Wave functions for the methane molecule

If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed

Analytical functions for the ground state potential surfaces of C3 (X 1 Σ g+) and HCN (X 1 Σ +)

Analytic functions have been obtained to represent the potential energy surfaces of C3 and HCN in their ground electronic states. These functions closely reproduce the available data on the energy, geometry, and force constants in all stable conformations, as well as data on the various dissociation products, and ab initio calculations of the energy at other conformations. The form of the resulting surfaces are portrayed in various ways and discussed briefly.

Potential energy functions for ground state surfaces of HCO and HNO

Analytical potential functions are reported for the ground state surfaces of HCO and HNO, the functions being derived from spectroscopic and ab initio data. Harmonized force fields have been deduced for the stable configurations of both molecules and vibration frequencies predicted for the metastable species COH and NOH.

MFN status and the choice of tariff regime

The gradualist approach to trade liberalization views the uniform tariffs implied by MFN status as an important step on the path to free trade. We investigate whether a regime of uniform tariffs will be preferable to discriminatory tariffs when countries engage in non-cooperative interaction in multilateral trade. The analysis includes product differentiation and asymmetric costs. We show that with the cost asymmetry the countries will disagree on the choice of tariff regime. When the choice of import tariffs and export subsidies is made sequentially the uniform tariff regime may not be sustainable, because of an incentive to deviate to a discriminatory regime. Hence, an international body is needed to ensure compliance with tariff agreement.

Dichotomous-choice contingent valuation with 'don't know' responses and misreporting

A new approach is presented that simultaneously deals with Misreporting and Don't Know (DK) responses within a dichotomous-choice contingent valuation framework. Utilising a modification of the standard Bayesian Probit framework, a Gibbs with Metropolis-Hastings algorithm is used to estimate the posterior densities for the parameters of interest. Several model specifications are applied to two contingent valuation datasets: one on wolf management plans, and one on the US Fee Demonstration Program. We find that DKs are more likely to be from people who would be predicted to have positive utility for the bid. Therefore, a DK is more likely to be a YES than a NO. We also find evidence of misreporting, primarily in favour of the NO option. The inclusion of DK responses has an unpredictable impact on willingness-to-pay estimates, since it impacts differently on the results for the two datasets we examine. Copyright (C) 2009 John Wiley & Sons, Ltd.

Consumer willingness to pay for in-flight service and comfort levels: A choice experiment

In the competitive aviation market as a result of the emergence of low cost carriers, charter airlines have had to reconsider their approach to service provision. Specifically, the reduction in service and comfort levels offered by the low cost airlines provides charter carriers with an opportunity to differentiate their product based on the quality of the offering. To consider this strategic option we employ an on-line choice experiment to examine consumer choices with respect to the bundle of services on offer when deciding to purchase a flight, With these data we use the Bayesian methods to estimate a mixed logit specification. Our results reveal that in principle passengers are willing to pay a relatively large amount for enhanced service quality. (C) 2008 Elsevier Ltd. All rights reserved.

The influence of age and gender on food choice: a focus group exploration

With 25% of the UK population predicted to be obese by 2010, the costs to individuals and society are set to rise. Due to the extra economic and social pressures obesity causes, there is an increasing need to understand what motivates and prevents consumers from eating a healthy diet so as to be able to tailor policy interventions to specific groups in society. In so doing, it is important to explore potential variations in attitudes, motivation and behaviour as a function of age and gender. Both demographic factors are easily distinguished within society and a future intervention study which targets either, or both, of these would likely be both feasible and cost-effective for policy makers. As part of a preliminary study, six focus groups (total n = 43) were conducted at the University of Reading in November 2006, with groups segmented on the basis of age and gender. In order to gather more sensitive information, participants were also asked to fill out a short anonymous questionnaire before each focus group began, relating to healthy eating, alcohol consumption and body dissatisfaction. Making use of thematic content analysis, results suggested that most participants were aware of the type of foods that contribute to a healthy diet and the importance of achieving a healthy balance within a diet. However, they believed that healthy eating messages were often conflicting, and were uncertain about where to find information on the topic. Participants believed that the family has an important role in educating children about eating habits. Despite these similarities, there were a number of key differences among the groups in terms of their reasons for making food choices. Older participants (60+ years old) were more likely to make food choices based on health considerations. Participants between the ages of 18–30 were less concerned with this link, and instead focused on issues of food preparation and knowledge, prices and time. Younger female participants said they had more energy when they ate healthier diets; however, very often their food choices related to concern with their appearance. Older female participants also expressed this concern within the questionnaire, rather than in the group discussions. Overall, these results suggest that consumer motivations for healthy eating are diverse and that this must be considered by government, retailers and food producers.

