借助单参数Lie群求首次积分的方法及其在陀螺系统的应用

讨论利用单参数Lie群求自治常微分方程组首次积分的方法, 并对经典陀螺系统找到其接受的一种非平凡单参数Lie群, 利用其所揭示的首次积分的特点就可用统一的思想容易地求出Euler, Lagrange及Kovalevskaya情形下的第4个首次积分, 指出并纠正了前人关于Kovalevskaya陀螺在x_G, y_G均不等于零的一般条件下第4个首次积分的错误.     

用两个单参数Lie群求三阶自治系统的积分因子

给出并证明了利用三阶自治系统接受的两个单参数Lie群的生成元求系统积分因子的力法.     

利用Lie群方法求Burgers-Huxley方程行波类首次积分

本文运用Lie群理论,证明了Burgers-Huxley方程的行波解所满足的二阶非线性方程在参数满足一定关系时,在经典意义下接受一个两参数Lie群,此时可用积分法求其首次积分.     

借助Lie群研究Burgers-KdV方程行波解的可积性

运用经典Lie群方法证明Burgers-KdV方程行波解所满足的二阶非线性常微分方程当且仅当参数满足特殊情况下,恰好接受一个两参数Lie群,并用不同的方法求出方程的两个相互独立首次积分.     

用两单参数李群求3阶自治系统的首次积分

在较一般的条件下,对3阶自治系统给出利用系统所接受的两个单参数李群的生成元计算首次积分的方法．     

用n-1个单参数李群求n阶自治系统的首次积分

在一般条件下,对n阶自治系统给出利用系统所接受的n-1个独立单参数李群的生成元计算首次积分的方法,并给出方程组有满足条件的非零解的充要条件.     

带有限性条件Abel群的自同态环和自同构群

给出了带极大或极小条件的Abel群A的自同构群以及自同态环的相伴Lie环是可解或幂零的充要条件.同时也给出了群A=Q_(π1)⊕Q_(π2)⊕…⊕Q_(πr)的自同构群是可解或幂零的充要条件,以及群A的自同态环的相伴Lie环是可解或幂零的充要条件.     

拟齐次系统的约化与约化Kowalevskaya指数

用所接受的单参数李群的特征定义拟齐次自治系统,并且对拟齐次系统进行约化,定义约化系统的约化Kowalevskaya指数,给出该指数与原拟齐次系统的Kawalevskaya指数之间的关系,对二维的拟齐次多项式系统,具体给出约化Kowalevskaya指数特征与拟齐次多项式首次积分的更深入关系.基于约化系统,证明拟齐次系统一般均存在局部的拟齐次首次积分组.     

可解二次Lie代数

一个带有非退化、对称不变双线性型的Lie代数称为二次Lie代数. 研究可解二次Lie代数的结构, 特别是Cartan子代数由半单元构成的可解二次Lie代数. 从上同调的观点出发给出了一种构造二次Lie代数的方法, 并证明了可解二次Lie代数均可用此方法构造.     

广义Toda链的τ-函数解与表示论

本文由Semenov-Tian-Shansky 约化定理所给出的完全可积Hamilton 系统的求解框架出发,利用Lie群、Lie代数表示论的方法;求得了广义Toda链的τ-函数解.     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

两种图多项式根的重数的一个注记

设P1，P2，……，Pt是几乎覆盖图G的l条不相交的路，s是没有被这些路覆盖的孤立点数．本证明：(i)匹配多项式μ(G，x)的非零根的重数最多是l，零根的重数最多l s。（ii)对于不含三角形的n阶图G，伴随多项式h(G，x)的非零根的重数最多是l，零根的重数最多是1/2(n l s)．(iii)对一种含三角形的所谓A型图，（ii）也成立．     

任意矩阵的特征值的扰动估计

设A和B是两个任意的n阶方阵,其特征值分别为{λ_1,…,λ_n}和{μ_1,…,μ_n}.本文对此两组特征值的如下“距离”的界给出了若干估计: B对于A的谱改变量 A与B的特征值的改变量这里的结果包含了Bauer-Fike定理,并且优于Kahan-Parlett/Jiang定理及Chu,施和肖所得出的结果.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

On the R-Order of Convergence of a Family of Methods for Simultaneous Extraction of Part of All Roots of Algebraic Polynomials

This note deals with the R-order of convergence of Weierstrass-Durand-Kerner-Dochev type single-step methods for the simultaneous determination of only a part of all roots of algebraic polynomials.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.