An explicit second order spectral element method for acoustic waves

The acoustic wave equation is here discretized by conforming spectral elements in space and by the second order leap-frog method in time. For simplicity, homogeneous boundary conditions are considered. A stability analysis of the resulting method is presented, providing an upper bound for the allowed time step that is proportional to the size of the elements and inversely proportional to the square of their polynomial degree. A convergence analysis is also presented, showing that the convergence error decreases when the time step or the size of the elements decrease or when the polynomial degree increases. Several numerical results illustrating these results are presented. Mathematics subject classifications (2000) 65M06, 65M70, 65M12 This work was supported by MIUR (PRIN 2001 “Metodi numerici avanzati per equazioni alle derivate parziali di interesse applicativo”).     

具有时滞的不确定离散时间系统时滞相关鲁棒镇定(英文)

基于状态观测器的设计,研究了不确定多时滞离散系统的鲁棒镇定问题,基于比较原理和不等式方法,给出了一个时滞相关鲁棒镇定条件。     

Radial Quantization in Rotating Space–Times

We examine the time discontinuity in rotating space–times for which the topology of time is S¹. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of time. Quantized radii emerge for which the associated tangential velocities are less than the speed of light. Using the de Broglie relationship, we show that quantum theory may determine the periodicity of time. A rotating Kerr–Newman black hole and a rigidly rotating disk of dust are also considered; we find that the quantized radii do not lie in the regions that possess CTCs.     

利用故障数据和估计的检查数据建立维修优化模型

利用时间延迟概念,根据故障记录数据和估计的检查数据建立了预防维修模型.通过对故障记录数据统计分析,提出了模型的假定条件.采用最大似然估计法,估计参数,包括缺陷发生率、不完全检查概率和时间延迟分布.建立了有关预防维修间隔期和总停机时间之间关系的检查模型,并根据估计参数和检查模型,计算最佳维修间隔期.     

PERSISTENCE AND STABILITY IN ARATIO‐DEPENDENT PREDATOR‐PREY SYSTEM WITH DELAY AND HARVESTING

ABSTRACT. . This paper aims to study the effect of time‐delay and combined harvesting on a Michaelis‐Menten type ratio‐dependent predator‐prey system. Dynamical behaviors such as persistence, stability, bifurcation, et cetera, are studied critically. Computer simulations are carried out to illustrate our analytical findings.     

带不同分布增量的随机和的局部渐近性

在Asmussen,Foss and Korshunov(J.Theoretical Probab.,2003,16(2):489-518)的基础上,讨论了支撑在(-∞,∞)上的不同分布的卷积的封闭性及带上述不同分布增量的局部渐近性.上述分布包括了常见的轻尾分布和重尾分布.     

Spurious,zeroth-order entropy generation along a kinked wall

Numerical entropy generation is studied in the case of steady, subsonic Euler flow along a kinked solid wall. For a standard upwind finite volume discretization the numerical entropy error, a component of the global discretization error, appears to be zeroth-order in mesh size. Two possible causes of the zeroth-order entropy error are studied. First an investigation is made of the local truncation error on a kinked grid. Although this error also appears to be zeroth-order in the neighbourhood of the kink, it probably does not cause the zeroth-order entropy error. Next a study is made of the existence of a singularity in the exact solution. Probably, the Euler flow solution is singular at the kink in the wall. The form of this likely singularity is unknown. Therefore the construction of a computational method which uses a priori knowledge about the singularity is not possible. Finally it is shown by numerical experiments that the subsonic Euler flow along a kinked wall still can be computed with vanishing entropy errors by using an appropriate sequence of continuously curved walls which converge to the kinked wall in the limit of zero mesh width.     

On the definition of an admitted Lie group for stochastic differential equations

A new definition of an admitted Lie group of transformations for stochastic differential equations involving Brownian motion is presented. The transformation of the dependent variables involves time as well, and it is proved that Brownian motion is transformed to Brownian motion. Applications to a variety of stochastic differential equations are presented.     

On open-loop and feedback attainability of a closed set for nonlinear control systems

In this note, we investigate the existence of controls which allow to reach a given closed set K through trajectories of a nonlinear control system. In the case where the set is sufficiently regular we give a condition allowing to find a feedback control law which ensures the existence of trajectories to reach the set. We also consider the case where all the trajectories reach K. When K is not necessarily attainable but only viable, we build a set-valued feedback for which the set is invariant. Our approach concerns continuous dynamics, possibly not C¹, so our methods do not come from geometric control theory. Furthermore, we do not require any regularity of the set K in order to obtain our results, except when we want to establish the existence of a feedback control law to achieve our goals.