On the regularization of an equation of the first kind with a multiple integration operator

The zero-order Tikhonov regularization method as applied to an equation of the first kind with a multiple differentiation operator is considered for the case when the solution belongs to a class from the domain of the adjoint operator. An estimate of the error of the approximate solution in the uniform metric is obtained, which is sharp with respect to the order, and the order is established. It is proved that the proposed method is optimal with respect to the order. Unimprovable estimates of the order of the modulus of continuity of the inverse operator are obtained.     

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.     

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.     

The Likelihood of the Parameters of a Continuous Time Vector Autoregressive Model

This paper provides a method of constructing the likelihood function of the parameters of a continuous time vector autoregressive model on the basis of discrete data without requiring the restrictions extant methods impose on the data that are capable of being rejected by a statistical test. In particular, the method does not rely on a steady-state assumption that can rule out unit root processes; it allows for weak assumptions on the innovations; and it allows for a mixture of skip-sampled and temporally-aggregated data. This revised version was published online in August 2006 with corrections to the Cover Date.     

On free semigroups of automaton transformations

It is established that the subset of freek-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach) in the set of allk-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 248–259, February, 1998. The author wishes to express his deep gratitude to Professor V. I. Sushchans'kii for permanent help and attention to the research. This research was partially supported by the ISSEP under grant No. GSU 051341.