贝卡的历险日记

担心着．担心着．北风来了,冰雪的脚步近了。一切都像没睡醒的样子．昏昏然紧闭着喉。山冷冻起来了．水凉起来了太阳在地平线下躲起来了．海豹偷偷地从水里钻出来．傻傻的．胖胖的．海洋里．浮冰上．瞧去．一大片一大片满是的．坐着．漂着．打两个滚．踢几块．水．赛几趟泳．捉几回迷藏。     

同分布的NA序列加权和的强大数律

讨论了同分布NA随机变量序列加权和的强大数律,所得结果推广了Z．D．Bai和P．E．Cheng及S．H．Sung的结果．     

到复Grassmann流形的多重调和映照的构造

本文给出了一些到复Ｇｒａｓｓｍａｎｎ流形的多重调和映照的构造定理,从而推广了莫小欢,Ｂｕｒｓｔａｌｌ　Ｆ． Ｅ．,Ｗｏｏｄ Ｊ． Ｃ．和 Ｕｄａｇａｗａ Ｓ．的结果．     

数学基础课是通向数学主流的门户

2007年．作者翻译T．Needham所写的《可视的复分析》（Visual Complex Analysis．Oxford Univ．Press．2006）一书．以为这是一本很好的教本．值得许多同志花一点时间读一下．译后有一些感想．因此写了一篇较长的译后记．主要思想即认为数学基础课是通向数学主流的门户．译本将由人民邮电出版社出版．现在征得出版社的同意,将这篇译后记发表于此．在发表时又作了一点补充．补写的文字放在方括号内．     

排球的发球问题

实际问题：在排球比赛中，地运动员站在后场发球．已知：排球的直径为0．21米（规定在20．69cm至21．327cm之间），排球场总长为18米，网高2．5米，女子网高为2．24米；为计算方便不妨取2．5米）．运动员采用跳发球的方式以水平方向发球，为了使发出的球落在界内．     

函数的基本概念

函数是高中数学的基础和主体内容．也是高中数学竞赛的重要内容． 有关函数基本概念的题目．涉及的知识面广，蕴涵的数学思想方法丰富．本文将结合近年来的数学竞赛试题，介绍一些处理函数的基本概念的方法．     

有关凸函数的一个定理的改进证明

文[1]．P5．引理1．1．3的证明过程比较复杂、难以理解,本文用另外一种方法(利用函数的单调性、凹凸性和拉格朗日中值定理)对该定理进行了证明．其证明方法比文[1]的证明方法简单、明了,并对定理的结论进行了推广．     

关于Levesque的信念逻辑的完备性

Ｈ．Ｊ．Ｌｅｖｅｓｑｕｅ最近为了研究非单调推理提出了含有两个模态词Ｂ，Ｎ的信念逻辑系统，并猜想它是完备的．本文提出了Ｔ~＊－集合的概念，并证明一句子集合如果是Ｔ~＊－集合，那么是可满足的．本文的定理是［１］中定理Ａ２的推广．并得到［１］中定理Ａ．２的一个简单的证明．     

具有p-Laplace算子的一类高阶奇异边值问题解的存在性

本文研究下面问题的正解其中Φp(s)=|s|p-2s,p>1．f在点x(i)=0,i=0,．．．,n-2可能是奇异的．证明建立在Leray-Schauder拓扑度和Vitali收敛定理的基础上．     

关于Fuzzy度量点式刻画的一点注记

本文中重新定义由一个点式Ｆｕｚｚｙｐ．ｑ．度量ｄ所诱导的Ｆｕｚｚｙｐ．ｑ．度量｛Ｄｒ｜ｒ＞０｝（代替［１］中的相关重域映射族）．在新的定义下，点式Ｆｕｚｚｙｐ．ｑ．（ｐ．）度量与Ｆｕｚｚｙｐ．ｐ．（ｐ．）度量之间有令人满意的──对应关系．     

任意Banach空间中线性算子的Moore-Penrose度量广义逆

在无空间严格凸的几何假定下,利用Banach空间几何方法给出了任意Banach空间中线性算子T的Moore-Penrose度量广义逆T~+的存在性、唯一性、极小性和线性性的充要条件,同时还讨论了T~+的一些性质,这些本质地将文献[8]的最近结果从严格凸Banach空间拓广至任意Banach空间．     

