可积性

We can realize the special Abel equation integrability and accurate solution by computer.

实现了计算机对该类方程可积性及其精确解的自动判定。

By using the interpolation mechanism of fuzzy system, an approach of building the series of fuzzy systems, which can uniformly approximate any continuous function on a compact domain to any accuracy, is given, and then the universal approximation theorem is generally proved.

利用模糊系统的插值模型来代替被控对象的真实模型，设计了一个自适应模糊控制策略；为保证系统的全局稳定性，增加了一个补偿控制律，它是根据模糊系统的逼近误差估计量来设计的，因此这里系统跟踪误差的收敛性不依赖于模型最小误差的平方可积性[70，71]。

Recursion formulas for quantities at infinity in this system were presented.

同时，计算了一类三次系统的前6个赤道环量，得到了系统在赤道邻域的可积性条件及在赤道附近存在5个极限环的系数条件，给出了一个平面三次系统在赤道附近分支出5个极限环的计算实例，并在不构造Poincare环域的情况下，指出了极限环存在的位置。

In first chapter,we discuss the〓-integrability of thegradients of the very weak solutions to non-linear elliptic systemsdivA=B(2)and〓-regularity of the very weak or the weak solutions to non-linearelliptic systems〓(3)in bounded domain Ω.

第一章讨论有界区域上的非线性椭圆型方程组〓（2）的很弱解的梯度的〓可积性和非线性椭圆型方程组〓（3）的很弱解与弱解的〓正则性。

This article use the improved integral inequalities with the deviate variable and some skills of inequalities as well as related knowledge about second-order differential equation,to obtain the following results: the classification of limit point case or limit circle case and boundedness for second order differential or difference equation with deviative variable,discussed the classification for certain n-order differential equations,Criteria for the classification of second order differential equation with deviative variable.

本文利用推广的具有偏差变元的积分不等式，结合不等式的一些技巧以及常微分方程的相关知识对一类二阶具有偏差变元的微分方程及一类二阶差分方程极限圆型的分类问题作了相关的研究工作，并且讨论了一类n阶具有偏差变元的常微分方程解的平方可积性与有界性和一类二阶非线性具有偏差变元的微分方程解的有界性。

The algorithm is linear recursive and easy to realized by a recursive function in computer algebra systems.

在最后一章，我们研究了具有任意有理共振奇点的复自治多项式微分系统(即线性部分特征值比为n∶—m型奇点)的可标准化，可积性，线性化问题。

By introducing the generatingfunction method,the integrability of FDIHS is proved,which is thesimplest way we know so far.

通过引入母函数方法，较简洁地证明了系统的可积性，包括守恒积分族的对合性与独立性，其中关于对合性的证明是迄今为止最为简洁的证明。

The growth of functions in these spaces depends on a weighted function ρ. We investigate the relation between growth and boundary values of the functions, and prove that a function or its radial derivative is in one of the spaces if and only if the p'integral average of the difference of its boundary value function is integrable or bounded.

研究这些函数空间中函数的增长性与边界值的关系，得到了函数或其径向导数属于相应空间的充分必要条件是其边界值差分的p次积分平均应具备一定的可积性或有界性。

Furthermore it describes the norm equivalence of therearrangement invariant martingale spaces acted by the greater operator and the smaller operator, and it represents the norm equivalence of these spaces acted by maximal operator and square operator more deeply.

第五章考虑了重排不变鞅空间框架下的一致可积性与上、下算子以及极大算子、均方算子作用在鞅及其相伴鞅所成空间上的有界性。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。