Oriented Mixed Area and Discrete Minimal Surfaces

Recently a curvature theory for polyhedral surfaces has been established, which associates with each face a mean curvature value computed from areas and mixed areas of that face and its corresponding Gauss image face. Therefore a study of minimal surfaces requires studying pairs of polygons with vanishing mixed area. We show that the mixed area of two edgewise parallel polygons equals the mixed area of a derived polygon pair which has only the half number of vertices. Thus we are able to recursively characterize vanishing mixed area for hexagons and other n-gons in an incidence-geometric way. We use these geometric results for the construction of discrete minimal surfaces and a study of equilibrium forces in their edges, especially those with the combinatorics of a hexagonal mesh.     

A novel preparation of macroscopic beads of porous silica

We report a new method for preparing porous silica beads using a high internal phase emulsion (HIPE) sol–gel templating method. The method uses a silica sol based HIPE and does not rely on a polymeric support to produce the final structure. As a result beads may be formed readily in large numbers. The beads have an open porous structure commensurate with the formation of a HIPE precursor phase. We also describe how the rheology of the HIPE reflects the formation of an open porous structure and how the viscosity of the HIPE can affect the shape of the beads and how HIPE destabilization may be used to vary the pore size.     

Cyclization and Isomerization Reactionsin Silylhydrazine Chemistry

 This review describes the synthesis and isomerization reactions of cyclic silylhydrazines. Topics of discussion are the ring expansion of the three-membered Si(SiN₂) to the four-membered (SiN)₂ ring by lithiation of the (SiN₂) ring and by thermal silyl group insertion into the N*N bond, the ring expansion of a three-membered (SiN₂) to a five-membered (CSi₂N₂) ring by SiCH₂ insertion into the Si*N bond, the formation of isomeric four- and six-membered (SiN₂)₂ rings, the synthesis of five- and six-membered silylhydrazine rings, and the expansion of a five-membered (N₂Si₂N)N ring to the isomeric six-membered (SiNN)₂ ring. The mechanisms of the isomerizations are explained by quantum chemical calculations, and the results are verified by crystal structure determinations.     

Counterexamples on L_p-maximal regularity

We establish a transference result for -maximal regularity for the abstract Cauchy problem on Banach space. From this result we deduce counterexamples to -maximal regularity In particular we obtain an operator B without any -maximal regularity although it admits bounded imaginary powers with for all . We also derive an operator which satisfies -maximal regularity on bounded intervals [0, T[ but not on the half line Received March 5, 1997; in final form October 10, 1997     

Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C

We study the rigid cohomology of the ordinary locus in some compact PEL Shimura varieties of type C with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent Hecke eigenforms. This generalises work of Coleman, and is a first step in an ongoing project to extend the cohomological approach to classicality to higher-dimensional Shimura varieties.     

Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

Comparisons between predictions of a Biot-Allard model allowing for angle-dependent elasticity and angle-and-porosity dependent tortuosity and transmission data obtained at normal incidence on water-saturated replica bones are extended to oblique incidence. The model includes two parameters which are adjusted for best fit at normal incidence. Using the same parameter values, it is found that predictions of the variation of transmitted waveforms with angle through two types of bone replica are in reasonable agreement with data despite the fact that scattering is not included in the theory.