Controlled modulation of mesoporosities in metal (M = Al, Fe) phosphate solids

Mesoporous solids which possess average pore diameters between 7 and 20 nm, depending on the composition, have been prepared. The solids have the general formula Al₁₀₀P_χM₂₀ where M = Al or Fe, and χ = 0, 4.5, 9, 18, 36, 72 or 144. The initial addition of phosphorus as phosphate transforms the originally crystalline oxide/oxides into amorphous solids. These amorphous materials possess a narrow pore size distribution: 80–90% of the pores lie within 1–2 nm of the average pore diameter. Subsequent incremental amounts of phosphorus transform the material into a crystalline solid whilst the pore size distribution becomes much wider and the maximum moves towards larger pore diameters. Substitution of 20% of the aluminium by iron results, at a low phosphorus content, in pores with smaller pore volumes and smaller surface areas.

The data in the dV_p/dD_p = > D_p) graphs, where V_p is the incremental pore volume and D_p is the average pore diameter, can be approximated using an admixture of Gaussian and Lorentzian curves. For low phosphorus contents the dV_p/dD_p = (D_p) curves have a mainly Gaussian profile but the gradual addition of phosphorus transforms them to Lorentzian-type curves. An attempt to approximate the histograms dV_p =(D_p) with the minimum number of distribution curves made up of the corresponding Gaussian and Lorentzian components indicates that each successive addition of phosphorus creates a dominant new pore component at a larger pore diameter. At the same time, the components at smaller pore diameters are diminished and eventually disappear as more phosphorus is added.     

Stereocontrolled addition to a penaldic acid equivalent: an asymmetric of threo-β-hydroxy-L-glutamic acid

The asymmetric synthesis of $\text{threo}$-β-hydroxy-L-glutamic acid (7) via a stereo-selective addition to the chiral penaldic acid equivalent 3 is described.     

Even more with the Lemke complementarity algorithm

This note presents a new termination result for the Lemke linear complementarity algorithm that unifies two previous results. Special cases include linear complementarity problems satisfying the Evers condition, and those whoseM matrix is copositive-plus.This research was partially supported by NSF Grant ECS-8312008.     

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.