查询词典 at infinity

According to the stability of vanishing points of the projected lines on the image of a group of lines at infinity, the algorithms for camera calibration and indoor visual navigation of the autonomous mobile platform based on parallels are proposed.

根据一组空间直线上的无穷远线素集在视平面上所形成的消失点对直线的平移具有稳定性的特点，提出了基于平行线的摄像机参数标定和自主移动平台室内视觉导航算法。

Then, we consider the Lyapunov-Schmidt reduction method from the Morse theoretical point of view. We prove that the critical groups at infinity of the reduced functional are isomorphic to those of the original functional.

接下来，我们从Morse理论的角度来考察著名的Lyapunov-Schmidt约化方法，证明了原泛函与约化后的泛函在无穷远处的临界群是同构的。

This paper studies a class of cubic system with planar polynomial.We use the qualitative theory of ordinary differential equations method of analysis, reached the following conclusions of four parts: First, we analyze the quality of all critical points of the system,and draw the conditions of existence of singular integrals for the system , in front based on the analysis, using Pioncare form series method to calculate the focal value of o(0,0). Finally, we also study the behavior of critical points at infinity.

中文摘要：本文研究了一类平面三次多项式系统，我们采用常微分方程的定性理论的分析方法，得出如下四个部分结论：第一部分，分析系统所有奇点的性态，并得出系统存在奇异积分直线的条件；在前面分析的基础上，用Pioncare形式级数法，计算出了系统在奇点o(0，0)的三个焦点量；最后，研究了系统无穷远奇点的性态。

4 We show that the Dirac operator in an external field has the same essential spectrum as the free Dirac operator provided the potential vanishes at infinity.

在4.3.4节，我们证明了狄拉克算子在外场中有着对应着无穷远处时零势能极限的自由狄拉克算子的相同的本质谱。

The decay rate of the corresponding strong solution at infinity is also given for some kinds of initial data with exponential decay.

若其初值以指数方式衰退，且空间可微，则此强解在之后的时间内也将以指数方式衰退。

However, for exterior problem, in order to ensure the uniqueness of the solution, the behavior of the solution at infinity must be specified, thus the modification for the expression of the solution and the constraint for the solution of boundary integral equation are needed.

对外边值问题，考虑到二维Dirichlet问题的解应当在无穷远处有界，故解的边界积分表达式要做修正，对积分方程的解要有约束，这样去解边界积分方程得出的解才等同于原问题的解。

The general Fredholm integral equation of the first kind with logarithmic kernel in 2 dimensions does not always have unique solution, especially for the unbounded problem, it depends on the asymptotic behaviour at infinity.

对二维问题，一般的带对数积分核第一类Fredholm 积分方程并不总是唯一可解的，特别是对外边值问题，解在无穷远处的形态有很大的影响。

Secondly, in the determination of the homography of the plane at infinity, it relies neither on projective reconstruction nor on the homography of a space plane, it needs only some image correspondences and epipoles, which are basic requirements for any camera self-calibration technique.

该方法主要优点在于：在确定无穷远平面的单应性矩阵的过程中，不需要射影重构，也不需要有限远平面信息，唯一所需要的信息是图象极点，从而简化了文献中现有的算法。

In addition, we prove that for a given set of camera motions such as {(R,t1),(R,t2)},if (t1 ,t2) are not linearly dependent, then the homography of the plane at infinity under this motion set can be linearly and uniquely determined.

另外同时给出了由极点确定关于无穷远平面单应性矩阵的充分必要条件。

The result with the reference of a point at infinity was derived from a newly proposed reference electrode standardization technique based on the equivalent distributed source theory.

其中无穷远点参考是通过一种基于等效分布源理论建立的参考电极校正技术处理后得到的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。