强Raney偏序集

引入强Raney偏序集的概念,讨论了强Raney偏序集的一些性质,证明了强Raney偏序集为超代数偏序集,定向完备的偏序集为强Raney偏序集当且仅当它既是Raney偏序集也是A-偏序集.     

模糊偏序集上理想完备的幂等性

主要讨论模糊偏序集上理想完备性的本质.并得到以下结论:模糊偏序集的理想完备是幂等的当且仅当理想完备上的广义Scott拓扑与Alexandroff拓扑是一致的.     

偏序集上一致连续性的等价刻画与性质

将一致小于关系移植到一般偏序集上,同时引入了上界小于关系,定义了偏序集的一致连续性和上界连续性.给出了一致连续偏序集的等价刻画,探讨了一致连续偏序集所具有的性质.主要结果有:(1)证明了偏序集上的一致连续性,上界连续性与s-超连续性均等价;(2)在交半格条件下,偏序集的一致连续性等价于它的每一主理想一致连续;(3)在并半格条件下,偏序集的一致连续性蕴含连续性,反之不成立;(4)一致完备的一致连续偏序集均是连续bc-dcpo,且每个主理想均为完全分配格;(5)在一致完备的条件下,一致连续性对主滤子,对闭区间,对Scott S-集以及对一致连续投射像均是可遗传的.文中也构造了若干实用的反例.     

偏序集的完备化

首先给出了偏序集的一些完备化的具体构造，又给出了关于完备格中完备子集的某些有用的定理，最终解决了关于偏序集的所有可能的完备化问题     

Z_S-相容连续偏序集及其相关范畴性质

引入了Zs-相客集系统的概念,讨论了Zs-相客连续偏序集的一系列性质.证明了Zs-相容连续偏序集范畴对偶等价于完全分配格范畴的一个满子范畴.     

拟可数逼近偏序集的网式刻画

在可数定向完备偏序集上引入了可数S-收敛网和拟可数S-收敛网的概念,基于此,分别给出了可数逼近偏序集和拟可数逼近偏序集的网式刻画。     

一类局部定向完备集及其范畴的性质

本文给出了局部定向完备集的概念及其在此结构下的一种新的双小于关系，从而进一步给出了一种新的连续性概念，接着讨论了局部定向完备集，连续的局部定向完备集等对象的一些性质，最后考察了三种范畴的笛卡儿闭性，并证明了范畴LDCPO是范畴ALG的反射满子范畴．     

偏序集的代数完备

引进一个偏序集的代数完备, 并且构造任意偏序集的一个代数完备.有最小元的并半格的代数完备正好是它的理想完备. 一个偏序集的代数完备同构于它的一个由下集作为元的完备格,并且这个完备格包含所有主理想. 基于代数完备的Galois联络的下扩张仍然是一个Galois联络.     

序半群的定向完备化

首先引入了序半群定向完备化的概念;其次证明了序半群的序理想之集和理想之集都是连续定向完备序半群,进而序半群的序理想之集和负序半群的理想之集是它们的定向完备化;最后得到了序半群范畴的几个满子范畴的反射子范畴。     

z-代数偏序集的范畴特征

讨论z-代数偏序集一些性质,主要证明z-代数偏序集范畴对偶等价于强代数格范畴的一个满子范畴.     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

Measure-theoretic pressure for subadditive potentials

By using the definition of topological pressure for subadditive potentials, we introduce a new definition of measure-theoretic pressure for ergodic measures of subadditive potentials on a compact metric space. Under some assumption, we show that this definition has a similar formalism to the definition of measure-theoretic pressure for ergodic measures of additive potentials on a compact metric space. As an application, assume that the subadditive potential is Hölder continuous, then for an expansive homeomorphism with the specification property, we study the relationship between the measure-theoretic pressure and the periodic points.     

