极限圆型Hamilton算子乘积的自伴性

本文讨论了极限圆型Hamilton算子乘积的自伴性,利用Calkin方法及奇异Hamilton系统自伴扩张的一般构造理论,给出了在极限圆型时判定Hamilton算子乘积自伴的一个充要条件.     

零膨胀集群数据层次回归模型的贝叶斯推断

零膨胀Poisson回归模型是研究零观测值过多的计数数据的常用工具,本文提出了一类拟合具有这类特征的集群数据的层次零膨胀泊松回归模型,并给出了相应的贝叶斯推断方法,参数估计通过Gibbs抽样获得,模型比较与选择则通过拟合优度检验与BIC准则实现.最后,利用一个船舶受损事故数据来展示本文方法的实现及应用.     

C1 Solutions of the Iterative Equation G(x, f(x), ..., fn(x)) =F(x)

In this paper we consider the iterative equation G(x,f(x),...,f n(x)) = F(x) on R,and give the existence of C 1 solutions near the fixed point of F,which generalize some results on the leading coefficient problem from the form of the polynomial-like iterative equations to the general form.     

A Note on the Estimation of Semiparametric Two-Sample Density Ratio Models

In this paper,a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation.A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function.Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution.So we can obtain the maximum empirical likelihood estimation (MELE) of parameters.Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm.     

On Products of Property b1

In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.     

A Brief Introduction to Fibrewise Topological Spaces Theory

Fibrewise topological spaces theory,presented in the recent 20 years,is a new branch of mathematics developed on the basis of General Topology,Algebra topology and Fibrewise spaces theory.It is associated with differential geometry,Lie groups and dynamical systems theory.From the perspective of Category theory,it is in the higher category of general topological space,so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance.This paper introduces the process of the origin and development of Fibrewise topological spaces theory.Then,we study the main contents and important results in this branch.Finally,we review the research status of Fibrewise topological spaces theory and some important topics.     

圆台和圆锥的一组性质

本文介绍用圆台侧面积和底面积来表示圆台的母线、高、底面与母线所成的角、体积的一种方法,供读者参考.定理若圆台的侧面积为S1,较大底面积S2,较小底面为S3,圆台母线成较大底面所成的角为θ,高为h,母线为l,体积为V,则     

用向量法证明平面几何问题

向量的线性运算和数量积运算都具有鲜明的几何背景,平面几何图形的许多性质都可以由向量的线性运算及数量积表示出来,因此,用向量法解决平面几何问题,不仅是一种全新的解题思路,对一些比较复杂的线段比例问题用向量法求解还是一种有效的捷径.下面是用向量法证平面几何题的几种常见类型,供同学们学习过程中参考.     

Approximation of integrable functions by general linear operators of their fourier series

The pointwise estimates of the deviation T n,A,B f (·) f (·) in terms of moduli of continuity .f and w.f there are proved. Analogical results on norm approximation with remarks and corollaries are also given. In the results there are used the essentially weaker conditions than these in [Mittal, M. L.: J. Math. Anal. Appl., 220, 434-450 (1998) Theorem 1, p. 437].