An inner product lemma

Given the operator product BA in which both A and B are symmetric positive‐definite operators, for which symmetric positive‐definite operators C is BA symmetric positive‐definite in the C inner product 〈x, y〉C? This question arises naturally in preconditioned iterative solution methods, and will be answered completely here. Copyright © 2004 John Wiley & Sons, Ltd.     

Effective stability for generalized Hamiltonian systems

An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems, dimensions of action variables and angle variables might be distinct.     

Hybrid numerical—experimental approach for investigation of dynamics of microcantilever relay system

The time average holography measurements of the vibrating microelectromechanical switch (MEMS) were performed in this study. Experimental measurement results exhibit good agreement with computer generated holographic interferogram analysis. The validation of experimental investigations versus numerical analysis provides the necessary background to analyze the dynamical characteristics of micromechanical systems in virtual numerical environments. Direct application of fringe counting techniques for reconstruction of motion from time average holograms cannot be straightforward if the analyzed micromechanical systems contain motion limiters. Modifications of a classical time average holographic technique enable qualitative analysis of MEMS and can be applied for investigation of dynamical properties of much broader classes of MEMS systems.     

190区超形变核中转动带的组态结构

通过系统研究A～190区超形变核中转动带的转动惯量、角动量顺排、旋称分裂随转动频率的变化规律, 结合我们用处理对力的粒子数守恒方法的计算结果, 对A～190区所有转动带的组态结构给出了一个整体的描述. 绝大多数超形变带都建立在强耦合轨道上, 例如中子[512]5/2, [624]9/2. 少数超形变带则建立在高j闯入轨道上, 即中子[761]3/2, [752]5/2. 根据我们提出的组态结构所进行的理论计算结果表明, A～190区所有转动带的一般行为、反常变化和带交叉都得到了满意的解释.     

微分代数多项式系统的可解集

本文对一般微分代数方程给出了几类可解集的概念，并讨论了多项式微分代数方程的可解集，得到子多项式系统具有唯一解。特别是有多于一个的解的条件，并得到了低次多项式在一定意义下的充分必要条件。     

彩票发行方案的合理性评价

本文根据目前常见的彩票销售规则及相应的奖金设置方案，综合分析了高项奖奖金额和低项奖中奖率对彩民的吸引力等因素，将发行方案的合理性问题归结为发行方案对彩民的吸引力上，引入了表示彩民心理趋向的偏好系数，构造了吸引力函数，同时综合考虑了封顶值等因素，对现行常见的29种彩票发行方案进行了综合评价。     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.