变换群

In exterior differentiation, one studies tensors, exterior algebra, tangent bundle, tangent vector fields, one-parameter groups action on a manifold, Frobenius's theorem, tensors fields, exterior differential form, integration on manifolds, Stokes's theorem etc.

外微分部分主要涉及外代数、切丛，光滑切向量场，单参数变换群，光滑张量场，外微分形式，Frobenius定理，外微分形式的积分，Stokes定理及其应用等。

ABSTRACT This dissertation describes our investigation of the geometric invariance and geometric invariant over projective transformation group, with the emphasis on the estimation of geometric constraints in image sequence and their applications in computer vision.

本论文介绍了作者对射影变换群上的几何不变性及几何不变量的研究，重点研究了序列图象间几何约束关系的估计及其在计算机视觉中的应用。

In this paper,all symmetries of the generalized kdv equation are obtained by means of infinitesimal generator of Lie group of transformation.

本文用Lie变换群的无穷小方法，求出了广义kdv方程的全部对称，并用特殊的对称将其化为常微分方程。

In chapter 1, as a preparative knowledge, the main results about symmetry theoryand Wus method are introduced, in addition some fundamental definitions, such as trans-formation group, infinitesimal operator, prolongation, first integral, infinitesimal criterionfbr invariance of an ODE, characteristic set are recalled.

第一章中作为预备知识简单介绍了对称理论和吴方法，并给出了一些基本概念和理论，如变换群、无穷小算子、算子延拓、首次积分、微分方程在对称下不变的判别准则和微分特征列集算法。

Discrete mechanics,dynamical equation,infinitesimal transformation group,symmetry,conserved quantity

中文关键词离散力学，动力学方程，无限小变换群，对称性，守恒量

The problem of invariance is both important and difficult in studies of neural retworks.

对不变性的认识，特别是对变换群下的不变性的认识，一直是神经网络系统研究中最重要的也是最困难的问题之一。

By applying the approach of the transformation of Lie group,the exact analytical solutions of the non-linear consolidation equation is obtained under different initial and boundary conditions. Based on this solution,the differences between that of large and infinite strain consolidation theories are analyzed.

运用变换群的方法求得了某些条件下大应变固结方程的完整解析解答，在此基础上与相同条件下的小应变固结论理做了比较，并通过对实例的计算，分析了不同假设条件下一维固结理论之间的差异。

An analytic solution of kinematic model was obtained via Lie transformation group. It shows that the velocity of particles flow is maximum when x=0. Through locating the maximum particles velocity distributing line and taking the line as the origin line of x coordinates, the modified kinematic model could simulate the eccentric discharging well.

通过Lie变换群得到"运动模型"的解析解，发现x=0时颗粒的垂直速度达到最大值，由此在确定颗粒最大速度分布线的基础上移动坐标使该线上x值均为0，对"运动模型"进行了修正，可以反映壁面对颗粒运动的影响，所得计算结果与实验测定吻合得很好。

With the combined method, some new types of solutions of the (2+1)-dimensionalcubic nonlinear Schr?

其次将求非线性发展方程精确解的广义射影Riccati方程法与求对称变换群的楼直接法框结合，研究了(2+1)-维色散长波方程，得到了一些新的类孤波解。

We prove strictly that under the action of any element of this transformation group, an dense orbit in symbolic dynamics becomes other dense ones.

我们证明了，符号动力系统中的一条稠轨在此变换群任一元作用下，变成另一条稠轨。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。