查询词典 arc hyperbolic function

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

The physical characteristics of various hyperbolic waves in Eular system are analysed. The shock physical characteristics and the conditions of forming the shocklet are discussed, detailedly. We are clear about the mechanism of shocklet excited by continuous waves.The physical mechanism of TS waves and the relation between shocklets and TS waves are studed in a systematic way.

从理论上分析了Eular系统中各种双曲波的物理性质，详细讨论了激波的物理特性和与产生激波的条件，明确了通过连续波动诱发激波物理机理，系统研究了TS波的在可压与不可压流动中的物理特性以及与激波的联系，分析了粘性对激波形成的影响。4。

Put forward a new method by transforming the second-order hyperbolic equationinto a first-order system of equations and derived the H_0~1 -norm and the L~2 -norm error estimates.

12提出一种新方法，通过转化双曲型方程中二阶时间导数项得到关于一阶时间导数的耦合方程组，然后进行离散，得到一个两层交替方向有限元格式，并得到H_0~1-模和L~2-模误差估计。

There is the Cauchy problem of hyperbolic system with weak damping in Chapter4. In the space of dimension N=1,3, exploiting the semigroup method, the global existence and the decay behavior of the solution with small initial data to problem (about problem with small initial data) is put forward.

当空间维数N=1，3和初值充分小时，利用半群理论得到问题整体解的存在性，并对于整体解给出一致衰减估计；当空间维数N=1 时，利用试验函数方法讨论解在有限时刻爆破的条件。

First of all, the report introduced evolution, achievments and problems in the study of anisotropy in the inner of earth. The first-order hyperbolic system of equations is work out, which is used to describe the wave motion in 2D transversely isotropic media. Utilizing the characteristics of free-divergence, We have imposed MacCormack theme that is used to simulate multicomponent records in anisotropic media and have developed a fast high order vectorized finite-difference algorithm adapted for the vector supercomputer.

本文首先阐述了地球内部介质各向异性研究的沿革、成就和问题，接着给出了描述二维横向各向同性介质中波动的一阶双曲型方程，利用其自由发散特性，构制了各向异性介质中多波多分量地震记录数值模拟的MacCormack算式，导出了适用于并行计算的二维横向各向同性介质中波动的有限差分模拟算子，该算子具有可并行化计算、相位差小等优点。

If the systems satisfy linearly degenerate or weakly linearly degenerate, the classical solutions to Cauchy problem for quasilinear hyperbolic system will exist as the initial data with compact support is small enough.

本章第一节，我们主要推导了波的分解公式，提出了弱线性退化、适配性条件和正规化坐标系的概念，并且给出了在正规化坐标系下一些关系式。

Hyperbolic tangent -- in radians !!!

双曲正切--以弧度为单位！！！

The conclusion results are positive. The shock wave with viscosity and heat conduction is validated a hyperbolic tangent type of soliton wave.

证实了有粘性和导热的激波是一类满足Sine-Gordon方程的双曲正切型孤立波。

2Based on the nonparametric model and the hyperbolic tangent model dynamic response analysis matlab based programs on the damper-structure coupled system were carried out.

2分别采用双曲正切模型和神经网络模型编制了Matlab程序，对安装有磁流变阻尼器的结构系统进行了动力响应分析。

Since it relates to hyperbolic tangent operation in the two layer weighted parallel interference cancellation algorithm it nearly can't by realized.

由于在双层加权并行干扰对消算法中涉及双曲正切运算，该算法几乎无法实现。

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。