An enantioselective 1,3-dipolar cycloaddition of 2-cyclo-hexene-1-one and azomethine ylide generated in situ from isatin and amino ester was developed by employing proline sulfonamide as the catalyst. Consequently, novel polycyclic spirooxindole scaffolds with three contiguous stereocenters were prepared in high yield (up to 95%) with excellent diastereo- (> 20:1 dr) and...
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....
Now in its 10th year, the Gramene database (http://www.gramene.org) has grown from its primary focus on rice, the first fully-sequenced grass genome, to become a resource for major model and crop plants including Arabidopsis, Brachypodium, maize, sorghum, poplar and grape in addition to several species of rice. Gramene began with...