Pollination biology of Syngonanthus elegans (Eriocaulaceae - Poales)

Studies on the pollination biology of Eriocaulaceae are scarce although particularly interesting because of its inclusion in the Poales, a predominantly wind-pollinated order. The pollination biology of Syngonanthus elegans (Bong.) Ruhland was studied during two annual flowering periods to test the hypothesis that insect pollination was its primary pollination system. A field study was carried out, including observations of the morphology and biology of the flowers, insect visits and pollinator behaviour. We also evaluated seed set, seed germination and seedling development for different pollination modes. Although seeds were produced by self-pollination, pollination by small insects contributed most effectively to the reproductive success of S. elegans, resulting in the greatest seed set, with the highest germination percentage and optimum seedling vigour. The. oral resources used by flower visitors were pollen and nectar that was produced by staminate and pistillate flowers. Self-pollination played a minor role and its consequence was inbreeding depression.

Reproductive biology of six Brazilian Myrtaceae: is there a syndrome associated with buzz-pollination?

The floral phenology and reproductive biology of six sympatric arboreal Myrtaceae species were studied in the coastal plain forest (Ubatuba, Brazil, 44 degrees 48`W 23 degrees 22`S), from September 1999 to April 2002. Flowering started in the transition from the driest to the most humid season (Sep/Oct) and lasted until March. The sequence with which the species flowered each year was consistently the same. However, the timing of flowering onset, peak, end, and overlap differed from one year to another. Myrtaceae species were classified as xenogamic according to the pollen:ovule ratios, but two of them seem to present some degree of self-compatibility. Flowers of all species opened at sunrise and lasted for I day. Bombus morio (Apidae: Bombini) was the most common visitor followed by Melipona rufiventris (Apidae: Meliponini). Buzz pollination in Myrtaceae was common at the study area and seems to be related to bees` behaviour and to some aspects of flowers` morphology.

Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.