Applying Methods from Differential Geometry to Devise Stable and Persistent Air Layers Attached to Objects Immersed in Water

We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribedconditions)and are mechanically stable and temporally persistent.In terms of physics,air-water interfaces are governed by theYoung-Laplace equation.Mathematically they are surfaces of constant mean curvature which represent solutions of a nonlinearelliptic partial differential equation.Although explicit solutions of this equation can be obtained only in very special cases,it is-under moderately special circumstances-possible to establish the existence of a solution without actually solving thedifferential equation.We also derive criteria for mechanical stability and temporal persistence of an air layer.Furthermorewe calculate the lifetime of a non-persistent air layer.Finally,we apply these tools to two examples which exhibit the symmetriesof 2D lattices.These examples can be viewed as abstractions of the biological model represented by the aquatic fernSalvinia.     

华模蛛科——采自中国的蜘蛛目一新科(蛛形纲,蜘蛛目)

记述了采自我国云南西双版纳雨林的1新科,华模蛛科Sinopimoidae fam.nov.,1新属,华模蛛属Sinopimoa gen.nov.,1新种,双色华模蛛Sinopimoa bicolor sp.nov..模式标本保存在中国科学院动物研究所.     

Structures of active melanocortin-4 receptor-Gs-protein complexes with NDP-α-MSH and setmelanotide

The melanocortin-4 receptor (MC4R),a hypothalamic master regulator of energy homeostasis and appetite,is a class A G-protein-coupled receptor and a prime target...     

The 33 kDa Protein of the Oxygen-Evolving Complex: a Multi-Gene Family in Tomato

A cDNA was isolated by chance from tomato which had a high similarityto a cDNA clone from potato known to code for the 33 kDa proteinof the oxygen-evolving complex [van Spanje et al. (1991) PlantMol. Biol. 17: 157]. The sequence of a previously describedpartial cDNA clone from tomato [Ko et al. (1990) Plant Mol.Biol. 14: 217] which has also a high similarity but is not identicalto the sequence described here indicates that tomato containsat least two genes coding for 33 kDa proteins per haploid genome.This conclusion is supported by Southern blot analysis. Thetissue specific expression of the corresponding genes is described. (Received September 28, 1992; Accepted February 15, 1993)