A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

     

Stopping rule for variable selection using stepwise discriminant analysis

Summary In general, when characterizing samples, such as ceramic samples or other types of samples, for first time by means of chemical elements, the analyst measures a large number of variables, many of which may not be very informative. In fact, some may even be unrelated to the issue at hand and blur the picture instead of making it clearer. In subsequent studies the analyst may wish to measure fewer variables for several reasons, such as being very time consuming; in cases where measurement time is important, such as on-line monitoring; in order to reduce cost or effort; etc. Therefore, the hope is to determine those variables that are most relevant without losing essential information and to remove the less productive information. The problem is how to perform this in an objective way and to capture crucial information using a multivariate analysis. This paper aims to describe and illustrate a stopping rule for the identification of redundant variables, and the selection of variable subsets, preserving multivariate data structure using stepwise discriminant analysis, selecting those variables that are in some senses adequate for discrimination purposes. One illustrative example using data sets obtained via INAA of ceramic samples from two archaeological sites is provided.     

Internal standardization for the determination of cadmium,cobalt, chromium and manganese in saline produced water from petroleum industry by inductively coupled plasma optical emission spectrometry after cloud point extraction

In the present paper a procedure is proposed for the determination of traces of Cd, Co, Mn and Cr in petroleum industry produced water by inductively coupled plasma optical emission spectrometry. The procedure is based on cloud point extraction of these metals, as their dithizonate complexes, into the surfactant-rich phase of octylphenoxypolyethoxyethanol surfactant (Triton X-114). Extractions were carried out in solutions with salinities between 10‰ and 70‰. Since residual salinity in the surfactant-rich phase caused differences in its transport to the plasma, yttrium was used as an internal standard to correct for this effect. The simultaneous metal extraction procedure was optimized by response surface methodology using a Doehlert design and desirability function. Enhancement factors of 21, 21, 9 and 19, along with limits of quantification of 0.093, 0.20, 0.73 and 1.2 μg L^− 1, and precision expressed as relative standard deviation (n = 8, 20.0 μg L^− 1) of 5.8, 1.2, 1.7 and 5.7% were obtained for Cd, Co, Mn and Cr, respectively. The accuracy was evaluated by spike recovery tests on the high salinity water samples with salinity of 40 and 63‰.     

Speed of adaptation in structured populations

Adaptation of populations takes place with the occurrence and subsequent fixation of mutations that confer some selective advantage to the individuals which acquire it. For this reason, the study of the process of fixation of advantageous mutations has a long history in the population genetics literature. Particularly, the previous investigations aimed to find out the main evolutionary forces affecting the strength of natural selection in the populations. In the current work, we investigate the dynamics of fixation of beneficial mutations in a subdivided population. The subpopulations (demes) can exchange migrants among their neighbors, in a migration network which is assumed to have either a random graph or a scale-free topology. We have observed that the migration rate drastically affects the dynamics of mutation fixation, despite of the fact that the probability of fixation is invariant on the migration rate, accordingly to Maruyama's conjecture. In addition, we have noticed a topological dependence of the adaptive evolution of the population when clonal interference becomes effective.     

Operator–valued Fourier multiplier theorems on Besov spaces

We investigate analytical properties of a measure geometric Laplacian which is given as the second derivative w.r.t. two atomless finite Borel measures μ and ν with compact supports supp μ ? supp ν on the real line. This class of operators includes a generalization of the well‐known Sturm‐Liouville operator as well as of the measure geometric Laplacian given by . We obtain for this differential operator under both Dirichlet and Neumann boundary conditions similar properties as known in the classical Lebesgue case for the euclidean Laplacian like Gauß‐Green‐formula, inversion formula, compactness of the resolvent and its kernel representation w.r.t. the corresponding Green function. Finally we prove nuclearity of the resolvent and give two representations of its trace.     

UPML formulation for truncating conductive media in curvilinear coordinates

This work presents a formulation based on UPML for truncating conductive media by using a local and non-orthogonal coordinate system to solve Maxwell’s equations by the FDTD method. The detailed procedure for obtaining the UPML equations for this case is shown and the complete equation set is provided.     

Vapor-liquid equilibrium data at 25°C for six binary systems containing methyl acetate or methanol,with dichloromethane,chloroform, or 1,2-trans-dichloroethylene

Isothermal vapor-liquid equilibrium (VLE) data, at 25° C were determined by a saturation method for each of the six methanol or methyl acetate binary systems with dichloromethane, chloroform, and 1,2-trans-dichloroethylene. The experimental data satisfy the Redlich-Kister consistency test, and were correlated with five Gibbs free energy models. All the binary mixtures of methanol with the chlorinated compounds exhibit strong positive deviations from ideality while the mixtures of methyl acetate with the chlorinated compounds present negative deviations from ideal behavior.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Asymptotic stability of semigroups associated with linear weak dissipative systems with memory

We study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations. We show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution. In the case of the lack of exponential decay, we find the polynomial rate of decay of the solution. Some examples are given.     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007