正规幂环和一致幂环

文[1]首次提出了HX环（幂环）的概念,文[2]探索了幂环的性质和结构,本文类似于幂群的研究,提出了正规幂环和一致幂环的概念,研究了它们的结构和它们之间的关系,对它们进行了分类,并讨论了它们的交与和,从而构造了它们的子环链和理想链。     

L-fuzzy拓扑空间中的相对T_i(i=0,1,2)分离性

以已有文献为基础,在L-fuzzy拓扑空间中引入了L-fuzzy相对Ti(i=0,1,2)分离性公理,给出了它们的特征刻画,讨论了它们之间的关系,并研究了它们的一系列基本性质,如可遗传性、L-fuzzy同胚不变性等.     

矩阵的旋转及其应用

讨论了一般矩阵A=(a_(ij))_(m×n)的六种旋转运算.首先,给出了它们的定义.其次,给出了它们的运算规律.最后,讨论了当它们为方阵时的行列式、特征值等相关结果与应用.     

信息量和熵的关系

介绍了信息量和熵,它们分别是信息科学和热力学中的概念,但是在实际应用中却有着十分紧密的联系,它们影响着人们对事物的发展变化进行的判断和决策.讨论了它们的关系,以及在具体实例中的应用.     

加密网格点二元局部基插值样条函数

1.简介 由于在理论以及应用两方面的重要性,多元样条引起了许多人的注意([6],[7]),紧支撑光滑分片多项式函数对于曲面的逼近是一个十分有效的工具。由于它们的局部支撑性,它们很容易求值;由于它们的光滑性,它们能被应用到要满足一定光滑条件的情况下;由于它们是紧支撑的,它们的线性包有很大的逼近灵活性,而且用它们构造逼近方法来解决的系统是     

多面体区域上非光滑函数的迹

本文给出了一类非光滑函数在多面体区域边界上的迹的定义,研究了它们的性质并给出了它们的结构形式.     

泛欧氏空间的Clifford群、扭群、旋群及它们的李代数

本文研究了泛欧氏空间的Clifford群、扭群、旋群,它们为Clifford代数中选出极好的一类子群.利用Clifford代数理论方法,获得了泛欧氏空间中Clifford群、扭群、旋群及其李代数的结构及它们之间的关系,并且得到了它们的李代数.     

复数域C上的一类非退化幂零李代数

本文讨论了复数域Ｃ上的有限维非退化李代数．并将它们与正交代数Ｂ_ｌ和 Ｄ_ｌ联系起来,从而得出它们的若干性质,同时也讨论了一类非退化幂零李代数并彻底 将它们刻划清楚．     

华罗庚域的Bergman核函数

给出了4类华罗庚域的Bergman核函数的显表达式.其关键之处有两点：一是给出了它们的全纯自同构群;二是引进了semi-Reinhardt域,并给出了它们的完备标准正交函数系.在此基础上,给出了它们的Bergman核函数的显表达式,这也是方法上的创新之处.     

准圆与准线的一种关联

从名称上看,圆锥曲线的准圆与准线名称都含准字,那么它们是否有某种关联呢?对此,笔者做了一点探究,得到了它们的     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.     

Spectral properties of sums of certain Kronecker products

We introduce two kinds of sums of Kronecker products, and their induced operators. We study the algebraic properties of these two kinds of matrices and their associated operators; the properties include their eigenvalues, their eigenvectors, and the relationships between their spectral radii or spectral abscissae. Furthermore, two projected matrices of these Kronecker products and their induced operators are also studied.     

Applicability and effectiveness of classifications models for achieving the twin objectives of growth and outreach of microfinance institutions

Measuring performance of microfinance institutions (MFIs) is challenging as MFIs must achieve the twin objectives of outreach and sustainability. We propose a new measure to capture the performance of MFIs by placing their twin achievements in a 2 × 2 grid of a classification matrix. To make a dichotomous classification, MFIs that meet both their twin objectives are classified as ‘1’ and MFIs who could not meet their dual objectives simultaneously are designated as ‘0’. Six classifiers are applied to analyze the operating and financial characteristics of MFIs that can offer a predictive modeling solution in achieving their objectives and the results of the classifiers are comprehended using technique for order preference by similarity to ideal solution to identify an appropriate classifier based on ranking of measures of performance. Out of six classifiers applied in the study, kernel lab-support vector machines achieved highest accuracy and lowest classification error rate that discriminates the best achievement of the MFIs’ twin objective. MFIs can use both these steps to identify whether they are on the right path to attaining their multiple objectives from their operating characteristics.     

Involutions of a Clifford Algebra Induced by Involutions of Orthogonal Group in Characteristic 2

Among the involutions of a Clifford algebra, those induced by the involutions of the orthogonal group are the most natural ones. In this work, several basic properties of these involutions, such as the relations between their invariants, their occurrences, and their decompositions, are investigated.     

A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９０８，Ｅ．Ｌａｎｄａｕｉｎｔｒｏｄｕｃｅｄｔｈｅｆｏｌｌｏｗｉｎｇｗｅｌｌｋｎｏｗｎｓｅｑｕｅｎｃｅｏｆｏｐｅｒａｔｏｒｓ［１］Ｌｎ［ｆ（ｔ）；ｘ］＝Ｋｎ∫１－１ｆ（ｔ）［１－（ｔ－ｘ）２］ｎｄｔ，　　　　（１．１）ｗｈｅｒｅ　　　　　Ｋｎ＝［∫１｛－１（１－ｔ２）ｎｄｔ］－１～ｎπ　　（ｎ→∞）．（１．１）ｗａｓｕｓｅｄｉｎｔｈｅｐｒｏｏｆｏｆｔｈｅＷｅｉｅｒｓｔｒａｓｓＴｈｅｏｒｅｍ．Ｓｉｎｃｅｔｈｅｎ，ｔｈｅａｐｐｒｏｘｉｍａｔｉｏｎｐｒｏｐ－ｅｒｔ…     

Some properties of factorizable Hopf algebras

A direct proof without modular category theory is given of a recent theorem of Etingof and Gelaki (1998) on the dimensions of irreducible representations. Factorizable Hopf algebras are characterized in terms of their Drinfeld double, and their character rings and the group-like elements of their duals are described.

     

Discrete finite element characterizations of source fields for volume and boundary constraints in electromagnetic problems

The consideration of electromagnetic field sources in potential formulations necessitates the definition of source fields. Such source fields are first defined for both volume and boundary constraints in static electromagnetic models. Then, automatic procedures are proposed to conveniently and efficiently characterize discrete source fields, with regard to their use in finite element formulations, their supports, their direct expression requiring no pre-computation, and their associated constraints. Two application examples are proposed to illustrate the approach.     

The variance and covariance of fuzzy random variables and their applications

The concepts of the variance and covariance of fuzzy random variables and their properties are introduced. Examples show their computation and applications in statistical estimation of parameters when samples or prior information are fuzzy. As their further applications the correlation function and the criterions of mean-square calculus for fuzzy stochastic processes are established.     

Planar groups of automorphisms of stable planes

(Semi-) planar groups of stable planes are introduced, and information about their size and their structure is derived. A special case are the stabilizers of quadrangles in compact connected projective planes (i.e. automorphism groups of locally compact connected ternary fields).