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In this thesis, we apply the equations of motion of steady Mach reflections and the oblique shock theory to derive polynomial expressions of the forms of f(r,Mo,P1) of downstream sonic and strong/weak separating conditions of reflected shocks of perfect-gas steady Mach reflections. We then obtain polynomial expressions of the forms of f(r,M0) for the limiting Mach angle condition of the above two expressions.

本论文首先应用稳态马赫反射流场运动方程式及斜震波关系式，推导出理想气体稳态马赫反射流场之反射震波下游之音速条件与反射震波之强弱分界条件之曲线解公式，并应用该曲线解公式来推导反射震波俱音速性质於Mach angle条件及反射震波俱强弱分界性质於Mach angle条件之公式。

Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.

首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。

Finally, we present an efficient algorithm for computing the minimal polynomial of a polynomial matrix. It determines the coefficient polynomials term by term from lower to higher degree.

最后，我们给出了一种计算多项式矩阵最小多项式或特征多项式的有效算法，它从低次项到高次项逐项确定最小多项式的系数多项式。

Considering that our algorithm also released the restrictions added on the input matrix in CHTB method and it is of lower computational complexity comparing with CHACM method, our algorithm is one of the good candidates for the computation of the minimal polynomial of a polynomial matrix.

本文提出的算法具有这样的优点：既去掉了CHTB方法的限制条件，又具有比CHACM方法更低的计算复杂性。

The Enneper's minimal surface is the unique cubic parametric polynomial minimal surface one can find and one can not find any high order polynomial minimal surface in the differential Geometry literatures.

极小曲面被广泛应用于建筑设计，飞机轮船制造业，在结构化学，材料科学，植物学，动物学等领域被用作各种模型，在这些应用领域已有很多文献出现，但是，在CAGD领域几乎还没有关于极小曲面造型方面的工作。

Sign pattern A is a SAP if every monic real polynomial of degree n can be achieved as the characteristic polynomial of a matrix with sign pattern A.

若给定任意一个n次首一实系数多项式f，都存在一个实矩阵B∈Q，使得B的特征多项式为f，则称A为谱任意符号模式。

An n×n sign pattern A is a spectrally arbitrary pattern if for any given real monic polynomial f of degree n, there is a real matrix B∈Q and B has characteristic polynomial f.

设A为n阶符号模式矩阵，若对任意给定的一个n次首1实系数多项式f，都存在一个实矩阵B∈Q，使得B的特征多项式为f，则称A为谱任意符号模式。

In this paper, introduces firstly a concept of polynomial coefficient matrix, and then the polynomial multiplication is masterly changed into the computing of matrix multiplication. Then a theorem is received. Throughout the process, the steps are very clear and the calculating is pretty simple.

该文首先引进了一个多项式系数矩阵的概念，然后巧妙地将多项式的乘法转变为矩阵乘法的运算，得到了一个定理，步骤清晰，计算简单。

In the temperature sensing, the theory of fiber Bragg grating temperature sensing has first been proposed, the characteristic of the FBG temperature sensing was analyzed, it was deduced that the sensitivity coefficients of first-order and second-order ,and experimental findings was protracted, the gained polynomial better inosculate with the theory value. The experiment was processed in the low temperature , the thermo-optic coefficient was emended in the polynomial of the normal temperature ,the result was accorded with the sensing character of the normal and low temperature ,and it was resolved that the theory account of the normal and low temperature did not accord with the experiment.

在温度传感方面，主要从光纤布拉格光栅的温度传感模式出发，对光纤布拉格光栅的温度传感特性进行了分析，推导出了光纤光栅的一阶与二阶温度灵敏度系数，并对实验数据进行了拟和，所得多项式和理论值吻合的很好，并对低温传感进行了实验，将在常温下得出的多项式进行了热光系数的修正，所得的结果同时符合常温与低温的传感特性，解决了低温与常温情况下的理论计算与实验的不一致性。

REPs extracted by polynomial fitting technique were unstable due to its high sensitivity to the spectral resolution, waveband range and the highest order of polynomial.

结果表明，叶片红边位置的计算结果对选择方法的依赖性很大，几种计算方法提取的红边位置与叶绿素含量的相关性均较好。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失