有限子集系的Sperner系

1９８０年，Ｋｏ-Ｗｅｉ Ｌｉｈ提出如下猜想：如果Ｆ是由Ｂ^ｎ中固定秩的不同元素生成的序理想，那么Ｆ是Ｓｐｅｒｎｅｒ系．本文证实了当Ｆ是由Ｘ的子集Ｙ的所有相同秩的元素生成的序理想，猜想是正确的     

有限子集系的Spernet系

１９８０年，Ｋｏ－Ｗｅｉ Ｌｉｈ提出如下猜想：如果Ｆ是由Ｂ＾ｎ中固定秩的不同元素生成的序理想，那么Ｆ是Ｓｐｅｒｎｅｔ系。本文证实了当Ｆ是由Ｘ的子集Ｙ的所有相同秩的元素生成的序理想，猜想是正确的。     

重分形Hausdorff测度的有限测度子集

设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度,ｑ,ｔ∈Ｒ,记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度,证明了当μ为测度时,Ｈ_μ^q,t的有限测度子集存在．     

一个子集树研究问题的解

In this paper, we solve a research problem on trees of subsets posed by F.R. McMorris. If a collection of subsets are chosen at random from the power set of a finite set X,we give the probability that the collection is a tree of subsets of X.     

有限型子集的Hausdorff测度

给出了有限型子集的Hausdorff测度的一个估计,改进了已有的结果。     

有限型子集的Hausdorff测度

给出有限型子集的Hausdorff测度的一个估计并在某些条件下给出计算公式。     

有限集合的子集族问题分类解析

将有限集合中符合某一特性的所有子集合，称之为有限集合的子集族．在各类集合问题中，与子集族相关的问题是其中极为重要的一类．这类问题题型新颖，解答灵活，给同学们的学习造成了一定的困难．本文拟对这类问题分类进行解析．     

R的紧致子集的一个刻画

借助离散子集和相对离散子集的概念,可给出R的紧致子集的一个刻画,证明了R的子集E是紧致子集当且仅当E的每一相对离散子集是有限手集。     

非线性Kelvin—Helmholtz波方程在有限维子集上的约化

本文发现无穷维可积的Kelvin-Helmholtz波方程可约化为某有限维子集(?)_1上的Hamiltonian系统,且在(?)_1上它的Lax对是自然相容的;在(?)_1上,其Lax对的空间和时间部分的解是一致的.     

Maximum Antichains in Random Subsets of a Finite Set

We consider the random poset (n, p) which is generated by first selecting each subset of [n]={1, …, n} with probability p and then ordering the selected subsets by inclusion. We give asymptotic estimates of the size of the maximum antichain for arbitrary p=p(n). In particular, we prove that if pn/log n→∞, an analogue of Sperner's theorem holds: almost surely the maximum antichain is (to first order) no larger than the antichain which is obtained by selecting all elements of (n, p) with cardinality n/2. This is almost surely not the case if pn=∞.     

Groups Saturated by a Finite Set of Groups

We study the periodic groups that are saturated by a finite set of finite (nonabelian simple) groups, obtaining some information about the elements of the saturating set.     

Sublattices of Lattices of Convex Subsets of Vector Spaces

Let Co(V) be a lattice of convex subsets of a vector space V over a totally ordered division ring . We state that every lattice L can be embedded into Co(V), for some space V over . Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional; in this case L also embeds into a finite lower bounded lattice of the form Co(V,)={X | X Co(V)}, for some finite subset of V. This result yields, in particular, a new universal class of finite lower bounded lattices.     

共球有限点集的k号心及其性质

在n维欧氏空间中,建立了n维共球有限点集的k号心概念,并据此导出了一串有关的平行线、共线点、共点线及共球点定理.     

Rado Partition Theorem for Random Subsets of Integers

For an l x k matrix A = (a_ij) of integers, denote by L(A) thesystem of homogenous linear equations a_i1x₁ + ... + a_ikx_k =0, 1 i l. We say that A is density regular if every subsetof N with positive density, contains a solution to L(A). Fora density regular l x k matrix A, an integer r and a set ofintegers F, we write if for any partition F = F₁ ... F_r there exists i {1, 2,..., r} and a column vector x such that Ax = 0 and all entriesof x belong to F_i. Let [n]_N be a random N-element subset of{1, 2, ..., n} chosen uniformly from among all such subsets.In this paper we determine for every density regular matrixA a parameter = (A) such that lim_n P([n]_N (A)_r)=0 if N =O(n) and 1 if N = (n). 1991 Mathematics Subject Classification:05D10, 11B25, 60C05     

Uniform Continuity of a Family of Weakly Regular Set Functions on Topological Spaces

Conditions for the uniform continuity of a family of weakly regular set functions defined on an algebra of subsets of a -topological space (T,) and taking values in an arbitrary topological space are found.     

凸距离空间内星形子集非扩张型映射不动点*

在本文中.我们给出包含一个集合的某种星形集的刻划及其性质.然后利用这些刻划和性质讨论凸距离空间的星形子集上非扩张型映射的不动点的存在问题,推广了丁协平、Beg和Azam的某些最近结果.最后还给出一个例子说明以上推广是本质上的推广.     

Berry–Esseen Bound for a Sample Sum from a Finite Set of Independent Random Variables

Let {X ₁,...,X _N} be a set of N independent random variables, and let S _n be a sum of n random variables chosen without replacement from the set {X ₁,...,X _N} with equal probabilities. In this paper we give an estimate of the remainder term for the normal approximation of S _n under mild conditions.