Optimisation of partial least squares regression calibration models in near-infrared spectroscopy: a novel algorithm for wavelength selection

A novel optimisation algorithm is presented for full spectrum calibration models in near-infrared (NIR) spectroscopy. The algorithm is used to investigate the affect of removing continuous spectral regions on parameters critical to the validity of the model (e.g. explained variance, bias etc.) and ultimately identify and remove problem areas of the spectrum. As an example of its application, this paper shows how to optimise partial least squares regression (PLSR) calibration models for predicting moisture content within an intact pharmaceutical product and how problems due to changes in the nature of samples since setting up the original model may be eliminated. On application of two validated calibration models to a new set of samples unacceptable results were obtained for bias (-0.26 and -0.21% m/m moisture content) between the NIR predicted values and the true values (Karl Fischer analysis). The optimisation algorithm identified small regions of the spectrum, which if included in development of the models contributed significant bias to the final prediction. On removal of these problem regions the calibration models were found to be equally accurate and precise, but with the added advantage of robustness to a variable region of the sample spectrum (bias reduced to -0.05 and -0.09% m/m).     

A minimum principle for molecular systems allowing the use of discontinuous wave functions

In this paper the minimum principle proposed for atomic systems by Hall, Hyslop and Rees [1] is generalized to molecules. It is shown that this generalization retains the advantage of admitting the use of a larger class of trial wave functions, for example those with discontinuities, than is possible in the usual minimum energy principle. The further advantage that the upper bounds obtained by this treatment are always at least as good as those of the Rayleigh-Ritz method is also preserved. The theory is applied to the H ion, potential energy curves are obtained for various “cut-off” wave functions, and the equilibrium internuclear distance is calculated. The optimization of the “cut-off” region so that the upper bound is minimized is also discussed.     

Marcus theory of outer-sphere heterogeneous electron transfer reactions: dependence of the standard electrochemical rate constant on the hydrodynamic radius from high precision measurements of the oxidation of anthracene and its derivatives in nonaqueous solvents using the high-speed channel electrode

The validity of Marcus theory for outer-sphere heterogeneous electron transfer for the electro-oxidation of a range of anthracene derivatives in alkyl cyanide solvents is investigated. The precision measurement of these fast electron transfers (k(0) >or= 1 cm s(-1)) is achieved by use of the high-speed channel electrode and, where necessary, fast-scan cyclic voltammetry. First, the solvent effect on the rate of electron transfer is studied by considering the first oxidation wave of 9,10-diphenylanthracene in the alkyl cyanide solvents: acetonitrile, propionitrile, butyronitrile, and valeronitrile. Second, the variation of k(0) for a series of substituted anthracenes is investigated by analyzing the voltammetric response of the one-electron oxidations of 9-phenylanthracene, 9,10-dichloroanthracene, 9-chloroanthracene, 9,10-dicyanoanthracene, 9-cyanoanthracene, 9-nitroanthracene, 9,10-diphenylanthracene, and anthracene in acetonitrile. It is shown that the rate of electron transfer of a single compound in different alkyl cyanides is determined by the longitudinal dielectric relaxation properties of the solvent, while differences in rate between the substituted anthracenes in acetonitrile can be quantitatively rationalized by considering their relative hydrodynamic radii. This makes possible the accurate prediction of electron-transfer rates for a molecule by interpolation of rate constants known for related molecules.     

Combustion of mixtures containing NaClO4, S and carbon

The thermoanalytical techniques e.g. DSC, TG/DTG and Hot Stage Microscopy have been used to examine the system of NaClO₄, S and charcoal mixtures. The results show that there is no reaction between NaClO₄ and S alone, but the presence of charcoal activates their reaction. Charcoal is oxidised by NaClO₄ prior to the melting of NaClO₄, showing a solid phase reaction. The presence of S activates the whole of the reaction to such a level that the mixture burns around 300C.

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Zusammenfassung Mittels DSC, TG/DTG und HSM wurde das System von Gemischen aus NaClO₄, S und Holzkohle untersucht. Die Ergebnisse zeigen, da\ sich zwischen NaClO₄ und S allein keine Reaktion abspielt, da\ diese Reaktion aber durch Gegenwart von Holzkohle aktiviert wird. Noch vor dem Schmelzen von NaClO₄ wird Holzkohle in einer Feststoffreaktion von NaClO₄ oxydiert. Die Gegenwart von S aktiviert die gesamte Reaktion in dem Ma\e, da\ das Gemisch bei 300C verbrennt.

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We wish to express our thanks to the Procurement Executive of the Ministry of Defence, UK for providing financial support for the research.     

A discrete look at localization

This article introduces a set of localized orthonormal functions to serve as basis functions for quantum calculations. They are defined to be eigenfunctions of the position operator in a function space. Their properties, including their variances, for a one-dimensional system are developed. The application to simple harmonic motion is considered as an example and, in particular, the time evolution of an initially localized function is calculated and shown to be periodic. The theory can be interpreted as producing a discrete quantization of space with Hamiltonian interactions that are predominantly between nearest neighbors. These functions can also be used in approximate calculations. To illustrate their accuracy, the example of a Morse oscillator treated as a perturbation of a harmonic oscillator is reconsidered. It is shown that the localized functions in a variational calculation lead to a result that is a good approximation for the lowest states. Furthermore, the use of a wave function that is defined only at discrete points can be justified as the first approximation to this, so that its accuracy can also be discussed. © 1995 John Wiley & Sons, Inc.     

Products of Tits geometries: A construction op cn geometries with non-classical residues

A method of Buekenhout and Sprague's is generalised to produce non-classical Tits geometries of type C_n for any n4.     

g-Jitter induced free convection near a stagnation point

 The effect of a small but fluctuating gravitational field, characteristic of g-jitter, on the flow near the forward stagnation point of a two-dimensional symmetric body resulting from a step change in its surface temperature has been considered in this paper. The transformed equations are solved numerically by a very efficient finite-difference method known as the Keller-box technique to investigate the effects on the shear stress and rate of heat transfer of variations in the Prandtl number, Pr, the forcing amplitude, a, and the forcing frequency, ω. It has been found that these parameters affect considerably the shear stress and the rate of heat transfer. Received on 28 February 2000     

On the existence of nearly Kirkman triple systems with subsystems

It is proved in this paper that the necessary and sufficient conditions for the existence of an incomplete nearly Kirkman triple system INKTS(u, v) are u ≡ v ≡ 0 (mod 6), u ≥ 3v. As a consequence, we obtain a complete solution to the embedding problem for nearly Kirkman triple systems.