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Shortest path Hamiltonian path and can be obtained over the shortest path and Hamiltonian path.

最短路径和哈密顿通路，可以求得多条最短路径和哈密顿通路。

By relaxing the assumption that the vehicle route is Hamiltonian tour for standard VRP, we study the open vehicle routing problem in which the route is Hamiltonian path.

松弛了标准VRP中车辆路线为哈密尔顿巡回的假设，研究了车辆路线为哈密尔顿路径的开放式车辆路径问题。

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。

In many physical situations, the Hamiltonian of the system is composed of an unperturbed Hamiltonian and a perturbation.

在很多物理情况下，系统的哈密顿量由未扰动哈密顿量与扰动势两部分所组成。

In this paper,we discuss the existence of solutions of asymptotically linear 2p-order Hamiltonian systems with the help of Morse index theory for associated linear Hamiltonian systems .

本文主要利用指标分类理论讨论了渐近线性2p-阶Hamiltonian系统的解的存在性。

It can be divided into two chapters.In chapter one ,we state a few usual notations,definitions and basic results.In chapter two, we first establish a Morse index theory for 2p-order linear Hamiltonian systems.Then as applications of the index theory ,we discuss nontrivial solutions for nonlinear Hamiltonian systems by making use of Leray-Schauder degree theory and Morse theory.

全文分为两章：第一章中给出了本文所要用到的一些基础知识和一些常用的记号；第二章先建立了线性2p-阶Hamiltonian系统的指标；作为此分类指标的应用，结合Leray-Schauder度理论及Morse 理论，讨论了渐近线性系统的非平凡解的存在性。

In 1997, Lenhard Ng Michelle Schultz[1] gave the definition of k -ordered Hamilton graphs,namely, let G be a Hamiltonian graph of order n,and for a positive integer k with k ≤n, we say that G is k -ordered if for every sequence S : v1 , v2,Λ,vk of k distinct vertices, there exists a hamiltonian cycle C of G such that the vertices of S are encountered on C in the specified order.

年， Lenhard Ng Michelle Schultz[1]给出k-可序( k ？ordered)哈密尔顿图的定义，即设G是n阶哈密尔顿图，对于正整数k，称G 是k -可序图，如果对于任意给定的k 个互不相同的顶点的有序子集S =( v1 ，v2，Λvk)( 2≤k ≤n)，存在G中的哈密尔顿圈C 包含S 且不改变其中元素的顺序。2000 年，R.J。

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

By using this newly developed index theory,we investigate the multiplicity of subharmonic solutions for nonlinear Hamiltonian systems and second order Hamiltonian systems.

应用这一指标理论，讨论Hamilton系统与二阶Hamilton系统次调和解的存在性。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。