Product of some elements of finite groups

In this paper, some sufficient and necessary conditions for the commutative product of two elements of finite groups are given. Moreover, some results are obtained by investigating the product of some elements.     

Meromorphic solutions of some types of complex differential-difference equations

Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we obtain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.     

一类积分不等式的推广

对一些基本的积分不等式进行了推广，给出了含有n个无关变元的更广泛的非线性积分不等式．利用所得的不等式讨论了某些非线性积分方程解的有界性．     

关于凸曲面的几个定义的关系

本文讨论了凸曲面的几种定义及其关系，发现有的定义是局部凸的定义，有的是整体凸的定义，有的则对于局部凸和整体凸都适合，最后给出了各种定义之间互推的证明，对于局部凸和整体凸定义之间不能推证的，则说明了原因．     

图的因子和因子分解的若干进展

本文综述了图的的因子和因子分解近年来的一些新结果。主要有图的因子与各种参数之间的关系,图有某种因子的一些充分必要条件,特别是图有ｋ－因子的一些充分条件以及关于图的因子分解和正交因子分解的一些新结果。文中提出了一些新的问题和猜想。     

高阶非线性常微分方程的可积类型

本文借助于Leibniz公式、复合函数的高阶导数公式以及变量替换的方法,给出了较为广泛的高阶非线性常微分方程的可积类型,有的还提供了通积分的表达式.所得结论推广了文献中的结果.最后列举了实例.     

高阶变系数泛函方程解的振动性

讨论了高阶变系数泛函微分方程解的振动性,并给出了这类高阶变系数函数方程解的若干新振动准则.结果推广了目前已有的某些结果.并且给出了在差分方程中的应用.     

颗粒随机分布复合材料热传导问题均匀化方法的理论分析

针对区域内颗粒随机分布复合材料的热传导问题给出了一种均匀化理论计算温度场.首先根据复合材料的特性以及通过用多尺度方法预测复合材料热传导参数的要求定义了一些基本的概率空间,然后结合材料的物理特性做合理的假设得到了在整个随机复合材料区域上的期望温度场与均匀化温度场之间的一种理论估计,从而说明了此均匀化温度场可以作为预测此类随机颗粒分布复合材料期望温度场的理论基础.     

关于图的团符号控制数

引入了图的团符号控制的概念,给出了n阶图G的团符号控制数γks(G)的若干下限,确定了几类特殊图的团符号控制数,并提出了若干未解决的问题和猜想.     

关于更新风险模型中破产概率的若干结果

进一步研究了更新风险模型中破产概率的问题，在假定索赔额分布是重尾时，证明了若干重要结果，得到了与经典的Crammer—Lunderberg模型相一致的结论．并义推广和改进了部分已有文献中的结果。     

多滞量二阶中立型方程的周期解

本文利用Fourier级数理论,讨论了一类多滞量二阶中立型方程的周期解问题,获得了若干确保周期解存在唯一的充分条件,并推广、改进和完善了一些相关文献的结果．     

-inclusion sets for eigenvalues of a tensor

In this paper, we mainly focus on new inclusion sets for eigenvalues of a tensor. First, we propose new inclusion sets for eigenvalues of a tensor, which are sharper than some existing inclusion sets, and obtain the law of distribution of the number of eigenvalues for a tensor. Second, two new classes of tensors are introduced. Third, some bounds on the spectral radii for nonnegative tensors are given. Fourth, some checkable sufficient conditions for the positive definiteness (positive semidefiniteness) of some classes of even-order real symmetric tensors are obtained.     

Galois Covers of Moduli of Curves

Moduli spaces of pointed curves with some level structure are studied. We prove that for so-called geometric level structures, the levels encountered in the boundary are smooth if the ambient variety is smooth, and in some cases we can describe them explicitly. The smoothness implies that the moduli space of pointed curves (over any field) admits a smooth finite Galois cover. Finally, we prove that some of these moduli spaces are simply connected.     

Comparisons of some weak forms of continuity

We investigate the interrelations of some families of weak forms of open sets and point out that some of them are the same. Also, we make comparisons of some weak forms of continuity and give decompositions of some of them.     

HX环的推广

在文[1,2]的基础上推广了HX环,提出了弱HX环的概念,并重新讨论了拟商环。证明了在正则条件下拟商环与弱HX环的统一性;同时也得到了一致弱HX环与普通商环的关系。     

Relationships among some chaotic properties of non-autonomous discrete dynamical systems

This paper is concerned with relationships among some chaotic properties of non-autonomous discrete dynamical systems. Some relationships among weak mixing, topologically weak mixing, generic chaos, dense chaos, and sensitivity are investigated. In addition, some equivalent conditions of sensitivity are given and the relationships between sensitivity and Li–Yorke sensitivity are obtained. These results generalize some existing results of autonomous discrete systems, some of which relax the corresponding conditions.     

关于内射模的P-平坦性

通过引用P-平坦模的定义,引入了右IPF环的概念,推广了右IF环的概念,这对研究IF环及QF环具有重要的作用,同时对右IPF环的性质作了一些刻画,得到了右IPF环的若干个等价命题;最后,用P-平坦模及右IPF环推出了正则环的一些等价条件．     

Quantale矩阵的广义逆及其正定性

给出Quantale矩阵{1}-广义逆的一种刻划以及存在的条件,给出Quantale矩阵M-P广义逆的定义,讨论Quantale矩阵M-P广义逆的若干性质,得到Quantale矩阵M-P广义逆的具体形式.引入Quantale矩阵正定性的概念,研究交换幂等Quantale上矩阵正定的一些性质,得到交换幂等Quantale上矩阵正定的一些等价刻画.     

Fuzzy HX环的推广

为改进Fuzzy HX环的结果,使之包含Fuzzy商环,提出了弱Fuzzy HX环的概念,研究了它的性质与结构,并重新讨论了拟Fuzzy商环,证明了在正则条件下拟Fuzzy商环与弱Fuzzy HX环的统一性：同时也得到了一致弱Fuzzy HX环与普通Fuzzy商环的关系。     

The Semigroup Characterizations of Positive Implicative BCK—algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ，，０）ｏｆｔｙｐｅ（２，０）ｗｉｔｈｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉ－ｔｉｏｎｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｉｍｐｌｉｅｓｘ＝ｙ．ＩｆａＢＣＩ－ａｌｇｅｂｒａ（Ｘ，，０）ｓａｔｉｓｆｉｅｓ（５）０ｘ＝０．ｔｈｅｎｉｔｉｓｃａｌｌｅｄａＢＣＫ－ａｌｇｅｂｒａ．ＩｎａＢＣＩ－ａｌｇｅｂｒａ，ｔｈｅｆ…