相同运算

The expanded formulas of Reed-Muller with fixed polarity and dual form of Reed-Muller are derived by using Kronecker matrix product operation. A simple and highly efficient transformation algorithm named decomposition method is proposed based on the transformational relation of the two expanded formulas with same polarity.

利用Kronecker矩阵积运算推导出了固定极性Reed-Muller和双重形式RM(dual form of Reed-Muller， DFRM)的展开式，并根据在相同极性下两者之间的转换关系，提出一种简洁高效的转换算法－分解法。

This is exactly what happens in a conventional logic gate as well.

这和在传统逻辑闸内的运算是完全相同的。

While matching, only the principal component directions corresponding to the rows of the same serial numbers in searching area are needed to be extracted for the computation of projection value so as to form the vectors of projection values. The distances between MM-vectors and the vectors formed by projection values are computed, and whether the two kinds of vectors are matchable should be in accordance to those distances.

在匹配时，只需抽取搜索区域中相同序号的列向相应的主元方向作投影运算，从而构成投影值向量，进而计算该向量与预处理中所得的最大最小值构成向量间的距离，从而根据距离的大小判断是否匹配。

We expect it will benefit the industry field to break through the optical measuring limits at present by offering some new ideas. Optical measuring research based on moire interferometry has developed for several decades. The main idea of this research is to utilize the moire effect caused by two superimposed gratings of identical or similar spatial frequency. One is the reference grating and it is a virtual grating created by a computer program in this research; The other grating is the image of grating projected on the measured surface by the DLP projector, and this grating will distort because of the different sloped profile of the surface. To superimpose the program-created grating and the captured distorted grating will derive the so-called moire effect. This research combined the basic theory of optical interferometry and moire effect to project the different phases of the projected grating fringes by the phase-shifting method and compute the principal value of arguments between -π,π. In the end, the phase unwrapping program based on discrete Fourier transform of solving PDEs is used to unwrap the phase of the measured surface, and finally the surface profile is derived by the optical measuring system.

以叠纹干涉术为基础的光学检测研究之发展早已行之有年，而在本研究中所采用的投影叠纹法(Projection moiré)之主要精神在於藉由两道空间频率相近或相同的光栅相互叠加而成的效应，其中一道为参考光栅，而本研究中的参考光栅是以程式产生可调整不同空间频率的虚拟光栅；另一道则为投影至待测物表面的光栅影像，而在起伏高度不一的待测表面上的光栅影像会受到待测物表面起伏状况不同而在观测方向产生光栅投影条纹影像的歪曲变形，将电脑产生的参考光栅与由影像撷取装置所获取投影於待测物表面的光栅影像作叠合，便会产生所谓的叠纹效应；利用基本的光学干涉理论与叠纹效应结合，本研究中以相移法来改变投影於待测表面的光栅相位，再以相移法的理论反运算出在带有待测面各点高度资讯之介於-π，π相位主幅角，再以离散傅立叶转换解偏微分方程的相位重建程式还原待测面的相位值，以得知待测面之表面轮廓。

Since two curves have the same coordinates and unit normal vector at the contacting point, the problem of the mesh of two planar curves is transformed into an ordinary differential equation by vector analysis. We have the solution to the equation by numerical method and computer calculation. After repeating the way of computing the solution to the equation, we have the contacting points.

因两曲线於接触点的位置相同，单位法线向量相等，由向量分析使曲线接触问题转变为常微分方程式，藉助数值计算与电脑运算得到方程式解，重覆计算方程式的解即可得每一接触点的位置。

This paper presents the cumulative-sum is a new data processing methods, It is a similar effect with the least squares method, it is more than simple arithmetic, Based on photoelectric effect measured Planck constant example, Introduced the methods for solving a linear equation with cumulative-sum method.

本文介绍的累积法是一种新颖的数据处理方法，它是一种效果与最小二乘法相同，比它更简明的运算方法，本文以光电效应法测普朗克常数实验为例，介绍了用普通累积法解一元线性方程的方法。

Based on it, a new efficient implementation of preconditioned conjugate gradient is put forward to solve the Gauss-Newton equation and save the cost on computation with the same exactly quadratic convergence to the traditional choleski factorization.

新算法与传统的使用Choleski技术的Gauss-Newton法具有相同的收敛速率，但在求解 Gauss-Newton方程组时减少了代数运算的计算量。

The slide rule is a mechanical device that uses the very same physical quantity -- length -- to represent numbers, and to help perform arithmetical operations with two or more numbers at a time.

该计算尺是一个机械装置使用相同的物理量-长度-代表人数，并协助执行算术运算与两个或两个以上的号码的时间。

As a minimum requirement, the algorithm should be able to align and superpose identical structures.

该运算法则最起码能排列和重叠相同的结构。

Two types of coefficients transforms are compared,The minimal number of nonzero digitals called Canonic Sign Digital and common substructure sharing mode are used to improve performance of raise cosine shape filter.

利用Canonic Sign Digit表示定点数并且实现高效的移加运算，实现定点数乘法可以极大减少硬件资源[1]，利用滤波器邻近抽头系数的特点进行相同项的合并共享进一步精简硬件资源[2]。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。