关于微分方程解的一致非常稳定性与一致距离有界性

讨论了一般非自治方程解的一致非常稳定性与一致距离有界性.     

基于Pena距离的加权最小二乘估计的影响分析

利用Pena距离对加权线性最小二乘估计的影响问题进行讨论,得到加权最小二乘估计的Pena距离的表达式,对其性质进行讨论,从而得到高杠异常点的判别方法.文中对Pena距离与Cook距离的性能进行了对比,得到在一定条件下Pena距离优于Cook距离的结论.并通过数值实验对此方法的有效性进行验证.     

ERM learning with unbounded sampling

The learning approach of empirical risk minimization (ERM) is taken for the regression problem in the least square framework. A standard assumption for the error analysis in the literature is the uniform boundedness of the output sampling process. In this paper we abandon this boundedness assumption and conduct error analysis for the ERM learning algorithm with unbounded sampling processes satisfying an increment condition for the moments of the output. The key novelty of our analysis is a covering number argument for estimating the sample error.     

On second order degree of graphs

Given a vertex v of a graph G the second order degree of v denoted as d 2(v) is defined as the number of vertices at distance 2 from v.In this paper we address the following question:What are the sufficient conditions for a graph to have a vertex v such that d2(v) ≥ d(v),where d(v) denotes the degree of v? Among other results,every graph of minimum degree exactly 2,except four graphs,is shown to have a vertex of second order degree as large as its own degree.Moreover,every K-4-free graph or every maximal planar graph is shown to have a vertex v such that d2(v) ≥ d(v).Other sufficient conditions on graphs for guaranteeing this property are also proved.     

一道高三模拟题的探究与推广

题目(江苏省南京市、盐城市2012届高三年级第一次模拟考试填空题第13题)设椭圆C:x2a2+y2b2=1(a>b>0)恒过定点A(1,2),则椭圆的中心到准线的距离的最小值是.解由x2a2+y2b2=1恒过定点A(1,2),得1a2+     

一道竞赛题的简解

题目（2006年全国初中数学竞赛（浙江赛区）初赛试题第13题）如图,正方形ABCD和正方形CGEF的边长分别是2和3,且点B,C,G在同一直线上,M是线段AE的中点,连结MF,则MF的长为.解析（坐标法）以BG所在直线为x轴,以BA所在直线为y轴,建立直角坐标系.则A（0,2）,F（2,3）,E（5,3）,AE中点M{...     

Outlier Mining Based on Principal Component Estimation

Outlier mining is an important aspect in data mining and the outlier mining based on Cook distance is most commonly used. But we know that when the data have multicoUinearity, the traditional Cook method is no longer effective. Considering the excellence of the principal component estimation, we use it to substitute the least squares estimation, and then give the Cook distance measurement based on principal component estimation, which can be used in outlier mining. At the same time, we have done some research on related theories and application problems.     

相似理论在深孔梯段爆破飞石距离计算中的应用

利用相似理论 ,推导了深孔梯段爆破中飞石距离的计算公式。结合三峡工程实际统计数据的回归分析导出了公式的具体表达式 ,讨论了公式的应用条件和进一步完善的研究思路。     

新的模糊数的模糊距离

文[1]中基于现有的模糊数的距离定义及模糊距离定义的缺陷进行分析并给出了改进的模糊数的距离定义。本文在此基础上给出新的模糊数的模糊距离定义,并给出相应的定理。     

一类拟线性抛物方程的吸引子及其均匀化

本文讨论了δtuε-divA(x/ε，↓Δuε)-kuε=f的整体吸引子A^ε与其均匀化后的方程δtu-divA(↓Δu)-ku=f的整体吸引子A^0之间的关系，并给出了A^ε与A^0之间距离的估计。