Anatomy of the floral scape of Bromeliaceae

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

Anatomia dos órgãos vegetativos e do escapo floral de Leiothrix crassifolia (Bong.) Ruhl., Eriocaulaceae, da Serra do Cipó-MG

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Anatomia do escapo floral de espécies brasileiras de Paepalanthus subgênero Platycaulon (Eriocaulaceae)

Foi estudada a anatomia dos escapos de 17 espécies de Paepalanthus subgênero Platycaulon, sendo 10 da sect. Divisi e sete da sect. Conferti. O trabalho foi realizado para caracterizar anatomicamente os escapos. como contribuição para o entendimento do grupo, uma vez que. morfologicamente, esse é o caráter laxonômico mais importante. Procurou-se, também, confirmar ou não o reconhecimento das duas seções dentro do subgênero. Para os estudos anatômicos utilizou-se material proveniente do Brasil, obtido de exsicatas de diferentes herbários e/ou coletado na Serra do Cipó, MG. Neste trabalho observou-se que Paepalanthus subg. Platycaulon é caracterizado morfologicamente por apresentar escapos pluricapitulados no ápice. Anatomicamente, as espécies estudadas da sect. Divisi apresentam escapos com vários cilindros vasculares, na região mediana e, ainda apresentam, em Paepalanthus vellozioides e P. spixianus, feixes vasculares corticais, características únicas na família. Diferentemente, as espécies avaliadas da sect. Conferti apresentam escapos com cilindro vascular único na região mediana, padrão análogo ao das demais Eriocaulaccae, e ainda apresentam, em Paepalanthus itatiaiensis, P. planifolius e P. paulensis, feixes vasculares medulares, que até então não haviam sido referidos para a família.

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Approximate analytical states of a polynomial potential: an example of symmetry restoration

An approximate analytical expression for the first two eigenvalues of the Schrodinger equation for the potential V(x) = Ax(4) + Bx(2) is achieved by using the Symanzik scaling symmetry. A kind of symmetry restoration when one of the potential parameters changes conveniently is observed. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

The symmetry group of Z(q)(n) in the Lee space and the Z(qn)-linear codes

The Z(4)-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the Z(4)-linearity to Z(q)n-linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (Z(q)(n), d(L)), as one of the most interesting spaces for coding applications. We establish the symmetry group of Z(q)(n) for any n and q by determining its isometries. We also show that there is no cyclic subgroup of order q(n) in Gamma(Z(q)(n)) acting transitively in Z(q)(n). Therefore, there exists no Z(q)n-linear code with respect to the cyclic subgroup.

D-n-forced symmetry breaking of O(2)-equivariant problems

We use singularity theory to classify forced symmetry-breaking bifurcation problemsf(z, lambda, mu) = f(1)(z, lambda) + muf(2)(z, lambda, mu) = 0,where f(1) is O(2)-equivariant and f(2) is D-n-equivariant with the orthogonal group actions on z is an element of R-2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Density-dependent coupling constants and charge symmetry breaking

The effect of the medium in the coupling constants implicate in a charge symmetry breaking on nuclear interactions. The amount of energy due to this modification can explain the Nolen-Schiffer anomaly.

Floral anatomy of Eriocaulon elichrysoides and Syngonanthus caulescens (Eriocaulaceae)

The floral anatomy of Eriocaulon elichrysoides Bong. and Syngonanthus caulescens (Poir.) Ruhland, from Brazilian mountain rock savannas (campos rupestres) was studied. The staminate flowers of E. elichrysoides present a diplostemonous androecium with six stamens, and those of S. caulescens present an isostemonous androecium with three stamens and three scalelike staminodes. Eriocaulon elichrysoides and S. caulescens have three nectariferous pistillodes located in the central portion of the receptacle. The pistillate flowers of E. elichrysoides present three simple styles while those of S. caulescens present three simple styles interspersed with three nectariferous appendices. Both the styles of E. elichrysoides and the nectariferous appendices of S. caulescens are vascularized by the dorsal vascular bundles of the carpels. The styles of S. caulescens lack vascularization. At the base of the gynoecium of E. elichrysoides there are six staminodes and there are three in the S. caulescens. Entomophily is suggested as the pollination syndrome in E. elichrysoides and S. caulescens as they present staminate and pistillate flowers with nectariferous structures. The ancestral character in Eriocaulon is probably given by the presence of the two staminal whorls. The staminate flowers of S. caulescens are probably derived from the reduction of a diplostemonous ancestral androecium. It remains open whether the pistillate flowers with nectariferous, appendices present an ancestral character or a derived one.

Floral development and embryology in the early-divergent grass Pharus

A detailed study of floral ontogeny, anatomy, and embryology in two (of six) species of Pharus is presented as part of a series of comparative investigations on early-divergent grasses. Pharus is a taxonomically isolated genus belonging to the earliest-diverging grass lineage with a true grass spikelet. It is unusual in possessing remarkably dimorphic florets: male florets possess two lodicules, six stamens, and a pistillode, whereas female florets lack lodicules entirely but possess six staminodes and a tricarpellary ovary with three stigmas. The rudimentary lodicules in male florets are initiated after the stamen whorls. There are most commonly six androecial organs, but in some florets, a five-staminate condition was observed, resulting from suppression of the abaxial stamen from the inner whorl, or even a four-staminate condition resulting from subsequent fusion of the two adaxial outer stamens (i.e., elements of both whorls). Thus, the pattern of floral zygomorphy in Pharus differs from that of many other grasses. Centrifixed anther attachment is reported for the first time in Pharus, resembling the condition in another early-divergent grass, Anomochloa, though anthers are introrse in Anomochloa compared with latrorse in Pharus. Anther wall development is of the reduced type in Pharus, in contrast to most other monocots. Microsporogenesis is of the successive type, as in many other monocots. The ovary develops from three distinct primordia and is unilocular with a single ovule and a pronounced ovary beak that is highly characteristic of Pharus. There is a hollow style, in contrast to the solid styles that are common in many other grasses. The embryo is highly differentiated, as in other grasses, with a distinct epiblast and a small cleft between the scutellum and the coleorhiza.

SOME CONSEQUENCES OF A SYMMETRY IN STRONG DISTRIBUTIONS

Some polynomials and interpolatory quadrature rules associated with strong Stieltjes distributions are considered, especially when the distributions satisfy a Certain symmetric property. (C) 1995 Academic Press, Inc.