求解

Then the shapes and amplitudes of geometrical imperfection can be determined through the decomposition of the correlation matrix.

这种求解拱结构随机几何缺陷的方法同样适用于其它结构中随机分布几何缺陷的分布方式及大小的求解。

The method for calculating the expression of the trapezoidal corrugation slow-wave structure is studied in detail,which uses Fourier series expandedness.

利用傅里叶级数展开，给出了一种求解梯形慢波结构表达式的方法。通过数值模拟，研究了级数展开次数对求解精度的影响。

In this paper we introduce the hyperbolic cosine function and construct the new hyperbolic cosine penalty function and algorithms, further more, we construct the new hyperbolic cosine multipier penalty function .

本文在传统形式的罚函数基础上引入双曲余弦函数做罚项，构造了新的对于一般约束优化问题的双曲余弦罚函数和求解迭代公式；进一步地，又提出了求解具有等式约束优化问题的双曲罚函数乘子法。

Then,the cosine value of central angle between the spacecraft and the descending node is solved by using cosine theorem of spherical geometry to avoid the cumbersome solving process by judging the flight direction of a satellite and the latitude of sub-satellite point in an original calculation model of image motion speeds.

通过球面几何的余弦定理直接求解航天器与降交点相对地心夹角的余弦值，避开了原像移速度计算模型中通过判断卫星飞行方向和星下点纬度来求解航天器与降交点相对地心夹角余弦值这一过程。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables,and the state and costate variables inside the time interval were approximated by Lagrange interpolation.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

To formalize this algorithm,crosscutting contract calculus and a set of contract elaboration rules are presented.

为了形式化这个算法，提出Crosscutting Contract演算和一组契约求解规则，并通过定义和证明契约完备性来保证契约求解过程的正确性。

These experimental results demonstrate that CUA adapts to both constrained and unconstrained problems, and has the virtues of occupying little memory, computing quickly and accurately, supplies the designers with sufficient convenience during the design stage.

这些例子验证了CUA既可以求解约束问题，也可以求解无约束问题，并且具有占用内存小、计算速度较快和精度较高的优点，可以为设计者在产品设计阶段提供便利。

The characteristic function of the probability density function of response variable is obtained by the high efficient multidimensional numerical integration method or convolution integral based on response surface method. Then the discrete probability density function of response variable is calculated using the fast Fourier inverse transform technique, at last the cumulative distribution function of the response variable can be quantitatively determined.

首先利用高效多维数值积分方法或基于响应面法的卷积积分求解功能函数的分布函数的特征函数，也就是进行Fourier正变换；然后利用快速Fourier逆变换数值求解功能函数的概率密度函数，进而求得失效概率。

A three- dimensional turbulence model in non-orthogonal curvilinear coordinates is proposed to investigate the impacts of vegetation on channel morphology. The model includes vegetation-induced drag force and vegetation density in the control equations to describe the effects of vegetation on flow structure, and solves sediment continuity equation to compute channel geometry.

本文建立曲线坐标系下的三维湍流模型研究水生植物对河道形态的影响，在水流控制方程中加入植物阻力项和植物密度项来描述水生植物对水动力特性的贡献，通过泥沙质量守恒方程求解河道变形，在适体网格中求解模型的控制方程。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。