随机截断数据非参数密度估计重对数律的充分和必要条件

本文利用一种直接的方法,无需通过经验过程的强逼近,建立了随机截断数据情形下,非参数密度估计重对数律的充分和必要条件,大大地改善了已有的相应的结果。     

随机截尾数据回归函数估计的重对数律

本文通过和W.Hardle处理完全数据情形时截然不同的方法,建立了随机截尾数据情形的回归函数估计的重对数律,作为本文特例(见定理3),大大地减少了文献[1]中主要结果的条件.     

带有不完全信息随机截尾试验下参数MLE的重对数律

在条件(Ψ)下,证明了带有不完全信息随机截尾试验中参数MLE的收敛速度符合重对数律,并且验证了指数分布、Weibull分布、对数正态分布满足条件(Ψ).     

B值独立随机元重对数律收敛速度的一般形式

本文讨论了Ｂ值独立同分布（ｉｉｄ）随机元重对数律收敛速度的一般形式,使得Ｄａｖｉｓ＾「１」及Ｇｕｔ＾「２,３」中的一些结果成为特款,同时减弱了Ｄａｖｉｓ结果中的矩条件,并且得到了Ｂ值ｉｉｄ随机元满足有界重对数律的一个充分性条件。作为应用,我们给出了随机足标和的相应结果。     

均值误差的随机加权逼近的重对数律──非独立同分布情况

讨论了独立不同分布情况下均值误差的分布估计问题,用随机加权法给出了精度为O(√lnlnn/n)的逼近分布.     

随机向量自正则和的重对数律

本文给出了独立随机向量序列自正则和的重对数律成立的一个充分条件.     

一维Wiener sausage长度的中偏差和重对数律

本文研究一维Wiener sausage.利用布朗运动的相关性质和收缩原理,得到p个Wiener sausage相交部分长度的中偏差和重对数律.     

有Edgeworth展式的分布的随机加权逼近的重对数律

本文研究了未知分布的逼近问题，利用随机加权法，给出了有Edgeworth展式的一类（未知）分布的模拟分布，证明了在一定条件下，模拟分布与未知分布的逼近精度达到O(n^-1√lnlnn），称之为随机加权逼近的重对数律。     

随机环境中可逗留随机游动的强极限边界

假定{(αi,βi),αi,βi∈(0,1),i∈Z}是一列i.i.d.的随机变量,γi=1-αi-βi,称{(αi,γi,βi),i∈Z}为随机环境.在这个环境上定义一个随机游动{Xk}(称为随机环境中可逗留随机游动):当在x状态时,它以概率αx向右游走一步,以概率βx向左游走一步,或者以概率γx逗留.本文获得了该过程能够游走的最大值的强极限边界.     

平稳随机场周期图的重对数律收敛性

对由二维平稳鞅差白噪声随机场构造的运动平均随机场，本文证明加权周期图的重对数律收敛性．     

A note on the disconnection number

We present a simple way to obtain all graphs with a given disconnection number if we know all the graphs with smaller disconnection number. Using this method we answer a question of Sam B. Nadler, i.e. we prove that there exist precisely 26 continua with disconnection number four. Some known results concerning disconnection number are also obtained as simple corollaries. Further we give some estimates on the number of distinct continua with a fixed disconnection number which concerns a problem of Sam B. Nadler.     

Odd connection and odd vertex-connection of graphs

In the last years, connection concepts such as rainbow connection and proper connection appeared in graph theory and received a lot of attention. In this paper, we present a general concept of connection in graphs. As a particular case, we introduce the odd connection number and the odd vertex-connection number of a graph. Furthermore, we compute and study the odd connection number and the odd vertex-connection number of graphs of various graph classes.     

An involution on increasing trees

We introduce a method to construct bijections on increasing trees. Using this method, we construct an involution on increasing trees, from which we obtain the equidistribution of the statistics ‘number of odd vertices’ and ‘number of even vertices at odd levels’. As an application, we deduce that the expected value of the number of even vertices is twice the expected value of the number of odd vertices in a random recursive tree of given size.     

合数是绝对假素数的充要条件

利用正整数模的特征数这一新概念给出了合数是绝对假素数的充要条件。以此为据，证明了绝对假素数是奇数，它无异于1的平方因数，并且至少是三个互异的奇素数的乘积；还给出了两个绝对假素数或两个大于1的奇数的乘积是绝对假素数的充要条件。     

与自反的n-color有序分拆相关的一些恒等式

首先,给出了偶数2v的自反的n-color有序分拆与v+1,v-1的n-color有序分拆之间的一个组合双射,并利用相应的计数公式得到了一个组合恒等式.其次,给出了正整数自反的n-color有序分拆数与Fibonacci数、Lucas数之间的一个关系式,并利用此关系式给出了偶数与奇数的自反的n-color有序分拆之间的一个组合双射.最后,给出了一些涉及正整数v的自反的n-color有序分拆数与其它有约束条件的有序分拆数之间的分拆恒等式.     

Combinatorial Aspects of Flashcard Games

We study a family of discrete dynamical processes introduced by Novikoff, Kleinberg, and Strogatz that we call flashcard games. We prove a number of results on the evolution of these games, and in particular, we settle a conjecture of NKS on the frequency with which a given card appears. We introduce a number of generalizations and variations that we believe are of interest, and we provide a large number of open questions and problems.     

Maillet determinants for real abelian number fields and its applications

In this paper, we define an analogue of the Maillet determinant in terms of Clausen function in [6], and we give a class number formula for a real abelian number field. We also give two applications of this class number formula.     

推广的奇轮的圆色数

图G的圆色数(又称"星色数")xc(G)是Vince在1988年提出的,它是图的色数 的自然推广.本文由奇轮出发构造了一族平面图,并证明了此类图的圆色数恰恰介于2和 3之间,填补了该领域的空白.     

关于自然数密度问题的思考

通过对首位数问题的研究,借鉴数论方法中的密率论,引入了自然数集合的统计密度的概念,将它进行了合理推广,并力图用初等微积分知识系统地建立了解决这一类问题的自然数集合对数密度理论.     

The shifted Turán sieve method on tournaments II

In a previous work [5], we developed the shifted Turán sieve method on a bipartite graph and applied it to problems on cycles in tournaments. More precisely, we obtained upper bounds for the number of tournaments which contain a small number of r-cycles. In this paper, we improve our sieve inequality and apply it to obtain an upper bound for the number of bipartite tournaments which contain a number of 2r-cycles far from the average. We also provide the exact bound for the number of tournaments which contain few 3-cycles, using other combinatorial arguments.