Finding the point on Bezier Curves with the normal vector passing an external point

Two algorithms for finding the point on non-rational/rational Bezier curves of which the normal vector passes through a given external point are presented. The algorithms are based on Bezier curves generation algorithms of de Casteljau's algorithm for non-rational Bezier curve or Farin's recursion for rational Bezier curve, respectively. Orthogonal projections from the external point are used to guide the directional search used in the proposed iterative algorithms. Using Lyapunov's method, it is shown that each algorithm is able to converge to a local minimum for each case of non-rational/rational Bezier curves. It is also shown that on convergence the distance between the point on curves to the external point reaches a local minimum for both approaches. Illustrative examples are included to demonstrate the effectiveness of the proposed approaches.

Case studies to demonstrate the range of applications of the Southampton Hand Assessment Procedure

The Southampton Hand Assessment Procedure (SHAP) was devised to assess quantitatively the functional range of injured and healthy adult hands. It was designed to be a practical tool for use in a busy clinical setting; thus, it was made simple to use and easy to interpret. This paper describes four examples of its use: before and after a surgical procedure, to observe the impact of an injury, use with prostheses, and during recovery following a fracture. The cases show that the SHAP is capable of monitoring progress and recovery, identifying functional abilities in prosthetic hands and comparing the capabilities of different groups of injuries.

Time-resolved gas-phase kinetic, quantum chemical and RRKM studies of reactions of silylene with cyclic ethers

Time-resolved kinetic studies of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reactions with oxirane, oxetane, and tetrahydrofuran (THF). The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at four or five temperatures in the range 294-605 K. All three reactions showed pressure dependences characteristic of third-body-assisted association reactions with, surprisingly, SiH2 + oxirane showing the least and SiH2 + THF showing the most pressure dependence. The second-order rate constants obtained by extrapolation to the high-pressure limits at each temperature fitted the Arrhenius equations where the error limits are single standard deviations: log(k(oxirane)(infinity)/cm(3) molecule(-1) s(-1)) = (-11.03 +/- 0.07) + (5.70 +/- 0.51) kJ mol(-1)/RT In 10 log(k(oxetane)(infinity)/cm(3) molecule(-1) s(-1)) = (-11.17 +/- 0.11) + (9.04 +/- 0.78) kJ mol(-1)/RT In 10 log(k(THF)(infinity)/cm(3) molecule(-1) s(-1)) = (-10.59 +/- 0.10) + (5.76 +/- 0.65) kJ mol(-1)/RT In 10 Binding-energy values of 77, 97, and 92 kJ mol(-1) have been obtained for the donor-acceptor complexes of SiH2 with oxirane, oxetane, and THF, respectively, by means of quantum chemical (ab initio) calculations carried Out at the G3 level. The use of these values to model the pressure dependences of these reactions, via RRKM theory, provided a good fit only in the case of SiH2 + THF. The lack of fit in the other two cases is attributed to further reaction pathways for the association complexes of SiH2 with oxirane and oxetane. The finding of ethene as a product of the SiH2 + oxirane reaction supports a pathway leading to H2Si=O + C2H4 predicted by the theoretical calculations of Apeloig and Sklenak.

Pitch range and vowel duration in the speech of children with Williams syndrome

This paper reports the pitch range and vowel duration data from a group of children with Williams syndrome (WS) in comparison with a group of typically developing children matched for chronological age (CA) and a group matched for receptive language abilities (LA). It is found that the speech of the WS group has a greater pitch range and that vowels tend to be longer in duration than in the speech of the typically developing children. These findings are in line with the impressionistic results reported by Reilly, Klima and Bellugi [17].

Bacterial, SCFA and gas profiles of a range of food ingredients following in vitro fermentation by human colonic microbiota.

It is now apparent that there is a strong link between health and nutrition and this can be seen clearly when we talk of obesity. The food industry is trying to capitalise on this by adapting high sugar/fat foods to become healthier alternatives. In confectionery food ingredients can be used for a range of purposes including sucrose replacement. Many of these ingredients may also evade digestion in the upper gut and be fermented by the gut microbiota upon entering the colon. This study was designed to screen a range of ingredients and their activities on the gut microbiota. In this study we screened a range of these ingredients in triplicate batch culture fermentations with known prebiotics as controls. Changes in bacteriology were monitored using FISH. SCFA were measured by GC and gas production was assessed during anaerobic batch fermentations. Bacterial enumeration showed significant increases (P ≤ 0.05) in bifidobacteria and lactobacilli with polydextrose and most polyols with no significant increases in Clostridium histolyticum/perfringens. SCFA and gas formation indicated that the substrates added to the fermenters were being utilised by the gut microbiota. It therefore appears these ingredients exert some prebiotic activity in vitro. Further studies, particularly in human volunteers, are necessary.

