Computing infima on convex sets, with applications in Hilbert spaces

Using intuitionistic logic, we prove that under certain reasonable conditions, the infimum of a real-valued convex function on a convex set exists. This result is then applied to problems of simultaneous approximation in Hilbert space and the corresponding operator space This enables us to establish that a bounded, weak-operator totally bounded, convex subset of is strong-operator located.

     

Clifford 代数,几何计算和几何推理

Clifford代数是一种深深根植于几何学之中的代数系统,被它的创始人称为几何代数．历史上,E．Cartan,R．Brauer,H．Weyl,C．Chevalley等数学大师都曾研究和应用过Clifford代数,对它的发展起了重要作用．近年来,Clifford代数在微分几何、理论物理、经典分析等方面取得了辉煌的成就,是现代理论数学和物理的一个核心工具,并在现代科技的各个领域,如机器人学、信号处理、计算机视觉、计算生物学、量子计算等方面有广泛的应用．本文主要介绍Clifford代数在几何计算和几何推理中的应用．作为一种优秀的描述和计算几何问题的代数语言,Clifford代数对于几何体,几何关系和几何变换有不依赖于坐标的、易于计算的多种表示,因而应用它进行几何自动推理,不仅使困难定理的证明往往变得极为简单,而且能够解决一些著名的公开问题,目前在国际上,几何自动推理已经成为Clifford代数的一个重要应用领域。     

离散时间模型下最大赤字问题

本文对引入利率的离散时间风险模型得到了破产前最大盈余的分布 ,破产前盈余、破产后赤字与破产前最大盈余的联合分布以及首达某一水平 x的时间分布的递推公式 ,对不带利率的模型得到了最大赤字、发生最大赤字的时间的分布     

Stochastic Convexity of the Poisson Mixture Model

This paper is devoted to the study of the compound Poisson mixture model in an actuarial framework. Using the s-convex stochastic orderings and stochastic s-convexity, several problems involving an unknown mixing parameter with given moments are examined; namely, the specification of the number of support points in a finite mixture model, and the derivation of extremal mixture distributions. The theory is enhanced with the derivation of theoretical and numerical bounds on several quantities of actuarial interest.     

Separable Banach space theory needs strong set existence axioms

We investigate the strength of set existence axioms needed for separable Banach space theory. We show that a very strong axiom, comprehension, is needed to prove such basic facts as the existence of the weak- closure of any norm-closed subspace of . This is in contrast to earlier work in which theorems of separable Banach space theory were proved in very weak subsystems of second order arithmetic, subsystems which are conservative over Primitive Recursive Arithmetic for sentences. En route to our main results, we prove the Krein-\v{S}mulian theorem in , and we give a new, elementary proof of a result of McGehee on weak- sequential closure ordinals.

     

面向21世纪师专数学专业培养目标的定位

分析了目前师专数学专业面临的现状,对该专业的培养目标进行了探索性的定位,并提出了课程改革的初步方案.     

浅析对数学史教育的认识与实施

数学史教育在大学数学教育中具有重要的意义.有助于学生理解数学知识的本质,培养学生的思维能力.有必要开设数学史课程或在专业课教学中渗透数学史知识;有适合学生的专门数学史教材;进行数学史教育要联系学生的数学知识,要深入浅出;要注意数学精神的宣传.     

The Gibbs' phenomenon from a signal processing point of view

Recently, Fay and Kloppers gave two proofs to show that the well-known Gibbs' phenomenon for Fourier series at a jump discontinuity depends only on the size of the jump and is a multiple of the integral 1/π ∫₀ ^π (sin x / x) dx. We give another proof, based upon low-pass filtering of the Fourier transform, that uses the observation that a truncated Fourier series for a function ? (x) is ‘very nearly’ equal to the convolution integral 1/π ∫ _-∞ ^+∞ ? (x - t)(sin nt / t) dt.     

Report on the activities of the working group on discrete mathematics

In the past decade there have been significant developments in computer technology and solution techniques for analysing business and industrial decision problems. In recent years good modelling systems have become available to ease the burden of model communication. Currently the single most important barrier to increased use of structured approaches to decision modelling is the acquisition of the necessary skills to initially develop models of complex decision systems. This paper examines the modelling process with reference to linear programming. Two related production planning problems are presented and their associated models developed. The relationship between the two problems is such that student modellers are forced to become involved in the important details of the problems and, by examining the nature of solution spaces in constrained optimisation, students are able to rapidly gain confidence and skills in modelling.     

Interpreting a graph and constructing its derivative graph: stability and change in students’ conceptions

This present study investigated engineering students’ conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the incorporation of computers for the purposes of seeing the power of visualization, investigating worked examples given in steps and solving various questions related to the worked examples, assisting conceptual understanding, and/or providing feedback besides lectures in the classroom. Students were tested before and after being exposed to instruction on differentiation and integration by a diagnostic test measuring their understanding of major aspects of calculus. Follow-up interviews were conducted with 18 students. Analyses of the results revealed that A-level student's performance was improving more than non-A-level students, particularly in computer groups. The analyses of the students’ written and oral responses in all groups indicated that prototypes, poor understanding of the notion of limit, confusion between the process and the product, and difficulties in using graphical information to give meaning to symbolic representation account for the errors and the misconceptions identified.