查询词典 generalized function

In part one,because there is no long-range order in one-dimensional(1D)system,generalized second-order Green's function theory isused to 1D spin-1 antiferromagnetic spin chain.The Haldane gapin the excitation spectrum appears naturally in the analytical re-sult;When k is zero,there is a gap 2Δ.

第一部分中，在长程序为零的条件下，我们应用推广的二级格林函数理论，讨论了自旋为1的反铁磁一维链，Haldane能隙在解析结果中自然地得出，在k＝0时，能谱中存在一个2Δ能隙，Δ＝0.5J。

In the second chapter, we mainly study the robust estimation of mean components in generalized semiparametric mixed models , including robust estimation of regression parameters and nonparametric function.

第二章主要研究了广义半参数混合效应模型均值部分的稳健估计问题，包括回归参数和非参数函数的稳健估计。

The dissertation focuses on performance gradient estimation and SRO algorithm of DES aswell as other related topics,such as modeling of DES and discrete event simulation,performancemeasure Hessian matrix estimation,Stochastic Approximationand so on.General Semi-Markov Processis adapted to describe behaviour of DES and discrete eventsimulation.A general result is obtained and applied to analyze strong consistency of performancegradient Perturbation Analysisestimator.Conditions for effectiveness of InfinitesimalPerturbation Analysisare also discussed.New PA algorithms,such as server PA,PA usingDirac generalized function,job sequence PA etc.,are proposed to deal with discreteparameters.Furthermore,strategies of combining PA algorithms with certain iterative rules areanalyzed widely in order to optimize DES parameters and some SRO algorithms are constructed toslove DES optimization problems.

论文将DES性能分析领域中性能梯度估计和单运行仿真优化作为主要的研究对象，探讨了与性能梯度估计有关的DES和离散事件仿真过程建模、高阶导数估计以及随机逼近等理论和方法；建立了具有一般性的DES和离散事件仿真的广义半Markov过程模型；获得了分析性能梯度估计量强相合性的理论结果和无穷小摄动分析算法应用的条件；提出了诸如服务台数目的摄动分析、奇异摄动分析、串联生产线和加工车间中工件加工序的摄动分析等一系列摄动的思想和算法，对连续参数和离散参数都进行了深入的研究；对摄动分析算法同优化规则结合实现仿真优化的策略也进行了广泛的分析，构造了新型的变界截尾的随机逼近算法，并用于DES的单运行仿真优化研究；最后，给出了DES性能分析方法的实证性研究结果。

The Hamiltonian function of this system was deduced and the system was inverted to generalized Hamiltonian control model.

导出了系统的哈密顿函数，并将系统转化为广义哈密顿控制系统。

Finally numerical examples with three shape functions are analyzed in detail. The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also one or higher orders derivative.

最后，通过多个数值算例的计算比较了三种形函数的计算结果，结果显示本文提供的MGMLS方法关于函数值和各阶导数值都具有很高的精度。

Based on the concept of zero-path tracking in homotopy which is generalized into minimum of energy function path tracking and considering that different homotopy path has greater impacts on convergence speed, a new method is put forward——the non-line homotopic BP algorithm.

本文在将同伦论中的零点路径跟踪概念推广到对多层前馈神经网络能量函数极小点路径跟踪的基础上，注意到不同的同伦路径对收敛速度的影响，提出了一种改进算法——非线性同伦BP算法。

Then,the system is linearized by variational approach,the local null controllability is proved by applying a generalized implicit function theorem and combining the property of the solution mapping.

首先得到了系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后给出系统零能控的结论。

In this project, we intend to combine the above mathematical ideas. First, we consider a wild family of dynamical systems which can be derived into a family of difference equations. Then using a generalized version of the implicit function theorem which we will establish, we want to show that for any dynamical systems near 「singular limit」, there exists a horseshoe structure and hence chaotic phenomena occur.

在此研究计画中，我们打算结合上述的数学结论与想法，进一步考虑一类能够转化成差分方程的动态系统函数族，使用即将建立的推广性隐函数定理，我们希望证明当参数接近奇异极限时，动态函数会具有马蹄结构所以有混沌现象。

Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping.

首先通过对系统线性化，构造泛函，利用对偶方程，给出控制函数具体形式的办法得到系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射好的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后利用局部零能控性和逼近能控性结合给出系统零能控的结论。

A new generalized object oriented Petri net model which can be used to evaluate the capability of equipment support was proposed. Its formal definition was given. The abstract place, abstract transition, message color and the message transferring function between objects were introduced in this model. This model has good modularity, inheritability, reusability, and maintainability, and can reflect flexibility and dynamic features of complex system. An example was given in the paper.

提出了一种可用于装备保障能力评估的增强型扩展的面向对象Petri网模型，给出了该模型形式化描述，引入了抽象库所、抽象变迁、消息颜色以及对象间的消息传递函数等新的概念，更好地体现了面向对象的思想，具有很好的模块性、继承性、重用性和可维护性，能够反映复杂系统的动态柔性特点，最后给出实例。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。