Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

On the enantioselectivity of aziridination of styrene catalysed by copper triflate and copper-exchanged zeolite Y: consequences of the phase behaviour of enantiomeric mixtures of N-arene-sulfonyl-2-phenylaziridines

By synthesising S-2-phenyl-N-(4-nitrophenyl)aziridine from S-phenylglycinol, it has been demonstrated that the aziridination of styrene by [N-(4-nitrobenzenesulfonyl)imino]phenyliodinane (nosyliminophenyliodinane, PhINNs) in the presence of S,S-2,2'-isopropylidene-bis(4-phenyl-2-oxazoline), catalysed by copper(II) triflate in CH(3)CN solution or heterogeneously by CuHY, has predominantly an R-configuration. The enantioselectivity of the aziridination of styrene by [N-arenesulfonylimino]-phenyliodinanes catalysed by copper-exchanged zeolite Y (CuHY), in conjunction with a chiral bis-oxazoline ligand, has been re-examined. In the case of PhINNs, it is shown that the product mixture of enantiomeric aziridines, on treatment with hexane, gives rise to a solid phase of low enantiomeric excess (ee) and a solution phase of high ee. Separation of the solid phase and recrystallisation afforded a true racemate (racemic compound), which has been confirmed by X-ray crystallography. The aziridine obtained from the solution phase could be recrystallised to produce the pure enantiomer originally in excess. A consequence of the new findings is that previous reports on the enantioselectivity of copper-catalysed aziridination, both in heterogeneous and homogeneous conditions, should be regarded with caution if the analytical procedure involved HPLC with injection of the enantiomeric mixture in a hexane-rich solvent. Such a method has been used in previous work from this laboratory, but has also been used elsewhere, following the procedure developed by Evans and co-workers when the (homogeneous) copper-catalysed aziridination by PhINTs was first discovered. Evidently, the change of substituent in the benzenesulfonyl group reduces the solubility in hexane, affording a solution phase of enhanced ee.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

Cobalt(iii) complexes as functional ligands for metal (oxide) surfaces

Co(iii) polyamine complexes with either two or three labile coordination sites bind strongly to high surface area metal oxides such as goethite or aluminium trihydroxide, and have been shown to act as passivating agents for aluminium flake in aqueous media, in addition to providing a potential method for surface functionalisation.     

The chip firing game onn-cycles

Spencer introduced a chip firing game on a line, which was generalized by Björner, Lovasz and Shor to graphs. This paper characterizes those configurations which may be repeated in a game, and analyzes the game forn-cycles.This research was funded by NSERC operating grants.     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

Dielectric relaxation in amorphous polyepichlorhydrin and polyepibromhydrin

The variation of the dielectric permittivity and loss factor with frequency and temperature has been measured for two polyethers with polar side groups, polyepichlorhydrin and polyepibromhydrin. Both polymers showed two distinct relaxation processes. The high-temperature relaxations correlate with the glass-to-rubber transition temperatures in accord with the WLF equation. For the low-temperature relaxations, attributed to rotational motion of the side groups, the activation energy for the bulkier—CH₂Br case is smaller than—CH₂Cl. This effect and the extreme broadness of these relaxations are explained by considering dipole-dipole interactions. Calculations for selected model conformations show that intramolecular dipole-dipole interactions are weak, but that inter-molecular dipole-dipole interactions can account for the observed order of activation energies.