图中含有D—闭迹的一个充分条件

设Ｇ是一个简单图，Ｌ＝ｕ１ｕ２…ｕｔ是Ｇ中的一个路，定义Ｌ的度ｄ（Ｌ）＝∑ｔｉ＝１ｄ（ｕｉ），其中ｄ（ｕｉ）为ｕｉ在Ｇ中的度数．本文证明了：若Ｇ是ｎ≥３阶几乎无桥的简单连通图，ＧＫ１，ｎ－１，且对Ｇ中任何两个无公共点的二长路Ｌ１，Ｌ２，有ｄ（Ｌ１）＋ｄ（Ｌ２）≥２ｎ－１，则Ｇ有一个Ｄ－闭迹，从而Ｇ的线图Ｌ（Ｇ）是Ｈａｍｉｌｔｏｎ图．     

2-连通图的Hamilton圈的一个充分条件

本文给出了２－连通图有Ｈａｍｉｌｔｏｎ圈的又一个充分条件．定理设Ｇ为有ｎ（ｎ＞３）个顶点的２－连通图，如果对Ｇ中任意两个顶点ｕ、ｖ，当ｄ（ｕ，ｖ）＝２时，都有ｍａｘ（ｄ（ｕ），ｄ（ｖ））≥ｎ／２，则Ｇ有Ｈａｍｉｌｔｏｎ圈．证用反证法．假设Ｇ没有Ｈａｍ...     

Cayley图的边Hamilton性

设Ｘ是有限群Ｇ的一个生成集．Ｃａｙ（Ｘ：Ｇ）表示生成集为Ｘ的Ｇ上的Ｃａｒｌｅｙ图，其顶点集为Ｇ，其边集为所有无序对［ａ，ｂ］组成的集合，其中ａ，ｂ∈Ｇ，ａ－１ｂ∈Ｘ∪Ｘ－１（Ｘ－１＝｛ｘ－１｜ｘ∈Ｘ｝）．若图的每条边都在的Ｈａｍｉｌｔｏｎ圈上，则称图是边－Ｈａｍｉｌｔｏｎ图．本文证明了：当Ｇ为ｐ－群或Ｈａｍｉｌｔｏｎ群时，若Ｘ含有Ｇ的中心元，则Ｃａｙ（Ｘ：Ｇ）是边－Ｈａｍｉｌｔｏｎ图．     

鞅差几何级数的重对数律

设｛Ｘｋ，Ｆｋ，ｋ≥０｝是（Ω，Ｆ，Ｐ）上的鞅差序列，在本文中我们讨论了以｛Ｘｋ｝为系数的幂级数Ｓ（β＝Σ∞ｋ＝０βｋＸｋ，当β↑１时的渐近行为，本文证明了：如果│Ｘｋ│≤ｃ，Ｅ（Ｘ＾２ｋ│Ｆｋ－１）＝１，则有下面的重对数律成立ｌｉｍβ↑１√１－β＾２／√２ｌｏｇｌｏｇ（１－β＾２）－１Ｓ（β）＝１ａ．ｓ。     

一类离散型奇异积分算子

设｛αｋ｝∞ｋ＝－∞为正数缺项序列，满足ｉｎｆｋαｋ＋１／ｄｋ＝α＞１，Ω（ｙ′）为Ｂｅｓｏｖ空间Ｂ０，１１（Ｓｎ－１）上的函数，其中Ｓｎ－１为Ｒｎ（ｎ２）上的单位球面．本文证明：若∫Ｓｎ－１Ω（ｙ′）ｄσ（ｙ′）＝０，则离散型奇异积分ＴΩ（ｆ）（ｘ）＝∑∞ｋ＝－∞∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）和相关的极大算子ＴΩ（ｆ）（ｘ）＝ｓｕｐＮ∑∞ｋ＝Ｎ∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）均在Ｌ２（Ｒｎ）上有界．上述结果推广了Ｄｕｏａｎｄｉｋｏｅｔｘｅａ和ＲｕｂｉｏｄｅＦｒａｎｃｉａ［１］在Ｌ２情形下的一个结果     

子集的交叉t－相交定理

设Ｘ为一个ｎ元集合，Ｃｎｋ为Ｘ的所有ｋ元子集全体，若Ａ∈Ａ，Ｂ∈Ｂ有｜Ａ∩Ｂ｜≥ｔ，则称（Ａ，Ｂ）为一个交叉ｔ－相交子集族．本文得到最大交叉ｔ－相交子集族和最大非空交叉２－相交子集族．证明如下两个结论．（１）若（Ａ，Ｂ）为一个交叉ｔ－相交子集族，且ａ≤ｂ及ａ＋ｂ≤ｎ＋ｔ－１，则｜Ａ＋Ｂ｜≤ｍａｘ｛（ｂｎ），（ａｎ）｝，且当（Ａ；Ｂ）＝（φ，Ｃｎｂ）或（Ｃｎａ，φ）时达到上界．（２）若（Ａ，Ｂ）为一个交叉２－相交子集族，且ａ＜ｂ，ａ＋ｂ≤ｎ－１及（ｎ，ａ，ｂ）≠（２ｉ，ｉ－１，ｉ）（ｉ为任意正整数），又Ａ，Ｂ均非空，则｜Ａ＋Ｂ｜≤１＋（ｂｎ）－（ｂ（ｎ－ａ））－ａ（（ｂ－１）（ｎ－ａ））且当（Ａ，Ｂ）＝（｛Ａ｝，Ｃｎｂ－｛Ｂ｜｜Ｂ｜＝ｂ，｜Ａ∩Ｂ｜≤１｝）时达到上界．     

