reagents NuCu(CN)Znl

Addition of functionalized zinc-copper reagents to the title complexes proceeds in a highly diastereoselective fashion to afford dienol complexes. The relative configurations of adducts 3d were determined by single X-ray diffraction analysis.     

脉冲序列的快速搜索法及可信度分析

对于周期脉冲序列的信号分选识别，可采用序列搜索的时域方法[1，2]。本文将大周期内完全重复的脉冲序列分解为多个“单周期信号”．并把它们均定义为周期性信号．同时，提出了序列搜索的一种软件实现方法及密集视频脉冲信号分选的变步长、信步长快速搜索法．在此基础上，本文针对序列搜索分选法的可信度计算公式进行了推导和分析，证实了这种方法的可行性和有效性．     

应用粒子动态分析仪研究水力旋流器流场

利用粒子动态分析仪(PDA),对水力旋流器内固相颗粒流场做了全面的测定,得出水力旋流器内固相颗粒的流态、浓度及粒度分布,为进一步查清水力旋流器的工作机理提供了重要理论依据。     

不等波纹函数低通原型的理论及应用

本文提出不等波纹函数低通原型，并对其理论进行初步探讨。切比雪夫函数及最平坦型巴特活兹函数皆为其特例。文中给出不等波纹函数的几个性质，最后给出两个应用实例，消除耦合环自感部分的影响；抑制高次模的微带圆盘腔带通滤波器。     

Studies of the compositions of Pd(II) hydrolysis products

The characterization of the clusters formed on alkaline hydrolysis of [PdCl₄]^2– was performed using¹⁷O,²³Na,³⁵Cl,¹³³Cs NMR and UV spectroscopy. The chemical composition of the clusters was found to be [Pd(OH)₂] _n ·nNaCl. No mononuclear oxo- or hydroxocomplexes were detected. The spatial structure of the clusters is stabilized by alkali metal cations.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 675–679, April, 1993.