Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary position feedback control of Kirchhoff's non‐linear strings

This paper is concerned with global stabilization of an undamped non‐linear string in the case where any velocity feedback is not available. The linearized system has an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by linear boundary control. Copyright © 2003 John Wiley & Sons, Ltd.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved.     

On a Generalized Cochrane Sum and Its Hybrid Mean Value Formula

The main purpose of this paper is to use a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a generalized Cochrane sum, and give an interesting mean value formula.2000 Mathematics Subject Classification: Primary—11F20; Secondary—11F99     

Large deviations and the generalized processor sharing scheduling for a two-queue system

We establish the optimal asymptotic decay rate of per-session queue length tail distributions for a two-queue system where a single constant rate server serves the two queues using the Generalized Processor Sharing (GPS) scheduling discipline. The result is obtained using the sample-path large deviation principle and has implications in call admission control for high-speed communication networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Application of stochastic optimal control to the suboptimal design of thrust-mass profiles

Stochastic optimal control techniques are applied to compare the performance of identical medium-range air-to-air missiles which have different thrust-mass profiles. The measure of the performance is the probability of reaching a lock-on-point with a favorable range of guidance and flight parameters, during a fixed time interval [0,t _f ], given that, during the flight, the trajectories of the missile are subjected to a variety of constraints including dynamic pressure constraints.     

Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

Lotka-Volterra型N-种群竞争系统的持久性和稳定性

本文研究一类具有无穷时滞的概周期Lotka-Volterra型N-种群竞争系统的持久性和全局渐近稳定性.一些新的充分条件被得到.     

~2样本深度的基本性质

本文讨论由L2深度修正得到的L2深度相应的样本深度的性质,得到了样本深度的相合性和渐近正态性,并证明了它在任意紧集上的一致相合性．最后,基于上述性质简要讨论了样本深度等高的一些性质．     

NA序列下经验分布函数的渐近正态性及其应用

本文在NA负相协序列下利用熟知的相依情形的大小块分割的方法,建立了经验分布函数的渐近正态性．作为在可靠性中的应用,得到了生存函数■(x)=P(X＞x)估计的渐近正态性．