问题求解

Therefore, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

因此，该问题的解答可归结为对一组无穷代数方程组的求解问题，并可利用截断有限项的方法对其进行计算。

And the prospect for the future of genetic algorithm in solving TSP is made.

最后，简单说明了混合遗传算法在求解TSP问题中的应用并对遗传算法解决TSP问题的前景提出了展望。

Chapter 5 solves the difficult degree-constrained minimum spanning tree problem by ant algorithm. Large number of tests and comparisons show the effectiveness of the searching strategy for highly constrained problem instances.

第五章对度约束最小生成树问题这个难题设计了相应的蚂蚁算法，通过大量试验求解并与其他算法作比较，发现这种蚂蚁搜索策略对于约束条件苛刻的问题实例来说，效果十分明显。

In two examples of bi-objective optimization for cantilever beam and rocket engine, linear weighted method and gradual easy constraint method and neighborhood cultivation genetic algorithm method were used to obtain Pareto Front.

并且在悬臂梁的优化问题中，对不同的定值点用目标点法求解优化问题的非劣解，结果说明不同的定值点对应不同的优化结果。

In order to improve the efficiency, an implementing scheme (according to the distribution of strain energy density) was suggested when to consider the fact that the high gradient usually appears only in a very local region, especially in the case of huge amount of computation. All programming has been finished on the platform of commercial codes Mathmatica and Fortran.4. A number of numerical examples and applications were presented to verify the proposed Bezier-Based Element Method. The engineering cases include: the belt die for diamond synthesize, the main frame of wire-rounded press, the hydraulic cylinder of open die forging press. The numerical results show that the BBEM has some good performances.

通过大量的数值算例来考证所构建的各种类型单元，并应用于人造金刚石年轮模具、钢丝缠绕预应力机架和液压机工作缸等实际问题的结构分析；结果表明：所构建的Bezier耦合单元具有描述较大梯度变化场(如位移场、应力应变场等)的能力，该方法不改变单元的大小和形状，保持单元的自由度数不变，而通过调节中间可动节点的位置改变单元内部的场分布，只需少量单元即可较精确地模拟较大的梯度变化；可为有效求解高梯度问题提供新思路，对实际工程应用具有重要意义。

A number of numerical examples and applications were presented to verify the proposed Bezier-Based Element Method. The engineering cases include: the belt die for diamond synthesize, the main frame of wire-rounded press, the oil cylinder of open die forging press. The numerical results show that the BBEM has some good performances. With few elements, the BBEM can lead to a high accuracy. If using same DOFs, the computing precision of BBEM is remarkable higher than that of the conventional FEM.

通过大量的数值算例来考证所构建的各种类型单元，并应用于人造金刚石年轮模具、钢丝缠绕预应力机架和液压机工作缸等实际问题的结构分析；结果表明：所构建的Bezier耦合单元具有描述较大梯度变化场（如位移场、应力应变场等）的能力，该方法不改变单元的大小和形状，保持单元的自由度数不变，而通过调节中间可动节点的位置改变单元内部的场分布，只需少量单元即可较精确地模拟较大的梯度变化；可为有效求解高梯度问题提供新思路，对实际工程应用具有重要意义。

Since the initial start of buried pipelines results in three-dimen-sional unstable heat transmission , and at initial start the temperature change of the soil around a pipeline is affected by the temperature inside the pipeline and the ground surface temperature annual fluctuation, the differential equation for heat transmission and the boundary value may be line...

埋地输油管道启输过程是三维非稳定传热问题，启输过程中管周土壤温度场的变化受管内热水温度和启输前地表面温度年波幅的影响，可将传热微分方程和边值条件线性组合成两个定解问题，用电子计算机进行数值求解，得出计算公式，以确定预热阶段管路任一点任一时刻的热水介质温度。

Based on the previous research about the ice-harvester tank, the paper further investigates the properties of tank at ice-filling and ice-melting, notifying the relation between the two rest angles, bringing out the method to optimize the tank"s dimensions, resolving the ice-filling problem according to the connection between the icepack and the tank"s underside, analyzing the ice-melting problem with discharge capacity.

本文在国内外有关片冰机蓄冰槽研究成果的基础上，对蓄冰槽在蓄冰和融冰时的特性做了进一步的研究，揭示了两个安息角的关系，提出了优化蓄冰槽尺寸的方法，根据冰床与蓄冰槽底面接触的情形求解蓄冰问题，用融冰能力分析融冰问题。

So we can use any 2D prestack procedure to process them, such as time migration, depth migration and velocity analysis.

它通过投影变换的方法，将三维叠前数据体投影为一系列的径向二维叠前数据体，从而将三维叠前问题转化为一系列的二维叠前问题来进行求解，使得三维叠前资料的偏移成像可以在中小型计算机上进行。

First, the stochastic dominance rules of the stochastic decision problems corresponding to the case with continuous decision variates and the case with partial information are studied, and an interactive procedure based on stochastic dominance rule is proposed for stochastic decision problems.

根据这类问题包含不确定性因素的特点，本文从随机资源分配问题的建模和求解一般随机优化模型的随机优势、随机规划方法两方面着手进行了研究，并研究了区域规划中的资源分配实例。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