Une définition dʼespace de modules locaux de structures CR

In this note, we propose a definition of local moduli space in a general framework including the case of CR structures on a fixed differentiable manifold. We show that it is the same as the notion of versal deformation space for complex structures. Finally, we test this definition on the spaces constructed in [5] and [6].     

构造自然数算术系统的一种新方法

用公理化方法来定义非空集上的二元关系〈，使得〈与该集合构成全序集，在全序集中给出最小元素原理的定义，再构造一个含有最小元素原理的适当公理系统来重新给出自然数的公理化定义，然后从构造的自然数公理系统中严格推导出一些基本命题，最后根据这些基本命题来完成对自然数算术系统的精确刻画，从而得到一种具体构造自然算术系统的新方法。     

Cognitive maps and fuzzy implications

A cognitive map is a collection of nodes linked by some arcs. Up to this point, there is unanimity in the literature about the previous definition. But if we look closer at the meaning of the nodes and links, we can see that there are crucial differences between the various authors. And these differences are not always explicit. In spite of this, it seems that many authors perform on the maps the same kind of analysis (strongly inspired by the book of Axelrod), even if these analyses are not consistent with their conception of a cognitive map. That is why it is important to clearly and formally define the kind of map used. In this paper, we propose a formal definition of a cognitive map relying on the concept of fuzzy implication. Thus in our framework, a node is a logical proposition and a link is an implication. Starting from our definition, we show some properties of this kind of maps and some analysis techniques.     

On the analogue of the Isidori relative degree definition for linear dynamical MIMO systems

This paper deals with the inversion problem for linear time-invariant dynamical systems. Earlier in this formulation the discussed issue has been addressed and solved for invertible systems that meet the definition of Isidori relative degree. But in fact, this problem is well-posed for a wider range of linear dynamical systems. In this paper we examine a particular case based on a definition that is similar to the definition of relative degree by Isidori. Presented here columnwise relative degree and its properties allow to consider and effectively solve the inversion problem for invertible systems that meet this definition.     

A multivariate IFR notion based on the multivariate dispersive ordering

In this paper we present a definition of multivariate increasing failure rate based on the concept of multivariate dispersion. This new definition is an extension of the univariate characterization of increasing failure rate distributions under dispersive ordering of the residual lives. We study this definition in the Clayton–Oakes model and the family of generalized order statistics. Copyright © 2009 John Wiley & Sons, Ltd.     

A RIEMANN-TYPE DEFINITION OF N-TH CESARO-PERRON INTEGRALS

In this paper, We give a varlational-type definition of (CnP) integrals. It is equivalent to the original definition of Perron-type and to the definition of Riemann-type, in this way the problem on definition of(CnP)′s Riemann-type has been solved completely.     

子空间非相似性度量(WWF-SSD)的三角不等式

2005年,W ang,W ang和Feng在国际期刊Pattern R ecogn ition上提出了用来刻画子空间非相似性的度量(WW F-SSD),而且利用这个度量设计人脸识别算法,取得了很好的效果.但是该文章中没能证明WW F-SSD满足一个距离必须具有的三角不等式性质.本文给出了WW F-SSD的一个矩阵形式等价定义.基于这个定义不但可以使利用M atL ab实现的算法更有效率,而且可以很直观的证明WW F-SSD不依赖于子空间标准正交基的选择这一性质.进一步,我们在这个定义的基础上,利用矩阵的有关性质证明了WW F-SSD的三角不等式,从而最终证明了WW F-SSD是距离.     

The elementary transformation of vector bundles on regular schemes

We give a generalized definition of an elementary transformation of vector bundles on regular schemes by using Maximal Cohen-Macaulay sheaves on divisors. This definition is a natural extension of that given by Maruyama, and has a connection with that given by Sumihiro. By this elementary transformation, we can construct, up to tensoring line bundles, all vector bundles from trivial bundles on nonsingular quasi-projective varieties over an algebraically closed field. Moreover, we give an application of this theory to reflexive sheaves.