n—反Abelian子群

从n-反换位子群的定义出发,得到了它的几条重要性质.作为应用,给出了一个群为n-反A belian群的一个充要条件及p-反A belian群的一个判别法.     

Minimal Non—Commutative n—Insertive Rings

Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n ⁴ elements and these rings have five (2p+4) isomorphic classes for p = 2 (p ≠ 2). This research is supported by the National Natural Science Foundation of China, and the Scientific Research Foundation for “Bai-Qian-Wan” Project, Fujian Province of China     

关于n—可解群与n—幂零群的两个结果

本文证明了下面主要结果：设Ｇ是ｎ－可解群，π是一些素数之集，若对任意ｐ∈∩π（Ｇ），（ｐ，ｎ（１－ｎ））＝１，则Ｇ的π－Ｈａｌｌ子群的个数ｒ＝ｋ１ｋ２．．．ｋｔ，每ｋｉ≡１（ｍｏｄｐ），某Ｐ∈π，且每ｋｉ整除Ｇ的一个主因子。     

On 2n—th—Order Eigenvalue Problem

In [1], Lu discussed the existence of positive solution for the BVPwhere f: [0, 1] × [0, ∞) → R is continuous and satisfies the following conditions(H1) There exists an M > 0 such that(H2) limx→∞ f(t, x)/x =∞uniformly for t [α,β] (0, 1) for some α < β and λ > 0 is a parameter.In this paper, the result of [1] is generalized to the following 2n-th-order BVPThe result of this paper isTheorem 1 Assume (H1) and (H2) hold. Then the BVP (3)-(4) has a positive solutionifλ > 0 is sm…     

关于S（n）—θ—闭空间

Ｄｉｋｒａｎｊａｎ与Ｇｉｕｌｉ引入了θ＾ｎ－闭包算子，定义了Ｓ（ｎ），Ｓ（ｎ）－闭和Ｓ（ｎ）－θ－闭空间，建立了Ｓ（ｎ）－θ－闭空间理论，并提出了６个公开问题，本文将从Ｓ（ｎ）－θ－空间的极小性和乘积性来介绍Ｓ（ｎ）－θ－闭空间理论的最新进展，文中的三个拓扑反例否定回答了Ｄｉｋｒａｎｊａｎ与Ｇｉｕｌｉ提出的４个公开问题。     

首达渗流中关于lin n→∞ Non—n的一个结果

在二维首达渗流中,设边上通过时间的分布为F(x),首达时aon的轨道(route)的最短长度为Non,人们猜测lim n→∞ Non/n 存在.本文对F(0)＜1/2的情形,就一类特殊的分布证明此猜想成立.     

(B n * GnSn) — Geometrien

A consequence of BENZ [3], [4] and ARTZY [2] is that the class of all (B ₂ ^* S₂)-geometries coinzides with the class of the chain geometries (K,K×K), K a commutative field. Therefore the tangency theorem holds in every (B ₂ ^* S₂)-geometry.In this paper we present a corresponding tangency theorem for (B ₃ ^* G₃S₃)-geometries and prove that up to isomorphisms the (B _n ^* G_nS_n)-geometries, n>1, are exactly the chain geometries (K,Kⁿ).     

Calderón——Zygmund 型算子及其交换子的有界性

本文得到了Calderón--Zygmund型算子及其与BMO函数或Lipschitz函数生成的交换子在Herz 型 Hardy空间上的一些有界性结果.     

Reduction of Volume—preserving Flows on an n—dimensional Manifold

A geometric reduction procedure for volume-preserving flows with a volume-preserving symme-try on an n-dimensional manifold is obtained.Instead of the coordinate-dependent theory and the concrete coordinate transformation,we xhow that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space.More generally,if it admits an r-parameter volume-preserving commutable symmetry,then the reduced folw preserves the corresponding (n-r)-dimensional volume form.     

n—Gorenstein环上的Gorenstein内射模

用Gorenstein内射刻画了n-Gorenstein环。     

从(n 1)/n×(n 1)=(n 1)/n (n 1)谈起

一问题的提出本刊2003年第5期刊载了《运用发现法解题》(以下简称《解题》)一文,文章在谈到“归纳发现法”时,提到这样一个例子: 1.观察下列各式     

Sur des notions de n—categorie et n—groupoide non strictes via des ensembles multi-simpliciaux (On the notions of a nonstrict n–category and n–groupoid via multisimplicial sets)

In this paper we first give a simplicial approach to the definition of a nonstrict n–category that we call a n–nerve following the idea that a category could be interpreted as a simplicial set (its nerve). Then we prove that for n=2 our construction is equivalent to the usual nonstrict 2–category (bicategory). Next,we give a simplicial definition of a nonstrict n–groupoïd, and we associate to any topological space a n–groupoïd n (X) which generalises the famous Poincaré groupoïd 1 (X) and embodies the n–truncated homotopy type of . Conversely, we construct for each n–groupoïd a geometric realisation and we show that the functors geometric realisation and Poincaré n–groupoïd induce an equivalence between the category of n–groupoids and the category of n–truncated topological spaces, when we localise both categories by weak equivalence.     

（m,n）—人主从对策的SP—解

1.引言 本世纪70年代初期,Chen C.I.,Simann M.和Cruz J.B.,Jr,首次把Stackelberg策略概念,引入到对策中来,建立了二人主从对策模型。由于这类对策有广泛的实际背景,因此,主从对策便成为80年代对策论中的一个热门方向。我们在[5]和[6]中提出了有多个“主人”和多个“从人”的(m,n)-人主从对策,并给出了SN-解,S∑-解和SQ-解的概念及其存在条件。     

The Median Formula and Related Inequalities in n—simplex

5l.TheMedianFormulaAseveryoneknows:in6ABC,letal=BC,a2=CA,a3=AB,;)11,)n2,n13aremedian1inesseparatelyonthethreeedgesBC,CA,AB,tI1entheequalityistrueasfollowsTheequality(l)iscalledmedianformulaofQABC,andwecanobtainfrom(l)Inthispaper,wesha1lextendtheequality(l)and(2)to,l-simplexin)l-EuclideanspaceH.Itisobtainedthemedianformulaof)I-simplex,andusingthisformula.wegetsomein-equalities.Themedianformulaofn-simp1exisobtainedasfollows:TheoremlFork=1,2,--',It 1andl相似文献   

On Ramsey—Turán type theorems for hypergraphs

LetH ^r be anr-uniform hypergraph. Letg=g(n;H ^r ) be the minimal integer so that anyr-uniform hypergraph onn vertices and more thang edges contains a subgraph isomorphic toH ^r . Lete =f(n;H ^r ,εn) denote the minimal integer such that everyr-uniform hypergraph onn vertices with more thane edges and with no independent set ofεn vertices contains a subgraph isomorphic toH ^r . We show that ifr>2 andH ^r is e.g. a complete graph then $$\mathop {\lim }\limits_{\varepsilon \to 0} \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} f(n;H^r ,\varepsilon n) = \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} g(n;H^r )$$ while for someH ^r with \(\mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} g(n;H^r ) \ne 0\) $$\mathop {\lim }\limits_{\varepsilon \to 0} \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} f(n;H^r ,\varepsilon n) = 0$$ . This is in strong contrast with the situation in caser=2. Some other theorems and many unsolved problems are stated.