Distribution and reproduction of the reef fish Petrus rupestris (Pisces: Sparidae) off the coast of South Africa

The red steenbras (Petrus rupestris) is endemic to the south and south-east coasts of South Africa and is the largest member of the family Sparidae. Morphometric relationships between length and mass are given for whole and eviscerated fish. The size distribution of P. rupestris is related to locality and water depth. Juveniles and sub-adults are common in shallow (< 50 m) Cape waters between False Bay and East London. Adults are more common offshore, in deep waters (> 50 m), especially off the coast between East London and Coffee Bay, throughout the year. P. rupestris were found to be rudimentary hermaphrodites. The development of the functional sexes, and the occurrence of sexual dichromatism, are described. Sexual maturity is attained at about 575 mm fork length in those fishes in the spawning areas. Reproductively ripe fishes were taken from Transkei, East London and a small collection was made from the Agulhas Bank. Peak spawning is between August and October. Current management regulations are discussed and advantages of large marine reserves in conservation of this mobile apex predator are outlined

The subtidal gully fish community of the eastern cape and the role of this habitat as a nursery area

The fish fauna of rocky subtidal gullies between Chelsea Point and Skoenmakerskop (South Africa) was sampled between October 1985 and September 1986 using rotenone to investigate the species composition and the importance of this habitat as a nursery area for marine linefish species. A total of 59 species belonging to 28 families were collected. The majority of these were cryptic fishes such as Clinidae and Cheilodactylidae. Sparidae and Serranidae were represented by juveniles of inshore species. The findings are discussed in relation to previous studies of intertidal pools in the eastern and western Cape, and it is concluded that shallow rocky inter-and infratidal areas are important nursery areas for numerous inshore fishes, including some species caught by recreational line fishermen. The results from this study suggest that previous intertidal studies have over-emphasized the importance of rock pools as nursery areas

The emission regions in X-ray binaries: dipping as a diagnostic

X-ray dipping in the black hole binary Cygnus X-1, the Galactic jet source GRO J1655-40 and in low mass X-ray binaries is discussed. It is shown that spectral analysis strongly constrains emission models. Measurement of dip ingress/egress times allows the sizes of extended emission regions to be determined, notably for the Accretion Disk Corona which is responsible for Comptonization in X-ray binaries. In LMXB, the radius of the ADC is shown to be between ~ 10^9 and ~ 5x10^10 cm, an appreciable fraction of the accretion disk radius. This is inconsistent with Comptonization models requiring a localized Comptonizing region, for example, in the immediate neighbourhood of the neutron star. Results from a survey of LMXB using ASCA and BeppoSAX reveal an approximate equality between the height of the blackbody emission region on the neutron star and the height of the inner radiatively-supported disk, suggesting either that there is a direct causal link, such as a radial accretion flow between the inner disk edge and the star, or an indirect link, as in the case of accretion flow creep on the surface of the neutron star as suggested by Inogamov & Sunyaev. Finally, the survey shows that the blackbody cannot originate on the accretion disk as the required inner radii in many sources are substantially less than the neutron star radius.Comment: solicited review paper presented at COSPAR 2000 "X-ray and Gamma-ray Signatures of Black Holes and Weakly Magnetized Neutron Stars"; accepted for publication in Advances in Space Research (2nd affiliation added

Book Reviews

Book Review 1Book Title: Early Life Histories of Fishes: New Developmental, Ecological and Evolutionary PerspectivesBook Author: Edited by E.K. BalonDr W. Junk, Dordrecht. 280 pp.Book Review 2Book Title: Comparative Aspects of Extracellular Acid-base BalanceBook Author: J.P. TruchotSpringer, 1987. 248 pp. 51 figures.Book Review 3Book Title: Insect Flight: Dispersal and MigrationBook Author: Edited by W. DanthanarayanaSpringer-Verlag, Berlin, 1986. 289 pp.Book Review 4Book Title:  The Mammalian Herbivore Stomach. Comparative Anatomy, Function and EvolutionBook Author: Peter LangerGustav Fischer, Stuttgart, 1988. 557 pages, 246 figures and 72 tablesBook Review 5Book Title:  Biology of the Integument. Vol. 2: VertebratesBook Authors: Edited by J. Bereiter-Hahn, A.G. Matoltsy & K.S. RichardsSpringer, Berlin, 1986. 855 pp.Book Review 6Book Title:  Advances in the Biology of Turbellarians and related PlatyhelminthesBook Author: Edited by Seth TylerDr. W. Junk Publishers, 1986. 357 pages; 253 figuresBook Review 7Book Title: Evolutionary Physiological EcologyBook Author: Edited by P. CalowCambridge University Press, Cambridge. 239 pp.Book Review 8Book Title: DragonfliesBook Author: Peter L. MillerCambridge University Press, Cambridge, New York and Melbourne, 1987. 84 pp

Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set

We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincare surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show that the hierarchical structure of the fractal set of singularities of the scattering functions is the same as the structure of the chaotic invariant set. Finally, we construct a symbolic encoding of the hierarchical structure of the set of singularities of the scattering functions and use concepts from the thermodynamical formalism to obtain one of the measures of chaos of the fractal set of singularities, the topological entropy.Comment: accepted in Phy. Rev.

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423