Some remarks on blvarlational bounds and the pointwise estimation of solutions

When a given equation can be realised in some Hilbert space H as an operator equation in the from A[d] then it is known that complementary variational bounds can be obtained for the inner product [d]. Recently it has been shown that complementary bivariational bounds can be obtained for the inner product [d]associated with the equation A[d]= f and an arbitary elementy [d]. These latter bounds are a natural starting point for investigatng pointwise estimatesd of solutions provided thta certain questions relating, on the one hand, to the self-adjointness and the invertibility of associated operators and on the other to the availability of a suitable large Hilbert space can be resolved. We show that if the underlying problem can be given an operator realisation in a suitably equipped Hilbert space then pointwise estimates of solution can be obtained     

Some remarks on conditional entropy

Summary Using a definition of conditional entropy given by Hanen and Neveu [5, 10, 11] we discuss in this paper some properties of conditional entropy and mean entropy, in particular an integral representation of conditional entropy (§ 2), and the decomposition theorem of the KolmogorovSina¯i invariant (§ 3) (see also [6–8] and [12]).There is an essential difference between Jacob's proof of the last called theorem [6] and the proof given below. The definition of a Lebesgue space, given by Rokhlin [7–9] and [12], is not used in this paper.     

模糊粒度空间的性质研究

在文献[16]基础上,进一步将模糊粒度空间推广到更一般地模糊等价关系上,研究了模糊粒度空间的性质,主要获得了3个结论.首先,引入了有序的等价关系集的概念,给出了下列的四个命题是等价的:(1) 给定一个模糊等价关系;(2) 给定一个等腰归一化伪距离;(3) 给定一个有序的粒度空间;(4) 给定一个有序的等价关系集.第二,通过模糊等价关系诱导的等腰归一化伪距离的投影距离和扩展距离,建立了模糊粒度空间上的距离,即是等腰归一化距离,并且给出了模糊粒度空间上距离度量的动态性质研究.最后,给出了模糊粒度空间与模糊等价关系之间的序关系,即它们的序是一致的.这些研究工作进一步完善了模糊粒度空间的理论,为模糊粒度计算提供了更为直观的数学理论和工具.     

ANTI FUZZY VECTOR SPACES（Ⅱ）

ＡＮＴＩＦＵＺＺＹＶＥＣＴＯＲＳＰＡＣＥＳ（Ⅱ）ＣｈｅｎＹｏｎｇｎｉａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，８３００５４，Ｘｉｎｊｉａｎｇ，Ｐ．Ｒ．Ｃｈｉｎａ）ＡＮＴＩＦＵＺＺＹＶＥＣＴ...     

内积空间中Witt定理的推广

在特征不是2的正交空间中,相关文献给出了Witt定理.华罗庚把它推广到体上的一些内积空间.把域上内积空间中的Witt定理推广到奇异内积空间,并给出相应的证明.     

The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements

The Hodge filtration of the module of derivations on the orbit space of a finite real reflection group acting on an ℓ-dimensional Euclidean space was introduced and studied by K. Saito [5] [6]. It is closely related to the flat structure or the Frobenius manifold structure. We will show that the Hodge filtration coincides with the filtration by the order of contacts to the reflecting hyperplanes. Moreover, a standard basis for the Hodge filtration is explicitly given.Partially supported by the Grant-in-aid for scientific research (No. 14340018 and 13874005), the Ministry of Education, Sports, Science and Technology, Japan     

Sets which are dense in the space of all Pettis integrable functions

Using the examples given by S.J. Dilworth and M. Girardi, we prove that the set of all nowhere Pettis differentiable functions is a G _δ -dense set in the space of all X-valued Pettis integrable functions on [0, 1]. Also an another example of a dense set in the space of all Pettis integrable functions is given.     

On hypersurface of a Finsler space with a special metric

In 1980, H. Izumi [3] introduced the concept of an h-vector. For the Finsler space whose metric is transformed by an h-vector, B. N. Prasad [10] obtained the Cartan connection. On the other hand, M. Matsumoto [7] presented a systematic theory of Finslerian hypersurface. M. Kitayama [4] obtained certain results for the Finslerian hypersurface given by β-changes. The purpose of the present paper is to derive certain properties of a Finslerian hypersurface given by an h-vector. The terminologies and notations are referred to Matsumoto [8].     

GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris‘ result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.