On Useful Conformal Tranformations In General Relativity

Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical purposes and represents a collection of exercises concerning local conformal transformations and dimensional reduction. To be published in "Gravitation and Cosmology

Forms on Vector Bundles Over Compact Real Hyperbolic Manifolds

We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.Comment: Int. Journ. Modern Physics A, vol. 18 (2003), 2041-205

Social cues in the expression of sequential alternative reproductive tactics in young males of the peacock blenny, Solaria pavo

Phenotypic change in response to variation in environmental cues has been widely documented in fish. Transitions in social dominance, in particular, have been shown to induce a rapid switch in reproductive phenotypes in many species. However, this effect has been mainly studied in adults and focused on behavioural transitions. The way social cues constraint the phenotypic development of juveniles remains poorly studied in fish. We tested the importance of social dominance and density in the phenotypic development of juveniles of the peacock blenny Solaria pavo. This species shows sequential male alternative reproductive tactics. In the first breeding season males can reproduce as nest-holders or as parasitic males (female-mimicking), or postpone reproduction; from the following season afterwards all males reproduce as nest-holders. Parasitic males have relatively larger testes that lack a testicular gland, present in the testes of nest-holders. The testicular gland is the main source of androgens in the testes and accordingly nest-holders have higher circulating androgen levels. In addition, exogenous androgen administration to parasitic males promotes the development of secondary sexual characters (SSC) only present in nest-holders such as a head crest and an anal gland. We raised juveniles under a high or low-density treatment and monitored social interactions for 1 month. No significant effect of density on the development of juvenile males was detected. However, within each replicate, the relative body size of juvenile males at the beginning of the experiment determined their dominance status, with dominant males developing towards the nest-holder morphotype. Dominant males engaged in more nest defence behaviour, showed larger testicular glands, had higher levels of 11-ketotestosterone (11-KT) and testosterone (T) and developed more SSC, as compared to subordinate males. However, these effects of social dominance were moderated by body condition as only dominant males in good body condition developed SSC. The effect of social dominance and of the area of the testicular gland on the development of SSC was mediated by 11-KT and on the expression of nest defence behaviour by T. Interestingly, in spite of the higher androgen levels and more pronounced morphologic development of SSC in dominant individuals, gonadal development was independent of social dominance and most fish still had underdeveloped testis at the end of the experiment. In conclusion, social dominance promoted the development of the testicular gland, an increase in circulating androgen levels and the development of SSC, but did not promote testicular development. This suggests a dissociation of mechanisms underlying sexual maturation and the expression of male reproductive traits. This dissociation seems to be the key for the occurrence of female-mimicking males in this species, which are sexually mature despite lacking the SSC typical of nest-holdets. (C) 2012 Elsevier Inc. All rights reserved.R&D Units Plurianual Program (R&D unit) from the Portuguese Foundation for Science and Technology (FCT) [331/2001]; FCT [SFRH/BD/6502/2001]; [POCTI/BSE/38395/2001]; [PTDC/MAR/71351/2006]info:eu-repo/semantics/publishedVersio

The ground state properties of the spin-1/2 transverse Ising chain with periodically varying bonds and fields

Using continued fractions we study the ground state properties of the spin-1/2 Ising chain in a transverse field with periodically varying interaction strengths and external fields. We consider in detail the chain having the period of modulation of interactions equals 2 and compare the results obtained with those corresponding to the spin-1/2 isotropic XY chain in a transverse field. In contrast to the behaviour of the transverse XY chain, the transverse Ising chain does not exhibit a step-like magnetization vs. field dependence caused by the alternation of bonds, its susceptibility exhibits a logarithmic singularity at the field determined by interaction strengths, and it is stable with respect to spin-Peierls dimerization.Comment: 11 pages, latex, 4 figure