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The condition for a 3D polynomial map to be equivariant is theoretically analyzed and proved.

研究了基于三维多项式映射的三维广义Julia集表示方法。

The expressions of polynomial and neural network are used to approximate angular error, it is demonstrated that the variance error by using neural network is smaller, which raises a higher request on the performance of the computer.

本文研究了误差模型的存贮方式问题，对于误差拟合采用了多项式法和神经网络方法，神经网络法的逼近程度高，但对计算机的性能要求也高。

A modified Euclidean algorithm was proposed by the generalization of synthetic division. It didn't judge the degree of polynomial and could decrease the complexity of decoding and hardware circuit and improve the decoding speed.

通过对综合除法进行推广，提出了一种改进型欧几里德算法，它不需要进行多项式次数的判断，能够降低译码的复杂度，减少硬件电路的复杂性，提高译码速度。

After that a 40 degree univariate polynomial equation can be obtained. Other variables can be computed by Euclidean algorithm and Gaussian elimination.

使用辗转相除法和高斯消去法可以直接快速的求出其他3个变元。

First, by using the properties of knots and the Jones polynomial, we research the relation between them, thereby involving in the projection diagram with n crossings, discuss the state S of the projection diagram L , through the properties of vertexgraph, Euler Formula, one studied the problem of the equal of the knots.

首先，我们利用纽结及琼斯多项式的性质研究了它们的关系，进而涉及了有n个交叉点的纽结投影图，对其投影图L的状态S进行讨论，并通过四岔地图，欧拉公式等性质，研究了纽结等价性问题。

Excess demand function ; polynomial function.

超额需求函数；多项式函数

The main results are: given n - 1 polynomials satisfying some conditions,then each polynomial can represent an excess demand function for corresponding commodity.

p1，p2，…，pn－1），s＝1，2，…，n—1，若满足条件：则Es，s＝1，2，…，n—1均为一个经济的超额需求函数。

Then obtains the judgment theorem and existence theorem of the rational root of the integral coefficient polynomial.

进而得出整系数多项式的有理根的一个判定定理和根的存在定理。

Here, the theory and the deducing process of the SEM based on the Legendre polynomial is given. The SEM can get a global diagonal mass matrix, which leads to a very simple explicit time difference scheme and high efficiency. Numerical simulation in the transversely isotropic medium are shown and the results approved that the SEM is a effective method for seismic wave modeling.

文中阐述了基于Legendre多项式的谱元法的理论和推导过程，该方法可以形成全局对角质量矩阵，在时间域使用显式的差分算法，提高运算效率，最后通过横向各向同性介质的数值计算，模拟结果表明该方法是一种有效的数值模拟方法。

Polynomial, first order decay exponential and wide kelvin-vogit models were used to fit material creep curves.

采用蠕变和粘弹性材料模型进行热压仿真分析，对仿真结果进行对比，选择热压仿真的材料模型。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。