数学化

The success of Indian mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension.

印度数学的成功主要归功于印度人对物体的数量或空间的扩展抽象成清晰化的数字的观念。

Several combining with middle school mathematics teaching Abstract: combining the number is the number of more abstract corresponding relation and the geometrical graph, combine to solve the problem of abstract concepts to materialize and intuitive, intuitive, abstraction, and systematic problem to reduce the difficulty of the problem, and to help students thinking transformation and training students' ability.

数形结合与中学数学教学摘要：数形结合就是把较为抽象的数量关系和与其对应的几何图形相互结合起来解决问题，使抽象的概念直观化、具体化，使直观的问题系统化、抽象化，从而达到降低难题的难度、帮助学生思维转换、培养学生能力的作用。

Then, the relations between the general nonlinear systems and its adjoint system were discussed, from which the sufficient and necessity conditions for exact linearization of general nonlinear control systems were obtained.

近20年来，由于微分几何等数学工具的引入，非线性控制系统的理论取得了长足的进展［1］，其中包括仿射非线性系统的精确线性化［2～4］。

A generalized mathematical model was developed to describe the distribution of over-potential.Dimensionless variables μ and ω that characterize the polarization and influence of side electrode reaction in the system,were derived from modeling.Adomian's decomposition methodADM）was used to solve the nonlinear differential equation of the model to obtain an approximate analytical solution,which was in the form of algebraic expressions of infinite power series.By the solution,the relationship between over-potential distribution and average selectivity could be easily calculated without solving the nonlinear model time and again.

建立了描述超电势分布的普遍化数学模型，归纳出表征电极极化和副反应影响的量纲1数μ和ω，并用ADM（Adomian's decomposition method）对该非线性微分方程模型求解；所获得的逼近解代数表达式，可方便地计算不同参数下超电势分布对平均选择性的影响，而毋需反复求解模型微分方程。

The physical and mathematical models of underground gasification are erected; a temperature field in the district of gasification is set up; the instance analysis on the computer analogue simulation machine has been carried out; systematic analysis and research on the variable rules of temperature and different components has also been taken and some important resultants about the best position for drilling and the relationship between adjustment and control and gasification stability have gained, which opens up a new field for the sight research of the control of the stability of underground gas of coal.

建立了钻孔调控气化的物理模型、数学模型及气化盘区温度场，并进行了计算机模拟仿真及实例分析，对温度及各组分的变化规律进行了系统的分析研究，得出了最佳调控钻孔位置及调控与气化稳定的关系等重要结论，为煤炭地下气化稳定控制的可视化研究开辟了新的领域。

According to Lagrange equation in analytic dynamics, the dynamic equations of the Double-Axis Gyro Stabilized Platform of a certain airborne SAR antenna are derived, its linear model and the transfer functions of other main parts in the DAGSP are given and at last the block diagram of DAGSP is given.

6利用分析力学原理，推导了某机载天线双轴陀螺稳定平台的动力学方程和线性化模型；给出了天线双轴陀螺稳定平台中各主要环节的传递函数及数学模型。

By observing and analyzing 3D structure of apple flower and inflorescence, we raised the 3D structure mathematical model of anthocaulus, receptacle, calyx, petal, androecium and pistil.

为了实现对苹果花及花序三维形态结构的交互设计、几何建模和真实感现实，提出了精确描述苹果花序三维形态结构的数学模型及可视化方法。

For the images of VSMCs cultured on the silicon membrane stretched by pulsatile flow, one method with eight steps based on difference arithmetic operators is proposed. Image enhancing, image graying, halation removing, Canny edge detection, mathematical morphology dilation, edge smoothing, mathematical morphological reconstruction are implemented according to the set sequence.

本文针对膜式张应力装置中体外培养血管平滑肌细胞图像，深入分析了该细胞力学实验中细胞图像的特点，提出了基于微分边缘检测算子的图像分割技术路线，依次为图像增强、灰度化、消除光晕、Canny边缘检测、数学形态学膨胀、区域填充、平滑边缘、形态学重建。

In 1869 Charles Meray, an apostle of the arithmetization of mathematics, gave a definition of the irrationals.

1869年查尔斯·梅雷作为数学算术化的革新者给出无理数的一个定义。

So a new model for ATC calculation is proposed——smooth ATC model based on security and stability.

从而建立了计算ATC的新的数学模型——同时考虑安全性与稳定性的光滑化ATC模型。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。