双曲函数

一种基于双曲函数的BP网络改进算法

An improved algorithm based on hyperbolic function of BP neural network

根据FAPopp相干理论及有关实验，生物光子的延迟辐射强度随时间服从双曲函数分布。

According to the coherence theory of F. A. Popp and some experiments , biological photon delayed radiation intensity obeys the hyperbolic function with time .

求解Burgers方程行波解的双曲函数展开法

The tanh-function method solving wave solutions of the Burgers equations

基于CORDIC算法实现双曲函数的计算

The Calculations for Hyperbolic Function Based on CORDIC Algorithm

扩展双曲函数级数方法和NLS方程的显式精确解

Extended Tanh-Function Expansion Method and New Explicit Exact Solutions of the NLS Equation

针对传统的CNN难于理论研究的缺点，利用非极性双曲函数代替传统CNN中的分段线性输出函数，构成了新的CNN。

For difficulties in academic analysis on state-equations , a new CNN is built by using a sigmoid function as the networks ' output instead of the traditional one .

将扩展的椭圆函数展开法应用到ModifiedImprovedBoussinesq方程，得到了新的解析周期解，包含冲击波解、孤波解和双曲函数解。

Extended elliptic function expansion method is applied to the solution of Modified Improved Boussinesq function , and new analytic periodic solutions to it is obtained , including the shock wave solution , solitary wave solution , and hyperbolic solution .

预测人口增长的数学模型通常采用3种函数，即指数函数、Logistic函数和双曲函数。

Three common mathematic models are always employed to predict the growth of regional or urban population , including exponential function ( Malthus model ), inverse hyperbolic function ( Keyfitz model ), and logistic function ( Verhulst model ) .

运用双曲函数法和吴方法，我们获得了Brusselator反应扩散模型新的显式精确行波解。

By using hyperbola function and Wu-elimination method , some new explicit and exact travelling wave solutions for the Brusselator reaction di ?

得到了新Hamiltonian振幅方程的丰富的行波解，包括双曲函数解，三角函数解，椭圆函数解，幂函数解等。

In this paper , some explicit and exact travelling wave solutions of the Hamiltonian amplitude equation are obtained which contain solitary wave solutions , trigonometric function solutions and Jacobian elliptic function solutions .

无需计算Jacobi椭圆函数，得到了无阻尼单摆运动方程的14种借Jacobi椭圆函数、双曲函数和三角函数表示的精确解。

Without calculating the Jacobi elliptic functions , 14 kinds of exact solutions expressed by various Jacobi elliptic functions , hyperbolic functions and trigonometric functions of the undamped single pendulum equation of motion are obtained .

于是我们系统地分析了Yan，Dai，Huang，Xie，Shang等在文献中提出的拓展的双曲函数法，结果显示这些方法只是数学形式不同，本质上是等价的。

So we systematically analyze the expansion of the hyperbolic function method proposed in the literature by Yan , Dai , Xie , Huang , Shang . However , the results show that these methods are mathematically different , but essentially equivalent .

提出一种双曲函数的方法，并且证明了这种变换方法可以从sinh-Gordon方程中得到。

A transformation method which is called hyperbolic function method is proposed . We show that this transformation can be obtained from the sinh-Gordon equation .

利用了Riccati方程已知的三角函数和双曲函数表示的解，得到了Ginzburg-Landau方程的多个包络波形式的精确解，并发现了频散系数和Landau系数之间的重要关系。

By using the known solutions expressed by triangle functions and hyperbolic functions of Riccati equation , a lot of envelope wave solutions for Ginzburg-Landau equation are obtained . And an important relation between dispersive coefficient and Landau coefficient is discovered .

近似方法包括两个数学近似，一个是用一阶惯性项的有限项和取代Bessel函数比，另一个是对双曲函数采用了无穷乘积。

Two mathematical treatments for the approximation are considered in the method . One is to substitute the Bessel function ratio by the sum of finite terms of the first order lag elements . The other is to adopt infinite products for hyperbolic functions .

将双曲函数展开式作为特殊的形式幂级数，通过形式幂级数运算获得双曲类型4组孪生恒等式，其中3组与Bernoulli数、Euler数有关。

Taking the expansion of hyperbolic function as a special formal power series , through the hyperbolic operation of formal power series , the author obtains four groups of twin identity of hyperbolic type , among which three groups are related to Bernoulli 's numbers or Euler 's numbers .

该方法可看作是双曲函数及一些相应扩展形式的概括，这种方法得到比其它方法更多的非线性微分差分sine-Gordon方程的孤立波，说明广义的tanh-sech法在求解非线性微分差分方程方面的有效性。

Compared with other method , many more solutions of nonlinear differential-difference sine-Gordon equation can be obtained by generalized tanh-sech method . This proves the efficiency of this method in solving the nonlinear differential-difference equations .

利用双曲函数方法，研究了具有广泛、深刻物理背景的Toda-Lattice系统，得到了它的显式精确解，这种方法也适用于求解其他离散的非线性方程（组）。

An algorithm is devised to obtained exact traveling wave solutions of differential-differential equations by means of hyperbolic function . For illustration , we apply the method to solve the discrete nonlinear Toda-Lattice system , and construct some explicit and exact traveling wave solutions successfully .

修正双曲函数法与非线性发展方程的精确解

Modified Hyperbolic Function Method and Exact Solutions to Nonlinear Evolution Equations

锚杆荷载传递机理分析的双曲函数模型

Hyperbolic function model to analyze load transfer mechanism on bolts

利用双曲函数法研究非线性方程的行波解

Traveling Wave Solutions for Nonlinear Evolutional Equations via a Hyperbolic Function Approach

双曲函数记录方式与其它记录方式的误差分析

Error Analysis on Hyperbolic Function and Other Recording Modes

寻找非线性演化方程精确解的新的双曲函数法

A new hyperbolic functions method for finding exact solutions of nonlinear partial differential equations

双曲函数型包层光纤光栅的特性研究

Study on the characteristic of fiber gratings with cladding being etched as hyperbolic function

最后，让我们的双曲函数反三角函数和照顾。

Finally , let 's take care of the inverse trig and hyperbolic functions .

层次双曲函数型网络的整体逼近理论及学习算法

The Universal Approximation Theory and Learning Algorithm of Hierarchical Hyperboloid Function Link Artificial Neural Networks

电子在双曲函数摇摆场和轴向导引场中的运动分析

Analysis on the electronic motion in combined hyperbolic functional wiggler and axial guide magnetic field

利用双曲函数级数的技术，研究了静态轴对称非线性标量方程的解析解。

This article arranges and disseminates the hyperbolic functions and the solution of differential equation .

厚松散层地表移动变形预计的双曲函数法

Applying hyperbolic function to predict the surface movement and deformation in the condition of thick alluvium

三角函数双曲函数及其导数积分公式的六边形记忆法

Hexagon Memory Method for the Derivative and Integral Formula of the Trigonometric and the Hyperbolic Function