The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from the eigenvalues and eigenfunctions of the Laplace-Beltrami operator determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete heat kernel and the...
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternative methods so far....
The P1 discretization of the Laplace operator on a triangulated
polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the
Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic...
Gender relations as well as the social situation of Manchu women have long been ignored in studies of the cultural evolution of the Manchu. By setting the discussion of Manchu women in the context of cultural adaptation, this study reintroduces gender and women's problems into the research on the Manchu...
Microbial ecology has been transformed by metagenomics, the study of the genetic in-formation in entire communities of organisms. In the following we develop metagenomic tools arising from the classic Wasserstein metric as applied to questions regarding the diversity between microbial communities. We provide a novel proof of the characteriza-tion of...
The South Pole ice core (SPC14), drilled in the field seasons of 2014/2015 and 2015/2016, is an intermediate length, 1,751-m ice core which preserves a 54,000-year record of past climate and atmospheric composition. The SPC14 ice core adds to the spatial grid of ice cores in Antarctica extending into the...
The demand for the development of sustainable energy is an all time high as we burn through limited fossil fuel reserves and as environmental concerns rise every year. Renewable energy sources such as wind and solar power have limitations due to inconsistent power supply that cannot meet the regular needs...