半正定Hermite矩阵的一个不等式

设Aj,Bj∈Cn×n(j =1,2, ,m)为半正定Hermite矩阵 ,本文建立了下列不等式∏mj=1detAj·detBj (1mn)mn ∑mj=1tr(AjBj) mn     

论我国教育产业中的不公平问题

教育产业不公平是当前教育研究的热点教育产业中的一个新问题。由于教育产业不公平而带来的诸多教育问题已广为人们关注。为此，研究教育产业中的不公平问题就具有相当重要的意义。本从我国教育产业不公平的表现形式、原因分析及对策研究三个方面探讨了这一问题。     

对贝尔不等式的误解

贝尔对自己的工作有两点误解:第一,贝尔用以导出贝尔不等式的隐变量理论具有一个极为特殊的性质:它原封不动地保留了全部经典概率论的运算规则,贝尔却把这种理论当成一般的"定域隐变量理论";第二,当贝尔从他的隐变量理论导出贝尔不等式时应用了两个命题,他把其中之一理解为"定域隐变量理论"的特征,而实际上导出贝尔不等式的却是另一命题.在此试图说明,没有定域隐变量理论也能导出贝尔不等式.此外,还考察了吉.洛查克对贝尔定理的异议.     

涉及单形的中线长的两个几何不等式

本文给出涉及n维单形的中线长度的两个几何不等式,证明了苏化明所提的一个猜想(数学季刊4(1)(1989))是正确的,最后,还提出了一个猜想。     

Social support and digital inequality: Does Internet use magnify or mitigate traditional inequities in support availability?

This study tested competing predictions about the implications of Internet use for traditional inequities in social support availability. Using survey data collected as part of the Pew Internet and American Life Project, inequities in social support availability stemming from demographic and network-related factors were examined among non-users, Internet users, and Internet users who also participated in a social network site (SNS). The results offered evidence consistent with the social compensation perspective. Traditional inequities in support availability related to age, race, and total network size persisted among respondents who did not use the Internet, but were less evident or absent among Internet users and/or Internet users who participated in an SNS. Using the Internet to connect with others appeared to be an important mechanism through which inequality in support availability was mitigated.     

一个无理不等式猜想的证明

本文利用微积分对n(√an-xn)≥a-xt的猜想给出了证明,并对相关问题进行了讨论.     

分数阶Feller算子下的反常扩散方程

建立了Feller算予以下的空间分数阶反常扩散方程,给出分数阶扩散方程Canchy问题的求解定理,借助定理、Fourier变换及伽利略变换不变性得到问题的精确解,并当α→2即θ→0时,问题的解与相应经典整数阶扩散（对流-扩散）方程的解一致．     

锐角三角形中线与角平分线的几个不等式

应用三角形不等式中重要的R-r-s方法,证明了锐角三角形的中线与内角平分线的两个不等式,提出了两个未解决的猜想不等式.     

一类广义多值向量变分不等式

研究了Hausdorff拓扑向量空间中一类广义多值向量变分不等式问题（GMVVIP）,把定义在凸集上的GMVVIP部分地推广到了非凸集并运用KKM定理得到了这类GMVVIP解的存在性定理．     

Suboptimal reliable guaranteed cost control for continuous-time systems with multi-criterion constraints

The suboptimal reliable guaranteed cost control （RGCC） with multi-criterion constraints is investigated for a class of uncertain continuous-time systems with sensor faults. A fauk model in sensors, which considers outage or partial degradation of sensors, is adopted. The influence of the disturbance on the quadratic stability of the closed-loop systems is analyzed. The reliable state-feedback controller is developed by a linear matrix inequalities （LMIs） approach, to minimize the upper bound of a quadratic cost fimction under the conditions that all the closed-loop poles be placed in a specified disk, and that the prescribed level of H∞ disturbance attenuation and the upper bound constraints of control inputs＇ magnitudes be guaranteed. Thus, with the above muki-criterion constraints, the resulting closed-loop system can provide satisfactory stability, transient property, a disturbance rejection level and minimized quadratic cost performance despite possible sensor faults.