A new genus and new species of fan worms (Polychaeta: Sabellidae) from Atlantic and Pacific Oceans-the formal treatment of taxon names as explanatory hypotheses

Members of Parasabella minuta Treadwell, 1941, subsequently moved to Perkinsiana, were collected during a survey of rocky intertidal polychaetes along the state of Sao Paulo, Brazil. Additional specimens, which are referred to two new species, were also found in similar habitats from the Bocas del Toro Archipelago, Caribbean Panama, and Oahu Island, Hawaii. A phylogenetic analysis of Sabellinae, including members of P. minuta and the two new species, provided justification for establishing a new generic hypothesis, Sabellomma gen. nov., for these individuals. Formal definitions are also provided for Sabellomma minuta gen. nov., comb. nov., S. collinae gen. nov., spec. nov., and S. harrisae gen. nov., spec. nov., along with descriptions of individuals to which these hypotheses apply. The generic name Aracia nom. nov., is provided to replace Kirkia Nogueira, Lopez and Rossi, 2004, pre-occupied by a mollusk.

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.