不变性

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。

The conventional matrix decomposition methods have been used to find the least-squares solutions of the abovementioned inconsistent matrix equations over given matrix set in many references, and the general expressions of these solutions were obtained. But it is difficult to determine the solution of Problem I by utilizing these expressions due to the fact that the orthogonal invariance of Frobenius norm does no hold for the general nonsingular matrices.

对于求上述不相容矩阵方程在给定矩阵集合上的最小二乘解，很多文献中利用传统的矩阵分解方法得到了其通解表达式，但是利用该表达式很难得到问题Ⅰ的解，这是因为一般的非奇异矩阵并不满足Frobenius范数的正交不变性。

Therefore, we often said easy is road of the change, but did not say easy to have the invariable principle, because the change is absolute, but the invariability is relative, and, also is simple.

所以，我们常说易是变化之道，而不说易有不变之理，因为变化是绝对的，而不变性则是相对的，并且，也是简易的。

Invariability of the rate law and activation energy of the decomposition on doping suggests that the complex behavior is not due to a change of mechanism.

不变性率法和活化能分解掺杂认为，复杂的行为，是不是因为要改机制。

In this paper, the form invariance of Nielsen equation for variable mass conservative mechanical system was studied.

形式不变性是不同于Noether对称性和Lie对称性的一种新的对称性理论。

The magnitude of pseudo-Zernike moments has rotational invariant property.

目前 ，伪 Zernike矩没有得到广泛的应用，其中的一个主要原因是，它不具备真正意义上的比例不变性。

Based on this notion and the invariance principle, a condition is proposed and proved, under which an invariant set of states of a switched system with Lyapunov stable subsystems can be stabilized by state feedback.

基于这个不变性原理以及输入对系统能量函数稳定的概念，利用多Lyapunov函数方法提出并证明了一类具有Lyapunov稳定子系统的切换系统的不变集可状态反馈镇定的条件。

The proposed method applies the ellipsoid invariant set to the estimated state and state estimation error. The conditions of invariance and feasibility of estimated state, as well as the stability of the closedloop system are given.

该方法采用双模控制策略，将不变椭圆集概念同时应用于观测器的状态方程和误差方程，给出估计状态不变性和控制输入可行性条件并给出了闭环系统的稳定性定理。

In the process of investigation on the torsional effect of quartz crystal, mirror symmetric conservative law is applied to ascertain the connection between the physical characteristics of leftwards spiral crystals and rightwards spiral crystals.

面对工程界对左旋石英晶体压电性质的描述不统一的现状，从晶体螺旋对称的本质出发，应用宇称不变性明确地建立了左、右旋晶体这两种客观实在物质的物理性质之间的联系，给出了建立这种联系的方法，并应用到了左旋石英晶体的三阶压电张量和四阶弹性张量的确定中。

By using methods of passivity and switching control of states of the linear subsystem, both stabilization of the linear subsystem and invariance of the specified region in state space can be guaranteed simultaneously. Hence, a sufficient condition for the robust invariance switching control of this class of systems was derived.

通过基于鲁棒严格无源技术和线性子系统状态反馈的切换控制来镇定线性子系统，同时保证了指定区域的正不变性，从而得到了该类系统鲁棒不变切换控制的充分条件。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。