大次和1—坚韧图中的最长圈

给一个图Ｇ，定义σ３（Ｇ）＝ｍｉｎ｛Σ＾３ｉ＝１ｄ（ｖｉ）│｛ｖ１，ｖ２，ｖ３｝｝是Ｇ的无关集｝，ｐ３（Ｇ）＝ｍｉｎ｛│Ｕ＾３ｉ＝１Ｎ（ｖｉ）‖｛ｖ１，ｖ２，ｖ３｝是Ｇ中使│ｎ＾３ｉ＝１Ｎ（ｖｉ）│≠０｝的无关集｝。本文证明了：设Ｇ是ｎ阶１－坚韧图，如果σ３（Ｇ）≥ｎ，则Ｇ包含长度至少为ｍｉｎ｛ｎ，２ｐ３（Ｇ）＋４｝的圈，为个结果推广了若干已知结果，也解决了Ｂｒｏｅｒｓｍａ－Ｈｅｕｖｅｌ－Ｖｅｌｄ     

2-阶邻域连通无爪图的Hamilton性

设Ｇ是无爪图．对ｘ∈Ｖ（Ｇ），若Ｇ［Ｎ（ｘ）］不连通，则存在ｙｉ∈Ｖ（Ｇ）－｛ｘ｝（ｉ－１，２），使｜Ｎ（ｙｉ）∩Ｋｉ（ｘ）｜≥２，且｜Ｎ（ｙｉ）∩Ｎ（Ｋｉ＋１（ｘ））｛ｘ｝｜≥２（ｉ模２），那么称无爪图Ｇ是强２－阶邻域连通的，其中Ｋ１（ｘ），Ｋ２（ｘ）分别表示Ｇ［Ｎ（ｘ）］的两个分支．本文证明了：连通且强２－阶邻域连通的无爪图是Ｈａｍｉｌｔｏｎ图．     

非退化扩散过程的极性的必要性

设Ｘ（ｔ）是一Ｎ维非退化扩散过程．设 Ｅ（０，∞）和 Ｆ ＲＮ都为紧集．本文给出了：Ｐ（Ｘ－１（Ｆ）∩Ｅ≠φ）＞０，Ｐ（Ｘ－１（Ｆ）≠φ）＞０和Ｐ（Ｘ（Ｅ）≠φ）＞０的充分条件．证明了：ｉ）设 Ｎ≥ ３，ａ）若 ｄｉｍ（Ｆ）＜Ｎ－２，则 Ｐ（Ｘ－１（Ｆ）＝φ）＝１； ｂ）若ｄｉｍ（Ｆ）＞Ｎ－２，则 Ｐ（Ｘ－１（Ｆ）≠φ）＞０； ｃ）存在 Ｆ１ ＲＮ，Ｆ２ ＲＮ，ｄｉｍ（Ｆ１）＝ｄｉｍ（Ｆ２）＝Ｎ－２，但有Ｐ（Ｘ－１（Ｆ１）＝φ）＝１，Ｐ（Ｘ－１（Ｆ２）≠φ）＞０．ｉｉ）设Ｎ＝１，ａ）若ｄｉｍ（Ｅ）＞１／２，则ｘ∈Ｒ１，Ｐ（Ｘ－１（ｘ）∩Ｅ≠φ）＞０；ｂ）存在Ｅ（０，∞），ｄｉｍ（Ｅ）＝１／２，使得ｘ∈Ｒ１，Ｐ（Ｘ－１（ｘ）∩Ｅ≠φ）＞０．以上这些结果，不仅仅是Ｂｒｏｗｎ运动的推广，即使就Ｂｒｏｗｎ运动的情形而言，其中有些结果也是新的．     

Hamiltonian图的泛圈性的一个充分条件

设Ｇ是一个ｎ阶图,若对于每一个ｋ（３≤ｋ≤ｎ）,Ｇ都含有长度为ｋ的圈,则称Ｇ为泛圈图． 在［１］中, Ｒ．Ｊ, Ｆａｕｄｒｅｅ等证明了如下结果： 定理Ａ设Ｇ是一个ｎ－阶２－连通图,δ（Ｇ）≥ｔ．若对于Ｇ中任意两个不相邻的点ｕ和ｖ,均有 ｜Ｎ（ｕ） ∪ Ｎ（ｖ）｜≥ｎ－ｔ,则 Ｇ是 Ｈａｍｉｌｔｏｎｉａｎ图． 根据 Ｂｏｎｄｙ在［４］中的想法：几乎任何一个 Ｈａｍｉｌｔｏｎｉａｎ图的非平凡的充分条件都可能蕴含着图的泛圈性质,自然有如下猜测：设图Ｇ满足定理Ａ的条件,则Ｇ是泛圈圈或者 ｎ＝２ｔ; Ｇ≌Ｋ_（ｔ,ｔ）…     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.