一类椭圆方程很弱解的正则性

得到了一类二阶椭圆方程Lu=f很弱解的一个临界情形的正则性结果。它指出：若|f|log^ |f|∈L^1(Ω)，则u∈L^n-2/n(Ω)。另外若对区域以及系数附加一定的正则性条件，并设|f|log^ |f|∈L^1(Ω),则|△u|∈L^n-1/n(Ω)。     

一类半线性椭圆边值问题的正对径解的存在性与多解性

通过考察当l→0或l→ ∞时f(r,l)/l的极限状态,研究了环域上的半线性椭圆方程△u f(r,u)=0的正对径解的存在性和多解性。     

一类非散度型椭圆方程解的梯度估计

得到了一类非散度型二阶椭圆方程解的梯度在 Lp中的局部估计 ,其中 p >0 .方程形式为 :L0 u+ b .　Δu -vu =f,L0 为具 H lder连续系数的非散度型椭圆算子 ,f有界可测 ,| b| 2 与 v均属于 Kato类     

一类非线性椭圆方程在环域上的正对径解的存在性与多解性

通过考察f(r,l)在有界区间上的性质建立了非线性椭圆方程Δu+f(r,u)=0在环域上的正对径解的存在性、非存在性与多解性.     

非齐次椭圆方程很弱解的比较原理（英文）

在一些适当的假设条件下,通过McShane扩张定理构造Lipschitz连续检验函数,本文得到了拟线性椭圆方程-div A(x,?u(x))=f(x, u)很弱解的比较原理,推广了齐次方程的相关结果.     

临界增长条件下一类半线性椭圆方程解的存在性

用变分方法研究了半线性椭圆方程Dirichlet迫值同题-△μ=f(x,μ） h（x）对几乎所有的x∈Ω，μ=0在δΩ上解的存在性，在临界增长情况下得到了所解的一个存在性定理．     

一类含凹凸非线性项拟线性椭圆方程的多重解

本文研究了一类拟线性椭圆方程,其中非线性项f在无穷远处(p-1)-次线性增长,非线性项g在无穷远处超线性增长.利用三临界点定理,获得了该类方程多重解的存在性,结果推广了Kristaly等人最近的相关结果.     

一类拟线性椭圆方程整体解的不存在性

这篇文章主要利用常微分技术讨论了一个二阶拟线性椭圆方程Lpu≡div（｜Du｜^p-2Du）=f（x,u）,x∈R^N的整体解的不存在性.我们只考虑2≤p〈N的情況并且在假设f（x,u）关于第二个变量u没有单调性的情况下得到整体解的不存在性结果.     

极限方程有奇性的一类四阶椭圆型方程混合边值问题解的渐近式

本文研究极限方程在部分边界上为退缩椭圆方程（椭圆－抛物）的一类四阶椭圆型方程混合边值问题解的渐近式。在适当的假设下，应用改进了的多重尺度法，求得其解除了半圆域的两个角点外，在整个半圆域中有任意阶的一致有效的渐近展开式。     

一类具奇异势的拟线性椭圆方程的无穷多解

本文用变分法和集中紧性原理获得了一类具奇异势的拟线性椭圆方程-Δ_pu=μ(|μ|~(P~*(s)-2)u)/(|x|~s) λf(x,u),u∈H_0~(1,p)(Ω)的无穷多解．     

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。