查询词典 integrable function

This paper gives an exact solution for free vibration of a physically nonuniform straight bar with vary-ing section by the use of a class of integrable linear ordinary differential equation.

本文应用可积的一类线性微分方程求出了非均质变截面弹性直杆振动问题的一个精确解，我们应用这一精确解验证了渐近解的精确度。

In addition, we also give the characteristic of uniformly integrable martingale in the rearrangement invariant martingale space and the relationship between one martingale and the accompanying martingale associated with it which is particular in the rearrangement invariant martingale space under the action of some most important martingale operators such as maximal operator, square operator, the greater operator and the smaller operator.

此外我们还考虑了重排不变鞅空间中的鞅是否一致可积的特征以及极大算子、均方算子和上、下算子在重排不变鞅空间及其相伴鞅空间上作用的特殊性质。

Our methods are based on soliton integrable theory, geometric singular perturbation theory, and Melnikov analysis.

其基本思想方法是基于孤子可积理论，Melnikov方法和奇异扰动理论的综合运用。

In chapter 1, we briefly introduce the near integrable systems, and give the background in physics and the developments in mathematics for the quintic and derivative nonlinear Schrodinger equations.

具五次和导数项的非线性Schrodinger方程具有广泛的物理应用背景，可视为非线性Schrodinger方程的扰动，进而可作为近可积系统进行较为精细的研究。

The quintic and derivative nonlinear Schrodinger equations has a extensive applications in various physical areas and can be considered the perturbation of the NLS equation. Further they are the near integrable systems.

具五次和导数项的非线性Schrodinger方程具有广泛的物理应用背景，可视为非线性Schrodinger方程的扰动，进而可作为近可积系统进行较为精细的研究。

This paper discusses the integrability of Riemann integral systematically: By analyzing the common characters of a lot of integral calculus, it abstracts the concept of Riemann integral and discusses its integrability of Riemann integral and then gets integrable functions.

摘要本文较为系统地讨论了积分的可积性：通过分析诸多积分概念的共性，抽象定义了积分并详细讨论了其可积性，得出了可积函数类。

This paper discusses the integrability of Riemann's integral theory systematically: By analyzing the common characters of a lot of integral calculus, it abstracts the concept of Riemann integral and discusses its integrability of Riemann's integral theory and then gets integrable functions.

摘要本文较为系统地讨论了积分可积性理论：通过分析诸多积分概念的共性，抽象定义了积分，详细讨论了其可积性理论，得出了可积函数类。

This dissertation studies some topics in soliton and integrable system,which mainly include as follows:exact solutions especially travelling wave solu-tions and solitary wave solutions,Painlevēproperty,transformation,similarity reduction,symmetries and their Lie algebra structure,generation ofsoliton hierarchy and their zero curvature representation,Hamiltonian struc-ture,Lax or Liouville integrability,nonlinearization of Lax pairs,applications ofWu's method and symbolic computation.

本文研究内容涉及到孤立子和可积系统的多个方面：精确解特别是行波解和孤波解，Painlevē性质、变换、相似约化、对称及其Lie代数结构、孤子族的生成及其零曲率表示，Hamilton结构，Lax和Liouville可积性、Lax组的非线性化以及吴方法和符号计算在上述研究中的应用。

We have a relation between the integrable system of IIB superstring on AdS〓S〓 and affined Toda theory.

根据Lax联络，我们可以得到经典的r矩阵以及相应的R矩阵。

For example, Donagi and Witten found that the spectral curves of these integrable many body systens are identified with the Seiberg-Witten curves of the Seiberg-Witten theory. More recently, Dijkgraaf and Vafa found the information about the superpotentials of the chiral fields in some N = 1 SUSY gauge theories from the planar diagram of certain matrix integral.

例如，Donagi和Witten等人发现可积系统的谱曲线和Seiberg-Witten理论中的Seiberg-Witten曲线相互等价，Dijkgraaf和Vafa等人从正则矩阵积分的平面图中找到了N=1的超对称规范理论中手征场的超势的一些信息，同时N。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。