求积分法

The relationship between transient response and shape design variables is highly non-linear, and the behavior of feasible domains is often not good, which may cause convergence difficulties. In order to improve convergence speed of iteration process, some algorithms the feasible domains adjusting, the adaptive move limit, the approximate line search and the approximate reanalysis, are adopted.

采用基于Newmark积分的直接求导法计算瞬态响应灵敏度，在序列二次规划算法中采用了可行域调整、近似—维搜索、自适应运动极限等改进技术，提高求解效率和收敛稳定性，以解决结构动态响应与设计变量的关系复杂、高度非线性，优化可行区域的性态不良等问题。

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared.

分别用无穷级数展开方法和数值积分计算中的高斯拉盖尔求积法对高能重离子碰撞中能量密度和粒子密度数值进行计算，并对结果及级数展开中的高次项和一次项的大小进行了比较。

Gust loading factor of displacement on three direction of the dynamic responses is obtained by the direct integral calculus method in time-domain.

利用时域内的直接积分法求出结构响应的时间历程，并且通过统计，得出了结构脉动响应三个方向的位移风振系数值。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用"去行去列法"和"置大数法"进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

It describes the heteroskedasticity character of interest rate by projecting the sample data onto the EGARCH (1, 1) auxiliary model, makes making the covariance matrix as moment conditions and uses EMM to estimate the parameters. EMM avoids the disadvantage of infeasible or computationally intensive of maximum likelihood functions.

通过将观测数据映射成EGARCH(1， 1)辅助模型描述利率行为的异方差特征，以协方差矩阵为矩条件，用有效矩估计方法得出模型参数，避免了最大似然估计法似然函数不可知或难以求积分的缺陷。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

This paper presents mechanical quadrature methods for solving the boundary integral equations of nonlinear boundary value problems.

本文提出了解非线性边值问题的边界积分方程的高精度机械求积法。

It is the purpose of this thesis to study the mechanical quadrature method and itssuper-convergence for solving first kind weakly singular Volterra integral equations.

本文旨在研究Volterra积分方程的机械求积法及其超收敛技术。

Moreover,according to this method,the deflection curve equation of other kinds of variable section beam will be also carried out.

本文利用积分法求出了变截面悬臂梁在各种不同载荷作用下的挠曲线方程，而对于其它类型的变截面梁，都可以按照这种方法去求解。

Analysis of tube-in-tube structure of variable cross-section in torsion;2. By assuming the structure to be continuous,the Hamiltonian dual system of coordination analysis is established for tube-in-tube structure s,in which the shears and flexures of the inter and the outer tubes are considered as Timoshenko beams.

在结构连续化假定的基础上，将内筒和外筒视为铁摩辛柯梁，同时考虑内筒和外筒的剪切与弯曲变形，建立了筒中筒结构协同分析的哈密顿对偶体系，导出了相应的状态空间方程，其系统矩阵具有辛矩阵的特性，可用精细积分法求该体系的高精度数值解。

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。