自由能展开式中点群的不可约表示的基函数

一个群的基函数的选择并非唯一，不同的基函数对应不同的表示矩阵。即使相同的表示矩阵，基函数也可以有不同的选择。在相变的宏观唯象理论中， 自由能展开式可由同一个表示矩阵的基函数来构造，因而给出不可约表示的基函数表就非常有意义。现有文献给出的32点群不可约表示的基函数只写到二次幂，而且有些文献中的同一个不可约表示所选取的不同的基函数却对应不同的表示矩阵，这样在构造群变换不变式时，就会出错。该文将基函数表写至三次幂, 这有助于准确、迅速地写出到六次幂群变换不变的自由能表达式。由新的基函数表发现十八种点群有三次幂的群操作不变式, 高温相属这些点群铁电体, 发生的本征铁电相变为一级相变。     

OUTLIER TEST IN RANDOMIZED LINEAR MODEL

In this paper, we give an approach for detecting one or more outliers inrandomized linear model The likelihood ratio test statistic and its distributions under the null hypothesis and the alternative bypothesis are given. Furthermore, the rebustneas of the test statistic in a certain sere is proved. Finally, the optimality properties of the test are derived.     

曲面论(一)--陈省身先生《微积分及其应用》之第四讲(2001.11.02)

1．曲面的标架 今天我们讲一点曲面论。微积分在曲面上应用的研究在整个数学里头是很要紧的。这是因为在曲面论中,曲面的这些性质往往扩充到其他更广的情形,而这些更广的情形变化到曲面的时候也有很多性质,在曲面的情形已经发生了。那么,曲面有个优点,就是我们假定它是在3维空间里头,所     

基于时态逻辑演算的程序验证

本文建立了时态逻辑演算。在该演算系统下,若能证明一程序抽象成的时态逻辑公式是定理,则该程序是完全正确的。     

图式流形

The discovery of manifold is a major advance in modern mathematics.In 1974,J.W.Morgan and D.P.Sullivan Surggest the concept of a Z/n manifold.We think that,it is more useful to suggest the concept of a graphlike manifold and research related topics.And these works will be done in this paper.     

Analytic invariant curves for a planar mapping

This paper is concerned with the existence of analytic invariant curves for a planar mapping. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. In this paper, we discuss not only the general case, but also the critical cases as well, in particular, the case where β is a unit root is discussed.     

Limit cycles and invariant parabola in a kukles system of degree three

In this article,the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola.For this class of second-order differential systems,it is shown that for certain values of the parameters the invariant parabola coexists with a center.For other values it can coexist with one,two or three small amplitude limit cycles which are constructed by Hopf bifurcation.This result gives an answer for the question given in[4],about the existence of limit cycles for such class of system.