Bootstrap for estimating the MSE of the Spatial EBLUP

This work assumes that the small area quantities of interest follow a Fay–Herriot model with spatially correlated random area effects. Under this model, parametric and nonparametric bootstrap procedures are proposed for estimating the mean squared error of the empirical best linear unbiased predictor (EBLUP). A simulation study based on the Italian Agriculture Census 2000 compares bootstrap and analytical estimates of the MSE and studies their robustness to non-normality. Results indicate lower bias for the non-parametric bootstrap under specific departures from normality.      

Mean‐risk optimization of electricity portfolios

We present a mathematical model with stochastic input data for mean‐risk optimization of electricity portfolios containing several physical components and energy derivative products. The model is designed for the optimization horizon of one year in hourly discretization. The aim consists in maximizing the mean book value of the portfolio at the end of the optimization horizon and, at the same time, in minimizing the risk of the portfolio decisions. The risk is measured by the conditional value‐at‐risk and by some multiperiod extension of CVaR, respectively.We present numerical results for a large‐scale realistic problem adapted to a municipal power utility and study the effects of varying weighting of risk. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generalizations of Pełczyński’s decomposition method for Banach spaces containing a complemented copy of their squares

Suppose that X and Y are Banach spaces isomorphic to complemented subspaces of each other. In 1996, W. T. Gowers solved the Schroeder-Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. However, if X ² is complemented in X with supplement A and Y ² is complemented in Y with supplement B, that is,

Hall’s and Kőnig’s theorem in graphs and hypergraphs

We investigate the relation between Hall’s theorem and K?nig’s theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall’s theorem, thereby showing that this class strictly contains all K?nig–Egerváry graphs. Furthermore, we give a generalization of Hall’s theorem to normal hypergraphs.     

Some Localization Properties of the Lp Continuous Wavelet Transform

We shall prove some simultaneous localization or concentration inequalities for the continuous wavelet transform. We will also show that simultaneous localization in the scale-time(space) is impossible, in the sense that the scale sections of the support of wavelet transform of a nonnull L^p-function can not have finite Lebesgue measure. Finally, some properties of the support of continuous wavelet transform of band-limited functions are studied.     

Gold nanoparticles produced in a microalga

An efficient biological route to production of gold nanoparticles which allows the nanoparticles to be easily recovered remains elusive. Live cells of the green microalga Chlorella vulgaris were incubated with a solution of gold chloride and harvested by centrifugation. Nanoparticles inside intact cells were identified by transmission electron microscopy and confirmed to be metallic gold by synchrotron based X-ray powder diffraction and X-ray absorption spectroscopy. These intracellular gold nanoparticles were 40–60 nm in diameter. At a concentration of 1.4% Au in the alga, a better than 97% recovery of the gold from solution was achieved. A maximum of 4.2% Au in the alga was obtained. Exposure of C. vulgaris to solutions containing dissolved salts of palladium, ruthenium, and rhodium also resulted in the production of the corresponding nanoparticles within the cells. These were surmised to be also metallic, but were produced at a much lower intracellular concentration than achieved with gold. Iridium was apparently toxic to the alga. No nanoparticles were observed using platinum solutions. C. vulgaris provides a possible route to large scale production of gold nanoparticles.     

Multiplicative processes and power laws in human reaction times derived from hyperbolic functions

In sensory psychophysics reaction time is a measure of the stochastic latency elapsed from stimulus presentation until a sensory response occurs as soon as possible. A random multiplicative model of reaction time variability is investigated for generating the reaction time probability density functions. The model describes a generic class of hyperbolic functions by Piéron?s law. The results demonstrate that reaction time distributions are the combination of log-normal with power law density functions. A transition from log-normal to power law behavior is found and depends on the transfer of information in neurons. The conditions to obtain Zipf?s law are analyzed.     

Mössbauer spectroscopy and X-ray diffraction study of FexMn0:70−xAl0:30 (0:40 < x < 0:70) alloys prepared by mechanical alloying

In order to study the structural and magnetic behaviour of Fe_xMn_0.70?xAl_0.30 (0.40≤x≤0.70) alloys prepared by mechanical alloying, Mössbauer spectroscopy and X‐ray diffraction techniques have been employed. All the alloys were prepared in 24 h and, in addition, for x=0.45 milling times of 4, 8, 12, 16 and 24 h were considered. X‐ray diffraction showed that all samples exhibit bcc‐type reflections. A slight decrease in grain size and a slight increase in lattice parameter with increasing Mn content were observed. For x=0.45, an increase in grain size with milling time has been evidenced. For this composition and 4 h of milling, the more intensive peak (1?1?0) was fitted with three peaks corresponding to that of Mn, Fe and the alloy, respectively. For 12 h milling only bcc peaks of the alloy were obtained. As the Fe concentration was increased beyond x=0.50, a phase change from paramagnetic to ferromagnetic, as well as an increment in the mean hyperfine field with x, was detected. For x=0.45 and 4 h of milling we registered the presence of both a single line, corresponding to the alloy, and a hyperfine field distribution with peaks in 27.5 and 23 T, as well as peaks at lesser fields. These peaks are associated to Fe sites with two or more Al and/or Mn atoms as next neighbours. These results are in agreement with those obtained by X‐ray diffraction.