代数正规类中的遗传根与强半单根

Puczylowski建立了一般代数对象类的根理论.本文在代数正规类中,用格论方法刻划一般遗传根和强半单根类,探究它们的一些性质,推广了已知各类代数系统的某些根论研究.     

具有散有限半序性质的BCI—代数

自日本数学家K.Iseki于一九六六年引入BCI-代数(见[1])以来,尤其是K.Iseki在一九八0年对BCI-代数理论做了一系列奠基工作(见[2-8])以来,BCI-代数理论的研究工作有了很大发展,取得了许多成果。在BCI-代数理论中一些类的研究一直是研究的主要方向之一。本文中作者要引入一类新的BCI-代数,使得BCI-代数类[9-10]、结合BCI-代     

可积代数正规类中半素代数类及半素一致代数类确定的上根

利用代数正规类中的理想乘积公理，引入可积代数正规类及可积代数正规类中素代数、半素代数类及一致代数类概念，讨论了可积代数正规类中半素代数类及半素一致代数类确定的上根性质。     

模糊蕴涵格理论

模糊蕴涵代数,在文献中简称为FI代数,最初由吴望名先生于1990年提出,至今已经有许多研究成果.文中综述有关FI代数的概念,性质等主要研究工作,同时给出这类代数的一些新的性质.重点强调构成格结构的FI代数,称之为模糊蕴涵格,简称为FI格.这类代数结构与模糊逻辑中几个重要的代数系统具有紧密的联系,文中将揭示这些联系,一些重要的模糊逻辑代数系统都是FI格类的子类.另外,所有正则FI格构成代数簇,即等式代数类.这个代数簇将在模糊逻辑与近似推理中发挥重要的作用.     

关于格蕴涵代数与BCK-代数

证明了格蕴涵代数与有界可换 Ｂ Ｃ Ｋ代数是两类相互等价的代数系统,借此得到了一类 Ｂ Ｃ Ｋ代数的结构定理     

无穷小量等价类集的代数结构

实现了无穷小量集合的分类,建立了两种无穷小等价类的分划,指出了无穷小等价类的存在性与元素结构,为寻求无穷小等价类的元素特征提供了理论基础.并在此基础之上,分析了无穷小等价类的代数结构,为进一步运用无穷小量进行各种运算提供了系统的理论基础.     

BL代数的(∈,∈∨q)-模糊滤子理论

对BL代数的(∈,∈∨q)-模糊滤子理论作系统研究。首先,在BL代数中引入(∈,∈∨q)-模糊对合滤子和(∈,∈∨q)-模糊结合滤子两类新概念,获得了这两类(∈,∈∨q)-模糊滤子的几个等价刻画。其次,详细讨论了BL代数中各类(∈,∈∨q)-模糊滤子间的关系,证明了一个模糊集为(∈,∈∨q)-模糊布尔(关联)滤子当且仅当它既是(∈,∈∨q)-模糊正关联滤子又是(∈,∈∨q)-模糊对合滤子。最后,以直观图示的方式对BL代数中各类(∈,∈∨q)-模糊滤子间关系进行了总结。     

Fuzzy蕴涵代数

本文讨论一个新的代数系统Fuzzy蕴涵代数,简称FI代数。FI代数是[0,1]值逻辑的蕴涵连接词的代数抽象,我们讨论了两类重要的FI代数—正则FI代数和HFI代数,并指出正则HFI代数与Boole代数的内在联系。     

吴文俊夏季学期讲座·强调数学教学

6月16日下午,由中科院研究生院数学系组织的院士系列讲座在中关村园区教学楼S204教室举行第三讲.此讲报告人是著名数学家和数学史家、中国科学院院士、第三世界科学院院士、中科院系统科学研究所名誉所长、首届国家最高科技奖获得者吴文俊.他的研究工作涉及代数拓扑学、代数几何、博奕论、数学史、数学机械化等众多领域.他在拓扑学的示性类理论、示嵌类理论、奇点理论及I*函子理论方面取得过杰出成果,并在我国率先研究代数几何学且取得重要成果,是我国数学机械化研究方向的主要开拓者,同时对中国古代数学史研究有独到的见解与成果。吴文俊…     

双重半伪补MS代数的正则滤子

正则滤子是刻画代数结构的工具,借助正则滤子同余关系有助于了解代数的内部结构.首先在双重半伪补MS代数上,引入正则滤子的概念,结合双重半伪补MS代数的运算属性,构造出具有正则滤子的最大同余关系;其次,利用双重半伪补MS代数具有正则滤子最小同余关系表达式,给出了具有正则滤子的最小同余关系与最大同余关系的等式关系.所得结论为其它分配格代数类正则滤子性质的研究提供了方法,丰富了分配格理论,为进一步研究分配格代数类的代数结构提供理论支持.     

Reliability analysis in uncertain random system

Reliability analysis of a system based on probability theory has been widely studied and used. Nevertheless, it sometimes meets with one problem that the components of a system may have only few or even no samples, so that we cannot estimate their probability distributions via statistics. Then reliability analysis of a system based on uncertainty theory has been proposed. However, in a general system, some components of the system may have enough samples while some others may have no samples, so the reliability of the system cannot be analyzed simply based on probability theory or uncertainty theory. In order to deal with this type systems, this paper proposes a method of reliability analysis based on chance theory which is a generalization of both probability theory and uncertainty theory. In order to illustrate the method, some common systems are considered such as series system, parallel system, k-out-of-n system and bridge system.     

