The Wigner function associated with the Rogers-Szego polynomials

A Wigner function associated with the Rogers-Szego polynomials is proposed and its properties are discussed. It is shown that from such a Wigner function it is possible to obtain well-behaved probability distribution functions for both angle and action variables, defined on the compact support -pi less than or equal to theta < pi, and for m greater than or equal to 0, respectively. The width of the angle probability density is governed by the free parameter q characterizing the polynomials.

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The use of the two-body energy to study problems of escape/capture Ernesto Vieira Neto1

The problem of escape/capture is encountered in many problems of the celestial mechanics -the capture of the giants planets irregular satellites, comets capture by Jupiter, and also orbital transfer between two celestial bodies as Earth and Moon. To study these problems we introduce an approach which is based on the numerical integration of a grid of initial conditions. The two-body energy of the particle relative to a celestial body defines the escape/capture. The trajectories are integrated into the past from initial conditions with negative two-body energy. The energy change from negative to positive is considered as an escape. By reversing the time, this escape turns into a capture. Using this technique we can understand many characteristics of the problem, as the maximum capture time, stable regions where the particles cannot escape from, and others. The advantage of this kind of approach is that it can be used out of plane (that is, for any inclination), and with perturbations in the dynamics of the n-body problem. © 2005 International Astronomical Union.

Revision of Nathan Banks type specimens of Bdellidae Dugès (Acari: Trombidiformes) of the Museum of Comparative Zoology, Cambridge

In this article, seven Bdellidae Dugès (Acari: Trombidiformes) of the Museum of Comparative Zoology, originally described by Nathan Banks are studied: Cyta americana (Banks, 1902), Bdella tenella Banks, 1896, Bdella utilis Banks, 1914, Bdella californica Banks, 1904, Bdella cardinalis Banks, 1894, Bdella peregrina Banks, 1894 and Bdella brevitarsis Banks. Bdella tenella and Bdella californica are transferred to the genera Spinibdella and Bdellodes, respectively. Bdella brevitarsis, previously a nomen nudum, is herein described for the first time under the genus Hexabdella. http://zoobank.org/urn:lsid: zoobank.org:pub:A18C8C10-8C8A-4873-AF0B-D1A9164CD7E8 © 2013 Copyright 2013 Taylor & Francis.