初等交换$p$群被内交换$p$群的中心扩张

Assume that N, F and G are groups. If there exsits a normal subgroup of G such that≌ G and G/≌ F, then G is called a central extension of N by F. In this paper, the central extension of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group of order p~3. Together with our previous work, all central extensions of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group.     

一种基于线性同余算法的伪随机数产生器

线性同余算法作为使用最为广泛的伪随机数产生算法,具有产生速度快、输出序列周期长等特点,但安全性能不佳的弱点始终制约着该算法在密码学领域的应用.本文在对线性同余算法详细分析的基础上,给出了一种不受乘数a选择限制的伪随机数产生器.该算法具有良好的伪随机性和安全性.     

有限局部环上对称矩阵的计数定理(I)

设$A_{n}(R)$是有限局部环$Z/p^{k}Z$上$n$阶对称矩阵的集合, 这里$n\geq 2$. $p$是大于$2$素数, $p\equiv1({\rm mod}4)$ 且$k>1$. 通过确定有限局部环$Z/p^{k}Z$上对称矩阵的标准型, 计算出$A_{n}(R)$在线性群${\rm GL}_{n}(R)$作用下的轨道数, 从而计算出由特定对称矩阵确定的正交群的阶以及与特定对称矩阵在同一轨道的对称矩阵的阶.     

A Generalization about Congruent Pairs on a Set

ＡＧｅｎｅｒａｌｉｚａｔｉｏｎａｂｏｕｔＣｏｎｇｒｕｅｎｔＰａｉｒｓｏｎａＳｅｔＨｕａｎｇＪｕｎｍｉｎ（黄骏敏）（ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃａｎｃｅｌｔｈｅｃｏｎｄｉｔｉｏｎ...     

Thermodynamics of saturated lanthanide nitrate-water systems

The thermodynamic properties of saturated aqueous lanthanide nitrate solutions were determined using recently published critically evaluated solubility and activity data. The variation of the thermodynamic functions and congruent melting points as a function of atomic number are interpreted in terms of changes in inner sphere coordination number in both the solid hexahydrates and in the aquo ions, and in terms of the double-double effect.Inconsistencies in experimental solubility data are generally caused by uncertainties in solid phase composition which is shown to be due to the very small Gibbs energies accompanying transitions from stable to metastable systems differing in the number of hydrating water molecules.Presentation to First International Symposium on Solubility Phenomena, University of Western Ontario, London, Ontario, August 21–23, 1984.     

矩阵的合同、相似与二次型

矩阵的合同关系、相似关系都是等价关系，它们虽然不同。但又有联系．对称矩阵是这两个知识点的交汇点。即两个实对称矩阵合同当且仅当它们相似．进一步得到二次型可以通过一个正交变换化为标准型。这一理论是高等代数教科书的重要内容。然而．现行的教科书对该理论的证明至少涉及到二次型、线性空间、线性变换和欧氏空间的内容．本文利用欧氏空间的正交性质给出这一理论新的简洁证明。以供教学参考之用。     

Congruent Pairs On a Set

ＣｏｎｇｒｕｅｎｔＰａｉｒｓＯｎａＳｅｔＺｈｕＺｕｏｔｏｎｇ；（朱作桐）ＨｕａｎｇＪｕｎｍｉｎ（黄军民）（ＮａｎｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｉｎｔｒｏｄ...     

Manifestation of a Photorefractive Effect in the Raman Scattering Spectra of Lithium Niobate Crystals of Variable Composition

Using the Raman scattering spectra, we investigated the ordering of the structural units in the cation sublattice and the photorefractive properties of lithium niobate single crystals of variable composition, i.e., nominally pure ones with different Li/Nb ratios and those doped with the nonphotorefractive cations Mg²⁺, Gd³⁺, and Y³⁺. It is shown that at low concentrations of Mg²⁺, Gd³⁺, and Y³⁺ the magnitude of the photorefractive effect is substantially determined by the ordering of the structural units of the cation sublattice. It has been found for the first time that the intensity of the line corresponding to the bridge valence vibrations of oxygen atoms in the octahedrons of NbO₆ is sensitive to the dipole ordering of the cation sublattice of the crystal. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 5, pp. 611–614, September–October, 2005.     

Finite p-groups with a minimal non-abelian subgroup of index p(Ⅱ)

We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich.     

广义Cholesky分解乘法扰动分析

0引言关于实对称矩阵的广义Cholesky分解和扰动问题是矩阵计算的重要问题,可参考文献[1-2].本文首先介绍已有的采用加法扰动的角度得到的广义Cholesky分解的一阶相对