A new approach to discretization applied to a continuous, nonlinear, sliding-mode-like control using nonsmooth analysis

This paper introduces a new approach to discretization of nonlinearcontrol laws with a Lipschitz property. The sampling time isdefined as a parameter, which must be selected sufficientlysmall so that the closed-loop system is stable. In contrastto similar results, the stabilizing effect of the control istaken into account. This can result in less conservative constraintson the minimum sampling frequency. The discretization techniquesare explained on a general nonlinear model and applied to thediscretization of a novel nonlinear, robust sliding-mode-likecontrol law. Similar robustness features as for continuous controlare demonstrated. Nonsmooth Lyapunov functions are used forthe discretized sliding-mode-like control introducing cone shapedregions of the state space. One of these cone shaped regionscoincides with a cone shaped layer around the sliding mode definedby the continuous sliding-mode-like control. A stability theoremusing nonsmooth Lyapunov functions is provided.     

Skilled workforce scheduling in Service Centres

The Skilled Workforce Project Scheduling Problem (SWPSP) is a complex problem of task scheduling and resource assignment that comes up in the daily management of many company Service Centres (SC). The SWPSP considers many real characteristics faced daily by the SC: client-company service quality agreements that establish maximum dates for the beginning and the end of tasks with penalties for delays, criticality levels indicating the client-priority in processing each task, generalized precedence relationships that can produce cycle structures, time period and percentage time lags and variable task durations depending on the worker executing the task. Furthermore, the SC workforce is made up of specialist workers characterised by efficiency levels showing their efficiency and speed executing the several types of tasks. Each worker has his or her own timetable.     

Limit theorems for random processes with random time substitution

In this paper we prove a theorem on sufficient conditions for the convergence in the Skorokhod space D[0, 1] of a sequence of random processes with random time substitution. We obtain almost sure versions of this theorem.     

超高速光电探测器

现代激光科学研究、核爆模拟、惯性约束核聚变（ICF）研究等领域需要测量半宽度100ps左右的超高速激光脉冲。超高速光电探测器就是探测光信号并转换成相应电脉冲的有力工具。     

Two-Sided Optimal Bounds for Green Functions of Half-Spaces for Relativistic <Emphasis Type="Italic">α</Emphasis>-Stable Process

The purpose of this paper is to find optimal estimates for the Green function of a half-space of the relativistic α -stable process with parameter m on ℝ ^d space. This process has an infinitesimal generator of the form mI–(m ^2/α I–Δ) ^α/2, where 0<α<2, m>0, and reduces to the isotropic α-stable process for m=0. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and we provide two-sided sharp estimates for the Green function for a half-space. As a byproduct we obtain some improvements of the estimates known for bounded sets. Our approach combines the recent results obtained in Byczkowski et al. (Bessel Potentials, Hitting Distributions and Green Functions (2006) (preprint). ), where an explicit integral formula for the m-resolvent of a half-space was found, with estimates of the transition densities for the killed process on exiting a half-space. The main result states that the Green function is comparable with the Green function for the Brownian motion if the points are away from the boundary of a half-space and their distance is greater than one. On the other hand for the remaining points the Green function is somehow related the Green function for the isotropic α-stable process. For example, for d≥3, it is comparable with the Green function for the isotropic α-stable process, provided that the points are close enough. Research supported by KBN Grants.     

定时截尾场合双参数威布尔分布的贝叶斯推断

给出了定时截尾下,双参数威布尔分布中参数及可靠性指标的Bayes估计,并且给出了未来观测值的贝叶斯预测问题.     

A blow-up result in a Cauchy viscoelastic problem

In this work we consider a Cauchy problem for a nonlinear viscoelastic equation. Under suitable conditions on the initial data and the relaxation function, we prove a finite-time blow-up result.     

Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations

In this paper we design higher-order time integrators for systems of stiff ordinary differential equations. We combine implicit Runge–Kutta and BDF methods with iterative operator-splitting methods to obtain higher-order methods. The idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently. We compare our new methods with the higher-order fractional-stepping Runge–Kutta methods, developed for stiff ordinary differential equations. The benefit is the individual handling of each operator with adapted standard higher-order time integrators. The methods are applied to equations for convection–diffusion reactions and we obtain higher-order results. Finally we discuss the applications of the iterative operator-splitting methods to multi-dimensional and multi-physical problems.     

ESTIMATION FOR THE ASYMPTOTIC BEHAVIOR OF THE DELAYED COMPETITION MODEL

In ecological dynamic systems, the competition between species is a very universal phenomenon, which can be described by the well-known Volterra-Lotka model in a diffusion form. Noticing that the living space usually changes in a seasonal manner and the population development of the species may also undergo time-delay im- pact, a developed form of this model is investigated in this article. The main approaches employed here are the upper-lower solution method and the energy-estimate technique. The results show that whether the species may sustain survival or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the time delay. For the survival case, the population evolutions of the two species may appear asymptotic periodicity with distinct upper bound and this bound depends heavily on the time delay. These results can be also checked by the intuitionistic numerical simulations.     

从x出发的漂移Brownian Motion的极值分布

该文研究了从x出发的正漂移Brownian Motion的极值问题，给出了关于这种随机过程的两种极大值的定义，并主要利用Brownian Motion的一些重要性质，比如正交不变性、时空齐次性及在有限停时上的强Markov性等，获得了两种极大值的分布函数的精确表达式。