Stability and other limit laws for exit times of random walks from a strip or a halfplane

We show that the passage time, T^*(r), of a random walk S_n above a horizontal boundary at r (r≥0) is stable (in probability) in the sense that as r→∞ for a deterministic function C(r)>0, if and only if the random walk is relatively stable in the sense that as n→∞ for a deterministic sequence B_n>0. The stability of a passage time is an important ingredient in some proofs in sequential analysis, where it arises during applications of Anscombe's Theorem. We also prove a counterpart for the almost sure stability of T^*(r), which we show is equivalent to E|X|<∞, EX>0. Similarly, counterparts for the exit of the random walk from the strip {|y|≤r} are proved. The conditions arefurther related to the relative stability of the maximal sum and the maximum modulus of the sums. Another result shows that the exit position of the random walk outside the boundaries at ±r drifts to ∞ as r→∞ if and only if the random walk drifts to ∞.     

Lyapunov stability of discontinuous dynamic systems

This paper derives necessary and sufficient conditions for thestability of dynamic systems in the sense of Lyapunov. Theseconditions are used to study the stability of discontinuousdynamic systems, which include fuzzy systems, hybrid systems,and impulsive differentia^! systems.     

On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations

In the rectangle D = (0,

Nanocomposite Mullite/Mullite Powders by Spray Pyrolysis

A mullite/mullite nanocomposite powder has been synthesized, composed of nanometer-size 3Al₂O₃·2SiO₂ (3/2) mullite precipitates within a matrix of the high alumina 2Al₂O₃·SiO₂ (2:1) mullite. Historically, the transition from the metastable high-alumina phase to the thermodynamically stable 3:2 phase of mullite has been thought to be a continuous process, involving a continuous solid solution between the two forms of mullite. In contradiction to this widely held view, our high resolution transmission electron microscopic characterization confirms that a first order phase transition between two distinct mullites occurs. The high degree of interface coherence between the precipitates and the matrix allows us to speculate that the mechanical properties of the matrix could be enhanced by a process similar to the precipitation hardening of metals.     

A PREDATOR-PREY SYSTEM WITH STAGE STRUCTURE AND HARVESTING FOR PREDATOR

In this paper, we consider a predator-prey system with stage structure and harvesting (where the predator population has two stages, an immature stage and a mature stage with harvesting, and the growth of the prey population is of Lotka-Volterra nature). We obtain the conditions of the globally asymptotic stability for three nonne-gative equilibria of this system.     

关于β稳定线公式的一个评注

指出β稳定线公式应在理论框架下通过自洽的计算决定.这与传统的β稳定线公式略有区别.本文还对在Hartree-Fock近似下的β稳定线公式给出了一个评注.     

The dynamics of random interfaces in phase transitions

A review is given of recent developments involving the dynamics of random interfaces formed in the evolution of metastable and unstable systems. Topics which are discussed include interface growth and nonequilibrium dynamical scaling. The possibility of there being dynamical universality classes in first-order phase transitions is also discussed. There are a large number of systems of experimental interest which include binary alloys, binary fluids, and polymer mixtures. Other systems studied by computer simulation include the kinetic Ising, Potts, andZ _N models.Work supported by NSF grant No. DMR-8013700.     

Perturbed steepest-descent technique in multiextremal problems

The steepest-descent technique dealing with the perturbed values of the objective function and its gradients and with nonexact line searches is considered. Attention is given to the case where the perturbations do not decrease on the algorithm trajectories; the aim is to investigate how perturbations at every iteration of the algorithm perturb its original attractor set.Based on the Liapunov direct method for attraction analysis of discrete-time processes, a sharp estimation of the attractor set generated by a perturbed steepest-descent technique with respect to the perturbation magnitudes is obtained. Some global optimization properties of finite-difference analogues of the gradient method are discovered. These properties are not inherent in methods which use exact gradients.The author is grateful to the referees for many useful suggestions.     

Solitons and Fractal Kerr Response

Optical solitary waves that propagate in a Kerr medium exhibiting a power-law nonlocal response are studied analytically. The first-principles stability analysis based on quantum field theory shows that within the whole range of the exponent (the fractal dimension) the solitary wave can be stabilized.     

食堂智能卡管理系统

本文全面介绍了通过使用最新推出的智能卡(IC卡)技术，结合51系列单片机而研制的食堂智能卡管理系统，替代了原食堂繁琐的饭票流通，实现了食堂管理的电脑化.