双曲函数论,theory of hyperbolic functions

1)theory of hyperbolic functions
双曲函数论

2)hyperbolic function
双曲函数
1.
A new hyperbolic functions method for finding exact solutions of nonlinear partial differential equations;
寻找非线性演化方程精确解的新的双曲函数法


2.
An improved algorithm based on hyperbolic function of BP neural network
一种基于双曲函数的BP网络改进算法


3.
The control strategy based on hyperbolic function is proposed and relative mathematical model is built.
为此讨论了车辆变速行为的一般规律,提出基于双曲函数的车辆变速控制策略,建立了相应的数学模型,并针对实例进行了具体分析。


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3)hyperbolic functions
双曲函数
1.
Bézier-like curves and surfaces based on hyperbolic functions;
基于双曲函数的Bézier型曲线曲面


2.
This article arranges and disseminates the hyperbolic functions and the solution of differential equation.
本文在文 [1]的基础上 ,对求解微分方程的双曲函数法进行了整理和推广 ,有一定新意 。


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4)Hyperbolic Function
双曲线函数
1.
The load-settlement relationship of skin friction q of every part of squeezed branch and corresponding settlement s of plate pile is presupposed as hyperbolic function,the necessary parameters are obtained based on the measured data,and compared with q-s relationship of measured every part.
假定支盘桩直桩段的桩侧摩阻力和含有分支或承力盘桩段的等效侧摩阻力q与相应桩土相对位移s的关系可用双曲线函数表示,根据实测数据采用最小二乘法求出所需系数,并用所得的双曲线与实测各分段的q-s关系进行对比。


2.
According to the data statistics of max transformation aside of pit to time, the paper established 3 typical hyperbolic function of displacement to time (depth).
根据实测软土基坑坑侧最大位移与时间关系资料,经统计分析建立了3种有代表性的位移与时间(挖深)的双曲线函数。


3.
According to analysis of the behavior of sand surrounding pile tips,a hyperbolic function is presented considering the compressibility of soil around pile tip which establishes certain relation between end bearing capacity and penetration at pile base.
对桩端周围土体的性状进行了分析,引入考虑桩端土体压缩特性双曲线函数,将桩端阻力的发挥同桩的刺入变形联系起来。



5)hyperbolic function method
双曲函数法
1.
A simple transformation,hyperbolic function method and exact solution for a class of reaction diffusion equation;
一个简单的变换,双曲函数法和一类反应扩散方程的精确解


2.
A united hyperbolic function method to find the solita ry wave solutions to nonlinear evolution equations was proposed,and two kinds of solitary wave solutions to the combined KdV-mKdV equation were obtained by this method.
提出一种统一的求解非线性演化方程孤波解的双曲函数法 ,并利用这种方法求出了组合KdV mKdV方程的钟状孤波解和激波状孤波解 。


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6)hyperbola function method
双曲函数法
1.
This paper found some exact solutions of Burgers equation with variable coefficients by the hyperbola function method, including solitary wave solutions and periodic solutions.
对双曲函数法进行了扩展,利用它找到了广义变系数Burgers方程在一定条件下的若干精确解,包括变速孤立波解和周期波解,许多解为首次所得。


2.
The hyperbola function method has been extendedand to find some exact solutions to Burgers equation with variable coefficients.
对双曲函数法进行了扩展,利用它找到了变系数Burgers方程在一定条件下的若干精确解,包括变速孤立波解和周期波解。


3.
Some new exact solutions for a class of the system of LS nonlinear equation are obtained by using the homogeneous balance method, hyperbola function method and trial function method.
利用齐次平衡法、双曲函数法、试探函数法求出了一类长短波方程多个新的精确解。


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补充资料：双曲点


双曲点
hyperbofic point

　　双曲点伪甲蜘众州d;roue两。几.，ecKa:TO，“a] l)曲面的双曲点(hyl犯面licpointofasurf加羌)是一个点，在该点的密切抛物面(璐以山山gp晚比ki均是双曲抛物面(hyl光而licP别旧加Ioid).在双曲点上1为咖.标形(I〕uPin让以i口trix)由一对共扼双曲线给出.EB.m~撰【补注】在双曲点上曲面有负C饱J骆曲率，反之，如果曲面在一个点上有负C饭u洛曲率，则这个点是双曲点.2)动力系统的双曲点(场详rbolicpointofad卵田汕习s岁记m)是系统 交=f(x)，x=(x:，二，戈)(*)的定义域中使得f(x’)二0的一个点x=x’，此时与叮归x在x二x’的值相等的矩阵A有k个正实部的本征值及n一k(O　　
说明：补充资料仅用于学习参考，请勿用于其它任何用途。

双曲函数论,theory of hyperbolic functions