《试论积分第一中值定理》一文的更正

本文指出文[1]中的引理2是错的,并且给出了一个命题来代替文[1]中的引理2,同时对文[1]中引理3的叙述与证明作了些修改,使之更完美,这样也就对文[1]中相应的有关叙述作了些调整.     

广义对角占优矩阵的3-块判定

本文用简捷的方法，讨论了广义对角占优矩阵的3-决判定，推广了文[2]、[3]的结果，同时指出了文[3]定理1中的一个错误.     

一组恒等式的q—模拟（Ⅱ）

A．Mercier讨论了一组恒等式。文[2]给出了其定理1－3的q-模拟形式。本文在[2]的基础上给出了其定理4－6的q-模拟形式，也推广了文[2]的结果。     

对D.A.Cohen的一个划分数不等式定理的再改进

关于正整数n的划分方法数，文[l]给出了定理．文[2]改进了文[1]的结果，本文又改进了文[2]的结果．     

也谈广义正定矩阵

本文对矩阵的正宛性作了进一步的推广，讨论了它们的一些性质，改进了文[1]、[2]的一些结果，并纠正了文[2]的一个错误结论。     

关于正值函数无积分收敛性判别法的讨论

文[1]给出了非负函数无穷积分收敛性的几个判别法，本文给出了比文[1]判别法更精细的一个判别法，同时，通过与文[2]中判别法的比较，说明它比文[1]中的判别法都强。     

一阶常微分方程可积的新类型

本文受文[2]的启示,推广了文[1]研究的一类可积的一阶常微分方程,给出了这类新的一阶常微分方程可积的充分条件及积分表达式。所得结论与文[2]的定理互不包含。     

正项级数高斯判别法的一个附注

文[1]中高斯判别法，实际上是文[2]的Bertran判别法，为了便于统一和推广，本文对文[1]的高斯判别法作了叙述与证明上的改进，最后与文[2]的Bertran判别法进行统一。     

可对角化的线性变换的多项式

讨论了可对角化的线性变换的多项式的一些性质，给出了n阶矩阵可对角化的一个充要条件，由此推广了文[1]、[2]、[3]中某些结果。     

h凸函数的判断准则

文[1]定义了区间上的h凸函数，并给出了它的若干等价命题，文[2]给出了它的若干性质。本文继续文[1，2]的工作，获得h凸函数的若干判别准则。     

S——“Bolzano—Weierstrass”性质

文[1]、[2]、[3]、[4]分别讨论了S—紧性和可数S—紧性,本文则讨论一种弱于S—紧性和可数S—紧性但对于半T_1空间类来说却等价于可数S—紧性的性质.这种性质称为S—“Bolzano—Weierstrass”性质或S—列紧性质,且要求这种空间的任何无限子集都具有空间内的半聚点.     

关于“模糊数的传递模糊排序”的注记

在文献[1]中,通过用t模取代文献[2]中的取小算子,得出了模糊数的一种传递性排序方法。但这种方法要求模糊数满足的条件过于严格。本文旨在指出:1)该方法实质上是按最小的t模进行排序;2)当取最大的t模时,该方法仅对一类非常特殊的模糊数成立。     

第二积分中值定理“中间点”渐近值的进一步完善

本文通过引入Beta函数．继续探讨了第二积分中值定理“中间点”，的一些渐近性质，得出一系列新结论．作为本文的结论包含了文[2—4]的所有结论．     

Fudenberg无名氏定理与平新乔先生的误读

文献[1]中平新乔先生陈述了一个十分特殊的无名氏定理.按平先生的说法,该定理的思想显而易见,因而没有给出证明,但文献[1]中的定理陈述却存在大量值得商榷的说法.通过讨论平新乔给出的这个定理,得出如下结论：（1）该定理陈述存在概念误用与逻辑不协调; （2）其限制条件模糊或冗余,对结论无实质性限定; （3）结论内容即便不是完全错误,也是无意义的.为澄清文献[1]中的混乱,对与之相关的Fudenberg无名氏定理的条件及结论给予了直观和简明的阐释.     

