Mean curvature flows and isotopy of maps between spheres

Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area‐decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc.     

Stainless steel capillary columns for high temperature gas chromatography

A layer of elemental silicon has been deposited on the surface of stainless steel tubing by means of chemical vapor deposition (CVD). Two kinds of capillary column were prepared from the deactivated tubing: cross-linked, silanol-terminated polydime-thylsiloxane wall coated open tubular (WCOT) columns and molecular sieve 13X porous layer open tubular (PLOT) columns. Unlike fused silica capillary columns, stainless steel WCOT and PLOT columns can be operated at temperatures in excess of 400°C. High temperature simulated distillation has been performed successfully with a macro bore WCOT column and rapid PNA (paraffin, naphthene, and aromatic) analysis with a multidimensional gas solid chromatographic (GSC) system using PLOT columns.