Hilbert-Smith Conjecture for K - Quasiconformal Groups

MSC 2010: 30C60

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Toward Clemens' Conjecture in Degrees between 10 and 24

1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.

Estádios de desenvolvimento dos órgãos reprodutivos dos machos de Panulirus echinatus Smith (Decapoda: Palinuridae)

Esta pesquisa caracteriza os estádios de desenvolvimento dos testículos e canais deferentes da lagosta Panulirus echinatus Smith, 1869 a partir da relação entre seus aspectos macroscópicos, microscópicos e a relação gonadossomática (RGS). Através de amostragem mensal (novembro de 1999 a outubro de 2000) foram capturados 1716 machos, empregando-se redes de espera de fundo. Retirou-se a região dorsal da carapaça para avaliação dos órgãos reprodutivos. Os testículos e canais deferentes foram dissecados, pesados, fixados em solução de Bouin e submetidos aos procedimentos histológicos. A análise microscópica dos órgãos reprodutivos foi avaliada pela presença ou ausência de espermatozóides nos testículos e canais deferentes. Esta, quando associada a macroscopia (mudança de cor, tamanho, diâmetro e desenvolvimento de espermatóforo) e a relação gonadossomática (RGS), possibilitou a caracterização de três estádios de desenvolvimento: imaturo, intermediário e maturo. Ficou evidenciada que a maturidade dos testículos precedeu a maturidade dos canais deferentes. Para avaliar se a RGS é um bom indicador quantitativo dos estádios de maturidade, um teste t (alfa = 0,05) foi usado e constatou diferença significativa nas médias da RGS. A RGS pode ser utilizada como indicadora dos estádios de maturidade para P. echinatus.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

The Lobel-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree at least some k is an element of N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r( T, T') of trees T, T' from the above classes.

Effect of Calcium on the in vitro Growth of Aechmea blanchetiana (Baker) L. B. Smith Plantlets

This work investigated the influence of different concentrations of calcium on the growth of plantlets of the bromeliad Aechmea blanchetiana cultured in vitro. Seedlings of A. blanchetiana were axenically cultured in liquid Murashige and Skoog basal medium supplemented with different concentrations of calcium (Ca; 1.5, 3, 4.5, 6, or 12 mM) without growth regulators. The resulting plantlets were cultured under 93 mol m-2 s-1 illumination, 12 hour photoperiod regime and 25C 1 for 120 days with subculture to fresh identical media every 30 days. The addition of calcium at 9.38 mM to MS modified medium increased the production of fresh and dry mass of plantlets, whilst chlorine from calcium chloride dehydrate (CaCl2 2 H2O) in excess (3.35 mM) decreased both the fresh and dry mass of plantlets.

Natural regeneration of Atlantic Forest species in the understory of Eucalyptus saligna Smith. in a former forest production unit at the Parque das Neblinas, Bertioga, SP

This study aimed at characterizing the potential for natural regeneration of native vegetation in the under-story of an earlier Eucalyptus saligna Smith production stand. The study was carried out at the Parque das Neblinas, Bertioga municipality, SP, in a 45 ha third rotation stand; which had been abandoned 15 years ago for natural regeneration to occur. The sampling was done in 24 plots of 20 x 40 m. The sampled area was of 19,200 m(2), with inventory made of 100% of the eucalyptus trees. All regeneration trees with a height >= 1.30 m and DBH >= 5.0 cm were measured, as well as adult individuals with DBH >= 5.0 cm; surveyed in two size classes. 1,417 individuals of E. saligna were measured, with a density of 738,02 individuals/ha and a basal area of 22.69 m(2)/ha. Among 2,763 natural regeneration individuals, 111 species belonged to 66 genera and 34 botanical families. The species represented 43.7% of the tree richness of neighboring native forest fragments. The total estimated density and the basal area were respectively 1,052.6 individuals/ha and 6.4 m(2)/ha of autochthonous trees with DBH >= 5.0 cm (Class 1); while for regeneration there were 3,864.58 individuals/ha, and 2.76 m(2)/ha of individuals with a height >= 1.30 m and DBH <5.0 cm (Class 2). Shannon diversity (H`) was 2.83 and 3.68, respectively, for Classes 1 and 2, and the corrected species richness for a 1000-individual sample (R(1000)) were 75.6 and 87.29 (Fisher`s a index) for the same classes. The majority of the species (34.84%) was typical from the understory of wet tropical forest and had zoochoric fruit dispersal (67.57%). The results indicate that, under these conditions, a eucalyptus forest is able to provide adequate regeneration niches for native vegetation, and may represent a sink habitat for local populations.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Book review of Mark McGillivray and Gary Smith's (eds.) "Australia and Asia", Melbourne: Oxford University Press, 1997. vii + 248 pp

The political capital invested in Australia's engagement with Asia over the past decade has sparked a lively discussion in the Australian academic community. The back cover of the book under review suggests that there are 'few bigger contemporary issues facing Australia than its relationship with Asia'. If the volume of scholarly material being produced on this issue is any indication, they are right. Like a number of similar works covering the shift in Australian foreign, defence, and trade policies towards Asia over the last decade, this book acknowledges a particular debt of gratitude to the Keating government for establishing regional engagement at the forefront of our national consciousness. Unlike some others however, this book seeks to place Australia's more recent 'discovery' of Asia into a broader historical framework.

A new social parasite in the ant genus Ectatomma F. Smith (Hymenoptera, Formicidae, Ectatomminae)

Ectatomma parasiticum Feitosa & Fresneau, a new ant species socially parasitic on Ectatomma tuberculatum (Olivier), is described from gynes discovered in Apazapan, state of Veracruz, Mexico, and reared in the laboratory. Ectatomma parasiticum is the first social parasite described in the Ectatomminae. This species can be distinguished from its host by morphological and behavioral features characteristic of the inquilines known in other ant subfamilies including reduced size, thickened petiole, and agonistic interactions with host species.

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighboring P-donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position, and interdonor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, while the magnitude of the double occupancy probability can affect the error rate.