析“爱A不A”固定格式

“爱A不A”固定格式蕴含着[十选择]的语义特征,即:爱A,就A;不爱A,就不A,它的语义与 语境、信息密切相关。爱A不A在句中有凸显焦点的作用,它有两种变式。     

Dynamic expression pattern of zebrafish bfabp （fabp7） during early embryogenesis

The expression of bfabp is correlated with the development of nervous system. Recently, a bfabp homologue (fabp7) was identified in zebrafish and its genomic structure, mRNA expression by RT-PCR and linkage mapping data were obtained. However, these studies did not provide the information of spatial and temporal expression pattern of fabp7 during zebrafish embryogenesis.     

Corrigendum to "Research progress on electrical signals in higher plants"

The authors would like to inform the readers that in the above mentioned paper,the word "Loosestrife" on p.533,the ninth line of the left-hand column should be replaced by "Desmodium motorium".In addition,the cited references[48,54-58]in the last sentence of the fourth paragraph of Section 3.3 "Patch-clamp recording technique" should be replaced by[48,54-57].The authors would like to apologize to the readers for these errors.     

Construction of Supramolecular Architectures via Self-assembly

1 Results In this paper we report supramolecular polymeric nano networks formed by the molecular-recognition-directed self-assembly between a calix[5]arene and C60[1]. Covalently-linked double-calix[5]arenes take up C60 into their cavities[2]. This complementary interaction creates a strong non-covalent bonding; thus,the iterative self-assembly between dumbbell fullerene 1 and ditopic host 2 can produce the supramolecular polymer networks (See Fig.1).     

凝聚半局部环的余维数

文[1]在正则局部环上证明了著名的Aushnder－Buchsbaum定理。文[2]将此定理推广到凝聚局部环上讨论，得到了更一般的结论。本文是在更广泛的凝聚半局部环上讨论此问题，推广了文[1]和文[2]的结论。该文中的环均指有单位元的交换环，模指幺模。     

Research of optimization to solve nonlinear equation based on granular computing

In this article, a real number is defined as a granulation and the real space is transformed into real granu-lar space[1]. In the entironment, solution of nonlinear equation is denoted by granulation in real granular space. Hence,the research of whole optimization to solve nonlinear equation based on granular computing is proposed[2]. In classicalcase, we solve usually accurate solution of problems. If can't get accurate solution, also finding out an approximate solutionto close to accurate solution. But in real space, approximate solution to close to accurate solution is very vague concept. Inreal granular space, all of the approximate solutions to close to accurate solution are constructed a set, it is a granulation inreal granular space. Hence, this granulation is an accurate solution to solve problem in some sense, such, we avoid to sayvaguely "approximate solution to close to accurate solution". We introduce the concept of granulation in one dimension real space. Any positive real number a together with movinginfinite small distance ε will be constructed an interval [a-ε,a ε], we call it as granulation in real granular space, denotedby ε(a) or [a]. We will discuss related properties and operations[3] of the granulations. Let one dimension real space be R, where each real number a will be generated a granulation, hence we get a granularspace R* based on real space R. Obviously, R∈R*. Infinite small number in real space R is only O, and there are three in-finite small granulations in real number granular space R* : [0], [ε] and [-ε]. As the graph in Fig. 1 shows. In Fig. 1,[-ε] is a negative infinite small granulation,[ε] is a positive infinite small granulation,[0] is a infinite small granulation.[a] is a granulation of real number a generating, it could be denoted by interval [a-ε,a ε] in real space [3-5].Letf(x)=0 be a nonliner equation,its graph in interval[-3,10]id showed in Fig.2.Where -3≤x≤10 Relation ρ(f‖,ε)is defied is follows:(x1,x2)∈ p(f‖,ε)iff |f(x1)- f(x2)|<εWhere ε is any given small real number.We have five appoximate solution sets on the nonliner equation f(x)=0 by ρ(f‖,ε)∧|f(x)|[a,b]max,to denote by granulations[xi1 xi2/2],[xi3 xi4/2],[xi5 xi6/2],[xi7 xi8/2]and[xi9 xi10/2]respectively,where |f(x)|[a,b]max denotes local maximum on x ∈[a,b].This is whole optimum on nonliear equation in interval [-3,10].We will get best opmension solution on nonliner equation via computing f(x)to use the five solutions dented by grandlation in one dimension real granlar space[2,5].