Inverse problems in queueing theory and Internet probing

Queueing theory is typically concerned with the solution of direct problems, where the trajectory of the queueing system, and laws thereof, are derived based on a complete specification of the system, its inputs and initial conditions. In this paper we point out the importance of inverse problems in queueing theory, which aim to deduce unknown parameters of the system based on partially observed trajectories. We focus on the class of problems stemming from probing based methods for packet switched telecommunications networks, which have become a central tool in the measurement of the structure and performance of the Internet. We provide a general definition of the inverse problems in this class and map out the key variants: the analytical methods, the statistical methods and the design of experiments. We also contribute to the theory in each of these subdomains. Accordingly, a particular inverse problem based on product-form queueing network theory is tackled in detail, and a number of other examples are given. We also show how this inverse problem viewpoint translates to the design of concrete Internet probing applications.     

一类非线性快慢系统非局部问题的摄动解

主要讨论了一类非线性快慢系统非局部问题的摄动解,在适当的条件下,根据不同边界层利用伸长变量和幂级数展开理论,构造了问题的形式渐近解,并利用微分不等式理论在整个区间上证明了形式渐近解的一致有效性,把奇摄动问题的摄动解推广到快慢系统非局部问题的摄动解.     

一类离散生态经济系统稳定性与分支研究

本文研究了一个离散生态经济模型的稳定性和分支问题.利用离散奇异系统理论,中心流形定理及Neimark-Sacker分支理论,得到了系统关于不动点的稳定性和Neimark-Sacker分支的有关结果,并与相应的连续模型进行对比分析.推广了文献[5]的结果.     

Idealized program packages and problems of positional control with incomplete information

The paper is devoted to developing the method of program packages as a tool for investigating problems of positional control with incomplete information. The method is embedded in the field of guaranteed control theory and was stipulated by a number of constructions from this theory. Under the assumption that an a priori given set of initial positions of a controlled system is finite, it is established that the solvability of a guaranteed guidance problem in the class of program packages (or, which is the same, in the class of positional strategies) is equivalent to the solvability of this problem in the class of considerably simpler program operators, namely, in the class of idealized program packages.     

Monotone optimal control for a class of Markov decision processes

This paper provides a unified framework to study monotone optimal control for a class of Markov decision processes through D-multimodularity. We demonstrate that each system in this class can be classified as either a substitution-type or a complement-type system according to the possible transition set, which can be used as a classification mechanism that integrates a variety of models in the literature. We develop a generic proof of the structural properties of both types of system. In particular, we show that D-multimodularity is a generally sufficient condition for monotone optimal control of different types of system in this class. With this unified theory, there is no need to pursue each problem ad hoc and the structural properties of this class of MDPs follow with ease.     

具有周期系数的两竞争种群系统的最优捕获策略

在竞争关系的生态模型基础上,通过引入周期性参数形成一个竞争的二维周期系统.对此非自治生态系统,利用比较定理探讨了系统的持续存在性;由Brouwer不动点定理及稳定性理论证明了其周期解的唯一存在性;最后,讨论了相应的最优控制问题,并给出了问题的最优收获策略Eopt(t).     

THE LIMIT CYCLES AND HOPF BIFURCATION OF A CLASS OF SIMPLIFIED HOLLING TYPE-IV PREDATOR-PREY SYSTEM WITH LINEAR STATE FEEDBACK

In this paper, a class of simplified Type-IV predator-prey system with linear state feedback is investigated. We prove the boundedness of the positive solutions to this system, and analyze the quality of the equilibria and the existence of limit cycles of the system surrounding the positive equilibra. By Hopf bifurcation theory, the result of having two limit cycles to the system is obtained.     

Boundary and initial-value methods for solving Fredholm equations with semidegenerate kernels

We develop a new approach to the theory and numerical solution of a class of linear and nonlinear Fredholm equations. These equations, which have semidegenerate kernels, are shown to be equivalent to two-point boundary-value problems for a system of ordinary differential equations. Applications of numerical methods for this class of problems allows us to develop a new class of numerical algorithms for the original integral equation. The scope of the paper is primarily theoretical; developing the necessary Fredholm theory and giving comparisons with related methods. For convolution equations, the theory is related to that of boundary-value problems in an appropriate Hilbert space. We believe that the results here have independent interest. In the last section, our methods are extended to certain classes of integrodifferential equations.     

弹性弦Dirichlet边界反馈控制的镇定与Riesz基生成

本文通过一端固定 ,一端 Dirichlet边界控制的一维波动方程说明系统是 Salamon- W eiss意义下适定和正则的 .由此说明 ,由 J.L.Lions引入的用于研究双曲方程精确可控性的 H ilbert唯一性方法是控制论中著名的对偶原理 .我们讨论了系统的指数镇定及闭环系统的广义本征函数生成 Riesz基和谱确定增长条件 .我们希望通过本文使读者对目前线性偏微分控制理论的一个新动向有一基本的了解 .