关于广义逆矩阵AT，S^（1,2）的刻画推广

本文通过一类秩等方程给出了AT,S^(1,2)、AT,S^(2)的一种刻画及一类秩等方程有解的充分必要条件，推广了文献[1]、[4]的结论，并改进了[4]关于矩阵A的Drazin逆Af的一类刻画的证明。     

广义逆AT，S^（2）的几种秩关系式

利用矩阵A的广义逆AT,S^（2）的Moore-Penrose逆表示式,得到了与广义逆AT,S^（2）相关的几种秩等式和不等式,并由此得到了加权Moore-Pensore逆,Moore-Pensore逆,Drazin逆及群逆的相应结论.     

广义逆A(2)T,S的一种计算方法

本文给出了利用特征多项式求矩阵广义逆AT，S^(2)的一种计算方法，并由此得到了加权M—P逆AM，N^ 、M—P逆A^ 、Drain逆Ad及群逆A9的相应计算方法，推广了文献[2]的结果．     

Blaschke张量的行列式为常数的2维子流形的研究

本文研究了S^(2+p)中2维子流形的莫比乌斯刚性问题.设M^(2)是^(2+p)维单位球S^(2+p)中的无脐子流形,M^(2)在S^(2+p)的莫比乌斯变换群下的四个莫比乌斯基本量为莫比乌斯度量g,Blaschke张量A,莫比乌斯形式Φ以及莫比乌斯第二基本形式B,利用不等式估计,证明了下列刚性定理:设x:M^(2)→S^(2+p)是^(2+p)维单位球S^(2+p)中莫比乌斯形式消失的2维紧致子流形,Blaschke张量A的行列式Det A=c(const)>0,若tr A≥1/4,那么x(M^(2))莫比乌斯等价于S^(2+p)中常曲率极小子流形或者S^(3)(1/√1+c^(2))中环面S^(1)(r)×S^(1)(√1/1+c^(2)-r^(2)),其中r^(2)=2-√1-64c/4(1+c^(2)).本文的证明补充了文献[3]中2维子流形情形.     

On Reducible Dehn Surgery （ Ⅱ ）

Let K be a knot in a 3-sphere S^3 and N( K ) be a regular neighbourhood of K in S^3. Let Mk = S^3 - intN (K), and T = э Mk. A slope r in T is a T-isotopy class of essential, unoriented, simple, closed curves in T. The distance between two slopes r1 and r2 in T,     

关于S^1上扩张映射的拓扑熵的改进

对献[1]中圆周上扩张映射的拓扑熵的结论给予了改进,得到了结论：设f∈C^r(S^1,S^1)是扩张映射,则ent(f)=log│deg(f)│。     

DIRECT EXPANSIONS FOR THE DISTRIBUTION FUNCTIONS AND DENSITY FUNCTIONS OF χ2-TYPE AND t-TYPE DISTRIBUTED RANDOM VARIABLES

Suppose that Z1,Z2…,Zn are independent normal random variables with common mean μ and variance σ^2. Then S^2=∑n n=1 (zi-z)^2/σ^2 and T =（n-1的平方根）-Z/（S^2/n的平方根） have x2n-1 distribution and tn-1 distribution respectively. If the normal assumption fails, there will be the remainders of the distribution functions and density functions. This paper gives the direct expansions of distribution functions and density functions of S^2 and T up to o(n^-1). They are more intuitive and convenient than usual Edgeworth expansions.     

Derivative estimates of averaging opera tors and extension

We study the derivative operator of the generalized spherical mean S^γt. By considering a more general multiplier m^Ωγ,b=Vn-2/2+γ(|ξ|)|ξ|^bΩ(ξ') and finding the smallest γ such that m^Ωγ,b is an Hp multiplier, we obtain the optimal range of exponents (γ,β,p)to ensure the H^p(R^n) boundedness of a^βS^γ1f(x). As an application, we obtain the derivative estimates for the solution for the Cauchy problem of the wave equation on H^p(R^n) spaces.     

广义逆A_T~(2),S的一个特征

给出了矩阵广义逆AT,B(2)的一个特征,并由此建立了AT,B(2)的一种算法.     

极大S2NS阵的分支数与非零元个数

一个实方阵A称为是S^2NS阵,若所有与A有相同符号模式的矩阵均可逆,且它们的逆矩阵的符号模式都相同.若A是S^2NS阵且A中任意一个零元换为任意非零元后所得的矩阵都不是S2NS阵,则称A是极大S^2NS阵.论文证明了当n≥5时,所有n阶极大S^2NS阵的分支个数所成之集合Fn为{1,…,n}／{2},而所有n阶极大S^2NS阵的非零元个数所成之集合S（n）,除去2n＋1到3n-4间的一段外,也得到了完全确定.     

ON A THEOREM OF A.A. LYAPUNOV

Abstract

In this note we obtain some extensions and an approximation of the Lyapunov convexity theorem by means of the bilinear integration of a set-valued function. The integration is performed successively with respect to a non-atomic, a direct sum and a Darboux vector measure. The necessary counterexamples are provided.     

A Priori and A Posteriori: A Bootstrapping Relationship

The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning, and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.     

有限群的一个类函数的模构造

本文研究了有限群上的一个类函数.通过计算它和不可约特征标的内积,证明了它是特征标并且通过复群代数的中心的正则表示给出了它的一个模构造.     

NAMING A COLUMN ON A SPREADSHEET

Spreadsheets use a meaningful algebra-like notation which, research suggests, can support pupils in developing an understanding of variables. This paper discusses the activity of Year 8 pupils who were taught to name a column on a spreadsheet, and who were asked to reflect upon their activity in a stimulated recall interview. More specifically, it considers the pupils' understanding of notation, such as 'A2' and 'm', which they used when constructing spreadsheet formulae. It is suggested that experience of naming columns may help pupils to develop a clearer sense of the notation as a variable, and to make links between their spreadsheet activity and use of standard algebraic notation [1].     

A REMARK ON A BMO MARTINGALE

Let M = (Mt,Ft) be a uniformly integrable continuous martingale with MO = 0. For1 5 p < cot we setIIMllBMO. = '3p II[E[IMoo ~ MTIplFT]]'/Pll.,where the supremum is taken over all stopping times T.Set BMO. = {M: IIMllBMO. < co}. It is well known that BMO. = BMO, (VI S p 5 q).F'urthermore, all 11.llBMO. norms are equivalent andIIi ~~if;llMllBMO. = SUP T P(T < co)i'where the supremum is taken over all stopping times T satisfying P(T < co) > 0. In the laterwe shall simply …     

A new characterization of A 5

Let G be a group and τ _e (G) the set of numbers of elements of G of the same order. In this paper, by τ _e (G), we give a new characterization of A ₅, where A ₅ is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ _e (G) = τ _e (A ₅) = {1, 15, 20, 24}.