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Firstly, in the frequency domain, differentiatial operator is decomposed into magnitude and phase operator, and the fractional order expressions of periodical signals, such as sine wave, cosine wave and complex exponent signal, are deduced.

首先，在频域中将微分算子分解为幅度算子和相们算子，导出正弦、余弦和复指数信号的分数阶微分表达式；然后考察矩形、三角形、梯形等常用周期信号的分数阶微分。

Among the method operator decomposed method was introduced Which can improve S/N ratio and continuity of section.

其中引入了算子分解法。这有利于改善剖面的信噪比和连续性。

Kinetic equations of multibody systems with scleronomic constraint s are projected along the feasible and unfeasible directons of the constiaints respectively,and generalized accelerations of the systems are decomposed along the two directons using the bases of constraint matrix and its orthocomplement.

通过约束矩阵及其正交补的两组基，将定常约束多体系统的动力学方程沿与约束相容和不相容的两个方向上投影，并将系统的广义加速度沿这两个方向进行分解，得到描述系统运动的纯微分方程和求约束力的公式，同时提出了违约修正的一种方法。

A new scheme for laser beam focus position error compensation is proposed, In this scheme, a decomposing compensation scheme, the compensation action along laser beam is decomposed to three orthogonal straight-line coordinates: X、Y、Z, without extra actuator.

论文提出了一种新的激光焦点位置误差补偿方案，该方案不需要专门的执行机构，而是将激光聚焦头沿着光轴方向的补偿运动分解到机床的X、Y、Z三个直线运动座标上，称为分解补偿方案。

It is proved that a signal can be decomposed into the linear superposition of a series of component signals by singular value decomposition using these two kinds of matrices. However, the component signals obtained by the first kind of matrix are orthogonal with each other, while those obtained by the second one are correlative with each other.

文中从理论上证明了在这两种矩阵方式下，奇异值分解都可以将信号表示为一系列分量信号的线性叠加，但是第一种矩阵获得的分量信号是彼此正交的，而第二种矩阵获得的分量信号则不具有正交性。

A wiener filter can be decomposed in multiple stages by a sequence of orthogonal transfer matrixes.

这一结论对进一步开展固定结构降维研究具有指导意义。

To begin with, the smoothing effect of error which is decomposed into orthogonal vectors in grid function space is analyzed. The error-reducing effect in orthogonal subspace which is developed from high frequencies and low frequencies component has been analyzed.

将协调有限元空间分解成高频子空间与低频子空间的直和，从而将误差的衰减变化转化为考虑高、低频子空间上的误差的高频与低频分量的衰减变化。

In this case the Hilbert space can be decomposed into an orthogonal direct sum of partial wave subspaces, which are the simultaneous eigenspaces of the angular momentum operators J^2,J_3 and the operator K which describes the spin-orbit coupling.

在此情形下希尔伯特空间可被分解为部分波子空间的直角方向的和，这子空间是本征角动量算符J^2，J_3和描述自旋轨道耦合算符K同时存在的本征空间。

This project has no second pollution with high efficiency which has strong oxidate and decomposed effect on pesticide remain of vegetables and fruits.

项目简介：本项目高效安全，无二次污染，对果菜中的农药残留有较强的氧化和降解作用。

The harmful gas such as formaldehyde, benzene, ammonia, TVOC still has bad smell, bacterium to wait with oxyhydrogen freedom radical reacts, be decomposed immediately hurtless carbon dioxide and water.

甲醛、苯、氨、TVOC等有害气体还有臭气、细菌等与氢氧自由基反应，马上被分解成无害的二氧化碳和水。

I'm not an actor. I'm a professor of paleontology.

我不是演员，我是古生物学教授

Spider Network Web site that is a very image of the name.

网络蜘蛛即Web Spider，是一个非常形象的名字。