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The given estimated values of variables in Newton method is a crucial problem for the final solutions, the solutions of the first order approximation of the Fourier series to land surface temperature were used to the input initial given values of the Newton numerical method.

在牛顿迭代解法中，很关键也很困难的一个问题是初始值的给定，本模型中牛顿迭代的初始值是傅立叶级数对地表温度一次逼近得到的结果。

This paper proposes a novel muiti-objective evolutionary algorithm, based on a novel crossover operation and improved crowding operation of NSGA-II ,in order to quicken further rate of convergence of solutions to Pareto optimal front and improve precision of solutions.

为了提高非劣解向Pareto最优前沿收敛的速度及进一步提高解的精度，本文在设计了一种新的杂交算子并改进了NSGA-II的拥挤操作的基础上，提出了一种基于分级策略的多目标演化算法。

Then the rigorous solutions for soil layer vibration are analytically derived by virtue of the separation of variables. By means of the orthogonal expansion technique, the coupling system solutions are finally obtained.

在这一背景下，本文考虑了饱和土的三维波动效应，采用解析方法对三维轴对称成层饱和土中完整桩及各类变阻抗桩的纵向耦合振动理论进行系统研究。

Taking HPAM solutions as an example, the unsteady flow of power-law fluid in eccentric annuli with the inner cylinder reciprocating axially is calculated; the distribution of velocity, flow rate and stability parameter is obtained; taking HEC solutions as another example, the flow of second order fluid in eccentric annuli with the inner cylinder moving axially is calculated too; the distribution of velocity and stress is obtained; the effect of eccentricity and axial movement on stress distribution on the outwall of the inner cylinder is analysed.

在理论上，分别用二阶流体和幂律流体模型描述聚合物驱油井产出液的非Newton流变性；分别建立了双极坐标系下二阶流体和幂律流体在内管做轴向往复运动的偏心环空中非定常流的控制方程及边界条件和初始条件方程；建立了幂律流体在内管做轴向往复运动的偏心环空中流动的稳定性参数和流体在内管壁上的压力分布计算公式；建立了二阶流体在内管做轴向运动的偏心环空中流动的流体在内管壁上的压力分布计算公式。

This paper presents a method to embed the original problem into separable parametric optimization problems and proves that the optimal solutions of the original problems are in the set of solutions of separable parametric optimization problems.

本文把原问题嵌入到可分的参数规划问题中，并证明了原问题的最优解包含在可分的参数规划问题的最优解集中。然后从最优解集中挑出原问题的最优解。

In this paper, the author is concerned with the problems that are to be solved in the field of Partial Difference Equations such as the following: the existence of oscillatory solutions of some partial difference equation, the asymptotic behavior of positive solutions of the same equation.

本文旨在研究当前偏差分方程领域中尚待解决的有关振动解的存在性及正解的渐近存在性等问题。

Chapter 2, we investigate the existence of multiple positive solutions of the neutral partial difference equations on the base of the existed results of partial difference and difference equations, and obtain some sufficient conditions for the existence of multiple positive solutions.

第二章，基于已有的偏差分方程和差分方程的结果，我们研究了高阶非线性中立型偏差分方程多正解的存在性问题，建立了判断多正解存在的充分条件，对前人的结果进行推广。

The results show that there exists different forms of soliton solutions and periodic solutions for this coupled system.

结果表明，这个系统存在不同形式的包络孤子解和周期解。

To obtain more practically optimal solutions for production planning in chemical enterprises, piecewise linear function and polynomial function were used to model nonlinear unit consumptions.The optimal solutions obtained by the two approaches were compared in case studies.

为了得到更切合实际的化工企业生产计划优化结果，采用分段线性函数和多项式函数对非线性单耗问题建模并进行比较。

Comparing the analytical solutions with numerical simulations, we found that our analytical solutions are precise when the point of incidence is not near the boundary of the medium.

通过数值模拟证明了该结果在不靠近样品边界的范围内都是准确的。

It has to be computed by the host for the actual clock rate.

主控制器可以用来计算实际的时钟速率。

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