The generator coordinate method in the unrestricted Hartree-Fock formalism

The generator coordinate method was implemented in the unrestricted Hartree-Fock formalism. Weight functions were built from Gaussian generator functions for 1s, 2s, and 2p orbitals of carbon and oxygen atoms. These weight functions show a similar behavior to those found in the generator coordinate restricted Hartree-Fock method, i.e., they are smooth, continuous, and tend to zero in the limits of integration. Moreover, the weight functions obtained are different for spin-up and spin-down electrons what is a result from spin polarization. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Influence diagnostics in Gaussian spatial linear models

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

Gaussian deconvolution: a useful method for a form-free modeling of scattering data from mono- and multilayered planar systems

A new method for analysis of scattering data from lamellar bilayer systems is presented. The method employs a form-free description of the cross-section structure of the bilayer and the fit is performed directly to the scattering data, introducing also a structure factor when required. The cross-section structure (electron density profile in the case of X-ray scattering) is described by a set of Gaussian functions and the technique is termed Gaussian deconvolution. The coefficients of the Gaussians are optimized using a constrained least-squares routine that induces smoothness of the electron density profile. The optimization is coupled with the point-of-inflection method for determining the optimal weight of the smoothness. With the new approach, it is possible to optimize simultaneously the form factor, structure factor and several other parameters in the model. The applicability of this method is demonstrated by using it in a study of a multilamellar system composed of lecithin bilayers, where the form factor and structure factor are obtained simultaneously, and the obtained results provided new insight into this very well known system.