Coefficient of variation and Power Pen's parade computation

Under the the assumption that income y is a power function of its rank among n individuals, we approximate the coefficient of variation and gini index as functions of the power degree of the Pen's parade. Reciprocally, for a given coefficient of variation or gini index, we propose the analytic expression of the degree of the power Pen's parade; we can then compute the Pen's parade.Gini index, Income inequality, Ranks, Har- monic Number, Pen's Parade.

Studies of the coefficient of variation of the magnitude of EEG signals

An analysis of the variation in magnitude of EEG signals in various frequency bands of anesthetized patients and normal sleeping volunteers was carried out. The coefficient of variation (CoV), i.e. the standard deviation/mean, within 10 second epochs was found to be quite constant throughout the whole of the EEG recordings and was typically about 0.46. This was found to be the case for both the patients and the volunteers. Histograms of the magnitudes indicated that the magnitudes are distributed as f(x)=βxe(-αx2) functions. However a CoV of 0.46 is consistent with f(x)=βxe(-αx3) functions. The non-stationary nature of the EEG is such that it is likely that while over short periods the EEG magnitudes are distributed as f(x)=βxe(-αx3) functions, variations of α over time mean that in the long term the EEG magnitudes are distributed as f(x)=βxe(-αx2) functions

Effect of concentration dependence of the diffusion coefficient on homogenization kinetics in multiphase binary alloy systems

Diffusion calculations were performed to establish the conditions under which concentration dependence of the diffusion coefficient was important in single, two, and three phase binary alloy systems. Finite-difference solutions were obtained for each type of system using diffusion coefficient variations typical of those observed in real alloy systems. Solutions were also obtained using average diffusion coefficients determined by taking a logarithmic average of each diffusion coefficient variation considered. The constant diffusion coefficient solutions were used as reference in assessing diffusion coefficient variation effects. Calculations were performed for planar, cylindrical, and spherical geometries in order to compare the effect of diffusion coefficient variations with the effect of interface geometries. In most of the cases considered, the diffusion coefficient of the major-alloy phase was the key parameter that controlled the kinetics of interdiffusion

Total variation regularization of multi-material topology optimization

This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is proposed which involves total variation regularization combined with a suitably chosen cost functional that promotes the diffusion coefficient assuming prespecified values at each point of the domain. The main difficulty lies in the delicate functional-analytic structure of the resulting nondifferentiable optimization problem with pointwise constraints for functions of bounded variation, which makes the derivation of useful pointwise optimality conditions challenging. To cope with this difficulty, a novel reparametrization technique is introduced. Numerical examples using a regularized semismooth Newton method illustrate the structure of the obtained diffusion coefficient.

Measures of Poverty and Inequality: A Reference Paper

This paper discusses various measures of poverty and inequality found in the literature. Inequality measures discussed include the range, the variance, the coefficient of variation, the standard deviation of logarithms, the Gini coefficient, Theil's Entropy measure and Atkinson's inequality measure. Of these the mean log deviation, the Theil index and the coefficient of variation have come to be known as the Generalised Entropy class of inequality measures. As far as poverty indicators are concerned the Foster-Greer-Thorbecke measures, a class of generalised decomposable poverty measures, have become very popular in the literature. The paper also discusses some Stata do-files that were written in order to calculate poverty and inequality measures, with application to the Income and Expenditure Survey data of 1995.Food Security and Poverty,