On rank, underdetermined systems and consistency

The concepts of rank, underdetermined systems and consistency in linear algebra are discussed in the context of a puzzle. The article begins with a specific example, moving on to a generalization of the example and then to the general n x n case. As well as providing a solution of the puzzle, the article aims to provide students with a greater understanding of these abstract ideas in linear algebra through the study of the puzzle.

π-dimerization of pleiadiene radical cations at low temperatures revealed by UV–vis spectroelectrochemistry and quantum theory

One-electron oxidation of the non-alternant polycyclic aromatic hydrocarbon pleiadiene and related cyclohepta[ c,d]pyrene and cyclohepta[c,d]fluoranthene in THF produces corresponding radical cations detectable in the temperature range of 293–263 K only on the subsecond time scale of cyclic voltammetry. Although the EPR-active red-coloured pleiadiene radical cation is stable according to the literature in concentrated sulfuric acid, spectroelectrochemical measurements reported in this study provide convincing evidence for its facile conversion into the green-coloured, formally closed shell and, hence, EPRsilent π-bound dimer dication stable in THF at 253 K. The unexpected formation of the thermally unstable dimeric product featuring a characteristic intense low-energy absorption band at 673 nm (1.84 eV; logεmax=4.0) is substantiated by ab initio calculations on the parent pleiadiene molecule and the PF6 − salts of the corresponding radical cation and dimer dication. The latter is stabilized with respect to the radical cation by 14.40 kcal mol−1 (DFT B3LYP) [37.64 kcal mol−1 (CASPT2/DFT B3LYP)]. An excellent match has been obtained between the experimental and TDDFT- calculated UV–vis spectra of the PF6 − salt of the pleiadiene dimer dication, considering solvent (THF) effects.

Integrated Arable Farming Systems and their potential uptake in the UK

Integrated Arable Farming Systems are examined from the perspective of the farmer considering the use of such techniques, and data are presented which suggest that the uptake of the approach may expose the manager to a greater degree of risk. Observations are made about the possible uptake of such systems in the UK and the implications this may have for agricultural and environmental policy in general.

Distributed systems and multimedia

Edited book to support level 3 undergraduate understanding.

Hospital catering systems and their impact on the sensorial profile of foods provided to older patients in the UK

Impaired sensorial perception is very common in older people and low sensorial quality of foods is associated with decreased appetite and dietary intake. Hospital undernutrition in older patients could be linked to sensorial quality of hospital food if the quality were low or inappropriate for older people. The aim of this study was to examine changes in the sensorial quality of different foods that occur as a result of the food journey (i.e. freezing, regeneration, etc.) in the most common hospital catering systems in the UK. A trained sensory panel assessed sensorial descriptors of certain foods with and without the hospital food journey as it occurs in the in-house and cook/freeze systems. The results showed effects of the food journey on a small number of sensorial descriptors related to flavour, appearance and mouthfeel. The majority of these effects were due to temperature changes, which caused accumulation of condensation. A daily variation in sensorial descriptors was also detected and in some cases it was greater than the effect of the food journey. This study has shown that changes occur in the sensory quality of meals due to hospital food journeys, however these changes were small and are not expected to substantially contribute to acceptability or have a major role in hospital malnutrition.

Reconciling model and information uncertainty in development appraisal

This paper investigates the effect of choices of model structure and scale in development viability appraisal. The paper addresses two questions concerning the application of development appraisal techniques to viability modelling within the UK planning system. The first relates to the extent to which, given intrinsic input uncertainty, the choice of model structure significantly affects model outputs. The second concerns the extent to which, given intrinsic input uncertainty, the level of model complexity significantly affects model outputs. Monte Carlo simulation procedures are applied to a hypothetical development scheme in order to measure the effects of model aggregation and structure on model output variance. It is concluded that, given the particular scheme modelled and unavoidably subjective assumptions of input variance, simple and simplistic models may produce similar outputs to more robust and disaggregated models.

Commodity futures prices: more evidence on forecast power, risk premia and the theory of storage

In this paper, we examine the temporal stability of the evidence for two commodity futures pricing theories. We investigate whether the forecast power of commodity futures can be attributed to the extent to which they exhibit seasonality and we also consider whether there are time varying parameters or structural breaks in these pricing relationships. Compared to previous studies, we find stronger evidence of seasonality in the basis, which supports the theory of storage. The power of the basis to forecast subsequent price changes is also strengthened, while results on the presence of a risk premium are inconclusive. In addition, we show that the forecasting power of commodity futures cannot be attributed to the extent to which they exhibit seasonality. We find that in most cases where structural breaks occur, only changes in the intercepts and not the slopes are detected, illustrating that the forecast power of the basis is stable over different economic environments.