双曲线函数

This course offers advanced topics for students who have learned ordinary differential equations. The course includes linear algebra which has topics as matrices, linear systems of equations, eigenvalue problems, vector differential and integral calculus. Fourier series, orthogonal functions, Fourier transforms and partial differential equations will also be introduced.

本课程为提供已有常微分方程式基础的同学修习，内容包括线性代数，矩阵运算，特徵值问题，向量的微分与积分，一阶线性微分方程组，傅力叶级数和正交函数，傅力叶转换，并将对椭圆，抛物线，双曲线型式的偏微分方程式作概略介绍。

This course offers advanced topics for students who have learned ordinary differential equations. The course includes linear algebra which has topics as matrices, linear systems of equations, eigenvalue problems, vector differential and integral calculus. Fourier series, orthogonal functions, Fourier

本课程为提供已有常微分方程式基础的同学修习、内容包括线性代数、矩阵运算、特徵值问题、向量的微分与积分、一阶线性微分方程组、傅力叶级数和正交函数、傅力叶转换、并将对椭圆、抛物线、双曲线型式的偏微分方程式作概略介绍。

On the basis of analyzing hyperbola and exponent models in common use, the power function model is presented.

在分析了岩体节理法向变形的对数模型、双曲线模型的基础上，提出了一种幂函数模型。

An hyperbolic function was proposed as a load transfer function to analyze the load transfer mechanism of a single pile.

选用双曲线荷载传递函数分析单桩的荷载传递规律。

Thus, modeling by 5 empirical equations showed that using hyperboloid and power function fitting the relationships are quite good.

鉴于此，选取5个经验方程进行建模，结果显示，对于胸径和CI、RCI、RC1、RC2间的关系用双曲线和幂函数方程拟合较为适宜。

Function graphing and analyzing: 2D, 2.5D functiongraphs and animations, extrema, root, tangent, limit,derivative, integral, inverse; sequence of number: arithmetic progression, geometric progression; analytic geometry: vector, line, circle, ellipse,hyperbola and parabola; solid geometry: spatial line, prism, pyramid, cylinder, cone, dado and sphere; Ability to save graph as data file or bmp file; Ability to save animation as AVI file; Ability to move, zoom in, zoom out and rotate the scene.

函数图表和分析：2D， 2.5D 函数图表和动画，极值，根，正切，极限，导数；序列号：等差数列，等比级数；解析几何：向量，矢量，直线，圆，椭圆，双曲线和抛物线；立体几何：空间线，棱柱，三角锥，圆柱，圆锥体，梯形台和球体；保存图形为数据文件或者图像文件的功能；保存动画为 AVI 文件的功能；移动，缩小，放大和旋转场景的功能。

This paper deals with the fertilizer rate for high—yield hybrid rice. By using the regression analysis, a hyperbola equation between soil natural nutrientsupplying rate and available nutrient content and a power functional equation between hybrid rice yield and nutrient uptake have been set up.

本文研究了高产杂交水稻的施肥量，通过回归分析建立的土壤养分自然供给量与土壤速效养分含量之间的双曲线方程和水稻产量与养分吸收量之间的幂函数方程，阐明了土壤养分自然供给量随土壤养分含量的变化而变化的规律和水稻产量与养分吸收量之间的关系。

The results show that the modified GM (1, 1) has the most satisfactory accuracy, while power function model and exponent function model are moderate in accuracy and hyperbolic model is relatively worse than the aforementioned ones.

结果表明，修正的GM(1， 1)模型模拟的荷载－位移曲线精度最高，幂函数模型和指数函数模型次之，双曲线模型相对较差。

On the basis of the achieved result and the effect of stress such as minor principal stress, intermediate principal stress, hydrostatic pressure, stress Lode degree, a generalized hyperbolic failure function adapted naturally with the envelope form of Mohr-Coulomb criterion is proposed for brittle rocks; and a smooth failure function acquired by Yu Maohong is also presented. Thus, a generalized polyaxial strain energy strength criterion is created.

在分析脆性岩石强度的静水压力、中间主应力、最小主应力以及应力Lode角等4种效应的基础上，提出子午面上与Mohr-Coulomb准则包络线自然衔接的广义双曲线型破坏函数及八面体偏平面上光滑角隅型破坏函数，从而建立非线性广义多轴应变能强度准则。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。