查询词典 arc hyperbolic function

Indeed, the reader who is slightly familiar with tessellations of the sphere, the Eaclidean plane and the hyperbolic plane, can easily prove the following result

事实上，稍微熟悉球面、欧几里得平面和双曲平面的分格的读者，都能容易地证明出下面的结果。

The third chapter discusses and proves Il"yashenko"s Theorem, that is, if every vertex on the polycycle of an analytic vector field in the real plane is hyperbolic, then limit cycles cannot accumulate on this polycycle.

第三章详细讨论和证明了Il'yashenko定理，即平面解析向量场的多边环上每一顶均为双曲奇点，则此多边环附近不能结集无限多个极限环。

Based on the priori knowledge of a point scattering - hyperbolic feature of subsurface objects in GPR B-Scan images, a method of ROI extraction with Neural Network is presented.

在分析了均匀介质中的目标回波特征一双曲线形态的产生机理和基本特征的基础上，提出了一种利用神经网络进行ROI提取的方案，根据GPR数据解译的特点，本文设计了相应的B-Scan图像预处理方法和神经网络结构、训练及测试方法，使用塑料管及其他目标的B-Scan实测数据对神经网络进行训练与测试。

Finally, we get local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems by the properties of bounded solutions to nonlinear nonautonomous equations.

最后运用非线性非自治中立型泛函微分方程有界解的性质，得到非线性自治动力系统在双曲平衡点的局部稳定流与局部不稳定流。

Finally,we get local stable manifolds andlocal unstable manifolds of near hyperbolic equilibrium point of nonlinearautonomous dynamical systems by the properties of bounded solutions to nonlinearnonautonomous equations.

最后运用非线性非自治中立型泛函微分方程有界解的性质，得到非线性自治动力系统在双曲平衡点的局部稳定流与局部不稳定流。

In this paper, we consider neutral functional differential equations and study the global existence of their solutions, stable subspaces and unstable subspaces of linear autonomous dynamical systems, local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems, periodic solutions and oscillation of the neutral equations.

本文主要研究中立型泛函微分方程解的整体存在性，自治线性动力系统的稳定子空间与不稳定子空间、自治非线性动力系统在双曲平衡点的局部稳定流与局部不稳定流，周期解与解的振动性。

By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map, it is shown whether the system has transversaUy homoclinicpoints and chaos in the sense of Smale horseshoes.

Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法，它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性。

In particular, the system generates bifurcation when 2c-a=0, and then the stable knot bifurcates a hyperbolic saddle point and stable convergence, which is so-called Pitchfork bifurcation. From 2c-a≤0 to 2c-a≥0, the attracting set A of the system is changed from single point to the union set of two different old orbits.

系统在2c-a=0时产生分岔，其稳定的结点分岔出一双曲鞍点和两个稳定的汇，这就是Pitchfork分岔，可见在2c-a≤0变化到2c-a≥0时，吸引集A从单点集变成为连接P和P的两异宿轨道的并。

The light curve of five kinds of landscape lianas commonly used in southern China were measured by LI-6400 portable photosynthesis system and fitted by non-rectangular hyperbolic model. Light compensation point, light saturation point, Pn,ɑ of the 5 lianas species were analyzed comparatively. The results indicated that there are significant differences in light response of photosynthesis among them.

采用Li-6400便携式光合测定仪对5种华南地区常用园林绿化藤本植物进行了光响应曲线的测定，并用非直角双曲线模型对其进行拟合，对比分析了5种藤本植物的光补偿点、光饱和点、最大净光合速率、最大表观量子效率。

In the fourth section, we stress on the study of the finite type rotation hypersurfaces, and obtain the classification of two and three dimensional spherical and hyperbolic rotation surfaces of finite type. It is proved that the parabolic rotation hypersurfaces are minimal or maximal.

第四节着重对有限型旋转超曲面进行了研究，得到二维和三维球型、双曲型有限型旋转曲面的分类结果，证明了有限型抛物型旋转超曲面是极小或极大超曲面。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。