Difference variance dispersion graphs for comparing response surface designs with applications in food technology

Variance dispersion graphs have become a popular tool in aiding the choice of a response surface design. Often differences in response from some particular point, such as the expected position of the optimum or standard operating conditions, are more important than the response itself. We describe two examples from food technology. In the first, an experiment was conducted to find the levels of three factors which optimized the yield of valuable products enzymatically synthesized from sugars and to discover how the yield changed as the levels of the factors were changed from the optimum. In the second example, an experiment was conducted on a mixing process for pastry dough to discover how three factors affected a number of properties of the pastry, with a view to using these factors to control the process. We introduce the difference variance dispersion graph (DVDG) to help in the choice of a design in these circumstances. The DVDG for blocked designs is developed and the examples are used to show how the DVDG can be used in practice. In both examples a design was chosen by using the DVDG, as well as other properties, and the experiments were conducted and produced results that were useful to the experimenters. In both cases the conclusions were drawn partly by comparing responses at different points on the response surface.

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Braneworlds scenarios in a gravity model with higher order spatial three-curvature terms

In this work we study a Hořava-like 5-dimensional model in the context of braneworld theory. The equations of motion of such model are obtained and, within the realm of warped geometry, we show that the model is consistent if and only if λ takes its relativistic value 1. Furthermore, we show that the elimination of problematic terms involving the warp factor second order derivatives are eliminated by imposing detailed balance condition in the bulk. Afterwards, Israel's junction conditions are computed, allowing the attainment of an effective Lagrangian in the visible brane. In particular, we show that the resultant effective Lagrangian in the brane corresponds to a (3 + 1)-dimensional Hořava-like model with an emergent positive cosmological constant but without detailed balance condition. Now, restoration of detailed balance condition, at this time imposed over the brane, plays an interesting role by fitting accordingly the sign of the arbitrary constant β, insuring a positive brane tension and a real energy for the graviton within its dispersion relation. Also, the brane consistency equations are obtained and, as a result, the model admits positive brane tensions in the compactification scheme if, and only if, β is negative and the detailed balance condition is imposed. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.

Coherence characteristics of random lasing in a dye doped hybrid powder

The photon statistics of the random laser emission of a Rhodamine B doped di-ureasil hybrid powder is investigated to evaluate its degree of coherence above threshold. Although the random laser emission is a weighted average of spatially uncorrelated radiation emitted at different positions in the sample, a spatial coherence control was achieved due to an improved detection configuration based on spatial filtering. By using this experimental approach, which also allows for fine mode discrimination and timeresolved analysis of uncoupled modes from mode competition, an area not larger than the expected coherence size of the random laser is probed. Once the spectral and temporal behavior of nonoverlapping modes is characterized, an assessment of the photon-number probability distribution and the resulting second-order correlation coefficient as a function of time delay and wavelength was performed. The outcome of our single photon counting measurements revealed a high degree of temporal coherence at the time of maximum pump intensity and at wavelengths around the Rhodamine B gain maximum.

Avaliação psicométrica da escala de atitudes em relação à estatística

RESUMO: O objetivo do estudo foi estimar a validade e confiabilidade da Escala de atitudes em relação à Estatística (EAE) quando aplicada a estudantes de Ciências Farmacêuticas. A amostra de 253 estudantes foi subdividida em duas partes. Sessenta por cento da amostra foi utilizada para explorar a estrutura fatorial e 40% para confirmá-la. Para verificar a reprodutibilidade da escala a mesma foi aplicada em duplicata a 40 estudantes. Aplicou-se o Teste de esfericidade de Bartlett e o índice Kaiser-Meyer-Olkin (KMO). A extração dos fatores foi realizada pela Análise de Componentes Principais. Realizou-se rotação ortogonal Varimax. Calculou-se o Coeficiente alfa de Cronbach (α) e o Coeficiente de Correlação Intraclasse (ρ). Realizou-se análise fatorial confirmatória. Elaborou-se um modelo hierárquico de segunda ordem (MHSO). O teste de esfericidade de Bartlett e o índice KMO foram excelentes (χ 2 =1835,815, p<0,001; KMO=0,935). Verificou-se dois fatores com valores próprios acima de 1 (λ=9,748; λ=2,086) explicando 59,2% da variância total. A questão 2 foi removida. Observou-se excelente consistência interna e reprodutibilidade. O modelo fatorial apresentou índices de qualidade de ajustamento bons (λ=0,59-0,86, χ 2 /gl=1,691, CFI=0,919, GFI=0,804, RMSEA=0,079). A validade discriminante dos fatores foi adequada. A EAE apresentou estrutura bifatorial na amostra com níveis de validade e confiabilidade adequados.