Adaptive designs for Phase I dose-finding studies

Improving methodology for Phase I dose-finding studies is currently of great interest in pharmaceutical and medical research. This article discusses the current atmosphere and attitude towards adaptive designs and focuses on the influence of Bayesian approaches.

Time-resolved gas-phase kinetic study of the germylene addition reaction, CH3C CCH3

Time-resolved kinetic studies of the reaction of germylene, GeH2, generated by laser. ash photolysis of 3,4-dimethyl-1-germacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with 2-butyne, CH3C CCH3. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 300-556 K. The second order rate constants obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1)) = (-10.46 +/- 10.06) + (5.16 +/- 10.47) kJ mol(-1)/ RT ln 10 Calculations of the energy surface of the GeC4H8 reaction system were carried out employing the additivity principle, by combining previous quantum chemical calculations of related reaction systems. These support formation of 1,2-dimethylvinylgermylene (rather than 2,3-dimethylgermirene) as the end product. RRKM calculations of the pressure dependence of the reaction are in reasonable agreement with this finding. The reactions of GeH2 with C2H2 and with CH3CRCCH3 are compared and contrasted.

Spatiotemporal behavior of the TIGGE medium-range ensemble forecasts

Using the recently-developed mean–variance of logarithms (MVL) diagram, together with the TIGGE archive of medium-range ensemble forecasts from nine different centres, an analysis is presented of the spatiotemporal dynamics of their perturbations, showing how the differences between models and perturbation techniques can explain the shape of their characteristic MVL curves. In particular, a divide is seen between ensembles based on singular vectors or empirical orthogonal functions, and those based on bred vector, Ensemble Transform with Rescaling or Ensemble Kalman Filter techniques. Consideration is also given to the use of the MVL diagram to compare the growth of perturbations within the ensemble with the growth of the forecast error, showing that there is a much closer correspondence for some models than others. Finally, the use of the MVL technique to assist in selecting models for inclusion in a multi-model ensemble is discussed, and an experiment suggested to test its potential in this context.

Effect of intensive vs. free range production on the fat and fatty acid composition of whole birds and edible portions of retail chickens in the UK

The primary objective was to compare the fat and fatty acid contents of cooked retail chickens from intensive and free range systems. Total fat comprised approximately 14, 2.5, 8, 9 and 15 g/100 g cooked weight in whole birds, skinless breast, breast with skin, skinless leg and leg meat with skin, respectively, with no effect of intensive compared with free range systems. Free range breast and leg meat contained significantly less polyunsaturated fatty acids (n-6 and n-3) than did those from intensive rearing and had a consistently higher n-6/n-3 ratio (6.0 vs. 7.9). Generally, the concentrations of long chain n-3 fatty acids were considerably lower than those reported in earlier research studies. Overall, there was no evidence that meat from free range chickens had a fatty acid profile that would be classified as healthier than that from intensively reared birds and indeed, in some aspects, the opposite was the case. (C) 2011 Elsevier Ltd. All rights reserved.

Benchmarking and valuation issues in measuring depreciation for European office markets

Purpose – The paper addresses the practical problems which emerge when attempting to apply longitudinal approaches to the assessment of property depreciation using valuation-based data. These problems relate to inconsistent valuation regimes and the difficulties in finding appropriate benchmarks. Design/methodology/approach – The paper adopts a case study of seven major office locations around Europe and attempts to determine ten-year rental value depreciation rates based on a longitudinal approach using IPD, CBRE and BNP Paribas datasets. Findings – The depreciation rates range from a 5 per cent PA depreciation rate in Frankfurt to a 2 per cent appreciation rate in Stockholm. The results are discussed in the context of the difficulties in applying this method with inconsistent data. Research limitations/implications – The paper has methodological implications for measuring property investment depreciation and provides an example of the problems in adopting theoretically sound approaches with inconsistent information. Practical implications – Valuations play an important role in performance measurement and cross border investment decision making and, therefore, knowledge of inconsistency of valuation practice aids decision making and informs any application of valuation-based data in the attainment of depreciation rates. Originality/value – The paper provides new insights into the use of property market valuation data in a cross-border context, insights that previously had been anecdotal and unproven in nature.