Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Avaliação de diferentes sistemas de cultivo in vitro para a micropropagação de Psychotria ipecacuanha (Brot.) Stokes

This work was carried out with Psychotria ipecacuanha, a Brazilian medicinal plant the roots of which contain emetine. The main objective was to develop a protocol for the micro-propagation of these species, by testing different culture techniques, the temporary immersion system, and the semi-solid and liquid media systems. In the semi-solid system, experiments were developed in flasks of two different sizes containing MS, B5, and WP media to which were added different growth regulators. Innoculum density was also evaluated. The liquid medium system consisted of MS medium supplemented with different growth regulators. For the temporary immersion system, the MS medium received an addition of 1.5mg/L BAP and 0.5mg/L GA3, and a reverse digital apparatus and vacuum pump were used. The liquid medium system with MS medium supplemented with 1.5mg/L BAP and 0.5mg/L GA3 presented the best results for shoot proliferation in a period of 30 days in culture (2.37 ± 0.32 shoots/explant). Cultures carried out for 90 days in the semi-solid system, using 8.5 × 5.5cm flasks and 3 explants per flask, developed 1.80 ± 0.20 shoots/explant, achieving 3.06 ± 0.51 cm of height adn presented superior survival ratio (96%). Explants cultured in temporary immersion system for 90 days showed 2.30 ± 1.10 shoots/explant achieving a growth of 2.08 ± 0.12 cm and 52% survival.

Phonon-assisted cooperative energy transfer and frequency upconversion in a Yb3+/Tb3+ codoped fluoroindate glass

Phonon-assisted cooperative energy transfer and frequency upconversion (UC) in Yb3+/Tb3+ codoped fluoroindate glass were investigated. Anti-Stokes quasiresonant excitation of Yb3+ ions was used to study the influence of multiphonon transitions in the UC process. A rate equation model was used to describe the temperature dependence of the UC emission intensities and the theoretical results are in good agreement with the experimental data.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

A simplified procedure for determination of clofentezine residues in fruits by liquid chromatography with UV detection

A rapid and sensitive method is described for the determination of clofentezine residues in apple, papaya, mango and orange. The procedure is based on the extraction of the sample with a hexane:ethyl acetate mixture (1:1, v/v) and liquid chromatographic analysis using UV detection. Mean recoveries from 4 replicates of fortified fruit samples ranged from 81% to 96%, with coefficients of variation from 8.9% to 12.5%. The detection and quantification limits of the method were of 0.05 and 0.1 mg kg-1, respectively.

A simplified spectrophotometric method for routine analysis of saccharin in commercial noncaloric sweeteners

A simple, rapid, and sensitive spectrophotometric method for routine analysis of saccharin in commercial noncaloric sweeteners is proposed. This method is based on the reaction of saccharin with tetrachloro-p-benzoquinone (p-chloranil) accelerated by hydrogen peroxide and conducted in an ethanol:acetone (4:1) medium, producing a violet-red compound (γ max = 550 nm). Beer's law is obeyed in a concentration range of 2.05 × 10 -4 to 3.00 × 10 -3 M with an excellent correlation coefficient (r = 0.9998). The detection limit was 1.55 × 10 -5 M, and the effect of interferences on the spectrophotometric measurements was evaluated. The proposed procedure was applied successfully to the determination of saccharin in noncaloric sweeteners. Recoveries were within 99.2-104.3% with standard deviations ranging from to 0.5-1.6%. Results of the proposed method compare very favorably with those given by the high-performance liquid chromatography method recommended by the Food and Drug Administration.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A simplified reflectometric method for the rapid determination of dipyrone in pharmaceutical formulations

This paper describes a simple, portable and environmentally friendly method for the rapid determination of dipyrone in pharmaceuticals by using diffuse reflectance spectroscopy. The proposed method is based on the reflectance measurements of the orange compound produced from the spot test reaction between dipyrone and p-dimethylaminocinnamaldehyde (p-DAC), in acid medium, using a filter paper as solid support. Experimental design methodologies were used to optimize the measurement conditions. All reflectance measurements were carried out at 510 nm and the linear range was from 1.42 × 10-4-2.85 × 10-3 mol L-1, with a correlation coefficient of 0.999. The limit of detection (LOD) and the limit of quantification (LOQ) were 1.20 × 10-5 mol L-1 and 4.00 × 10-5 mol L-1, respectively. The intraday precision and interday precision were studied for 10 replicate analyses of 7.90 × 10-4 mol L-1 dipyrone solution. The coefficients of variation were 1.1 and 0.9%, respectively. The proposed method was applied successfully to the determination of dipyrone in commercial brands of pharmaceuticals. No interferences were observed from the common excipients in formulations. The results obtained by the proposed method were favorably compared with those given by the Brazilian Pharmacopoeia procedure at 95% confidence level. ©2007 Sociedade Brasileira de Química.

A simplified method for determining the high frequency induction motor equivalent electrical circuit parameters to be used in EMI effect

The aim of this paper is to present a simple method for determining the high frequency parameters of a three-phase induction motor to be used in studies involving variable speed drives with PWM three-phase inverters, in which it is necessary to check the effects caused to the motor by the electromagnetic interference, (EMI) in the differential mode, as well as in the common mode. The motor parameters determination is generally performed in adequate laboratories using accurate instruments, such as very expensive RLC bridges. The method proposed here consists in the identification of the motor equivalent electrical circuit parameters in rated frequency and in high frequency through characteristic tests in the laboratory, together with the use of characteristic equations and curves, shown in the references to be mentioned for determining the motor high frequency parasite capacitances and also through system simulations using dedicated software, like Pspice, determining the characteristic waveforms involved in the differential and common mode phenomena, comparing and validating the procedure through published papers [01].

Antinucleon spectra in the Dirac equation with scalar and vector Wood-Saxon potentials

We analyze here the spin and pseudospin symmetry for the antinucleon spectra solving the Dirac equation with scalar and vector Wood-Saxon potentials. In relativistic nuclear mean field theories where these potentials have large magnitudes and opposite signs we show that contrary to the nucleon case where pseudospin interaction is never very small and cannot be treated perturbatively, for antinucleon systems this interaction is perturbative and an exact pseudospin symmetry is possible. This result manifests the relativistic nature of the nuclear pseudospin symmetry. © 2009 American Institute of Physics.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.