求积

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

In chapter two ,we determine the crossing number of the cartesian product of five graphs on 6-vertex with path.

第二章：我们确定了6个7阶图与路的笛卡尔积图的交叉数；第三章：我们证明了4个五阶图与星图的笛卡尔积交叉数；第四章：我们求出了完全三部图K_(1，m，n)的交叉数。

According to the frequency-domain convolution theorem, we can prove the peak frequency and phase are frequency and phase of the harmonic wave signal.

根据频域卷积定理证明最大峰值点的频率和相位就是信号的实际频率和相位，依据由卷积关系得出的关于幅值的方程求出校正幅值。

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。

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。

Thirdly, a multi-component form of equation(8)in reference[40]is worked out, then its Hamiltonian structure is presented byuse of the extended trace identity. Nextly, the expanding integrable model ofmulti-component integrable equation hierarchy is obtianed.

最后，将文献[40]中Liouville可积的方程族(8)式扩为多分量的形式，然后利用扩展的迹恒等式得到了该多分量方程族的HamiIton结构，接下来求出了多分量方程族的一类扩展可积模型。

After convolving the image model with the edge detection operators of second derivative model, a plane fitting in the least squares sense is used to detect the zero crossing points as edge points.

使用二阶导数型边缘检测算子对图象模型进行卷积后，用均方误差最小的准则对卷积后的图象进行平面拟合，并求出零交点作为图象的边缘点。

Also it can minimize leakage errors involved in fast fourier transform based measurement and can be pre-emphasized by keeping low crest factor.

与伪随机信号的周期反卷积不同，扫频信号通常都是由非周期反卷积求脉冲响应，这使脉冲响应的长度可以大于信号的长度。

DFT using the convolution nature for two complex sequence of linear convolution.

利用DFT的卷积性质求两个复序列的线性卷积。

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。