Calculating the tetrahedral bond angle using spherical polars and the dot product

A proof using the methane tetrahedroid bond angle can be obtained by using spherical polar coordinates to calculate the Cartesian coordinates of the hydrogen atoms, then using the dot product of vectors.

Rotational symmetry of a methane molecule and the bond angle

The rotational symmetry of a methane molecule can be used to great advantage to calculate the bond angle. The problem is worked out in this article.

Steric stabilisation of the P_P bond in a bulky tetraorganodiphosphine: synthesis, characterisation and X-ray structure determination of tetrakis(2,4,6-triisopropylphenyl)diphosphine

We report the synthesis and characterisation of tetrakis(2,4,6-triisopropylphenyl)diphosphine. Synthesis is effected by the treatment of PCl3 with an excess of 2,4,6-triisopropylphenyllithium (or the equivalent Grignard reagent) in 70% yield. While under normal circumstances the triarylphosphine would be expected, excessive bulk prevents this, and the resulting diphosphine is, unusually, stable to PP cleavage by further organolithium moieties. The compound is stable, both thermally (m.p. 185°C) and to air and water in the solid state, although conversion to the equivalent diorganophosphinate ester is effected by boiling ethanolic solutions in air. Crystallisation from hexane/ethanol afforded pale yellow crystals of X-ray quality. The molecule is characterised by m.p., IR, NMR, elemental analysis (C, H, P) and MS. The X-ray structure shows an antiperiplanar conformation with a PP separation of 2.2461(16) Å. Comparisons are made with other diphosphines, the title compound being only the fourth simple diphosphine to be structurally characterised.

Towards an improved understanding of farmers' behaviour: the integrative agent-centred (IAC) framework

An effective approach to research on farmers' behaviour is based on: i) an explicit and well-motivated behavioural theory; ii) an integrative approach; and iii) understanding feedback processes and dynamics. While current approaches may effectively tackle some of them, they often fail to combine them together. The paper presents the integrative agent-centred (IAC) framework, which aims at filling this gap. It functions in accordance with these three pillars and provides a conceptual structure to understand farmers' behaviour in agricultural systems. The IAC framework is agent-centred and supports the understanding of farmers' behavior consistently with the perspective of agricultural systems as complex social-ecological systems. It combines different behavioural drivers, bridges between micro and macro levels, and depicts a potentially varied model of human agency. The use of the framework in practice is illustrated through two studies on pesticide use among smallholders in Colombia. The examples show how the framework can be implemented to derive policy implications to foster a transition towards more sustainable agricultural practices. The paper finally suggests that the framework can support different research designs for the study of agents' behaviour in agricultural and social-ecological systems.

Appraiser behaviour and appraisal smoothing: some qualitative and quantitative evidence

There is a substantial literature which suggests that appraisals are smoothed and lag the true level of prices. This study combines a qualitative interview survey of the leading fund manager/owners in the UK and their appraisers with a empirical study of the number of appraisals which change each month within the IPD Monthly Index. The paper concentrates on how the appraisal process operates for commercial real estate performance measurement purposes. The survey interviews suggest that periodic appraisal services are consolidating in fewer firms and, within these major firms, appraisers adopt different approaches to changing appraisals on a period by period basis, with some wanting hard transaction evidence while others act on ‘softer’ signals. The survey also indicates a seasonal effect with greater effort and information being applied to annual and quarterly appraisals than monthly. The analysis of the appraisals within the IPD Monthly Index confirms this effect with around 5% more appraisals being moved at each quarter day than the other months. More November appraisals change than expected and this suggests that the increased information flows for the December end year appraisals are flowing through into earlier appraisals, especially as client/appraiser draft appraisal meetings for the December appraisals, a regular occurrence in the UK, can occur in November. January illustrates significantly less activity than other months, a seasonal effect after the exertions of the December appraisals.

A micro-level simulation for the prediction of intention and behaviour

In this contribution we aim at anchoring Agent-Based Modeling (ABM) simulations in actual models of human psychology. More specifically, we apply unidirectional ABM to social psychological models using low level agents (i.e., intra-individual) to examine whether they generate better predictions, in comparison to standard statistical approaches, concerning the intentions of performing a behavior and the behavior. Moreover, this contribution tests to what extent the predictive validity of models of attitude such as the Theory of Planned Behavior (TPB) or Model of Goal-directed Behavior (MGB) depends on the assumption that peoples’ decisions and actions are purely rational. Simulations were therefore run by considering different deviations from rationality of the agents with a trembling hand method. Two data sets concerning respectively the consumption of soft drinks and physical activity were used. Three key findings emerged from the simulations. First, compared to standard statistical approach the agent-based simulation generally improves the prediction of behavior from intention. Second, the improvement in prediction is inversely proportional to the complexity of the underlying theoretical model. Finally, the introduction of varying degrees of deviation from rationality in agents’ behavior can lead to an improvement in the goodness of fit of the simulations. By demonstrating the potential of ABM as a complementary perspective to evaluating social psychological models, this contribution underlines the necessity of better defining agents in terms of psychological processes before examining higher levels such as the interactions between individuals.

European CMBS pricing: bond, mortgage and real estate characteristics

The recent global economic crisis is often associated with the development and pricing of mortgage-backed securities (i.e. MBSs) and underlying products (i.e. sub-prime mortgages). This work uses a rich database of MBS issues and represents the first attempt to price commercial MBSs (i.e. CMBSs) in the European market. Our results are consistent with research carried out in the US market and we find that bond-, mortgage-, real estate-related and multinational characteristics show different degrees of significance in explaining European CMBS spreads at issuance. Multiple linear regression analysis using a databank of CMBSs issued between 1997 and 2007 indicates a strong relationship with bond-related factors, followed by real estate and mortgage market conditions. We also find that multinational factors are significant, with country of issuance, collateral location and access to more liquid markets all being important in explaining the cost of secured funding for real estate companies. As floater coupon tranches tend to be riskier and exhibit higher spreads, we also estimate a model using this sub-set of data and results hold, hence reinforcing our findings. Finally, we estimate our model for both tranches A and B and find that real estate factors become relatively more important for the riskier investment products.

Effective elements of cognitive behaviour therapy for psychosis: results of a novel type of subgroup analysis based on principal stratification

Background. Meta-analyses show that cognitive behaviour therapy for psychosis (CBT-P) improves distressing positive symptoms. However, it is a complex intervention involving a range of techniques. No previous study has assessed the delivery of the different elements of treatment and their effect on outcome. Our aim was to assess the differential effect of type of treatment delivered on the effectiveness of CBT-P, using novel statistical methodology. Method. The Psychological Prevention of Relapse in Psychosis (PRP) trial was a multi-centre randomized controlled trial (RCT) that compared CBT-P with treatment as usual (TAU). Therapy was manualized, and detailed evaluations of therapy delivery and client engagement were made. Follow-up assessments were made at 12 and 24 months. In a planned analysis, we applied principal stratification (involving structural equation modelling with finite mixtures) to estimate intention-to-treat (ITT) effects for subgroups of participants, defined by qualitative and quantitative differences in receipt of therapy, while maintaining the constraints of randomization. Results. Consistent delivery of full therapy, including specific cognitive and behavioural techniques, was associated with clinically and statistically significant increases in months in remission, and decreases in psychotic and affective symptoms. Delivery of partial therapy involving engagement and assessment was not effective. Conclusions. Our analyses suggest that CBT-P is of significant benefit on multiple outcomes to patients able to engage in the full range of therapy procedures. The novel statistical methods illustrated in this report have general application to the evaluation of heterogeneity in the effects of treatment.