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We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in$R$^{3}away from the nuclei.

The problem of compressive-sensing (CS) L2-L1-TV reconstruc- tion of magnetic resonance (MR) scans from undersampled k-space data has been addressed in numerous studies. However, the regularization parameters in models of CS L2-L1-TV reconstruction are rarely studied. Once the regu- larization parameters are given, the solution for an MR reconstruction model is xed and is less eective in the case of strong noise. To overcome this shortcoming, we present a new alternating formulation to replace the standard L2-L1-TV reconstruction model. A weighted-average alternating minimization method is proposed based on this new formulation and a convergence analysis of the method is carried out. The advantages of and the motivation for the pro- posed alternating formulation are explained. Experimental results demonstrate that the proposed formulation yields better reconstruction results in the case of strong noise and can improve image reconstruction via exible parameter slection.

Surface segmentation is a fundamental problem in computer graphics. It has various applications such as metamorphosis, surface matching, surface compression, 3D shape retrieval, texture mapping, etc. All orientable surfaces are Riemann surfaces, and admit conformal structures. This paper introduces a novel surface segmentation algorithm based on its conformal structure. Each segment can be conformally mapped to a planar rectangle, and the transition maps are planar translations. The segmentation is intrinsic to the surface, independent of the embedding, and consistent for surfaces with similar geometries. By using segmentation based on conformal structure, the mapping between surfaces with arbitrary topologies can be constructed explicitly. The method is rigorous, efficient and automatic. The segmentation can be applied to surface morphing, construct conformal geometry image, convert mesh to Spline