Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined.As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, we must pass from the solution of the artificial system (driven by parametric noise) to that of the original one (driven by external noise, that is known). Moreover, introducing this invertible nonlinear transformation into the Itô’s rule for the original system driven by external input, one can derive the Itô’s rule for systems driven by a parametric type excitation, directly. In this latter case one can see how natural is the presence of the Wong–Zakai correction term or the presence of the hierarchy of correction terms in the case of normal and Poissonian white noise, respectively. Direct transformation on the Fokker–Planck and on the Kolmogorov–Feller equation for the case of parametric input are found.     

Note on ‘Construction of Double Sampling s‐Control Charts for Agile Manufacturing’

He and Grigoryan (Quality and Reliability Engineering International 2002; 18 :343–355) formulated the design of a double‐sampling (DS) s control chart as an optimization problem and solved it with a genetic algorithm. They concluded that the DS s control charts can be a more economically preferable alternative in detecting small shifts than traditional s control charts. We explain that, since they only considered the average sample size when the process is in control, their conclusion is questionable. Copyright © 2006 John Wiley & Sons, Ltd.     

Fast and accurate 4‐node quadrilateral

An accurate and variationally consistent 4‐node quadrilateral element is introduced where high coarse mesh accuracy and low mesh distortion sensitivity are characteristic qualities, even when incompressibility is approached for plane strain. One‐point quadrature integration procedure is adopted and a new improved stabilization technique is developed. Orthogonality conditions are utilized so that the patch test is satisfied for arbitrary quadrilaterals. Several numerical examples including a convergence rate study are presented which confirm the excellent performance of this element. Copyright © 2004 John Wiley & Sons, Ltd.     

Markov analysis of qualitative dynamics1

Common sense sometimes predicts events to be likely or unlikely rather than merely possible. We extend methods of qualitative reasoning to predict the relative likelihoods of possible qualitative behaviors by viewing the dynamics of a system as a Markov chain over its transition graph. This involves adding qualitative or quantitative estimates of transition probabilities to each of the transitions and applying the standard theory of Markov chains to distinguish persistent states from transient states and to calculate recurrence times, settling times, and probabilities for ending up in each state. Much of the analysis depends solely on qualitative estimates of transition probabilities, which follow directly from theoretical considerations and which lead to qualitative predictions about entire classes of systems. Quantitative estimates for specific systems are derived empirically and lead to qualitative and quantitative conclusions, most of which are insensitive to small perturbations in the estimated transition probabilities. The algorithms are straightforward and efficient.     

On a three-dimensional axisymmetric boundary-value problem of nonlinear elastic deformation: Asymptotic solution and exponentially small error

In this paper, we study a three-dimensional axisymmetric boundary-value problem of a slender cylinder composed of a nonlinearly elastic material subjected to an axial force. Starting from the field equations, after a transformation and proper scalings, we identify a small variable and two small parameters, which characterize the present problem. Then, by an approach involving compound series-asymptotic expansions, a nonlinear ODE is derived, which governs the axial strain (the first-term in the series expansion). By imposing the zero radial displacement conditions at two ends, we manage to get the analytical solution of the axial strain, from which all other physical quantities can be deduced and thus the three-dimensional displacement field can be determined. Graphical results are presented, which show that there are two boundary layers near the two ends while the middle part is in a state of almost uniform extension. The asymptotic structure of the analytical solution is derived, which offers clear explanations to the structure of the deformed configuration and shows that the thickness of both boundary layers is of the order of the radius. We also point out the relevance of the present results to the St. Venant’s problem. In particular, we obtain the explicit uniformly-valid exponentially small error term, when the obtained deformed configuration is compared to the configuration of a uniform extension.     

Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

This paper deals with the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems have certain special properties. These properties are explored and used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated by an application to a time-optimal problem for a class of underwater vehicles.     

基于Delphi的报童模型的实现与动态仿真

已往库存论中的决策模型,它是把现实过程用数学的方法进行分析,得到决策值,但不能看到决策的过程,不能反映出现实生活中的不确定性、动态性。运用Delphi 7.0和SQL server 2000对销售过程进行了动态仿真,利用Newsboy模型的推广(S,s)订购策略来监控库存并做出决策,这样就体现出此过程的不确定性、动态性;且举出了一个仿真商品销售的实例,对其中的一些关键技术,如何仿真、算法的实现等进行了阐述。     

一种探测二维电磁目标的新方法

电磁目标的探测对通信而言有着十分重要的意义。本文描述一种收敛迅速、结果准确、抗强随机噪声的探测二维电磁目标的新方法。首先从体等效原理出发得到一个积分方程组，此方程组可求解散射问题。随后，对此方程组求变分，变形后得到散射场变化与介电参数变化之间关系的矩阵方程，即反演方程。文中列举了几个例子，通过数值实验结果证明本法收敛速度快、反演精度高、适应复杂目标的能力强，能抗强随机噪声干扰     

PMMA／PBA乳胶IPN阻尼材料的研究

用乳液聚合方法合成了一系列的互穿聚合物网络，其中包括：ＰＭＭＡ／ＰＢＡ和Ｐ（ＭＭＡ－ｃｏ－ＰＭＡ）／ＰＢＡ乳胶互穿聚合物网络（ＬＩＰＮ），ＰＭＭＡ／ＰＢＡ乳胶双向互穿聚合物网络（ＬＢＩＰＮ）以及ＰＭＭＡ／ＰＢＡ界面交联互穿聚合物网络（ＩＣＬＩＰＮ）。动态力学谱和拉伸试验结果表明：（１）ＰＭＭＡ／ＰＢＡ互穿聚合物网络的两组分相容性和阻尼性能可通过ＭＭＡ和ＰＭＡ共聚来改善；（２）双向互穿技术是一种行之