自由群的直积的检验元素的注记

本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.     

幂格与商格的关系的注记

研究了分配格上的幂格,给出了格的相对凸子格的概念,得到了分配格上的幂格的一个充要条件,建立了幂格与商格的联系.     

含有共轭三键的高聚物的掺杂机制的探讨

本文从实验事实出发,对含有共轭三键的共轭高聚物——聚丁二炔的掺杂及电导的特点进行了详细的分析;对聚丁二炔晶体掺杂的机制进行了初步的探讨;从结构相变的角度出发,提出了一个掺杂模型,并从能量的角度估算了由于掺杂引起链段结构改变所需的能量,较好地解释了聚丁二炔晶体掺杂未取得成功的原因.     

基于GRA-DEA模型的有关农民收入的九城市的评价

有关农民收入,文章以山西省九个城市为例进行了评价.首先用灰色关联分析法分析了2016年这些城市的有关数据,筛选出影响农民收入的主要因素;其次构建了指标体系,利用数据包络分析法对有关农民收入九个城市进行了DEA有效性评价;再次对非DEA有效的城市,借助投影公式探索了改进方法;最后得出了九城市分为两类的结论,提出了针对性的建议.     

关于特征值的平方和的注记

探讨了特征值的平方和这一计算问题,指出了常用方法的不足之处,并在深入研究方阵相似的基础之上弥补了这一不足,彻底解决了这一问题,此外运用这种方法还能解决特征值高次幂之和与多项式之和的计算问题.最后文中给出了一种新的计算特征值平方和的方法,这种方法能够回避第一种方法的不足,但缺点是不易推广.     

环的投射自由性的研究

引进了两类新环,进而研究了其投射自由性,得到了群环上的模结构,推广了Quillen-Suslin定理.     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

关于图的最大亏格的结果

提供了一类新的上可嵌入图类,并且得到了一类直径为2的二连通伪图以及一类直径为4的重图的最大亏格的紧下界,这推广了Skoviera的一个结果．     

函数的商的不定积分

本文给出了函数的商的不定积分公式,揭示了该公式的应用方法.     

曲面的切平面引入方式的比较

对比研究了同济大学版高等数学教材和华东师大版数学分析教材引入切平面的方式，梳理了它们引入的思路，揭示了不同引入方式背后的思想.针对不同的专业，给出了教学方法上的建议，旨在提高学生学习的兴趣，丰富学生的数学思想.     

Subinverses of fuzzy matrices

A matrix operation is examined for fuzzy matrices and interesting properties of fuzzy matrices are obtained using the operation. Particularly some properties concerning subinverses and regularity of fuzzy matrices are given and the largest subinverse is shown by the properties. The properties are closely related to inverses of fuzzy matrices and fuzzy equations. Moreover fuzzy preorders are examined using the matrix operation and basic properties are obtained. The results are considered to be useful for the theory of fuzzy matrices.     

Prosperity properties of TU-games

An important open problem in the theory of TU-games is to determine whether a game has a stable core (Von Neumann-Morgenstern solution (1944)). This seems to be a rather difficult combinatorial problem. There are many sufficient conditions for core-stability. Convexity is probably the best known of these properties. Other properties implying stability of the core are subconvexity and largeness of the core (two properties introduced by Sharkey (1982)) and a property that we have baptized extendability and is introduced by Kikuta and Shapley (1986). These last three properties have a feature in common: if we start with an arbitrary TU-game and increase only the value of the grand coalition, these properties arise at some moment and are kept if we go on with increasing the value of the grand coalition. We call such properties prosperity properties. In this paper we investigate the relations between several prosperity properties and their relation with core-stability. By counter examples we show that all the prosperity properties we consider are different. Received: June 1998/Revised version: December 1998     

Coefficient rings of numerical semigroup algebras

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show that arithmetic and set-theoretic properties of a numerical semigroup ring are properties of an equi-gcd numerical semigroup algebra.

     

Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation

Properties of coefficients of the Slevinsky-Safouhi formula are derived. These properties are: matrix and orthogonality properties; the characterization of a zero array; generating functions; asymptotics; and, recurrence relations for computing a sum as efficiently as possible. These properties are useful in a numerical or computational setting.     

MTL代数的特征定理

对于逻辑系统代数结构的研究,是一个十分重要的研究课题.近期提出的BL代数,R_0代数,MTL代数就是这个方向具有代表性的研究成果.本文讨论MTL代数的性质与结构,给出这种代数的几个特征定理,澄清这种代数与其它代数结构的关系.鉴于单位区间中由左连续t-范数诱导的剩余蕴涵与MTL代数的紧密联系,本文还考察了这种模糊蕴涵的特征性质.     

Equivalence of several characteristics of dual switched linear systems

This paper is concerned with the equivalence of several dynamic characteristics between mutually dual switched linear systems, both discrete- and continuous-time cases are considered. Two systems are mutually dual means that their system matrices are transpose of each other. The dynamic properties considered in this paper include four types: exponential stability, global uniform asymptotic stability, attractivity, and weak attractivity. It is shown that every one of the four dynamic properties of a switched linear system implies each of the four dynamic properties of its dual system, and vice versa. The main results enable us to investigate these dynamic properties of switched system by virtue of study related to the corresponding properties of its dual system, thus providing an alternative way to explore the dynamics of switched systems. A numerical example is provided to illustrate the obtained theoretical conclusions.     

Analysis of plain-weave composites

The paper analyzes the mechanical properties of plain-weave composites by employing different micromechanical models. Their in-plane and flexural properties are estimated using analytical approaches, including the rule of mixtures and one-dimensional composite beam and two-dimensional mosaic models. The expressions of effective material properties are obtained for one-, two-, and three-ply woven composites. The results obtained are in agreement with published data.     

Some properties of explicitly quasiconcave functions

Quasiconcave functions are characterized by the convexity of the upper level sets. This paper presents the additional properties which are required to characterize explicitly quasiconcave functions, which include the strictly quasiconcave functions. These additional properties are expressed in terms of the properties of and relationships between the level set, the upper level set, the boundary, and the profile of the upper level set.     

Structure of H0R characters the ring R

For a commutative ring R, its related characterizations are given by investigating the structure and properties of H0R. Furthermore, by virtue of H0 structure, some important characterizations of CPF properties and connected properties on K0R are obtained from related rings.     

Derivation of preservation conditions for properties of mathematical models

A general method for deriving conditions for the preservation of properties of any mathematical models is proposed. No constraints on the properties under consideration are imposed. No a priori specification of any part of these conditions, except connection predicates for pairs of variables corresponding to each other in the definitions of properties, is required. Examples are given.