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The problem isdiscussed and the error caused by using the approximate formula proves to be superior to that caused by using the homogeneous Taylor's polynomial and an expression is proved to be similatr to the remainder in Taylor's formula.

由讨论这个问题出发，证明了用这种近似式产生的误差，优于用同阶Taylor多项式产生的误差，并给出这个误差的一个类似于Taylor公式余项的表达式。

Whence, the homomorphism proof system from formulas in MU(1) is complete, and this proof system and the tree resolution proof system can be transformed mutually in polynomial time on the size of proof.

从而，由 MU(1)中的公式构成的同态证明系统是完备的，并且由 MU(1)中的公式构成的同态证明系统与树消解证明系统之间是多项式等价的。

The analytic expression for such kind of hypersurfaces is given. Consequently, any umbilical Lorentzian isoparametric hypersurfaces of type Ⅱ with minimal polynomial^2 of A are the parallel hypersurface of M.

并且形算子A的最小多项式为(λ0a)^2的任何Ⅱ型全脐洛伦兹等参超曲面局部地与上述超曲面的平行超曲面叠合，从而完成了S(上标 n+1 下标 1)中的Ⅱ型全脐洛伦兹等参超曲面的分类。

Compared with the previous polynomial interpolating method, this method can avoid ill-conditioned matrices in the process of the calculation and obtain more accurate values.

相比于以前介绍的多项式方法，此方法不但能避免矩阵的病态，而且提高了计算的精度和效率。

The transcendental characteristic equation is converted into a polynomial equation at the imaginary axis without any substitutions.

针对具有单输入反馈控制的单时滞电力系统，提出了一种求解时滞稳定裕度的简便方法。

The transcendental characteristic equation is converted into a polynomial equation at the imaginary axis without any substitutions. This method needs less computation than the CTCR method.

该方法将含有指数项的特征方程在虚轴上转化为多项式方程进行研究，无需任何中间变量代换，处理方法简单，计算量小。

In this dissertation, segmentation, description and recognition of objects are studied systematically by the variogram function and implicit polynomial curve.

本文引进变差函数和隐含多项式曲线理论对景物图像中的物体分割、描述和识别作了较为系统的研究。

In fact, polynomial patches of degree 5 or higher tend to be noisy.

事实上，多项式片面数的程度5或增高趋势倍受争议。

To compensate for the incomplete projection data, polynomial interpolation method is proposed to deduce more projection data from the available ones. Furthermore ,with the Chapman model assumption of electron density distribution, a method to expand the view angle and evalute the projection data under low elevation angle is presented.

本文提出了用多项式插值的方法增加接收站观测数据，并根据对电离层垂直方向Chapman模型的假设，提出了扩展投影角度的方法，以估算观测中无法得到的低仰角投影数据。

The 3 order Yeoh constitutive model is used to describe the mechanical behavior of carbon-filled rubbers, the aging deterioration rule of carbon-filled rubber is discussed by thermal aging test, and an incomplete quadratic polynomial model is established by Response Surface method, which can describe the variation of performance with aging time and temperature of aged rubber.

用响应函数法建立了橡胶性能随老化时间、温度变化的二次不完全多项式模型，定量描述了材料热老化性能的变质规律。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