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Shortest path problem is a basic problem in the combinatorial optimization. The objective in the network is time-varying.

在组合优化过程中，往往需要获得从起点到终点之间的最短路，而其所考虑的目标可能是一个与时间相关的变量。

Since last year and this year the fund to purchase products, there are varying degrees of shrinkage.

因为去年和今年购买的基金产品，都存在了不同程度的缩水。

With intensifying exploitation of the resources, the grassland and shrubby vegetation in the region has been damaged to a varying extent.

随着黄河源区资源开发力度逐步加大，草场和灌丛植被遭到不同程度的破坏，生态环境日趋恶化。

The languages of some groups outside modern Tibet, such as Dzongkha, Sikkimese, Sherpa, and Ladakhi, are more distant varieties descended from archaic Tibetan, and which bear varying degrees of similarity to modern Tibetan.

他们保留着同现代藏语不同程度的相似性。包括各种藏语方言在内，说藏语的人口大概有6百万。

A silver chloride {100} T-grain emulsion and a series of cubic silver halide emulsions were prepared by varying the parameters correctly during nucleation and growing processes of grains.

通过调变乳剂制备的各项参数，成功地制备了系列立方体卤化银乳剂及氯化银{100}面扁平颗粒乳剂。

The description of network delays including characteristics and effects are also covered and the uniformed mathematic models for NCSs with four different structures are derived. Furthermore, the controller basing on state prediction and compensating time delay is designed. Sufficient and necessary stability conditions for systems with different transmission policies such as perfect transmissions, delayed transmissions and time-varying transmissions are obtained as simple eigenvalue tests of certain test matrices. And in the end, effects of model error over maximum communication interval are analyzed. Numerical examples show the feasibility and efficiency of the proposed methods.

首先介绍了网络控制系统中数据包的传输情况以及基于模型结构方法的基本思想，并针对四种不同拓扑结构的控制网络分析了网络时延的性能，进而给出了统一的数学模型；然后，提出了基于状态预测的具有时延补偿功能的状态反馈控制器的设计方法，并针对完美传输、延时传输及时变传输三种数据传输策略，分别研究了控制系统的稳定性问题；最后分析了模型误差对最大通讯间隔的影响；仿真结果表明了设计及控制方法的正确性和有效性。

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。

As to system＇s uncertainty such as time varying characteristics, grey multiple step error correction method took the place of the conventional single step error correction method.

针对对象特性时变等不确定因素，该文以灰色多步误差预测校正替代原有算法的当前一步误差校正，可以更为有效的克服模型失配等因素的影响。

As to system s uncertainty such as time varying characteristics, grey multiple step error correction method took the place of the conventional single step error correction method. The new method could effectively overcome the bad influence of some factors such as model mismatch.

针对对象特性时变等不确定因素，该文以灰色多步误差预测校正替代原有算法的当前一步误差校正，可以更为有效的克服模型失配等因素的影响。

Information is presented volumetrically in microliters of liquid consumed rather than simply a number of licks on the sipper tube with varying amount of liquid consumed.

消耗的液体体积以微升计，而不是简单地用每次饮水体积变化的舔吸水管的次数来计。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。