The eigenvalue problem for solitary waves of a boussinesq equation,via a generalization of the rouché theorem

We consider the study of an eigenvalue problem obtained by linearizing about solitary wave solutions of a Boussinesq equation. Instead of using the technique of Evans functions as done by Pego and Weinstein in [R. Pego and M. Weinstein, Convective Linear Stability of Solitary Waves for Boussinesq equation. AMS, 99, 311–375] for this particular problem, we perform Fourier analysis to characterize solutions of the eigenvalue problem in terms of a multiplier operator and use the strong relationship between the eigenvalue problem for the linearized Boussinesq equation and the eigenvalue problem associated with the linearization about solitary wave solutions of a special form of the KdV equation. By using a generalization of the Rouché Theorem and the asymptotic behavior of the Fourier symbol corresponding to the eigenvalues problem for the Boussinesq equation and the Fourier symbol corresponding to the eigenvalues problem for the KdV equation, we show nonexistence of eigenvalues with respect to weighted space in a planar region containing the right-half plane.     

Analysis of cocaine and two metabolites in dried blood spots by liquid chromatography with fluorescence detection: a novel test for cocaine and alcohol intake

An original HPLC method coupled to spectrofluorimetric detection is presented for the simultaneous analysis in dried blood spots (DBS) of cocaine and two important metabolites, namely benzoylecgonine (its main metabolite) and cocaethylene (the active metabolite formed in the presence of ethanol). The chromatographic analysis was carried out on a C8 column, using a mobile phase containing phosphate buffer (pH 3.0)-acetonitrile (85:15, v/v). Native analyte fluorescence was monitored at 315 nm while exciting at 230 nm. A fast and feasible sample pre-treatment was implemented by solvent extraction, obtaining good extraction yields (>91%) and satisfactory precision values (RSD<4.8%). The method was successfully applied to DBS samples collected from some cocaine users, both with and without concomitant ethanol intake. The results were in good agreement with those obtained from plasma samples subjected to an original solid-phase extraction procedure on C8 cartridges. The method has demonstrated to be suitable for the monitoring of cocaine/ethanol use by means of DBS or plasma testing. Assays are in progress to apply this method on the street, for the control of subjects suspected of driving under the influence of psychotropic substances.     

Simultaneous determination of disulfiram and bupropion in human plasma of alcohol and nicotine abusers

An isocratic high-performance liquid-chromatographic method has been developed for the simultaneous determination of disulfiram and bupropion in human plasma samples. Analyses were carried out on a C₈ reversed-phase column using a mobile phase composed of 50% acetonitrile and 50% aqueous phosphate buffer, containing triethylamine. Diode-array detection was used, operating at a wavelength of 250 nm. For the clean-up of plasma samples, a solid phase extraction procedure, based on C₂ cartridges, was implemented. Extraction yields of the analytes were satisfactory, being always higher than 84%. The calibration curve was linear over the 5–500 ng mL^-1 plasma concentration range for both disulfiram and bupropion. The method showed a high sensitivity (limit of detection of 1.5 ng mL^-1) and satisfactory precision, selectivity and accuracy. The application to human plasma samples obtained from some alcohol and nicotine abusers also gave good results.     

Entropy, entropy flux and entropy rate of granular materials

The aim of this work is to analyze the entropy, entropy flux and entropy rate of granular materials within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas that follows from the Boltzmann equation differs from the one of a simple fluid due to the presence of a term which can be identified as the entropy density rate. From the knowledge of a non-equilibrium distribution function-valid for processes closed to equilibrium-it is obtained that the entropy density rate is proportional to the internal energy density rate divided by the temperature, while the entropy flux is equal to the heat flux vector divided by the temperature. A thermodynamic theory of a granular material is also developed whose objective is the determination of the basic fields of mass density, momentum density and internal energy density. The constitutive laws are restricted by the principle of material frame indifference and by the entropy principle. Through the exploitation of the entropy principle with Lagrange multipliers, it is shown that the results obtained from the kinetic theory for granular gases concerning the entropy density rate and entropy flux are valid in general for processes close to equilibrium of granular materials, where linearized constitutive equations hold.     

