Computational Aspects of the Calculation of Isometry Groups in General Relativity

We describe the ideas behind the package 'isometry', implemented in Maple to calculate isometry groups of dimensions 2, 3 and 4 in General Relativity. The package extends the functionality of previous programs written to perform invariant classification of space-times in General Relativity. Programming solutions used to surmount problems encountered with the calculation of eigenvectors and the determination of the signs of expressions are described. We also show how the package can be used to find the Killing vectors of a space-time.

Allometric growth of two species of Ephemeroptera from Neotropical mountains streams

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Development of secondary sexual characters in the seabob shrimp Xiphopenaeus kroyeri (Heller 1862) (Crustacea, Decapoda, Penaeidae): a scanning electron microscope study

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Biological parameters and population structure of Psammobatis extenta in Ubatuba region, north coast of the State of São Paulo, Brazil

Specimens of the zipper sand skate Psammobatis extenta were collected in the region of Ubatuba off the northern coast of the State of São Paulo, Brazil, monthly for once year (January - December 2000), at 25- to 40-m isobaths. A total of 123 individuals were caught. The total length (TL) of females averaged 224.6 mm, and of males 217 mm. The overall sex ratio was 1:1. Analysis of the length-weight relationship indicated the existence of positive allometry in females, and isometry in males. The length at onset of sexual maturity was determined for both sexes; females reached sexual maturity at smaller sizes than males (TL50 = 230.7 and TL50 = 237.7 mm respectively). Females showed functional parity of both ovaries and uteri. Females that were pregnant or were carrying vitellogenic oocytes were observed during nine of 12 months of the survey, indicating a continuous reproductive cycle. Psammobatis extenta was most abundant from January to April, and again from June to October. Most individuals were collected at the 40-m isobath. Both adults and neonates were collected in the study area. However, adolescent skates were scarce, which either indicates differential occupation of the area, or suggests that the shallow waters of the continental shelf are used as breeding grounds.

Relative growth and morphological sexual maturity of Chasmagnathus granulatus (Crustacea, Varunidae) from a mangrove area in southeastern Brazilian coast

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

Conformal structures and twistors in the paravector model of spacetime

Some properties of the Clifford algebras Cl-3,Cl-0, Cl-1,Cl-3, Cl-4,Cl-1 similar or equal to C circle times Cl-1,Cl-3 and Cl-2,Cl-4 are presented, and three isomorphisms between the Dirac-Clifford algebra C circle times Cl-1,Cl-3 and Cl-4,Cl-1 are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU( 2,2) and the group $pin(+)(2,4) is also investigated, in the light of a suitable isomorphism between C circle times Cl-1,Cl-3 and Cl-4,Cl-1. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $ pin(+)(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian R-4,(1) spacetime.We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra C circle times Cl-1,Cl-3 using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over R-4,R-1 is also used to describe conformal maps, instead of R-2,(4). Our formalism sheds some new light on the use of the paravector model and generalizations.

Bioecology of the uçá-crab, Ucides cordatus (Linnaeus, 1763), in Vitória Bay, Espírito Santo State, Brazil

A biologia de Ucides cordatus na Baía de Vitória (ES) foi avaliada como subsídio ao manejo populacional. As amostragens ocorreram mensalmente durante um ano (outubro/1998 a setembro/1999), com análise biométrica (LC = largura da carapaça; PE = peso total úmido) e de fatores abióticos em quatro transectos, com quatro faixas cada (margem à região supratidal). A densidade foi de 3,7±1,5 caranguejos.m-2, com incremento em direção à região supratidal, sendo a profundidade das galerias de 1,1±0,3 m. A salinidade da água intersticial diferiu entre as faixas, sendo mais elevada na região supratidal. Houve correlação significativa entre a abundância de exemplares e alguns fatores ambientais, o mesmo ocorrendo quanto as tocas abertas e fechadas. A razão sexual evidenciou um predomínio de fêmeas (1,0M:1,6F), particularmente entre 50 e 75 mm LC. A maior incidência de tocas fechadas ocorreu em agosto e setembro, enquanto as fêmeas ovígeras foram registradas de janeiro a abril. A relação PE/LC mostrou isometria para os machos (PE=0,425.10-3 LC3,0014; R²=0,99) e fêmeas (P=0,439.10-3 LC2,97; R²=0,99). Para o total da população a média de tamanho (LC) e peso (PE) foi de 54,6±11,8 mm e de 77,5±42,4 g, respectivamente. Os dados evidenciam que a população encontra-se sobrexplotada, requerendo manejo adequado para a viabilidade da atividade extrativa na área estudada.

Relating propelinear and binary G-linear codes

In this paper we establish the connections between two different extensions of Z(4)-linearity for binary Hamming spaces, We present both notions - propelinearity and G-linearity - in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary G-linear codes are propelinear codes, and translation-invariant propelinear codes are G-linear codes. (C) 2002 Elsevier B.V. B.V. All rights reserved.

RELATIVE GROWTH OF THE SPECKLED SWIMMING CRAB ARENAEUS-CRIBRARIUS (LAMARCK, 1818) (BRACHYURA, PORTUNIDAE), NEAR UBATUBA, STATE OF SAO-PAULO, BRAZIL

Arenaeus cribrarius is a mainly tropical crab that occurs in the Western Atlantic Ocean, Brazil being its type-locality. The species ranges from Vinevard Sound, Massachusetts, USA to La Paloma, Uruguay. Information about this species is scarce. The relative growth of A. cribrarius was analyzed, based on some morphometric relations, where the carapace width, excluding lateral spines (CW), was used as an independent variable. A total of 403 specimens (189 males and 214 females), was collected in Ubatuba, State of São Paulo, Brazil, with otter-trawls. The animals were sexed and sorted to maturation phase (juvenile or adult). Some measurements were made: carapace (length and width excluding lateral spines), abdomen (greatest width of the fifth somite in females and the sixth in males) and major chela (greatest length, width and height, dactylus length). This study was made by the application of the power function (y=a.x(b)) which was fitted to the data and the pattern of growth established for each parameter by the ''b''-value (constant of allometry), as positive allometry (b>1), negative allometry (b<1) or isometry (b=1). The morphometric relations of the carapace showed a tendency to isometry. In females, the abdominal width grew in positive allometry, higher in juveniles (b=1.33) than in adults (b=1.18). In this case, an overlap and discontinuity was noticed between the phases over a carapace width range of 55 to 70 mm, where the puberty molt occurs. The majority of relationships showed that the major chela of the males grew in positive allometry, however, the greatest allometric difference between the phases was observed towards the propodus length with 1.09 as juvenile and 1.26 as adult ''b''values. In the males, this variable showed an inflection between the CW range of 45' to 55 mm, where the transition to the maturation phase occurs. The relative growth of this species is similar to those of previously studied species. This indicates, that the propodus length and the abdominal width are the morphometric variables most appropriate to estimate the size of the beginning of the sexual maturity for males and females of this species, respectively.

Estudo clínico e eletromiográfico da dinâmica do sistema mastigatório em pacientes adultos com paralisia cerebral

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma abordagem de isometria em sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aprendendo isometria com mosaicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)