Non-homogeneous Tb Theorem for Bi-parameter g-function

The main result of this paper is a bi-parameter Tb theorem for Littlewood-Paley g-function, where b is a tensor product of two pseudo-accretive function. Instead of the doubling measure, we work with a product measure μ = μn × μm, where the measures μn and μm are only assumed to be upper doubling. The main techniques of the proof include a bi-parameter b-adapted Haar function decomposition and an averaging identity over good double Whitney regions. Moreover, the non-homogeneous analysis and probabilistic methods are used again.

基于能量优化的数据参数化方法

构造一条通过一组给定数据点的参数样条曲线的关键之一是选取节点。本文提出了一种基于离散能量模型的确定节点参数的新方法,该方法首先通过极小化离散能量模型的目标函数确定参数样条曲线在节点处的最佳切向角,然后以最佳切向角为参变量来计算节点参数。该方法所得到的方程为线性方程,便于求解。本文最后通过实例对新方法与累加弦长方法、向心参数化方法、修正弦长参数化方法以及ZCM方法进行了比较。