The maximum and minimum degrees of random bipartite multigraphs

In this paper the authors generalize the classic random bipartite graph model, and define a model of the random bipartite multigraphs as follows:let m = m（n） be a positive integer-valued function on n and ζ（n,m;{pk}） the probability space consisting of all the labeled bipartite multigraphs with two vertex sets A ={a₁,a₂,...,a_n} and B = {b₁,b₂,...,b_m}, in which the numbers t_ai,b_j of the edges between any two vertices a_i∈A and b_j∈ B are identically distributed independent random variables with distribution P{t_ai,b_j=k}=pk,k=0,1,2,...,where pk ≥0 and ∞Σk=0 pk=1. They obtain that X_c,d,A, the number of vertices in A with degree between c and d of G_n,m∈ζ（n, m;{pk}） has asymptotically Poisson distribution, and answer the following two questions about the space ζ（n,m;{pk}） with {pk} having geometric distribution, binomial distribution and Poisson distribution, respectively. Under which condition for {pk} can there be a function D（n） such that almost every random multigraph G_n,m∈ζ（n,m;{pk}） has maximum degree D（n）in A? under which condition for {pk} has almost every multigraph G（n,m）∈ζ（n,m;{pk}） a unique vertex of maximum degree in A?     

浅谈函数的周期性和对称性问题

周期性是函数的一个重要性质,是研究函数图象及性质的重要工具,尤其是一些问题中所隐含的周期性更成为解题的关键所在,而且成为近几年来各种测试的一个命题热点,特别是将函数     

最小二乘法、最小一乘法与方差、线性回归方程

1问题的提出高中数学新课标教材的统计部分(必修3与选修1-2或2-3)中涉及到方差定义与线性回归方程的确定.方差反映的是样本数据χi,i=1,2,3,     

有关拓扑学与覆盖粗糙集的一些结论

引入了拓扑覆盖的概念,并结合最小描述元对有限论域上的拓扑覆盖加于研究,得出了拓扑覆盖的最简覆盖和基与最小描述元之间的关系.介绍了在基于有限论域U上的覆盖,构造U上的一个拓扑的方法.并且在最小描述元的基础上将划分下的粗糙隶属函数推广至一般覆盖下的粗糙隶属函数,而后介绍了其相关运用.     

2010年全国高中数学联赛加试试题及参考答案

试题一、(本题满分40分)如图1,锐角三角形ABC的外心为O,K是边BC上一点(不是边Bf的中点),D是线段AK延长线上一点,直线BD与AC交于点N,直线CD与AB交于点M.求证:若OK⊥MN,则A,B,D,C四点共圆.     

一道德国数学奥赛试题的简解及思维过程

2008年德国数学奥林匹克有一题如下.题目求最小的常数c,使得对所有的实数x,y,有1+(x+y)2≤c(1+x2)(1+y2).     

Two new least-squares mixed finite element procedures for convection-dominated Sobolev equations

Two new least-squares mixed finite element procedures are formulated for solving convection-dominated Sobolev equations. Optimal H(div;Ω)×H ¹(Ω) norms error estimates are derived under the standard mixed finite spaces. Moreover, these two schemes provide the approximate solutions with first-order and second-order accuracy in time increment, respectively.     

极大代数上线性系统的3维最小实现的研究

研究了极大代数上线性系统的3维最小实现问题,给出了特征方程为λ<'3> c<,0>λ<'0>=c<,2>λ<'2> c<,1>λ,当c<,1>=c<'2><,2>,c<,0>=C<,1>C<,2>时,无穷序列{g<,2>}<,0><'∞>存在3维最小实现的充要条件.     

A method to quantitatively estimate rainfall rate above water surface based on different spectra shapes generated by rainfall

A method combined with the nonlinear least-square regression to quantitatively estimate rainfall rate over water surface from the different spectrum shapes generated by rainfall in some frequency bands was presented.About 2000 min spectrum data generated by rainfall have been collected in an open-lake in Xiamen city.As a result,the spectrum shape in 15-30 kHz is fitted to log-linear law which allows classification of rain into three categories from the spectrum slope:no rain,drizzle(rainfall rate>10 mm/h)and heavy rain(rainfall rate>10 mm/h).Then,rainfall detection is made and rainfall rate is quantified in drizzle time with Logistic model in the frequency bands of 2-15 kHz,and the rainfall rate in heavy rainfall also quantified with log-linear regression.Finally,all measured spectrum data are used to calculate rainfall rate with the algorithm.The results show that the estimated rainfall rates are comparably coincident with the synchronously measured ones.The average error of accumulative rainfall per min is only l%-4%.     

基于反馈和多最小二乘支持向量机的分数阶混沌系统控制

根据分数阶线性系统的稳定理论,将混沌系统分成稳定的线性部分和相应的非线性部分.设计主动控制器,对非线性部分进行补偿,从而将分数阶混沌系统控制到平衡点.为了提高主动控制器的补偿能力,提出基于反馈的多最小二乘支持向量机(M-LS-SVM)拟合模型.通过减聚类方法将输入空间划分为一些小的局部空间,在每个局部空间中用LS-SVM建立子模型.为解决子模型相互之间的严重相关问题,提高模型的精度和鲁棒性,各个子模型的预测输出通过主元递归(PCR)方法连接.仿真实验表明该方法有助于提高补偿精度和系统响应指标. 关键词： 分数阶 混沌系统 多最小二乘支持向量机 反馈