hyperbolic function meaning in English
双曲函数
双曲线函数
双曲型函数
Examples
- A general class of solutions to nonlinear scalar equations with static cylindrical symmetry is obtained in the form of a hyperbolic function series . these solutions can be used to describe a long . straight global string
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.在物理上.这些解描述了无限长的直整体弦 - Spline curves defined in the space constructed by polynomial and hyperbolic functions are studied in this paper . the main research contents and achievements are as follow : firstly , we generate the cardinal extended complete chebychevian ( ect ) - systems on the space constructed by polynomial and hyperbolic functions , then introduce the algebraic - hyperbolic b - spline space and identify the dimension law and zero properties . the existence of a basis of splines with minimal compact supports is demonstrated , and functions named non - uniform algebraic - hyperbolic b - splines are obtained by solving certain linear equations with a block matrix
本文主要研究定义在多项式和双曲函数构成的空间上的样条曲线,其内容和完成结果如下:一、生成由多项式和双曲函数构成的空间上的一组典范式ect ( extendedcompletechebychevian )组及其对偶, ,证明非均匀代数双曲b样条空间的维数定理和零点定理,直接通过解块矩阵线性方程组得到具有最小紧支撑的非均匀代数双曲b样条函数,进而构造非均匀代数双曲b样条曲线,还具体给出低阶的表示 - In section 1 , some nonlinear wave equations of this part discussing are recommended ; in section 2 , the elementary tool of this part utilizing is mentioned , namely , the hyperbolic function method ; in section 3 , seme exact solitary wave solutions to these nonlinear wave equations are attained
本部分由三节组成，第一节介绍了所讨论的几类非线性波动方程；第二节介绍了本部分所使用的基本工具，即，双曲函数方法；第三节给出了这些非线性波动方程的若干精确孤立波解。 - The mostly conclusion of this part is as follows , on the conditon of travelling wave , the exact solitary wave solutions to some nonlinear wave equations such as sawada - kotera equation , kaup - kupershmidt equation , the fifth order kdv equation , fisher - kolmogorov equation , on the help of the computer algebraic system ( maple ) , are explicitly established by making use of the hyperbolic function method . this part is maken up of three sections
本部分的主要结论如下，利用双曲函数展开法，在行波条件下，对sawada - kotera方程， kaup - kupershmidt方程，五阶kdv方程， fisher - kolmogorov方程，等几类非线性波动方程求解，将其孤立波表示为双曲函数的多项式，从而将非线性波方程的求解问题转化为非线性代数方程组的求解问题，并借助于计算机代数系统求解非线性代数方程组，最终获得了这些非线性波动方程的若干精确孤立波解。 - The mathematics - mechanization method is applied the field of differential equations . many algorithm for constructing solitary wave solutions for a class of nonlinear wave equations are given , and implemented in a computer algebraic system , such as the hyperbolic tangent function method and the hyperbolic function method etc . exact solitary wave solutions of a great deal of nonlinear equations are gained
将机械化数学方法应用于偏微分方程领域，建立了构造一类非线性波方程的精确孤立波解的许多算法，如，双曲正切函数展开法，双曲函数方法等，并在计算机数学系统上加以实现，因而推导出了一批非线性波方程的精确孤立波解。