A New Coherent States Approach to Semiclassics Which Gives Scott’s Correction

We introduce a new semiclassical calculus by generalizing the standard coherent states. This is applied to the semiclassical expansion for the sum of negative eigenvalues of Schrödinger operators which leads to a new proof of the Scott correction for non-relativistic molecules.Work partially supported by an EU TMR grant, by a grant from the Danish research council, and by MaPhySto – Centre for Mathematical Physics and Stochastics, funded by a grant from The Danish National Research Foundation. ©2003 by the authors. This article may be reproduced in its entirety for non-commercial purposes.     

Chiral rhodium(II,II) dimers catalyzed enantioselective intramolecular aziridination of sulfonamides and carbamates

The asymmetric intramolecular aziridination of unsaturated sulfonamides and carbamates catalyzed by chiral dirhodium(II,II) complexes were achieved in good yields (up to 95%) and enantioselectivity (up to 76% e.e.).     

Geometry of Four-Vector Fields on Quaternionic Flag Manifolds

 The purpose of this paper is to describe certain natural 4-vector fields on quaternionic flag manifolds, which geometrically determine the Bruhat cell decomposition. These structures naturally descend from the symplectic group Sp(n), and are related to the dressing action given by the Iwasawa decomposition of the general linear group over the quaternions, GL _n (). Received: 3 April 2002 / Accepted: 15 January 2003 Published online: 21 March 2003 Communicated by L. Takhtajan     

Bulk viscosity damping for accelerating convergence of low Mach number Euler solvers

In solution of the Euler equations in the steady state external flows, error or residual waves are blamed for decelerating the convergence. These waves may be damped by adding a bulk viscosity term to the momentum equations. We analyse effects of this term on the linearized differential equations, and study its explicit and implicit implementation in one and two space dimensions. Optimum values of the bulk viscosity damping (BVD) are discussed. After generalization to two space dimensions, its performance both alone and in combination with a soft wall boundary condition and residual smoothing in central differencing codes is reviewed. It is shown that BVD is complementary to them, and acts independently of them. Finally, application of BVD in solution of low Mach number flows is considered, to show how it can strongly stabilize and accelerate these low Mach number computations. Copyright © 2003 John Wiley & Sons, Ltd.     

On non-inflectional solutions of non-uniform elasticae

We study buckled states of non-uniform elasticae and show that solutions having pairs of loops not separated by inflection points appear if and only if there is an (isolated) minimum in the bending stiffness. Such solutions lie on branches disconnected from the trivial solution in the global bifurcation diagram and so we obtain partial information regarding the qualitative structure of the latter.     

Investigation of the Pore Texture of SnO2-CeO2 Composite Oxides

Gas adsorption techniques have been used to study the pore texture changes occurring in composite SnO₂-CeO₂ materials of varying Sn: Ce atom ratios on calcination at temperatures up to 1273K. The data show that the uncalcined materials are largely microporous in nature, but changes in specific surface area, pore sizes and pore volume occur at an early stage in the calcination process with the formation of mesopores. However, significant changes occur at calcination temperatures>673 K at which point the mesopores are substantially reduced, and at 873 K and above the mean pore size increases greatly finally giving non-porous solids after calcination at 1273 K.     

Proof of the ionization conjecture in a reduced Hartree-Fock model

Summary The ionization conjecture for atomic models states that the ionization energy and maximal excess charge are bounded by constants independent of the nuclear charge. We prove this for the Hartree-Fock model without the exchange term.Oblatum 3-V-1990Work supported in part by the U.S. National Science Foundation grant DMS-9002416