Distances between critical points and midpoints of zeros of hyperbolic polynomials

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

Relaxation algorithm to hyperbolic states in Gross-Pitaevskii equation

A new version of the relaxation algorithm is proposed in order to obtain the stationary ground-state solutions of nonlinear Schrodinger-type equations, including the hyperbolic solutions. In a first example, the method is applied to the three-dimensional Gross-Pitaevskii equation, describing a condensed atomic system with attractive two-body interaction in a non-symmetrical trap, to obtain results for the unstable branch. Next, the approach is also shown to be very reliable and easy to be implemented in a non-symmetrical case that we have bifurcation, with nonlinear cubic and quintic terms. (c) 2006 Elsevier B.V. All rights reserved.

Casimir energy in a small volume multiply connected static hyperbolic preinflationary universe

A few years ago, Cornish, Spergel and Starkman (CSS) suggested that a multiply connected small universe could allow for classical chaotic mixing as a preinflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated the Casimir energy for static multiply connected fat space-times. Because of the interest in small volume hyperbolic universes (e.g., CSS), we generalize the DHI calculation by making a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static universe, whose spatial sections are the Weeks manifold, the smallest universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.

On the birth of a closed hyperbolic universe

We clarify and develop the results of a previous paper on the birth of a closed universe of negative spatial curvature and multiply connected topology. In particular we discuss the initial instanton and the second topology change in more detail, This is followed by a short discussion of the results.

Casimir energy in multiply connected static hyperbolic universes

We generalize a previously obtained result for the case of a few other static hyperbolic universes with manifolds of nontrivial topology as spatial sections.

A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Geometrically uniform hyperbolic codes

In this paper we generalize the concept of geometrically uniform codes, formerly employed in Euclidean spaces, to hyperbolic spaces. We also show a characterization of generalized coset codes through the concept of G-linear codes.

A and B mode ultrasonography in preoperative evaluation of lens and posterior segment of dogs eyes with cataract

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

Ultrasonographic analysis of senile cataractous lens of dogs and its correlation to phacoemulsification

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

Elementary particles under the lens of the black holes

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

Thermal-optical properties of Ga : La : S glasses measured by thermal lens technique

In this work the quantitative theoretical treatment for two beam mode mismatched thermal lens spectrometry is applied to investigate the thermo-optical properties of chalcohalide (chalcolgenides and halides mixture) glasses. For the three kinds of glass studied the thermal diffusivity varied between 2.5 and 2.7 x 10(-3) cm(2) s(-1). Using these results and supposing Dulong-Petit specific heats we estimated the thermal conductivity and temperature ratio of optical path length (ds/dT) and temperature coefficient of refractive index (dn/dT). All samples had positive ds/dT(similar to 3.3 x 10(-6) K-1) and negative dn/dT (similar to -26 x 10(-6) K-1). The difference between these parameters and the change of signal are consequences of the expansion coefficient (13 x 10(-6) K-1) and refractive index (n similar to 2.6) of chalcohalides. (C) 1999 Elsevier B.V. B.V. All rights reserved.

ISOLATION AND IN-VITRO HYDROLYSIS OF GLOBULIN G1 FROM LENTILS (LENS-CULINARIS, MEDIK)

The major globulin fraction from lentil seeds was investigated with respect td in vitro hydrolysis by trypsin and chymotrypsin. Globulin was isolated by a NaCl-ascorbate extraction procedure and purified by DEAE-cellulose chromatography and gelfiltration chromatography on Sepharose CL-6B. The purity and identification of the protein were performed by PAGE. The native globulin, with a molecular weight of 375 kD, was resolved by SDS-PAGE into twelve polypeptides with molecular weights ranging from 61 to 14.5 kD. Native and heated globulin GI was hydrolyzed with trypsin and chymotrypsin. SDS-PAGE indicated that native globulin was more resistant to digestion than heated protein. Amino acid analysis of the major globulin revealed that glutamic acid was present in the largest concentration, followed by aspartic acid, arginine and leucine. As is also the case for other legumin-like globulins, lentil GI was deficient in sulfur-containing amino acids.

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.