Gel'fand-Levitan equation for deletion of states from Coulomb spectra

The Gel'fand-Levitan formalism is used to study how a selected set of bound states can be eliminated from the spectrum of the Coulomb potential and also how to construct a bound state in the Coulomb continuum. It is demonstrated that a sizeable quantum well can be produced by deleting a large number of levels from the s spectral series and the edge of the Coulomb potential alone can support the von Neumann-Wigner states in the continuum. © 1998 Elsevier Science B.V.

Two-body Dirac equation approach to the deuteron

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ = 1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved.

Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrödinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schrödinger equation. A particular scaling is used in the equation, which permits us to evaluate the wave-function normalization after the numerical solution. We have a two-point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, be equal for large distances. In order to obtain fast convergence, the secant method is used. © 1999 The American Physical Society.

Pollen viability in Syagrus romanzoffiana and S. coronata (Arecaceae)

Palms of the Syagrus genus have several natural hybrids in Brazil. They are widely cultivated around the world as ornamental palm. S. romanzqffiana is the parental of natural hybrids with other Syagrus species that are potentially useful as palm cultivated for heart of palm production. The objective of this work was to evaluate the pollen grains viability got from plants grown in the Experimental Nursery of the FCAVJ/UNESP, Jaboticabal, SP, Brazil. Pollen grains were sampled from inflorescence in three occasions: in the right day of anthesis, one day before and one day after anthesis. For each day, the inflorescence was subdivided in apical, medium and basal portions where pollen grains were collected. The results shown that: a) for S. coronata there was no statistical differences in pollen viability (pollen viability average = 92.89%); b) for S. romanzoffiana the average pollen viability was 87.27%, 87.47% e 86.85% before, during and after the anthesis, respectively. The basal portion pollen grains had lower viability (85.19% - p<0.01) than those from the medium (88.17%) and the apical (88.46%) portion of the inflorescence. These results shown that both species have no problems with pollen viability and can be used as parental of hybrids with other Syagrus species.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

Galilean covariance and the Duffin-Kemmer-Petiau equation

We use a five-dimensional approach to Galilean covariance to investigate the non-relativistic Duffin-Kemmer-Petiau first-order wave equations for spinless particles. The corresponding representation is generated by five 6 × 6 matrices. We consider the harmonic oscillator as an example.

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.

Economic viability and selection of irrigation systems using simulation and stochastic dominance

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

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.

Viability of Streptococcus mutans on transparent and opaque toothbrushes.

PURPOSE: The objective of this study was to evaluate the viability of the microorganism Streptococcus mutans on toothbrushes made of opaque and transparent materials. METHODS: Twenty-eight toothbrushes (14 opaque and 14 transparent) were inoculated in tubes with brain heart infusion (BHI) broth of a standard strain of S. mutans and incubated in candle jars at 37 degrees C for 24 hours. Both the opaque and transparent toothbrushes were removed at T = 0 h (control); T = 0.5 h; T = 1 h; T = 2 h; T = 4 h; T = 8 h; and T = 24 h. Individual toothbrushes were subjected to agitation in a saline solution and samples of the solution were diluted and inoculated in Bacitracin Sucrose Agar--SB-20. RESULTS: After half an hour (T2) there was a significant decrease in the number of microorganisms on the transparent and opaque toothbrushes, respectively 6.0 x 10(5) and 9.4 x 10(5), when compared to the control. After the T3 = 1 hour, T4 = 2 hours, T5 = 4 h, the number of microorganisms decreased from 4.1 x 10(5); 2.1 x 10(5); 1.4 x 10(5); and 9.2 x 10(5); 5.7 x 10(5); 1.2 x 10(5) to zero (0.0) in T6 = 8 h, respectively on the transparent and opaque toothbrushes. The reduction in viable microorganisms was more obvious with the transparent toothbrushes, although the number of viable microorganisms was not significantly different for the two types of toothbrushes at the end of the experiment, T5 = 1.4 x 10(5) (transparent) and T5 = 1.2 x 10(5) (opaque). CONCLUSIONS: With both opaque and transparent toothbrushes, the number of microorganisms decreased with time. A reduction in the number of microorganisms on the transparent toothbrushes was observed following inoculation and incubation. This suggests the transparent toothbrushes inhibit the viability of the S. mutans.

Effect of air humidity on the egg viability of predatory mites (Acari: Phytoseiidae, Stigmaeidae) common on rubber trees in Brazil

Rubber pest mites, Calacarus heveae and Tenuipalpus heveae, reach economic damage levels at the end of the rainy season and the beginning of the dry season in Brazil. Therefore, low humidity adaptation might be an important characteristic for predatory mites to successfully control pest organisms. This study determined the effect of the relative humidity (RH) levels of 30-100% on the hatching of larvae of Amblyseius acalyphus, Euseius citrifolius, Iphiseiodes zuluagai, Metaseiulus camelliae, Agistemus floridanus and Zetzellia malvinae at 25 ± 0.5°C. These predatory mites are common on rubber trees in the state of São Paulo and might be used for introduction in the major rubber tree production regions in the state of Mato Grosso. At 70% RH or higher, viability was 70% or higher for all species, indicating that their performance might be higher during the rainy season than during the dry season. Eggs of E. citrifolius and M. camelliae presented higher viability at the lower relative humidity levels than those of other species, indicating that these species might have higher chance to persist in the dry season. It is suggested that M. camelliae should be further evaluated for introduction in the state of Mato Grosso, considering that this mite is not yet present in that area. © Springer 2006.