二次公式

It's the first time that from the angle of computational mathematics combined with the structure model of parallel machine, the parallel degree of the relevant algorithms in orthopaedics clinic engineering modeling system, such as piecewise cubic Lagrange interpolation formula, piecewise cubic Hermite's interpolation formula, cubic spline, Chebyshev multinomial fitting algorithms, least square method and contour curve multinomial algorithms, were discussed.

论文首次从计算数学的角度并结合并行机的结构模式出发，讨论了在骨科临床工程造型系统中可能涉及的如分段三次拉格郎日插值公式、分段三次埃尔米特插值公式、三次样条函数、切比雪夫多项式拟合算法，最小二乘法以及轮廓曲线多项式求值算法的并行度。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

In Chapter 4 and Chapter 5, we discuss the quadratic finite element space with Regular mesh and the one with Criss-Cross mesh. We can respectively obtain the finite element asymptotic expansions and extrapolations in these situations. The high accuracy combination formulas are constructed.

在本文的第四、五章中，我们将在第二、三章中所使用的方法分别推广到Regular网格与Criss-Cross网格下的二次有限元空间中，得到了这两种情形下的有限元的渐近展式与外推结果，并构造出了相应的高精度组合公式。

Secondly, the problem of observer design for Lipschitz switched nonlinear systems is considered. By proposing a proper switching strategy and utilizing Schur complement formula and the related notion of LMI, we design a quadratically stable observer which can be used for both finite and infinite switched nonlinear systems. The main result is given in the form of linear matrix inequality. Simulations validate the correctness of the presented algorithms. The simplicity of the design algorithm makes it easy to be carried out.

通过设计适当的切换策略，利用Schur补公式和线性矩阵不等式的相关知识，给出了一种全局二次稳定的观测器的设计方案，这种方案适用于有限和无限切换系统，主要结果以线性矩阵不等式的形式给出，通过仿真实例验证了所提方案的正确有效性，该部分设计思路简单、易实现。

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.

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。

Based on the force and moment balances on the shaft and compressor frame, mathematical formulation of shaft bearing loads, unbalanced force and moment acting on the frame were made in terms of balance weight design parameters such as masses and installations of the upper and lower balance weights.

分析了在二次平衡中，主、副平衡重的安装角为任意值的条件下涡旋压缩机的动力特性，推导了在保证机架受力情况最好的条件下，通过改变平衡重的安装角来控制主轴承受力的设计公式，从而确保了轴承的使用寿命，提高了压缩机的可靠性。

Applying theories of Vector geometry and differential calculus, this paper aims to infer the internal force and geometry equations for curved beam, whose axis curve is parabola and being distributing-load.

目的 对形心轴线为二次抛物线形曲线梁的内力、几何方程进行理论分析与公式推导。

The conicoid fitting method used for transforming GPS elevation, and the basic structure and mathematic formulas of BP algorithm of neural networks are introduced briefly in this paper.

简要介绍了转换 GPS高程的二次曲面拟合法，以及神经网络 BP算法的基本结构和数学公式。

The formula to solve the weighting matrice is suggested.

此外，文中还讨论了线性二次型控制的逆问题，给出了求解相应的加权矩阵的公式。

D models are the most widely spread in the world of turbo-machinery for its simplicity, but they are indeed purely empirical correlations which not only fail to provide detailed information inside one or more components, but also require significant effort to recreate themselves if engine operating conditions or component representations change; quasi 3-D models have been the workhorses for compressor and turbine design for many years, and the primary benefit of using quasi 3-D system models is to facilitate the design and detail analysis of a particular component across the range of possible boundary conditions; Full 3-D models are gradually replacing quasi 3-D ones by virtue of requiring no exit flow angle model and loss model and being capable of predicting secondary flow in cascade.

零维模型由于使用时简单易行，因此在涡轮发动机的仿真中得到广泛应用，但零维模型作为纯粹的经验关系式无法反映部件内部的流动细节，并且一旦部件有少许改动则新特性的建立耗费巨大；准三维模型由于能够详细地提供部件内部的流动情况，方便设计而成为涡轮和压气机设计的主要工具；全三维数学模型正逐步取代准三维模型在涡轮设计中的主导作用，同后者相比前者能够预测叶轮机械内的二次流动，在粘性流计算时不需要气流角和损失的经验公式，因此拥有巨大的发展前景。

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。