THE STRUCTURE OF $\[\Pi \]$ SPACE (II)

This paper continues the study of [1]. In this paper, the author discusses when a subspace of $\[\Pi \]$ space is a complete subspace, and gives the structure of general linear subspaces (in particular, that of closed linear subspaees),     

ON THE INVARIANCE PRINCIPLE FOR $\[\rho \]$-MIXING SEQUENCES OF RANDOM VARIABLES

In this note the author establishes the invariance principle for $\[\rho \]$-mixing sequences under combinations of moment assumptions and $\[\rho \]$-mixing rates. The result answers a problem from a recent survey paper of Peligrad.     

ON $\[\sigma \]$-FINITE INTEGRALS ON $\[{C^*}\]$-ALGEBRAS

This paper considers positive linear functionals $f$ defined on a dense-subalgebra which is an analogue of the continuous functions with compact supports, of a $\[{C_*}\]$-algebra $\[{L^1}\]$-spaces associated with $f$ are studied. Also introduced is an analogue of the bounded Borel functions vanishing at infinity.     

ON THE DIOPHANUNE EQUATION $\[\sum\limits_{i = 0}^N {\frac{{{x_i}}}{{{d_i}}}} \equiv 0\]$ (mod 1) AND ITS APPLICATIONS

The number $\[A({d_1}, \cdots ,{d_n})\]$ of solutions of the equation $$\[\sum\limits_{i = 0}^n {\frac{{{x_i}}}{{{d_i}}}} \equiv 0(\bmod 1),0 < {x_i} < {d_i}(i = 1,2, \cdots ,n)\]$$ where all the $\[{d_i}s\]$ are positive integers, is of significance in the estimation of the number $\[N({d_1}, \cdots {d_n})\]$ of solutiohs in a finite field $\[{F_q}\]$ of the equation $$\[\sum\limits_{i = 1}^n {{a_i}x_i^{{d_i}}} = 0,{x_i} \in {F_q}(i = 1,2, \cdots ,n)\]$$ where all the $\[a_i^''s\]$ belong to $\[F_q^*\]$. the multiplication group of $\[F_q^{[1,2]}\]$. In this paper, applying the inclusion-exclusion principle, a greneral formula to compute $\[A({d_1}, \cdots ,{d_n})\]$ is obtained. For some special cases more convenient formulas for $\[A({d_1}, \cdots ,{d_n})\]$ are also given, for example, if $\[{d_i}|{d_{i + 1}},i = 1, \cdots ,n - 1\]$, then $$\[A({d_1}, \cdots ,{d_n}) = ({d_{n - 1}} - 1) \cdots ({d_1} - 1) - ({d_{n - 2}} - 1) \cdots ({d_1} - 1) + \cdots + {( - 1)^n}({d_2} - 1)({d_1} - 1) + {( - 1)^n}({d_1} - 1).\]$$     

COMPLETE DISTRIBUTIVITY OF AN l-GROUP

This paper gives twelve equivalent topological conditions to the complete distributivityof an O(D)-contractible 1-group.     

ON GROUPS OF ODD ORDER AND RANK $\[ \le 2\]$

The least commonmultiple of dimensions of chief factors of a finite solvable group is called the rank of the group. The groups of odd order with trivial Fratttini subgroups all of whose subgroups but itself have ranks are completely determined (Theorem A). For an odd number a necessary and sufficient condition for the groups of order n all to be of rank $\[ \le 2\]$ is obtained (Theorem B).     

複合形在歐氏空間中的實現問题Ⅰ

<正> 在拓撲發展之初很早就知道一個抽象的n維單純複合形(有限或無限)必可在2n+1維歐氏空間及R~(2n+1)中得到實現,它的證明也很簡單(例如見[1]§2或[2]第Ⅲ章§2).從這一定理知道2n+1維的歐氏空間實際上已包括了所有想像得到的n維複合形,可是是否有不能在R~m中實現但能在R~(m+1)中實現的     

ON FINITE GROUPS OF ORDER $\[2_{pq}^3\]$

Zhang Yuanda has determined the groups of order $\[2_{{p^2}}^3\]$ (p is an odd prime$\[ \ne 3,7\]$). Now this paper is to determine the structures of groups of order $\[2_{pq}^3\]$(p,q are odd primes and p相似文献   

