A Variational Approach to Discontinuous Problems with Critical Sobolev Exponents

We employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form − Δu = λh(x)H(u − a)u^q + u^2* − 1 in R^N, where λ, a > 0 are parameters, h(x) is both nonnegative and integrable on R^N, H is the Heaviside function, 2* is the critical Sobolev exponent, and 0 ≤ q < 2* − 1. We obtain existence, multiplicity and regularity of solutions by distinguishing the cases 0 ≤ q ≤ 1 and 1 < q < 2* − 1.     

Compact Clifford–Klein Forms of Homogeneous Spaces of SO(2, n)

A homogeneous space G/H is said to have a compact Clifford–Klein form if there exists a discrete subgroup of G that acts properly discontinuously on G/H, such that the quotient space \G/H is compact. When n is even, we find every closed, connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford–Klein form, but our classification is not quite complete when n is odd. The work reveals new examples of homogeneous spaces of SO(2, n) that have compact Clifford–Klein forms, if n is even. Furthermore, we show that if H is a closed, connected subgroup of G = SL(3, R), and neither H nor G/H is compact, then G/H does not have a compact Clifford–Klein form, and we also study noncompact Clifford–Klein forms of finite volume.     

Eigenvalues and normalized eigenfunctionsof discontinuous Sturm-Liouville problem with transmission conditions

In this study, discontinuous Sturm-Liouville problems which contain eigenvalue parameters both in equation and in the boundary conditions are investigated. We introduce an operator-theoretic interpretation, extend some classic results for regular Sturm-Liouville problems and obtain asymptotic approximate formulae for eigenvalues and normalized eigenfunctions. By modifying some techniques of [2, 6, 7] we obtain asymptotic formulae for eigenvalues and normalized eigenfunctions. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in [2].     

A classicalN-body simulation of groups of galaxies

Summary Groups of galaxies are simulated by Monte Carlo technique. The mass distribution of the groups is assumed to follow a power law. Furthermore a linear relationship between mass and luminosity is considered. The calculated velocity dispersion is compared with the observational data and provides an estimate of the range in which the galaxy masses are distributed. It is shown, in this case, that the mass discrepancy can cover up two orders of magnitude, such as pointed out in the literature. The authors of this paper have agreed to not receive the proofs for correction. Supported by Conselho Nacional de Desenvolvimento Cientifico e Tecnológico, CNPq (Brasil).     

Laboratory measurements on molecules of astrophysical interest

Summary The infra-red absorption bands of a representative polycylic aromatic hydrocarbon (PAH) molecule, coronene, have been examined in the laboratory at various temperatures up to 240 °C. This paper is devoted to a systematic analysis of the temperature variations of the integrated band intensity. A tentative interpretation of the observed behaviour is given in terms of anharmonicity effects. These new laboratory results may be helpful in the context of the attribution of the ?unidentified? infra-red band to PAH molecules. In addition, for the first time thermal-emission spectra of three different PAHs recorded at 240 °C are presented. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

ISO spectroscopy: the study of active galaxies

Summary Infrared spectroscopy can greatly help in the understanding of the active galaxies phenomena, having the advantage over optical and UV spectroscopy of penetrating those nuclei heavily obscured by absorbing dust. The standard photoionization code CLOUDY by Ferland has been used to predict the intensities of the infrared ionic fine-structure lines. Examples of line ratio diagrams are presented which constrain the two main free parameters of the models (gas density and ionization parameter), and separate line emission in the different regions of active galaxies (Seyfert and LINER type nuclei, coronal emission region, starbursts). Moreover, some line ratio diagrams can disentangle emission-line components from shock excited and photodissociated gas. Finally we show that the observations of these infrared lines will be possible in the near future with the ISO (Infrared Space Observatory) spectrometers. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

SN1987A; n-stars, s-stars and the observational evidences

Summary We discuss a SN model with s-matter in the core, compatible with the set of experimental results obtained on SN 1987A by ν-detectors and gravitational antennas.     

Characterisation and identification of proteinaceous binding media (animal glues) from their amino acid profile by capillary zone electrophoresis

A capillary electrophoretic method for identifying different species of proteinaceous binders--collagen, egg white, and milk casein--is described. It allows characterisation of the proteins on the basis of the amino acid profiles obtained after their acidic hydrolysis. The profiles of the underivatised amino acids are recorded directly by capillary zone electrophoresis at pH 2.26 with the aid of a conductivity detector, thus eliminating the need for a derivatisation step. Identification is carried out by means of different relative peak areas of the amino acids. A scheme is given for identification, which is based on the main markers, hydroxyproline, proline, glycine, glutamic acid, and serine and valine.     

Multiple solutions for strongly resonant nonlinear elliptic problems with discontinuities

We examine a nonlinear strongly resonant elliptic problem driven by the -Laplacian and with a discontinuous nonlinearity. We assume that the discontinuity points are countable and at them the nonlinearity has an upward jump discontinuity. We show that the problem has at least two nontrivial solutions without using a multivalued interpretation of the problem as it is often the case in the literature. Our approach is variational based on the nonsmooth critical point theory for locally Lipschitz functions.