79Br NMR spectroscopy as a practical tool for kinetic analysis

⁷⁹Br NMR spectroscopy has been used to monitor a series of reactions in which the bromide ion is produced, including the Menschutkin reaction of pyridine with a range of substituted benzyl bromides and a Heck coupling process. In cases where the process could also be monitored using ¹H NMR spectroscopy, the kinetic analyses using heteronuclear magnetic resonance spectroscopy were shown to be completely consistent. Both the utility of the process in following reactions which may be difficult to analyse using other techniques and the practical limitations associated with solvent choice are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

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The empirical harmonic potential function of diborane

A total of 114 spectroscopic data accumulated from 6 isotopic species of diborane have been used to permit a precise determination of the empirical harmonic potential function to be made for the first time. Of the 33 independent force constants, 30 can be determined with numerical significance. The physical significance of the values is probably best demonstrated by the rather close correspondence throughout with scaled ab initio force constants from two sources, only one rather large disagreement in magnitude being found. The potential function reproduces all known frequency, isotopic frequency shift, Coriolis ζ, and centrifugal distortion Δ data to high accuracy. It is used to calculate parameters which will be of value to further spectroscopic and structural studies, to enable accurate analyses to be made of a number of major Fermi resonance interactions present in the spectra, and to explain the anomalously small Coriolis interaction between the infrared active rocking and wagging fundamentals. The advantages of alternative symmetry coordinate definitions are considered, particularly in relation to making comparisons between diborane and ethylene.     

Weighted norm inequalities for convolution operators and links with the Weiss Conjecture

We study convolution operators on weighted Lebesgue spaces and obtain weight characterisations for boundedness of these operators with certain kernels. Our main result is Theorem 3 which enables us to obtain results for certain kernel functions supported on bounded intervals; in particular we get a direct proof of the known characterisations for Steklov operators in Section 3 by using the weighted Hardy inequality. Our methods also enable us to obtain new results for other kernel functions in Section 4. In Section 5 we demonstrate that these convolution operators are related to operators arising from the Weiss Conjecture (for scalar-valued observation functionals) in linear systems theory, so that results on convolution operators provide elementary examples of nearly bounded semigroups not satisfying the Weiss Conjecture. Also we apply results on the Weiss Conjecture for contraction semigroups to obtain boundedness results for certain convolution operators.     

Decay of a polariton mode generated by difference mixing

An experiment to determine the life-time of a pulsed polariton is analysed. (i) The phase matching condition for a complex refractive index is discussed, and (ii) decay curves are presented for both polariton branches.