The roles of diffusivity and curvature in patterns on surfaces of revolution

We address the question of finding sufficient conditions for existence as well as nonexistence of nonconstant stable stationary solution to the diffusion equation _ut=div(a∇u)+f(u)$u_t=\mathrm{div}(a\mathrm{\nabla }u)+f(u)$ on a surface of revolution with and without boundary. Conditions found relate the diffusivity function a and the geometry of the surface where diffusion takes place. In the case where f is a bistable function, necessary conditions for the development of inner transition layers are given.     

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.     

On positive solutions for a class of quasilinear elliptic systems

We investigate the existence and properties of solutions for a class of systems of Dirichlet problems involving the perturbed phi-Laplace operators. We apply variational methods associated with the Fenchel conjugate. Our results cover both sublinear and superlinear cases of nonlinearities.     

Synthesis of new fluorous modular chiral ligand derivatives from amino alcohols and application in enantioselective carbon–carbon bond-forming alkylation reactions

N-Trifluoracyl β-chalcogeno amides and N-perfluoracyl β-thio amide ligands were prepared by a simple and efficient reaction sequence. These new ligands were evaluated in palladium-catalyzed alkylation of rac-(E)-1,3-diphenyl-2-propenyl acetate in the presence of dimethyl malonate and an enantioselectivity of up to 99% was obtained. After catalysis, the fluorous ligand can be easily recovered by liquid–liquid extraction and reused without loss in the activity.     

Determination of the mineral composition of fresh bovine milk from the milk-producing areas located in the State of Sergipe in Brazil and evaluation employing exploratory analysis

In this work, the mineral composition of fresh bovine milk obtained from the milk-producing areas of the Brazilian State of Sergipe was examined. A dry-ashed digestion method and the ICP OES technique were used for the quantification of mineral elements (e.g., Ca, Mg, K, Na, P, Sr and Zn) in 27 samples of milk collected from properties located in milk-producing areas around Nossa Senhora da Glória. The following ranges of values (% m/v) were obtained: 0.063 to 0.117 for Ca; 0.060 to 0.114 for P; 0.024 to 0.064 for Na; and 0.087 to 0.164 for K. The ranges of values (mg L^− 1) for the other mineral elements were also found: 0.68 to 1.89 for Sr; 2.46 to 5.73 for Zn; and 54.2 to 109.9 for Mg. Additionally, the exploratory evaluation of the 27 milk samples was performed using principal component analysis (PCA) involving seven variables dealing with the effect of different management systems (conventional and organic) on milk composition. The results show that there are indeed differences between the mineral composition of milk from properties that use organic practices and those that use conventional management practices.     

Thermal analysis of hair treated with oxidative hair dye under influence of conditioners agents

This research aimed the effect on Caucasian hair tresses treated with oxidative hair dye, either incorporated or not with conditioners agents, analyzed by Differential Scanning Calorimetry (DSC) and Thermogravimetric analysis (TG). The formulations of hair dyes were emulsions oil-in-water with light blond color containing or not the conditioners agents: silanetriol and panthenol; PEG-12 dimethicone; hydrolyzed silk, hydrolyzed milk protein, and lactose. Each dye (1.5 g) was applied in the hair tress (2.0 g/20.0 cm of length of Caucasian light-brown), previously treated, more 1.5 g of hydrogen peroxide 20 vol during 40 min. Evaluation of mass loss of the different hair sample demonstrates that these chemical hair treatments impair the hair fibers, reduced their moisture content with respect to the untreated hair. The incorporation of conditioners agents (silanetriol and panthenol; PEG-12 dimethicone; hydrolyzed silk, hydrolyzed milk protein, and lactose) in oxidative hair dyes types did not decrease the damage caused on the tresses by the coloring process quantified by TG/DTG. However, the DSC curves demonstrated those conditioners agents (silanetriol and panthenol; PEG-12 dimethicone) dislocated the beginning of the third event in 20 °C and they inhibited the presence of the fourth event, having characterized thermal protection to the hair.     

Luminescence quantum yield determination for molecules adsorbed onto solid powdered particles.

A new methodology for the determination of the fluorescence quantum yield of dyes adsorbed onto microcrystalline cellulose is presented and applied to rhodamine 101, cresyl violet and auramine O. It is based on a previously reported method by Ruetten and Thomas (J. Phys. Chem., 1998, 102, 598-606), which is not applicable to the dyes used in the present study. It uses ground-state diffuse reflectance spectra obtained with and without filters, which prevents the luminescence of the dye from reaching the integrating sphere and the photodetector. New equations are presented here, correcting for the fluorescence emission of the dye, which depends on the detector sensitivity. Cut-on filters, which have a transmittance close to unity in the absorption region, and close to zero in the emission region, of the dye are used to obtain corrected reflectance spectra. The influence of the substrate was also taken into account. This methodology may be applied to other probes and surfaces or emissions of a different nature (i.e., phosphorescence or delayed fluorescence), and constitutes a very simple and general procedure to solve the important problem of luminescence quantum yield determination of probes adsorbed onto solid powdered surfaces.     

On an inequality by N. Trudinger and J. Moser and related elliptic equations

It has been shown by Trudinger and Moser that for normalized functions u of the Sobolev space ??^{1, N} (Ω), where Ω is a bounded domain in ?^N, one has ∫_Ω exp(α_N|u|^{N/(N ? 1)})dx ≤ C_N, where α_N is an explicit constant depending only on N, and C_N is a constant depending only on N and Ω. Carleson and Chang proved that there exists a corresponding extremal function in the case that Ω is the unit ball in ?^N. In this paper we give a new proof, a generalization, and a new interpretation of this result. In particular, we give an explicit sequence that is maximizing for the above integral among all normalized “concentrating sequences.” As an application, the existence of a nontrivial solution for a related elliptic equation with “Trudinger‐Moser” growth is proved. © 2002 John Wiley & Sons, Inc.