Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors

SOLUTION OF MULTIPHASE HEAT CONDUCTION PROBLEMS VIA THE GENERALIZED INTEGRAL TRANSFORM TECHNIQUE WITH DOMAIN CHARACTERIZATION THROUGH THE INDICATOR FUNCTION

The Generalized Integral Transform Technique (GITT) has appeared in the literature as an alternative to conventional discrete numerical methods for partial differential equations in heat transfer and fluid flow. This method permits the automatic control of the error and is easy to program, since there is no need for a discretization. The method has being constantly improved, but there still a vast number of practical problems that has not being solved satisfactory. In several brands of engineering, the transport equations have to be solved for a combination of different phases or materials or inside irregular domains. In this case, the mathematical resource of the Indicator Function can be employed. This function is a representation of the phases or parts of the domain with the numbers 0 and 1 for each phase. According to the method, the Indicator Function is defined by Poisson’s equation, which is added to the system of the transport equations. An integral is done along the curve that defines the interface that will generate the source term in Poisson’ equation used to calculate the Indicator Function distribution. The solution of the system of equations is done using the common GITT approach. Then, an analytical expression for each transformed potential of the indicator function and the other variables are available. Once the transformed potentials are known, the Indicator Function can be analytically operated, and the interface can be represented by an analytical continuous function. In this work, the use of the GITT in conjunction with the Indicator Function is proposed. The methodology is described and some previous results are presented. GITT is applied to a two-dimensional heat conduction problem in a multiphase domain with an irregular geometry, inside a square domain. The methodology presented here can be extended to all brands of convection-diffusion problems already solved via GITT

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we are able to obtain complete agreement with the results obtained in intrinsic coordinates. In particular, we have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.Comment: Extended version of GRG publication, with some typos etc correcte

Kepler detection of a new extreme planetary system orbiting the subdwarf-B pulsator KIC10001893

KIC10001893 is one out of 19 subdwarf-B (sdB) pulsators observed by the Kepler spacecraft in its primary mission. In addition to tens of pulsation frequencies in the g-mode domain, its Fourier spectrum shows three weak peaks at very low frequencies, which is too low to be explained in terms of g modes. The most convincing explanation is that we are seeing the orbital modulation of three Earth-size planets (or planetary remnants) in very tight orbits, which are illuminated by the strong stellar radiation. The orbital periods are P1=5.273, P2=7.807, and P3=19.48 hours, and the period ratios P2/P1=1.481 and P3/P2=2.495 are very close to the 3:2 and 5:2 resonances, respectively. One of the main pulsation modes of the star at 210.68 {\mu}Hz corresponds to the third harmonic of the orbital frequency of the inner planet, suggesting that we see, for the first time in an sdB star, g-mode pulsations tidally excited by a planetary companion. The extreme planetary system that emerges from the Kepler data is very similar to the recent discovery of two Earth-size planets orbiting the sdB pulsator KIC05807616 (Charpinet et al. 2011a).Comment: 6 pages, 5 figures, accepted for publication in Astronomy and Astrophysic

Biologia do percevejo Tibraca limbativentris (Heteroptera: Pentatomidae) em arroz e milho.

Este trabalho teve como objetivo avaliar o desenvolvimento de T. limbativentris quando alimentado com colmos de arroz e milho.Pôster - graduação

Performance ninfal do percevejo Euschistus heros (Heteroptera: Pentatomidae) alimentado com Amaranthus sp.

O objetivo desse trabalho foi avaliar a capacidade do caruru (Amaranthus sp.) de alimentar e possibilitar o desenvolvimento das ninfas de E. heros até a fase adulta.Apresentação oral - Pós-graduação

Gene duplication in an African cichlid adaptive radiation

Background Gene duplication is a source of evolutionary innovation and can contribute to the divergence of lineages; however, the relative importance of this process remains to be determined. The explosive divergence of the African cichlid adaptive radiations provides both a model for studying the general role of gene duplication in the divergence of lineages and also an exciting foray into the identification of genomic features that underlie the dramatic phenotypic and ecological diversification in this particular lineage. We present the first genome-wide study of gene duplication in African cichlid fishes, identifying gene duplicates in three species belonging to the Lake Malawi adaptive radiation (Metriaclima estherae, Protomelas similis, Rhamphochromis “chilingali”) and one closely related species from a non-radiated riverine lineage (Astatotilapia tweddlei). Results Using Astatotilapia burtoni as reference, microarray comparative genomic hybridization analysis of 5689 genes reveals 134 duplicated genes among the four cichlid species tested. Between 51 and 55 genes were identified as duplicated in each of the three species from the Lake Malawi radiation, representing a 38%–49% increase in number of duplicated genes relative to the non-radiated lineage (37 genes). Duplicated genes include several that are involved in immune response, ATP metabolism and detoxification. Conclusions These results contribute to our understanding of the abundance and type of gene duplicates present in cichlid fish lineages. The duplicated genes identified in this study provide candidates for the analysis of functional relevance with regard to phenotype and divergence. Comparative sequence analysis of gene duplicates can address the role of positive selection and adaptive evolution by gene duplication, while further study across the phylogenetic range of cichlid radiations (and more generally in other adaptive radiations) will determine whether the patterns of gene duplication seen in this study consistently accompany rapid radiation

The type N Karlhede bound is sharp

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spacetimes are properly $CH_2$, i.e., curvature homogeneous of order 2 but non-homogeneous. This means that tetrad components of $R, \nabla R, \nabla^{(2)}R$ are constant, and that essential coordinates first appear as components of $\nabla^{(3)}R$. Covariant derivatives of orders 4,5,6 yield one additional invariant each, and $\nabla^{(7)}R$ is needed for invariant classification. Thus, our class proves that the bound of 7 on the order of the covariant derivative, first established by Karlhede, is sharp. Our finding corrects an outstanding assertion that invariant classification of four-dimensional Lorentzian manifolds requires at most $\nabla^{(6)}R$.Comment: 7 pages, typos corrected, added citation and acknowledgemen