Directional maximal operators with smooth densities.

We study directional maximal operators on Rn with smooth densities. We prove that if the classical directional maximal operator in a given set of directions is weak type (1, 1), then the corresponding smooth-density maximal operator in that set of directions will be bounded on Lq for q suitably large, depending on the order of the stationary points of the density function. In contrast to the classical case, if q is too small, the smooth density operator need not be bounded on Lq. Improving upon previously known results, we also establish that if the density function has only finitely many extreme points, each of finite order, then any maximal operator in a finite sum of diadic directions is bounded on all Lq for q > 1

Proposals for optimization of laser welding in prosthetic dentistry

This paper points out each key parameter involved in laser welding and discusses the parameters' effects on weld microstructure and defects detected inside the weld. Solutions are proposed to adjust the parameters to provide an optimal dental assembly. Metallurgical effects as well as defects are briefly discussed. A welding procedure adapted to different compositions of dental alloys is proposed