Tachyonization of the ΛCDM cosmological model

In this work a tachyonization of the ΛCDM model for a spatially flat Friedmann–Robertson–Walker space–time is proposed. A tachyon field and a cosmological constant are considered as the sources of the gravitational field. Starting from a stability analysis and from the exact solutions for a standard tachyon field driven by a given potential, the search for a large set of cosmological models which contain the ΛCDM model is investigated. By the use of internal transformations two new kinds of tachyon fields are derived from the standard tachyon field, namely, a complementary and a phantom tachyon fields. Numerical solutions for the three kinds of tachyon fields are determined and it is shown that the standard and complementary tachyon fields reproduces the ΛCDM model as a limiting case. The standard tachyon field can also describe a transition from an accelerated to a decelerated regime, behaving as an inflationary field at early times and as a matter field at late times. The complementary tachyon field always behaves as a matter field. The phantom tachyon field is characterized by a rapid expansion where its energy density increases with time.     

Determination of thermodynamic pKa values of benzimidazole and benzimidazole derivatives by capillary electrophoresis

Thermodynamic pK_a values for benzimidazole and several substituted benzimidazoles were determined by CE. Electrophoretic mobilities of benzimidazoles were determined by CE at different pH levels and ionic strengths. The dependence of electrophoretic mobilities on pH was used to obtain pK_a values at different ionic strengths. Extrapolations to zero ionic strength were used to determine the thermodynamic pK_a values. Using this method the thermodynamic pK_a values of 15 benzimidazoles were determined and found to range from 4.48 to 7.38. Results from the CE measurements were compared with spectrophotometric measurements which were evaluated at wavelengths where the highest absorbance difference for varying pH was recorded. The two analytical techniques were in good agreement.     

Stability of post-fertilization traveling waves

This paper studies the stability of a family of traveling wave solutions to the system proposed by Lane et al. [D.C. Lane, J.D. Murray, V.S. Manoranjan, Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs, IMA J. Math. Appl. Med. Biol. 4 (4) (1987) 309-331], to model a pair of mechanochemical phenomena known as post-fertilization waves on eggs. The waves consist of an elastic deformation pulse on the egg's surface, and a free calcium concentration front. The family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration. This work establishes the spectral, linear and nonlinear orbital stability of these post-fertilization waves for small values of the coupling parameter. The usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation. Nonetheless, exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established. We show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase-modulated traveling wave.     

Conidial pigmentation is important to tolerance against solar-simulated radiation in the entomopathogenic fungus Metarhizium anisopliae

The importance of conidial pigmentation to solar UV radiation tolerance in the entomopathogenic fungus Metarhizium anisopliae var. anisopliae, was estimated by comparing the effects of exposure to simulated solar UV radiation on the wild-type parent strain U.S. Department of Agriculture (USDA)-Agricultural Research Service (ARS) Collection of Entomopathogenic Fungal Cultures (ARSEF) 23, which has dark green conidia, and three groups of color mutants with yellow, purple and white conidia. The comparisons included inactivation levels and the kinetics of germination of conidia exposed or not exposed to simulated solar UV radiation. In addition to significantly inactivating the conidia of different mutants, exposure to radiation delayed for several hours the germination of surviving conidia of the wild type and all mutants. In general, mutants with white conidia were more sensitive to simulated solar UV radiation than mutants with purple conidia, which were more sensitive than mutants with yellow conidia, which in turn were more sensitive than the green wild strain. A significant variation in tolerance to simulated solar radiation was observed among mutants within each color group, particularly among mutants with yellow conidia. Revertants with green conidia, DWR 179 and DWR 176, were obtained from the very sensitive UV mutants DWR 148 (yellow conidia) and DWR 149 (purple conidia), respectively. These revertants had levels of tolerance to simulated solar UV radiation similar to those of the wild-type ARSEF 23. This observation is strong evidence of the importance of green conidial pigmentation for tolerance to simulated solar UV radiation, a factor that could be manipulated to produce M. anisopliae strains with more tolerance to solar UV radiation.     

Influence of different extraction methods on the yield and linalool content of the extracts of Eugenia uniflora L

This work has been developed using a sylvestral fruit tree, native to the Brazilian forest, the Eugenia uniflora L., one of the Mirtaceae family. The main goal of the analytical study was focused on extraction methods themselves. The method development pointed to the Clevenger extraction as the best yield in relation to SFE and Soxhlet. The SFE method presented a good yield but showed a big amount of components in the final extract, demonstrating low selectivity. The essential oil extracted was analyzed by GC/FID showing a large range of polarity and boiling point compounds, where linalool, a widely used compound, was identified. Furthermore, an analytical solid phase extraction method was used to clean it up and obtain separated classes of compounds that were fractionated and studied by GC/FID and GC/MS.     

Moduli of curves and spin structures via algebraic geometry

Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type and on computations of Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the number of marked points and the genus of the curves.