A Littelmann-type formula for Duistermaat-Heckman measures

Given a compact Hamiltonian T-manifold M, some component of whose moment map is a Palais-Smale Morse function, we give a formula for the Duistermaat-Heckman measure (the Fourier transform of the equivariant symplectic volume) as a sum of volumes of simplices. Unlike previous formulae for this measure, this sum has only positive terms. In the case of M a flag manifold, our results are an asymptotic version of Littelmann's multiplicity result in representation theory [9]. Oblatum 5-I-1998 & 25-I-1998 / Published online: 14 October 1998     

Zeros of the Whittaker function associated to Coulomb waves

The zeros in the complex z plane of the Whittaker function W_c/z,µ(z),closely related to spherical waves in the quantum-mechanicalCoulomb problem, are investigated for varying real values ofthe parameters c and µ     

Polyurethanes. IV. Effect of poly(propylene glycol) tacticity on the properties of block copolyether-urethanes

Block copolyèther–urethane–ureas containing isotatic polypropylene glycols were synthesized and their dynamic mechanical properties compared to the analogous atactic structures. At poly(propylene glycol) molecular weights below 1000, tacticity appears to have little effect on the stress–strain properties of the block copolymers. At higher molecular weights, the ability of the isotatic polyglycol segments to crystallize under strain can effect cyclic deformation properties.     

Total synthesis of the immunosupressant (-)-pironetin (PA48153C)

[reaction: see text]. Total synthesis of the immunosuppresant pironetin has been achieved by a synthetic route in which the connections between starting materials and the desired structure are readily discerned. Key steps include a diastereoselective Lewis acid mediated crotylstannane aldehyde addition, a highly selective Lewis acid promoted Mukaiyama aldol reaction, an anti-selective SmI2 reduction of a beta-hydroxyketone, and finally a lactone annulation reaction.     

Supercritical carbon dioxide processing of fluorinated surfactant templated mesoporous silica thin films

The effect of processing mesoporous silica thin films with supercritical CO2 immediately after casting is investigated, with a goal of using the penetration of CO2 molecules in the tails of fluorinated surfactant templates to tailor the final pore size. Well-ordered films with two-dimensional hexagonal close-packed pore structure are synthesized using a cationic fluorinated surfactant, 1-(3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,10-heptadecafluorodecyl)pyridinium chloride, as a templating agent. Hexagonal mesopore structures are obtained for both unprocessed films and after processing the cast films in CO2 at constant pressure (69-172 bar) and temperature (25-45 degrees C) for 72 h, followed by traditional heat treatment steps. X-ray diffraction and transmission electron microscopy analysis reveal significant increases in pore size for all CO2-treated thin films (final pore diameter up to 4.22 +/- 0.14 nm) relative to the unprocessed sample (final pore diameter of 2.21 +/- 0.20 nm) before surfactant extraction. Similar pore sizes are obtained with liquid and supercritical fluid treatments over the range of conditions tested. These results demonstrate that combining the tunable solvent strength of compressed and supercritical CO2 with the "CO2-philic" nature of fluorinated tails allows one to use CO2 processing to control the pore size in ordered mesoporous silica films.