The exact proability that the roots of quadratic,cubic, and quartic equations are all real if the equation coefficients are random

Suppose that the coefficients of a polynomial equation are Independent random variables defined on subsets of real numbers, The purpose of this paper is to find the exact probability that all roots of a random polynomial equation are real. Since a polynomial equation of degree higher than four with arbitrary coefficients cannot be solved algrebraically, this paper will consider quadratic, cubic and quartic equations only. The general results are obtained in each case, Also, a number of special cases are furnished.     

中国城市软实力评价及实证研究

为了有效地将软实力概念和理论运用到城市发展实践中,文章界定了城市软实力的内涵,区分了软实力资源、中介、建构效果,从人口素质、自然环境、文化资源、社会和谐、传播力度、建构效果这六个方面入手,提出了城市软实力的结构方程模型并进行了实证检验.同时,运用该模型,对中国大陆287个地级及以上城市软实力进行了排序,有针对性地提出了城市软实力建设的一些着力点.     

用Excel软件求解线性规划和某些数学问题的方法

介绍了用Excel软件求解线性规划的方法,在此基础上给出了用该软件求解不等式问题和线性方程组的方法.     

Substitute or Complement? Spousal Influence on Volunteering

Social scientists have documented the influence of family statuses on volunteering, ignoring intrafamily effects. Using newly issued data from the Current Population Survey on the volunteer behavior of 19,626 American couples, we test two competing theories concerning spousal influences on volunteering. Substitution theory predicts that spouses will trade off volunteer work; complementarity theory predicts that spouses’ volunteer work is positively linked. Using structural equation methods to control for simultaneity bias, we find support for the complementarity theory. The wife’s influence, however, is stronger than the husband’s. Spousal influence is stronger if both spouses volunteer in the same domain. The findings underline the importance of close relationships in mobilizing volunteer workers.     

Rangwala-Rao方程的显式精确解及其分支

运用动力系统的几何理论、分支理论及大量的积分运算,求出了Rangwala Rao方程的型如u(x,t)=ei(φ(ξ)-ωt)a(ξ),ξ=x-vt的5种显式精确孤波解.本文包含了以往文献所得的结果,且给出了若干新解.     

关于Diophantine方程x3-8=py2

在p是奇素数的假设下,证明了如果p=12r2 1,其中r是偶数,则方程x3-8=py2没有适合gcd(x,y)=1的正整数解(x,y).     

Baker方法的若干应用(ⅩⅤ)

设a、b、n是正整数本文运用Baker方法证明了：当n≥2·108或者2＜n＜2·108且ab＞（4nn2／（n-1））2／（n-2）时方程。axn-by＝±1至多有1组正整数解（x，y）．上述结果基本上证实了Siegel的一个猜想．     

Observer,Self‐, and Partner Reports of Hostile Behaviors in Romantic Relationships

The present study examines how different observers of romantic relationships differ in their reports of hostility. Using confirmatory factor analysis with structured means, the results from 236 young adults and their romantic partners indicated that (a) the correlations among targets’ self‐reports, partners’ reports, and observers’ reports of targets’ behaviors were moderate; (b) targets’ self‐reports of their own level of hostility were lower than their partners’ reports of them; (c) young couples who were living together demonstrated a higher level of hostility than dating couples; and (d) women showed a higher level of hostility toward their partners than did men.     

分布式时延范台坡方程的Hopf分岔

分析了分布式时延的范台坡方程,将平均时延作为分岔参数,证明了模型经历了Hopf分岔过程,用图示Hopf理论获得了判定分岔周期解的稳定性和分岔方向的准则。并应用数字仿真的例子证明了理论分析的正确性。     

Optimal model averaging estimation for correlation structure in generalized estimating equations

Longitudinal data analysis requires a proper estimation of the within-cluster correlation structure in order to achieve efficient estimates of the regression parameters. When applying likelihood-based methods one may select an optimal correlation structure by the AIC or BIC. However, such information criteria are not applicable for estimating equation based approaches. In this paper we develop a model averaging approach to estimate the correlation matrix by a weighted sum of a group of patterned correlation matrices under the GEE framework. The optimal weight is determined by minimizing the difference between the weighted sum and a consistent yet inefficient estimator of the correlation structure. The computation of our proposed approach only involves a standard quadratic programming on top of the standard GEE procedure and can be easily implemented in practice. We provide theoretical justifications and extensive numerical simulations to support the application of the proposed estimator. A couple of well-known longitudinal data sets are revisited where we implement and illustrate our methodology.