Fractional Type Integral Operators on Variable Hardy Spaces

Given certain n × n invertible matrices A ₁, . . . , A _m and 0 ≦ α < n, we obtain the \({H^{p(.)}(\mathbb{R}^n) \to L^{q(.)}(\mathbb{R}^n)}\) boundedness of the integral operator with kernel \({k(x, y) = |x - A_1y|^{-\alpha_1} . . . |x - A_my|^{-\alpha_m}}\) , where α ₁ +  . . . + α _m = n ? α and p(.), q(.) are exponent functions satisfying log-Hölder continuity conditions locally and at infinity related by \({\frac{1}{q(.)} = \frac{1}{p(.)} - \frac{\alpha}{n}}\) . We also obtain the \({H^{p(.)}(\mathbb{R}^n) \to H^{q(.)}(\mathbb{R}^n)}\) boundedness of the Riesz potential operator.     

A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization

Intensity Modulated Radiotherapy Treatment (IMRT) is a technique used in the treatment of cancer, where the radiation beams are modulated by a multileaf collimator allowing the irradiation of the patient using non-uniform radiation fields from selected angles. Beam angle optimization consists in trying to find the best set of angles that should be used in IMRT planning. The choice of this set of angles is patient and pathology dependent and, in clinical practice, most of the times it is made using a trial and error procedure or simply using equidistantly distributed angles. In this paper we propose a genetic algorithm that aims at calculating good sets of angles in an automated way, given a predetermined number of angles. We consider the discretization of all possible angles in the interval [0 \(^{\circ }\) , 360 \(^{\circ }\) ], and each individual is represented by a chromosome with 360 binary genes. As the calculation of a given individual’s fitness is very expensive in terms of computational time, the genetic algorithm uses a neural network as a surrogate model to calculate the fitness of most of the individuals in the population. To explicitly consider the estimation error that can result from the use of this surrogate model, the fitness of each individual is represented by an interval of values and not by a single crisp value. The genetic algorithm is capable of finding improved solutions, when compared to the usual equidistant solution applied in clinical practice. The genetic algorithm will be described and computational results will be shown.     

Realization of 2D convolutional codes of rate \frac{1}{n} by separable Roesser models

In this paper, two-dimensional convolutional codes constituted by sequences in $(\mathbb F ^n)^{\mathbb{Z }^{2}}$ where $\mathbb F $ is a finite field, are considered. In particular, we restrict to codes with rate $\frac{1}{n}$ and we investigate the problem of minimal dimension for realizations of such codes by separable Roesser models. The encoders which allow to obtain such minimal realizations, called R-minimal encoders, are characterized.     

PIXE analysis of Tillandsia usneoides for air pollution studies at an industrial zone in Central Mexico

In order to find out if there is a relation between atmospheric particulate matter composition and human health effects, metals and other elements measurement are performed. Analysis of atmospheric aerosols collected in filters is the usual method to achieve this task. Biological monitors provide an advantageous alternative way of sampling, since there is no need of special sampling devices, and accumulation time can be as long as desired. In this study, Tillandsia usneoides a reliable air pollution biological monitor that occurs naturally throughout Mexico was used to monitor air quality of Tula–Tepeji corridor at central Mexico. This area is considered critical zone because of atmosphere contaminants high concentration. Some biomonitors were transplanted from a clean environment to four sites at the Tula corridor. Plants samples were collected every two weeks from February to April 2008. PM₁₀ sampling in filters was also performed simultaneously at three locations where T. usneoides was transplanted, for a comparison. Chemical composition was determined by PIXE. Results showed that T. usneoides incorporates anthropogenic elements reaching maximal levels after 6 to 10 weeks approximately. Since results obtained with biomonitors agree with those obtained with aerosol filters, T. usneoides could be employed as a first approximation to provide insights of the atmospheric pollution level previous to a detailed study using filters.     

The transition from fracton to phonon states in a Sierpinski triangle lattice

Lattice dynamics of a Sierpinski triangle submitted to different levels of disorder was studied via atomistic Green’s functions. It was found that there is a critical level of disorder that separates two regions of thermal transport. The first is characterized by a fast destruction of fracton states and the formation of spatially extended phonon states. The second region is characterized by a transition from extended to localized phonon states as predicted by the Anderson model.     

Drying of solids with irregular geometry: numerical study and application using a three-dimensional model

This article proposes a numerical solution for the diffusion equation applied to solids with arbitrary geometry using non-orthogonal structured grids for the boundary condition of the first kind. A transient three-dimensional mathematical formulation written in boundary fitted coordinates and numerical formalism to discretize the diffusion equation by using the finite volume method, including numerical analysis of the computational solution are presented. To validate the proposed solution, the results obtained in this work were compared with well-known numerical solution available in literature and good agreement was observed. In order to verify the potential of the proposed numerical solution, it was applied to describe mass transfer inside ceramic roof tiles during drying. For that, it was used experimental data of the drying kinetics at the following temperatures: 55.6; 69.7; 82.7 and 98.6 °C. An optimization technique using experimental dataset has been presented to estimation of transport properties. The obtained statistical indicators enable to conclude that the numerical solution satisfactorily describes the drying processes.     

Niobium oxide solid catalyst: esterification of fatty acids and modeling for biodiesel production

Biodiesel can be obtained from fatty acid raw materials through esterification. The reactivity of lauric, palmitic, stearic, oleic, and linoleic fatty acids with methanol using powdered niobic acid as a heterogeneous catalyst was investigated in this work, both experimentally (in a batch reactor) and theoretically. A 2³ experimental design was used, with methanol/fatty acid molar ratio, catalyst concentration, and temperature as main factors. An empirical model demonstrated that temperature is the most important variable. Fourteen heterogeneous and 56 homogeneous‐like kinetic models were tested. A homogeneous‐like model considering zero order for all species and inhibition by water was the most adequate for experiments without catalyst. A homogeneous‐like model considering a second‐order reaction in relation to the fatty acid and no water inhibition was the most adequate for niobic acid catalyzed reaction. Molecular modeling confirmed the experimental results showing that the reactivity is directly related to the increase of unsaturated bonds and the reduction of carbon chain length. The polarity of the fatty acid is determinant in the reactivity. At the molecular level, reaction occurs between the HOMO orbital of methanol and LUMO orbitals of fatty acids and reactivity is higher when the energy difference between these orbitals is lower. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterisation of foxing stains in eighteenth to nineteenth century drawings using non-destructive techniques

The reddish-brown, brown or yellowish stains of circular or irregular shape known as foxing spots have been fully described in conservation literature but still, this phenomenon does not find any scientific agreement since many hypotheses have been raised concerning their origin. In this work a contribution to foxing definition not only focussed on its appearance but also reported on its chemical information. For this purpose foxing stains present in drawings from two Portuguese artists dated from the eighteenth to nineteenth centuries were observed under ultra-violet light and optical microscope and analysed by three non-invasive spectroscopy techniques. The observations carried out on the stains provided information on their surface morphology. The use of energy-dispersive X-ray fluorescence revealed a variation on the elemental content between foxing and paper region. Although the results from X-ray diffraction analysis showed no signs of cellulose degradation in foxing stains, Fourier-transformed infrared analysis revealed the presence of oxide groups. Both the information on the chemical nature and surface morphology of the stains achieved in this study will contribute to increase foxing formation information and develop future protocols for conservation purposes.