A SORT OF POLYNOMIAL IDENTITIES OF $\[{M_n}(F)\]$ WITH CHAR $\[F \ne 0\]$

Let $F$ denote a field, finite or infinite, with characteristic $\[p \ne 0\]$. In this paper, the author obtains the following result: The symmetric polynomial on $t$ letters $$\[{S_{sym(t)}}({x_1},{x_2}, \cdots ,{x_t}) = \sum\limits_{x \in sym(t)} {{X_{\pi 1}}{X_{\pi 2}} \cdots {X_{\pi t}}} \]$$ is a polynomial identity of $\[{M_n}(F)\]$ when $\[t \ge pn\]$, and this is sharp in the sense that if $\[t \le pn - 1\]$,it is not a polynomial identity of $\[{M_n}(F)\]$.     

SOME NONLINEAR EVOLUTION EUQATIONS WITH LAX PAIR OF $\[3 \times 3\]$ MATRICES

For some NEEs with Lax pairs of $\[3 \times 3\]$ matrices, the author presents the Backlund transformations(in Darboux form) and the corresponding Modified equations. The method deriving the Backlund transformations and the Modified equations can be considered as an extension and development of the mehtod in [1].     

Orlicz序列空间的（弱）正规结构和（LD）性质

本文讨论赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间ＬＭ，主要结果如下：（１）ＬＭ具有Ｌａｍｉ－Ｄｏｚｏ性质     

THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS FROM L^P （R^n） TO TRIEBEL-LIZORKIN SPACES

Let (→b)=(b1,…,bm),bi∈Λβi(Rn),1≤i≤m,0＜βi＜β,0＜β＜1,[(→b),T]f(x)=∫Rn,(b1(x)-b1(y))…(bm(x)-bm(y)))K(x-y)f(y)dy where K is a Calder(o)n-Zygmund kernel.In this paper,we show that[(→b),T] is bounded from Lp (Rn) to Fβ,∞p(Rn),as well as[(→b,Iα)] from Lp(Rn) to Fβ,∞p(Rn),where 1/q=1/p-α/n.     

Hardy空间上Fourier级数的Cesaro求和

研究了Hardy空间上Cesaro 算子的有界性.证明极大Cesaro算子的强型和弱型有界估计.其弱有界性估计是精确的.推广和加强了已有研究结果.     

SYNTOPOFORMIC SPACES (SYNTOPOGENOUS LIMIT SPACES)

Abstract

Császár generalized the uniform spaces, the proximity spaces and the topological spaces to syntopogenous spaces. Cook and Fischer generalized the uniform spaces to uniform limit spaces. Finally Marny generalized the proximity spaces to proximal limit spaces. Analogously we generalize the syntopogenous spaces to syntopoformic spaces (syntopogenous limit spaces). These spaces include all the above mentioned in a suitable sense. We extend some of the well-known results of compactness and completeness to syntopoformic spaces.     

SUPERCATEGORIES OF THE CATEGORY OF NEARNESS SPACES

Abstract

The framework in which nearness spaces were defined by H. Herrlich [1] and [2], leads one to consider the supercategory Pow of the category Near of nearness spaces, having as objects all pairs (X,ξ), where X is a set and ξ ? P(P(X)) is any subset of the power set of the power set of X, and as morphisms f: (X,ξ) → (Y,n) all functions f: X → Y such that, if A ? ξ then fA □ {f(A) | A ξ A} ? η. In this paper we show that the full subcategories of Pow comprising the objects satisfying subsets of the prenearness space axioms lie in a lattice of bireflections or bicoreflections. This serves as a first step towards the aim of characterizing all bireflective (resp. bicoreflective) and even all initially complete subcategories of Pow.     

Banach空间的渐近赋范性质与（S）性质

本文证明渐近赋范性质与（ｓ）性质具有对偶性，并且给出一个Ｂａｎａｃｈ空间为ＨａｈｎＢａｎａｃｈ光滑的充要条件。     

BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES

The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces.     

连通度量空间的映象

拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli 和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或FrEchet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math Soc.上提出的问题.     

Orlicz空间的局部U性质

给出Ｏｌｉｃｚ空间是局部Ｕ空间的充要条件。