凸序列不等式的控制证明

利用控制不等式理论简洁地证明了一类凸序列不等式 (包括著名的 Nanson不等式的几个推广 ) ,并给出若干应用 .     

Quantum Inequality for Negative Energy Density States of Massive Dirac Field in Four-Dimensional Spacetime

Negative energy density and the quantum inequality are examined for the Dirac field. A proof is given of the quantum inequality for negative energy densities in the massive Dirac field produced by the superposition of two single particle electron states.     

关于自组凯尔文电桥的测量不确定度

凯尔文电桥是国内大学基础物理实验所开设的实验内容之一，且多为自组式．关于自组凯尔文电桥的测量精度与桥路参数精度之间的关系，有些实验教材已有推导，但尚未涉及与两低阻相邻电压接头间跨桥电阻的定量关系，不注意这一点，会给测量结果带来一定的误差．本文就实际中常用的等双臂凯尔文电桥从理论上定量地推出了这一关系，进而给出了跨桥电阻可忽略时的适当阻值．     

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.     

The Iyengar Type Inequalities with Exact Estimations and the Chebyshev Central Algorithms of Integrals

In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated.     

中立型脉冲微分方程正解的存在性

本文利用Banach压缩映射原理，讨论了中立型时滞脉冲微分方程正解的存在性。     

四阶非线性边值问题解的存在性与上下解方法

该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.     

Sobolev-Hardy不等式与临界双重调和问题

该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ，这里Ω包含R^N是包含0的有界光滑区域，u∈H0^2(Ω），μ∈R是参数，0≤s≤2,△^2=△△表示双重拉普拉斯算子，当f(x,u)=u^p,p=2N/N-4时，上述问题就是一个临界双重调和问题，该文运用Sobolev-Hardy不等式和变分方法，得到它的解的存在性的一些结果。     

浅谈家用吊扇的调速方法

家用吊扇的核心部分是单相异步电动机,此绕组如图1,有一主绕组(工作绕组)与一串联电容器C的副绕组(启动绕组)相并联.这样做可使二绕组的电流在相位上相差90°,从而形成旋转磁场.转子的转动过程与三相异步电动机相似.