时标上的二阶变时滞动力方程的振动准则

利用广义Riccati技巧及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力方程的振动性,得到了一些新的振动准则.     

具有强迫项的二阶非线性时滞微分方程的振动性

利用广义Riccati技巧和积分平均技巧,研究具有强迫项的二阶非线性时滞微分方程的振动性态,得到了这类方程振动的若干新的区间判别准则.     

一类边值问题的振动准则

本文考虑一类中立型泛函偏微分方程的边值问题。我们的主要工具是平均技巧，利用有关的泛函微分不等式来建立这类边值问题解的振动准则。     

一类二阶微分方程解的振动性质

利用积分平均技巧研究二阶微分方程(r(t)(x(t) )x′(t) )′ q(t) f(x(t) ) g(x′(t) ) =0 .解的振动性质 ,得到了一些保证此方程所有解振动的充分条件 .特别 ,本文的结果改进了文 [1 ]的主要结果 .     

时标上具正负系数的三阶阻尼动力方程的振动性

研究了时标上一类具有正负系数和阻尼项及非线性中立项的三阶动力方程的振动性,运用Riccati变换技术,结合大量不等式技巧,得到了该方程的几个新的振动准则,这些准则推广和改进了一些已知的结果,最后以具体例子来说明了本文的结论.     

二阶矩阵微分系统的区间振动准则

本文利用矩阵Riccati技巧,平均技巧及矩阵不等式,建立形如[P(t)Y']' Q(t)Y=0的二阶矩 阵微分系统的一些新的区间振动准则.所得结果推广,改进和包含一系列已有的结论,并能应用于已知 准则不能适用的若干情形.     

二阶矩阵微分系统的区间振动准则

本文利用矩阵Riccati技巧,平均技巧及矩阵不等式,建立形如[P(t)Y']'+Q(t)Y=0的二阶矩阵微分系统的一些新的区间振动准则.所得结果推广,改进和包含一系列已有的结论,并能应用于已知准则不能适用的若干情形.     

补数速乘技巧

有补数关系的两个数列相乘，有几种速乘技巧，归纳为：     

带阻尼项的非线性矩阵微分系统的振动性

通过定义新的预备解及利用矩阵Riccati技巧、平均技巧及矩阵不等式,给出了带阻尼项的二阶非线性矩阵微分系统(P(t)X′(t))′+R(t)X′(t)+Q(t)F(X′(t))G(X(t))=0的一些振动性准则;所得结果推广和改进了已有文献的相关结果。     

具有分布偏差变元的二阶中立型方程的振动准则(英文)

利用Riccati变换及积分平均技巧,建立一类具有非线性中立项及分布偏差变元的二阶中立型方程的振动准则,我们的结果推广并改进了一些已有的结果.     

Error analysis of the combination technique

Summary. The combination technique is a method to reduce the computational time in the numerical approximation of partial differential equations. In this paper, we present a new technique to analyze the convergence rate of the combination technique. This technique is applied to general second order elliptic differential equations in two dimensions. Furthermore, it is proved that the combination technique for Poisson's equation convergences in arbitrary dimensions. Received September 25, 1997 / Revised version received October 22, 1998 / Published online September 7, 1999     

A new globalization technique for nonlinear conjugate gradient methods for nonconvex minimization

It is well-known that the HS method and the PRP method may not converge for nonconvex optimization even with exact line search. Some globalization techniques have been proposed, for instance, the PRP+ globalization technique and the Grippo-Lucidi globalization technique for the PRP method. In this paper, we propose a new efficient globalization technique for general nonlinear conjugate gradient methods for nonconvex minimization. This new technique utilizes the information of the previous search direction sufficiently. Under suitable conditions, we prove that the nonlinear conjugate gradient methods with this new technique are globally convergent for nonconvex minimization if the line search satisfies Wolfe conditions or Armijo condition. Extensive numerical experiments are reported to show the efficiency of the proposed technique.     

Probabilistic diversification and intensification in local search for vehicle routing

This article presents a probabilistic technique to diversify, intensify, and parallelize a local search adapted for solving vehicle routing problems. This technique may be applied to a very wide variety of vehicle routing problems and local searches. It is shown that efficient first-level tabu searches for vehicle routing problems may be significantly improved with this technique. Moreover, the solutions produced by this technique may often be improved by a postoptimization technique presented in this article, too. The solutions of nearly forty problem instances of the literature have been improved.     

A reliable aftertreatment for improving the differential transformation method and its application to nonlinear oscillators with fractional nonlinearities

A new aftertreatment technique is developed in this paper to deal with the truncated series derived by the differential transformation method (DTM) to obtain approximate periodic solutions. The proposed aftertreatment technique splits into two types, named as (Sine-AT technique, SAT) and (Cosine-AT technique, CAT). It is shown that the differential transformation method with the proposed aftertreatment technique is very effective and convenient for a class of nonlinear oscillatory problems with fractional nonlinearities without any need for Padé approximants or Laplace transform.     

基于有效Monte Carlo模拟的外汇期权组合非线性VaR模型

为了克服极小概率事件发生概率估计的困难,提出了把重要抽样技术发展到外汇期权组合非线性VaR模型中,估计出组合损失概率。为了进一步达到减少模拟估计误差目的,在重要抽样技术基础上使用分层抽样技术,进行更有效的Monte Carlo模拟。数值结果表明,重要抽样技术算法比常用Monte Carlo模拟法的计算效率更有效;而重要抽样技术和分层抽样技术相结合算法比重要抽样技术算法更有效地减少模拟所要估计的组合损失概率的方差,有着更高的计算效率。     

A useful technique for piecewise deterministic Markov decision processes

This note presents a technique that is useful for the study of piecewise deterministic Markov decision processes (PDMDPs) with general policies and unbounded transition intensities. This technique produces an auxiliary PDMDP from the original one. The auxiliary PDMDP possesses certain desired properties, which may not be possessed by the original PDMDP. We apply this technique to risk-sensitive PDMDPs with total cost criteria, and comment on its connection with the uniformization technique.     

Singular differential game numerical techniques

This paper develops a numerical technique to solve a class of zero-sum differential games with singular control. By using this technique and the application of inverse systems, a near-optimal closed-loop technique is developed to generate a numerical solution to this class of problems.     

6σ管理和统计技术

从6σ名称,绿带、黑带的评定标准和培训内容都体现了统计技术是6σ管理的核心技术。DMAIC统计技术应用模式虽有不足,最大功绩是使应用统计技术简单化,实际应用者认识了统计技术的重要性。     

On caustics associated with the linearized vorticity equation

The linearized vorticity equation serves to model a number of wave phenomena in geophysical fluid dynamics. One technique that has been applied to this equation is the geometrical optics, or multi-dimensional WKB technique. Near caustics, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to determine an asymptotic solution of the linearized vorticity equation and to study associated wave phenomena on the caustic curve.     

KKM技巧及其应用

本文介绍KKM技巧,并用以建立了新的抉择定理和重合定理,它们是[2,10,11,15,16]等近期文献中一些重要结果的推广.