A comparative evaluation of functions for partitioning nitrogen and amino acid intake between maintenance and growth in broilers

The results from three types of study with broilers, namely nitrogen (N) balance, bioassays and growth experiments, provided the data used herein. Sets of data on N balance and protein accretion (bioassay studies) were used to assess the ability of the monomolecular equation to describe the relationship between (i) N balance and amino acid (AA) intake and (ii) protein accretion and AA intake. The model estimated the levels of isoleucine, lysine, valine, threonine, methionine, total sulphur AAs and tryptophan resulting in zero balance to be 58, 59, 80, 96, 23, 85 and 32 mg/kg live weight (LW)/day, respectively. These estimates show good agreement with those obtained in previous studies. For the growth experiments, four models, specifically re-parameterized for analysing energy balance data, were evaluated for their ability to determine crude protein (CP) intake at maintenance and efficiency of utilization of CP intake for producing gain. They were: a straight line, two equations representing diminishing returns behaviour (monomolecular and rectangular hyperbola) and one equation describing smooth sigmoidal behaviour with a fixed point of inflexion (Gompertz). The estimates of CP requirement for maintenance and efficiency of utilization of CP intake for producing gain varied from 5.4 to 5.9 g/kg LW/day and 0.60 to 0.76, respectively, depending on the models.

An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken

A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.

A comparative evaluation of functions for the analysis of growth in male broilers

Data from six studies with male broilers fed diets covering a wide range of energy and protein were used in the current two analyses. In the first analysis, five models, specifically re-parameterized for analysing energy balance data, were evaluated for their ability to determine metabolizable energy intake at maintenance and efficiency of utilization of metabolizable energy intake for producing gain. In addition to the straight line, two types of functional form were used. They were forms describing (i) diminishing returns behaviour (monomolecular and rectangular hyperbola) and (ii) sigmoidal behaviour with a fixed point of inflection (Gompertz and logistic). These models determined metabolizable energy requirement for maintenance to be in the range 437-573 kJ/kg of body weight/day depending on the model. The values determined for average net energy requirement for body weight gain varied from 7(.)9 to 11(.)2 kJ/g of body weight. These values show good agreement with previous studies. In the second analysis, three types of function were assessed as candidates for describing the relationship between body weight and cumulative metabolizable energy intake. The functions used were: (a) monomolecular (diminishing returns behaviour), (b) Gompertz (smooth sigmoidal behaviour with a fixed point of inflection) and (c) Lopez, France and Richards (diminishing returns and sigmoidal behaviour with a variable point of inflection). The results of this analysis demonstrated that equations capable of mimicking the law of diminishing returns describe accurately the relationship between body weight and cumulative metabolizable energy intake in broilers.

A comparative evaluation of functions for describing the relationship between live-weight gain and metabolizable energy intake in turkeys

The suitability of models specifically re-parameterized for analyzing energy balance data relating metabolizable energy intake to growth rate has recently been investigated in male broilers. In this study, the more adequate of those models was applied to growing turkeys to provide estimates of their energy needs for maintenance and growth. Three functional forms were used. They were: two equations representing diminishing returns behaviour (monomolecular and rectangular hyperbola); and one equation describing smooth sigmoidal behaviour with a fixed point of inflexion (Gompertz). The models estimated the metabolizable energy requirement for maintenance in turkeys to be 359-415 kJ/kg of live-weight/day. The predicted values of average net energy requirement for producing 1 g of gain in live-weight, between 1 and 4 times maintenance, varied from 8.7 to 10.9 kJ. These results and those previously reported for broilers are a basis for accepting the general validity of these models.

Food choice in an interdisciplinary context

Reform of agricultural policies, notably the continuing elimination of production-enhancing subsidies, makes it possible for policies to respond to social issues such as the rural environment and health in future. In this paper, we draw on a Rural Economy and Land Use (RELU) research project which is examining the potential for the development of healthy food chains and the implications for human health and the environment. One of the key issues to be addressed is consumers' willingness to pay for the nutritionally enhanced food products from these new chains, but it is evident that only a partial understanding can be gained from a traditional economics approach. In the paper, we discuss how economists are beginning to incorporate views from other disciplines into their models of consumer choice.

Choice of designs and doses for early phase trials

This paper reviews state-of-art statistical designs for dose-escalation procedures in first-into-man studies. The main focus will be on studies in oncology, as most statistical procedures for phase I trials have been proposed in this context. Extensions to situations such as the observation of bivariate outcomes and healthy volunteer studies are also discussed. The number of dose levels and cohort sizes used in early phase trials are considered. Finally, this paper raises some practical issues for dose-escalation procedures.

Describing long-term trends in precipitation using generalized additive models

With the current concern over climate change, descriptions of how rainfall patterns are changing over time can be useful. Observations of daily rainfall data over the last few decades provide information on these trends. Generalized linear models are typically used to model patterns in the occurrence and intensity of rainfall. These models describe rainfall patterns for an average year but are more limited when describing long-term trends, particularly when these are potentially non-linear. Generalized additive models (GAMS) provide a framework for modelling non-linear relationships by fitting smooth functions to the data. This paper describes how GAMS can extend the flexibility of models to describe seasonal patterns and long-term trends in the occurrence and intensity of daily rainfall using data from Mauritius from 1962 to 2001. Smoothed estimates from the models provide useful graphical descriptions of changing rainfall patterns over the last 40 years at this location. GAMS are particularly helpful when exploring non-linear relationships in the data. Care is needed to ensure the choice of smooth functions is appropriate for the data and modelling objectives. (c) 2008 Elsevier B.V. All rights reserved.