Search

We propose and analyze a semidiscrete parametric finite element scheme for solving the area-preserving curve shortening flow. The scheme is based on Dziuk's approach [SIAM J. Numer. Anal., 36 (1999), pp. 1808--1830] for the anisotropic curve shortening flow. We prove that the scheme preserves two fundamental geometric structures of the flow with an initially convex curve: (i) the convexity-preserving property, and (ii) the perimeter-decreasing property. To the best of our knowledge, the convexity-preserving property of numerical schemes which approximate the flow is rigorously proved for the first time. Furthermore, the error estimate of the semidiscrete scheme is established, and numerical results are provided to demonstrate the structure-preserving properties as well as the accuracy of the scheme. [ABSTRACT FROM AUTHOR]

The phylogeny of foliicolous taxa in Pilocarpaceae was reconstructed using Bayesian and maximum likelihood analyses of concatenated ITS and mtSSU sequences. Sixty-six new partial sequences representing 36 taxa were generated and 29 sequences were downloaded from GenBank. Our results indicate that Lasioloma R. Sant. is nested within a paraphyletic Calopadia Vězda, whereas Fellhanera Vězda is polyphyletic and the phylogenetic relationships of Eugeniella Lücking et al. and Sporopodium Mont. with Fellhanera require further investigation. In addition, Tapellaria parvimuriformis W. C. Wang & J. C. Wei is described as a new species from Khao Yai National Park, Thailand, and is characterized by its small muriform ascospores, grey campylidia with a pale base, and short conidia. Eight new records of foliicolous lichens for Thailand are also listed. [ABSTRACT FROM AUTHOR]