Exact Solutions of Extended Boussinesq Equations

The problem addressed in this paper is the verification of numerical solutions of nonlinear dispersive wave equations such as Boussinesq-like system of equations. A practical verification tool for numerical results is to compare the numerical solution to an exact solution if available. In this work, we derive some exact solitary wave solutions and several invariants of motion for a wide range of Boussinesq-like equations using Maple software. The exact solitary wave solutions can be used to specify initial data for the incident waves in the Boussinesq numerical model and for the verification of the associated computed solution. The invariants of motions can be used as verification tools for the conservation properties of the numerical model.     

A study of the epoxidation of 6-deoxyhex-5-enopyranosides. 1,5-Dicarbonyl derivatives and novel synthetic routes to D-xylo-hexos-5-ulose and D-lyxo-hexos-5-ulose

The work described deals with the isolation and characterization of epoxides from 6-deoxyhex-5-enopyranosides and preliminary exploration of their synthetic potential. Prolonged epoxidation reaction times led to their hydrolysis in situ and gave novel protected D-hexos-5-ulose derivatives (sugar 1,5-dicarbonyls). Some reactions of the hexos-5-uloses were studied, and in some cases septanoside (seven-membered-ring saccharide) derivatives were isolated. Novel routes to D-xylo-hexos-5-ulose and D-lyxo-hexos-5-ulose, of interest as intermediates in the synthesis and biosynthesis of inositols and aza sugars, are also described. The structures of the epoxides and novel hexos-5-uloses were established by NMR and X-ray crystallographic methods.     

The Design and Implementation of Usable ODE Software

In the last decade it has become standard for students and researchers to be introduced to state-of-the-art numerical software through a problem solving environment (PSE) rather than through the use of scientific libraries callable from a high level language such as Fortran or C. In this paper we will identify the constraints and implications that this imposes on the ODE software we investigate and develop. In particular, the way a numerical solution is displayed and viewed by a user dictates that new measures of performance and quality must be adopted. We will use the MATLAB environment and ODE software for initial value problems, boundary value problems and delay problems to illustrate the issues that arise and the progress that has been made. One of the major implications is the expectation that accurate approximations at off-mesh points must be provided. Traditional numerical methods for ODEs have produced approximations to the underlying solution on an associated discrete, adaptively chosen mesh. In recent years it has become common for the ODE software to also deliver approximations at off-mesh values of the independent variable. Such a feature can be extremely valuable in applications and leads to new measures of quality and performance which are more meaningful to users and more consistently interpreted and implemented in contemporary ODE software. Numerical examples of the robust and reliable behaviour of such software will be presented and the cost/reliability trade-offs that arise will be quantified.     

Structure of 9,10-di(9,9-dioctylfluorenyl)anthracene in the solid and in solution

A new example of magnetic nonequivalence of chemically equivalent atoms is identified from the proton and carbon resonance spectra of 9,10-di(9,9-dioctylfluorenyl)anthracene with the aid of its conformation in the crystalline state. Molecular modeling suggests that it has a similar conformation in solution.     

13C CP MAS NMR of halogenated (Cl,Br, I) pharmaceuticals at ultrahigh magnetic fields

This work reports significantly improved spectral resolution of ¹³C CP MAS NMR spectra of chlorinated, brominated and iodinated solid organic compounds when such spectra are recorded at ultrahigh magnetic field strengths. The cause of this is the residual dipolar coupling between carbon atoms and quadrupolar halogen nuclides (chlorine‐35/37, bromine‐79/81 or iodine‐127), an effect inversely proportional to the magnetic field strength which declines in importance markedly at 21.1 T as compared to lower fields. In favorable cases, the fine structure observed can be used for spectral assignment, e.g. for Cl‐substituted aromatics where the substituted carbon as well as the ortho‐carbons show distinct doublets. The experimental results presented are supported by theoretical modeling and calculations. The improved spectral resolution in the studied systems and similar halogenated materials will be of particular interest and importance for polymorph identification, drug discovery and quality control in the pharmaceutical industry. Copyright © 2009 John Wiley & Sons, Ltd.     

Single-molecule magnet behavior for an antiferromagnetically superexchange-coupled dinuclear dysprosium(III) complex

A family of five dinuclear lanthanide complexes has been synthesized with general formula [Ln(III)(2)(valdien)(2)(NO(3))(2)] where (H(2)valdien = N1,N3-bis(3-methoxysalicylidene)diethylenetriamine) and Ln(III) = Eu(III)1, Gd(III)2, Tb(III)3, Dy(III)4, and Ho(III)5. The magnetic investigations reveal that 4 exhibits single-molecule magnet (SMM) behavior with an anisotropic barrier U(eff) = 76 K. The step-like features in the hysteresis loops observed for 4 reveal an antiferromagnetic exchange coupling between the two dysprosium ions. Ab initio calculations confirm the weak antiferromagnetic interaction with an exchange constant J(Dy-Dy) = -0.21 cm(-1). The observed steps in the hysteresis loops correspond to a weakly coupled system similar to exchange-biased SMMs. The Dy(2) complex is an ideal candidate for the elucidation of slow relaxation of the magnetization mechanism seen in lanthanide systems.