E-凸Fuzzy集和E-反凸Fuzzy集

研究了广义凸Fuzzy集和广义反凸Fuzzy集以及它们的性质。通过将凸Fuzzy集和E-凸集相结合,提出了一种新的广义凸Fuzzy集———E-凸Fuzzy集,使得凸Fuzzy集成为它的特例,并对E-凸Fuzzy集的性质进行了初步研究。然后,类似地,通过将反凸Fuzzy集和E-凸集相结合,提出了一种新的广义反凸Fuzzy集———E-反凸Fuzzy集,使得反凸Fuzzy集成为它的特例,并对E-反凸Fuzzy集的性质进行了初步研究。     

K-Drop凸空间与局部K-Drop凸空间

引入了Banach空间的局部k-drop凸性质，研究了k-drop凸与局部k-drop凸的一些性质以及两者之间的关系，并用单位球的切片统一而简洁地处理了这两个性质．     

非常极凸空间

本文使用非常极凸的定义，证明了非常极凸和非常光滑是互为对偶空间且严格介于弱k凸和非常凸之间的空间，最后得到了非常极凸的一些特征．     

有界凸圆型域上的准凸映照

本文研究星形映照的一类子族——有界凸圆型城上的准凸映照,并讨论了它与星形映照及凸映照的关系,建立其与凸映照同形的增长定理和掩盖定理．     

Banach空间上凸集的凸性

以Banach空间的一般凸集为研究对象,将Banach空间的凸性研究推广到了内部非空的凸集上．打破了从单位球出发研究Banach空间几何的具有局限性的研究方法,给出了严格凸集的若干特征刻画及性质,并得到了严格凸集和光滑集之间的对偶定理．     

完全k凸与局部完全k凸的关系

本文讨论了完全ｋ凸与局部完全ｋ凸之间的关系，它包含了Ｐｏｌａｋ和Ｓｉｍｓ的结果。此外我们还给出局部一致凸空间的两个新特征，这些特征刻划了ＬＵＲ，Ｌ－ｋＲ和Ｌｋ－ＵＲ之间的关系。     

灰色凸集及其基本性质

本文给出了灰色凸集的定义．并证明了灰色凸集具有一般凸集完全类似的性质．     

关于k-强极凸空间

本文证明k-强极凸是严格介于k-非常极凸和k-极凸之间的凸性.利用k-强极凸的概念,得到k-强极凸的一些特征.     

k-Drop凸空间的特征

通过研究局部k-drop凸空间的一些性质,得出了k-drop凸性质与自反且k-严格凸是等价的,同时k-drop凸空间具有商遗传性.     

欧氏空间凸多面体极点凸组合表示定理的推广

使用切面技术、归纳法等证明了欧氏空间中凸集极点的存在性,进一步证明了空间中一般有界闭凸集(不只局限于凸多面体)中任意一点同样可表示为极点的凸组合.方法独到.     

关于(余)反射的等价性和可扩张性及其应用

该文研究了（余）反射的等价性和可扩张性及应用，得到的主要结果如下：(1) 余反射余代数范畴和反射代数范畴是等价的．(2) 反射和余反射都具有可扩张性．使用这些结果可以用来推广和化简［1-4］中部分结论     

Estimating a survival function with incomplete cause-of-death data

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a “self-consistency” approach are considered. The solution sets corresponding to both approaches are found. They are infinite and identical. Only some of the solutions are consistent; i.e., the MLEs and self-consistent estimators are not consistent in general. Two estimates are thus proposed and their asymptotic properties are studied. It is shown that both estimates are strongly consistent and converge to Gaussian processes. The covariance structures of these Gaussian processes are derived.     

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.     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

由格蕴涵代数诱导的伴随半群

给出由格蕴涵代数诱导出的伴随半群及有关概念 ,详细讨论伴随半群中的元素即格蕴涵代数的左映射的性质 ,得到它们的几个等价条件。最后讨论由格蕴涵代数诱导的两个双格半群与伴随半群之间的关系 ,并证明这些半群是幂等的当且仅当它们是由格 H蕴涵代数所诱导     

An introduction to Minkowski geometries

The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students’ understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.     

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.     

Games with vector payoffs

Two-person games are defined in which the payoffs are vectors. Necessary and sufficient conditions for optimal mixed strategies are developed, and examples are presented.     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

On covering mappings on solenoids

Covering mappings on the dyadic solenoid are studied. Some results stated by Zhou Youcheng (2000) are discussed in a more detailed way by indicating certain inaccuracies in their proofs. These are either corrected or supplemented, or else suitable counterexamples are constructed. Some open questions are asked and connections with related results are considered.