二次公式

Secondly, in our methods, the essential geometry of the image single axis geometry may be specified by six parameters and this may be estimated from one conic and one fundamental matrix (a total of 12 parameters) or may be minimally estimated from two conics (a total of 10 parameters).

本文证明了单轴旋转运动的不变量可以通过一个基本矩阵和一条二次曲线来确定，在这种情况下，由于基本矩阵的自由度为7，二次曲线的自由度为5，所需确定的参量个数仅为12，大大减少了不变量的计算量；本文同时证明单轴旋转运动的不变量可以通过最少两条二次曲线来确定，在这种情况下所需确定的参量个数仅为10，该方法是目前同类算法中参数最少的；本文提出了用多条二次曲线求解单轴旋转运动的不变量的最大似然估计算法，其所需确定的参量个数为6+2n，其中n为二次曲线的个数，该公式更深刻地反映了二次曲线与不变量的参数关系。

The principle of the fractal-interpolated surface was discussed. The formula and the theorem of fractal dimension of the fractal-interpolated surface were analyzed. The numerical analysis of height anomaly fit by the fractal interpolated surface and the result comparison with the quadric polynomial surface model with practical data were given.

本文论述了分形插值曲面的原理，分析了分形插值曲面的计算公式，讨论了分形插值曲面的维数估计方法和公式，用实际数据进行了分形插值曲面拟合高程异常的数值分析以及与二次多项式曲面拟合模型结果的比较。

In this paper, we construct the differential equation to solve the unconstrained optimization problem. Such methods solving the ill-conditioned problems are very effective. It indicates that the asymptotically stable region of explicit the Euler method to solve the differential equation equals to the descent region of the gradient method to solve the original unconstrained optimization problem.

我们发现，在用Euler方法求解二次优化问题的等价动力系统的方程时，由方法的步长确定的稳定区域对应于这些方法所得到的迭代公式的步长满足单调下降算法的条件确定的单调下降区域，因此我们可以利用这个性质构造解无约束优化问题的数值方法而不采用标准的常微分方程的数值求解公式。

We know that the solutions of quadratic, cubic and quartic can be expressed by radicals. As to the solution of the quintic which has became an issue for past two or three hundred years, it was not solved until 1832 a great young Mathematician of French named Galois who recommended group theory that proved a polynomial of degree 5 and over 5 can't be solvable by radicals.

中文摘要我们知道二次、三次及四次的方程式都可以用根式表示，至於五次方程式的解迟迟无法解决，这个问题持续了两三百年，直到1832年，一位法国青年Galois在其决斗前夕，在他的遗书中，这位伟大的青年数学家引进了群的理论，证明了：五次及五次以上的方程式，不可能有公式解。

The observation results reveal the difference between surrounding rock pressures of shallow tunnel calculated by exiting methods and test results is large, pressure figure seems cat ear, surrounding rock pressure of deep tunnel belongs to clastic pressure, the test result is consistent with result by modified KAKE formula, the invert stress properties of shallow tunnel and deep tunnel are different, the axial force of lattice girder is at pressure in majority, and the stress of second lining is relatively small in loess highway tunnel.

实测结果表明：现有浅埋隧道围岩压力公式计算结果与实测结果偏差较大，其分布呈"猫耳朵"形状；深埋隧道围岩压力属形变压力，其实测值与修正卡柯公式计算结果较为一致；深埋与浅埋隧道中仰拱的受力性态有所不同；格栅拱钢筋轴力以受压为主；黄土公路隧道二次衬砌受力相对较小。

So, the approximate calculating formula of parabola and the length of ellipse arc is developed by the method of finding experience formula from point of view of simplifying the calculating process and getting certain accura...

本文从既能简化计算又能达到一定精度的设想，通过找经验公式的方法给出了计算机抛物线及椭圆弧长的近似公式，并给出了常用区间上计算抛物线和椭圆弧长的一次式和二次式。

Questions in this content area are based on an understanding of the quadratic formula, rational and radical expressions, absolute value equations and inequalities, sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers.

中等代数（ 15 ％）。这方面的考试内容包括理解二次公式，有理式及根式，绝对值方程和不等式，序列，方程组，二次不等式，函数，建模，矩阵，多项式的根以及复数。

A formula was proposed to explain the effects of secondary-scattering in the electron impact experiment, based on this formula, and the secondary-scattering coefficient as a function of the scattering angle was investigated.

在一定假设下利用公式解释了在电子碰撞实验中二次散射效应对实验测量的影响，并在此公式的基础上研究了对CO不同跃迁的二次散射系数随角度的变化关系。

By the utilization of the symmetric characteristic of the tensor, algebra relation between the elements in the tensor and refraction index ellipsoid equation, an approach base on Attenuated-total-reflection technology was proposed for the measurement of the QEO coefficient of the organic polymer.

有机聚合物材料的二次电光系数是衡量其二次电光效应的一个重要参数，其可以用一个6×6阶的张量来表示。利用该张量的对称特性、各个元素之间的已知关系以及折射率椭球公式，本文提出了一种基于衰减全反射技术的测量有机聚合物二次电光系数的方法。

Theory; the spatial meshing theory includes comparative motion, comparative differential and conjugative curved surface; and the application of meshing theory includes gear drive and worm drive. The spatial meshing theory is the main part of the course.

课程的重点讲解内容有曲线的参数方程、切线、法面、弧长、曲率、空间曲线的基本公式、挠率及平面曲线的基本公式等；曲面第一和第二基本公式，法曲率、主方向和主曲率、欧拉公式、短程挠率、欧拉公式和贝特朗公式推广、相对法曲率和相对短程挠率等；刚体的绝对和相对运动速度、相对微分和绝对微分、相对速度和相对微分、轨迹曲面的法曲率和短程挠率等；空间共轭曲面的啮合条件、诱导法曲率、两类界限点、等距共轭曲面、空间啮合的二次接触原理等；蜗杆传动的数学模型建立及啮合特性分析方法等。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。