求积公式

For interpreted preceding N terms of inner product of arithmetic progression with 2-order symmetric sequence with property of sequence the expression is be made up of the same like with generalized diagram multiplication method symmetric formula.

利用对称数列性质分析等差数列与二阶对称数列的内积，建立与广义图乘法对称型公式一致的数列内积的对称型公式。用算例说明公式在求弯矩、数列和概率中的应用

Realization of an algorithm MSDP for minimal disjoint sum of products based on the recurrent formula with the sharp # operation. MSDP algorithm can be used to any kind of two-value structure functions (coherent or non-coherent).

根据所提出的递推原理及公式，利用立方体的锐积#运算，给出并实现了一个求最小不交积之和的算法MSDP，并对算法的各主要步骤进行了讨论。

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。

Under the one-dimensional situation, it introduces mainly the Newton-Cotes formula, the Gaussian quadrature formula, the numerical integration rule of sharp oscillatory function, the numerical integration rule by the methods of sampling and so on.

在一维情形下，主要介绍了Newton-Cotes公式，Gauss型求积法则，急速振荡函数的数值积分法则，抽样法求数值积分的法则等。

Proceeding by Bubnov-Galerkin method in combination with numerical method based on the quadrature formula the problem was reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.

根据Bubnov-Galerkin法，结合基于求积公式的数值方法，将问题简化为求解具有松弛奇异核的非线性积分－微分方程的问题。

By adapting the existed numerical methods for ordinary and delay differential equations, and matching certain suitable numerical quadrature formulas, Rosenbrock methods are constructed for delay integro-differential equations, the stability criteria of the methods are derived.

通过改造现有常及离散型延迟微分方程的数值方法，并匹配以适当数值求积公式，构造了求解时滞积分微分方程的Rosenbrock方法，导出了其稳定性准则。

Then, using the second-order central difference to discretize the time derivative of the displacement, and applying the quadrature formula to the mass matrix, a fully discrete lumped mass Morley element method i...

然后利用中心差分格式离散时间方向的二阶导数，再利用适当的求积公式得到薄板弯曲问题的集中质量Morley元全离散格式。

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。

The Romberg formula is a successful example of peecise solution,wish is worked out from linear combination few approximate solutins.

Romberg求积公式以精度高而著称，而且也是用几个粗造的近似值的线性组合得到较为精确值的成功典范，因而在数值积分中广为运用。

Report : Programming Environment : Newton MATLAB7 K polynomial interpolation procedures to achieve Romberg of Quadrature program Gaussian out PCA Elimination of the program.

详细说明：计算方法实验报告：编程环境：MATLAB7.0 牛顿K次插值多项式的程序实现龙贝格求积公式的程序实现高斯列主元消去法的程序实现。

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。