苯并寡聚乙二氧链螺旋体的合成

以对甲氧基苯酚、对苄氧基苯酚、对苯二酚和四乙二醇二磺酸酯这些简单化合物为原料,通过磺酸酯与酚的亲核取代反应及苄基保护、钯碳氢化去保护策略制备得到了4种新颖的苯并寡聚乙二氧链螺旋体化合物.     

空气中PM2.5的动态扩散及宏观预测

以PM2.5扩散、衰减模式为研究对象,分析探究了PM2.5的扩散规律、危机治理及其后5年的治理问题.首先通过主成分分析法,建立了PM2.5与其它污染物之间的多元非线性对数模型.同时引入相对湿度的影响因素对模型进行再度优化,提高了模型的拟合优度.运用统计学原理,得出采集点之间的PM2.5具有较高的协同性.另外分析了静态下PM2.5污染物颗粒的受力和漂移模式和从点源、面源两方面分析了PM2.5动态扩散模式,建立了PM2.5的扩散偏微分方程模型.根据建立的扩散模型,对突变的污染物浓度确定安全区域的范围.最后建立综合费用和专项费用的多目标优化模型,利用贝叶斯支持向量机方法对PM2.5进行宏观预测,并运用系统动力学理论对目标值进一步优化,并对不同治理模式进行对比分析.     

几何凸（凹）函数积分的上（下）界比较及其一般结果

运用齐次函数的分析性质,在基本不等式中插入了一个齐次加权＂平均＂,推广加细了基本不等式.作为特例,得到了加权的对数,指数平均不等式,从而部分解决了文[1]提出的问题.     

Properties of the weighted logarithmic matrix norms

Mingzhu Liu Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China Email: ghu{at}hit.edu.cn, ghuca{at}yahoo.ca Email: mzliu{at}hit.edu.cn Received on January 31, 2006; Accepted on December 9, 2006 In this paper, we are concerned with the properties of the weightedlogarithmic matrix norms. A relation between the elliptic logarithmicmatrix norm and the weighted logarithmic matrix norm is given.Based on Lyapunov equations, two weighted logarithmic matrixnorms are constructed which are less than 1-logarithmic matrixnorm and -logarithmic matrix norm, respectively. Then, an iterativescheme is presented to obtain the logarithmically -efficientmatrix norm. Numerical examples are given to illustrate theresults.     

Large deviations viewpoints for a heavy-tailed β-mixing sequence

Let {Xn; n ≥ 1} be a stationary sequenceof non-negative random variables with heavy tails. Under mixing conditions, we study logarithmic asymptotics for the disp(Sn ＞ nx) ≈ n-αx+1 for appropriate values of x, where α is a specific parameter. The related conjecture proposed by Gantert is investigated. As a by-product, the so-called supremum large deviations principle is also studied.     

含结构零2×2表中风险比齐性检验的样本量研究

本文研究了在临床和流行病学中出现的K个独立含结构零的2×2列联表.利用风险比推导出基于Wald型,基于对数变换型以及基于Score型的三个检验统计量,以检验层间齐性假设,获得了分别基于这三个检验统计量的控制功效的样本量公式和数值实验结果.模拟研究表明基于Score检验和基于对数变换检验的样本量公式比基于Wald检验的样本量公式更精确,更能有效保证预先给定的功效.推广了基于列联表问题的假设检验方法.     

Tensor logarithmic norm and its applications

Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi‐norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems. Copyright © 2016 John Wiley & Sons, Ltd.     

一类函数的对数完全单调性

通过对参数λ,μ的讨论,主要利用函数的单调性理论,已有对数完全单调函数的性质以及幂函数的积分表达式研究了函数Gλ,μ(x)及函数[Gλ,μ(x)]-1的对数完全单调性,并在此基础上得到了一定条件下函数Gλ,μ(x)及[Gλ,μ(x)]-1对数完全单调的充要条件.     

两个不等式的加强与证明

本文利用幂平均加强了林同坡不等式和Ｓｔｏｌａｒｓｋｙ不等式，并给出了证明．