求解过程

Because this equation has the character of parabolic type in mathematics, it could provide a very accurate and powerful tool for computing fluid mechanics and heat transfer characteristics in micro-tubes after fully developed region.

我们为了方便计算程式的求解过程，将三维的圆形微管流简化为二维轴对称x-r方向的平面流场，并求解边界层方程式。

The constraints with different linearity in this model are dealt with by an approach that combines successive linearization with piecewise linearization, and in the solving process the security and stability constraints of transmission lines are directly considered to avoid the low-efficiency of both model and solution due to the passive calibration and modifying working constraints in Newton method.

对模型中线性度不同的约束，采用逐次线性化和逐段线性化相结合的方法处理。在求解过程中直接考虑线路安全稳定约束，避免了牛顿法被动校验和变更约束带来的模型和求解的低效性。

A problem of cable force optimization of cable-stayed bridge is equated as a nonlinear implicit optimization model. In the mathematical model, the object function is minimizing summation of bending strain energy and axial strain energy, and the constrain conditions are nonlinear and related to reasonable finished dead state. The optimization model is solved by projection gradient method, fully considering all kinds geometric nonlinearity.

把超千米级斜拉桥的索力优化问题归结为非线性隐式优化的数学模型，以系统最小弯压应变能为目标，根据合理成桥状态指定各种非线性约束条件，利用投影梯度法进行优化问题的求解，求解过程中充分考虑了各种几何非线性的影响。

Its most advantage is: it is suitable for any complex geology structure, the"iterative"ray tracing method is based on Fermat"minimum travel time principle", it uses Taylor expansion and finds the solution segmentally and iteratively, then modifies the initial ray path.

迭代射线追踪方法是根据Fermat最小旅行时原理，应用Taylor展开，分段迭代求解，再逐次修改初始射线路径，完成全射线路径的迭代求解过程，其最大优点是计算的速度快，追踪射线效率高。

In order to avoid the singular problem in matrix operations,a step-by-step method is developed to compute the model parameters during the process of parameter finding.

利用环形邻域构建马尔可夫模型，在模型参数求解过程中，为了避免矩阵奇异，设计了模型参数分步求解算法。

The error compensation is introduced in the interpolation algorithm to increase the interpolation point's solution precision of the parametric curve, and the reasonable simplification of the compensation expression is carried in the solution process to decrease the calculation load of interpolation.

通过引入误差补偿值以提高参数曲线插补点的求解精度，在求解过程中对误差补偿值进行合理简化以降低插补计算量。

Based on boson-fermion model, we illustrate how to get the flow equations and how to solve spectral function of this model.

基于玻色子—费米子模型介绍了该方法的求解过程，以及如何利用流方程求解系统的谱函数。

Adding boundary conditions in whole equations in the wavelet Galerkin method frequently does with its of differential equations. The result can derive by solving transcendental equation, which make unknow quantity number and the number of system of equation become nonuniformity.

经常采用的小波Galerkin方法对微分方程边界条件的处理，均是将边界条件作为附加方程补充到整体方程中，从而求解超越方程组得到原方程的解，这导致了求解过程出现的方程组个数与未知量个数不一致。

Based on the Hertzian contact theory, the pressure distribution on balls of a pair of angular contact ball bearing under three dimensional loading conditions was analyzed.

本文首先介绍了Hertz接触理论的基本特点与求解过程，对于实际存在的有限长线接触问题进行了详细讨论并完成了对该问题基本积分方程的一维数值求解。。。

Finally, we mainly investigate the following three problems:(1) The problem of portfolio selection with transaction costs is formulated as a bi-objective programming model, but it is no-differentiable and difficult to solve. With a transformation, we can transform the nondifferentiable nonlinear programming problem to a linear program.

然后主要做了如下三个方面的工作：（1）针对带交易费的最优证券组合选择问题可以表示为一类不可微非线性规划模型，但其求解比较困难的特点，提出了一种新的化简方法，一次变换即可将该类不可微非线性规划模型转化为一个线性规划模型，不仅简化了求解过程，而且还减少了最终的线性规划问题的变量个数。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。