The calculation of accurate normal coordinates I: general theory, and application to methane

The calculation of accurate and reliable vibrational potential functions and normal co-ordinates is discussed, for such simple polyatomic molecules as it may be possible. Such calculations should be corrected for the effects of anharmonicity and of resonance interactions between the vibrational states, and should be fitted to all the available information on all isotopic species: particularly the vibrational frequencies, Coriolis zeta constants and centrifugal distortion constants. The difficulties of making these corrections, and of making use of the observed data are reviewed. A programme for the Ferranti Mercury Computer is described by means of which harmonic vibration frequencies and normal co-ordinate vectors, zeta factors and centrifugal distortion constants can be calculated, from a given force field and from given G-matrix elements, etc. The programme has been used on up to 5 × 5 secular equations for which a single calculation and output of results takes approximately l min; it can readily be extended to larger determinants. The best methods of using such a programme and the possibility of reversing the direction of calculation are discussed. The methods are applied to calculating the best possible vibrational potential function for the methane molecule, making use of all the observed data.

"I don't know what you are trying to establish": The socio-environmental 'problems' of visual impaired children

This paper uses the social model of disability to examine visually impaired children's experiences of their housing and neighbourhoods and finds that they did not experience any significant problems with the design of them. The source of their problems was within these environments, and was caused by factors such as the intensity of movement, for example, from flows of traffic. We conclude by discussing the social policy implications of these findings.

Insulin, glucagon-like peptide 1, glucose-dependent insulinotropic polypeptide and insulin-like growth factor I as putative mediators of the hypolipidemic effect of oligofructose in rats

The addition of oligofructose as a dietary fiber decreases the serum concentration and the hepatic release of VLDL-triglycerides in rats. Because glucose, insulin, insulin-like growth factor I (IGF-I) and gut peptides [i.e., glucose-dependent insulinotropic polypeptide (GIP) and glucagon-like peptide-1 (GLP-1)]) are factors involved in the metabolic response to nutrients, this paper analyzes their putative role in the hypolipidemic effect of oligofructose. Male Wistar rats were fed a nonpurified diet with or without 10% oligofructose for 30 d. Glucose, insulin, IGF-I and GIP concentrations were measured in the serum of rats after eating. GIP and GLP-1 contents were also assayed in small intestine and cecal extracts, respectively. A glucose tolerance test was performed in food-deprived rats. Serum insulin level was significantly lower in oligofructose-fed rats both after eating and in the glucose tolerance test, whereas glycemia was lower only in the postprandial state. IGF-I serum level did not differ between groups. GIP concentration was significantly higher in the serum of oligofructose-fed rats. The GLP-1 cecal pool was also significantly higher. In this study, we have shown that cecal proliferation induced by oligofructose leads to an increase in GLP-1 concentration. This latter incretin could be involved in the maintenance of glycemia despite a lower insulinemia in the glucose tolerance test in oligofructose-fed rats. We discuss also the role of hormonal changes in the antilipogenic effect of oligofructose.

Operator space structure of JC*-triples and TROs, I

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension

How do I know if my forecasts are better? Using benchmarks in Hydrological ensemble prediction

The skill of a forecast can be assessed by comparing the relative proximity of both the forecast and a benchmark to the observations. Example benchmarks include climatology or a naïve forecast. Hydrological ensemble prediction systems (HEPS) are currently transforming the hydrological forecasting environment but in this new field there is little information to guide researchers and operational forecasters on how benchmarks can be best used to evaluate their probabilistic forecasts. In this study, it is identified that the forecast skill calculated can vary depending on the benchmark selected and that the selection of a benchmark for determining forecasting system skill is sensitive to a number of hydrological and system factors. A benchmark intercomparison experiment is then undertaken using the continuous ranked probability score (CRPS), a reference forecasting system and a suite of 23 different methods to derive benchmarks. The benchmarks are assessed within the operational set-up of the European Flood Awareness System (EFAS) to determine those that are ‘toughest to beat’ and so give the most robust discrimination of forecast skill, particularly for the spatial average fields that EFAS relies upon. Evaluating against an observed discharge proxy the benchmark that has most utility for EFAS and avoids the most naïve skill across different hydrological situations is found to be meteorological persistency. This benchmark uses the latest meteorological observations of precipitation and temperature to drive the hydrological model. Hydrological long term average benchmarks, which are currently used in EFAS, are very easily beaten by the forecasting system and the use of these produces much naïve skill. When decomposed into seasons, the advanced meteorological benchmarks, which make use of meteorological observations from the past 20 years at the same calendar date, have the most skill discrimination. They are also good at discriminating skill in low flows and for all catchment sizes. Simpler meteorological benchmarks are particularly useful for high flows. Recommendations for EFAS are to move to routine use of meteorological persistency, an advanced meteorological benchmark and a simple meteorological benchmark in order to provide a robust evaluation of forecast skill. This work provides the first comprehensive evidence on how benchmarks can be used in evaluation of skill in probabilistic hydrological forecasts and which benchmarks are most useful for skill discrimination and avoidance of naïve skill in a large scale HEPS. It is recommended that all HEPS use the evidence and methodology provided here to evaluate which benchmarks to employ; so forecasters can have trust in their skill evaluation and will have confidence that their forecasts are indeed better.