分段可微函数

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

Using normal distribution transform probability model to represent a laser range scan.Not need features corresponded,but transform the discrete scan date to the piecewise continuous and differentiable probability density function,and using Newton's algorithm to optimize scan matching,so can build the 2D global map.

利用正态分布转换概率模型来表示激光扫描，不需利用特征对应，而是通过将扫描得到的离散数据点转换成分段连续可微的概率密度函数，并利用牛顿优化算法来进行扫描匹配，从而建立2维全局地图。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新