The geometry of a vorticity model equation

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\ge 2$.Comment: 24 page

The Cellular Structure of Selected Apple Varieties

Apple cultivars (Sauergrauech, Klarapfel, James Grieve, Granny Smith, Mcintosh, Robinette) which had different textures based on sensory and instrumental analysis (particularly in firmness and mealiness) were examined by conventional scanning electron microscopy (SEM), cold-stage SEM (cryoSEM) and confocal scanning laser microscopy (CSLM) using various preparative procedures. Advantages, lim itations and artifacts of each technique are discussed. SEM with glutaraldehyde-fixation and criticalpoint- drying produced minimal tissue distortion and the fracture pattern and appearance of mealy versus non mealy tissue was different. Freeze-drying unfixed tissue caused cell collapse and firm versus soft varieties could not be differentiated. Freeze-fracturing and cryoSEM of apple ti ssue with varying textures revealed the degree of cell adhesion between frozen hydrated cells. CSLM provided more information on the three-dimensional internal structure of intact fresh apple tissue and cell cohesiveness . Details of structural elements were enhanced by staining with acridine orange