二阶脉冲积微分方程周期边值问题的解

利用上下解和不动点定理，给出了二阶混合型脉冲积微分方程周期边值问题解的存在性。     

一类积分微分包含的周期解

研究了一类积分微分包含的周期解,利用Kakutani不动点定理和Tichonoff不动点定理给出了凸和非凸两种情形下周期解存在的充分条件.     

二阶脉冲积微分方程周期过值问题的解(英)

利用上下解方法和不动点定理，给出了二阶混合型脉冲积微分方程周期边值问题解的存在性．     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

共振条件下一类方程无界解和周期解的共存性

讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性．利用Poincare映射轨道的性质,给出了无界解的存在性条件．在此条件下,Poincare-Bohl定理,得到了方程的一个周期解,进而说明共振条件下这类方程无界解和周期解的是可以共存的．最后,给出了一个无界解和周期解共存的具有等时位势的方程实例．     

一类高维非自治系统周期解的存在性和唯一性

该文利用Schauder和Roth不动点定理,讨论了一类高维非自治系统周期解的存在性和唯一性,给出了其存在周期解和存在唯一周期解的一组充分性判据.     

YoshiZawa型周期解定理和Massera型周期解定理研究进展简介

微分方程解的有界性和周期解的存在性是檄分方程理论研究中的两个重要课题，二者之间有着紧密的联系．在解的有界性与周期解的存在性的研究中，Yoshizawa周期解定理和Massera周期解定理是非常重要的结果，具有重要的理论意义和应用价值．本文以Yoshizawa型周期解定理和Massera型周期解定理的研究为主，简要介绍泛函微分方程周期解理论研究方面的一些新进展。     

一类n维非自治系统的周期解

本文应用Ｓｃｈａｕｄｅｒ和Ｒｏｔｈ不动点定理，给出了周期系统存在周期解的一组充分性条件，推广了文「１」「２」的结果。     

一类具有HollingⅢ型食饵—捕食系统的周期解存在性

利用重合度理论中的延拓定理研究非自治周期食饵—捕食系统的非平凡周期解存在性,给出了周期解存在的充分条件.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

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.     

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.     

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.     

Radius of convexity of certain classes of analytic functions

We consider the classes of analytic functions introduced recently by K.I. Noor which are defined by conditions joining ideas of close-to-convex and of bounded boundary rotation functions. We investigate coefficients estimates and radii of convexity.     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

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。