A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions

This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained

Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of the global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page

Solution of the Cauchy Problem for a Time-Dependent Schoedinger Equation

We construct an explicit solution of the Cauchy initial value problem for the n-dimensional Schroedinger equation with certain time-dependent Hamiltonian operator of a modified oscillator. The dynamical SU(1,1) symmetry of the harmonic oscillator wave functions, Bargmann's functions for the discrete positive series of the irreducible representations of this group, the Fourier integral of a weighted product of the Meixner-Pollaczek polynomials, a Hankel-type integral transform and the hyperspherical harmonics are utilized in order to derive the corresponding Green function. It is then generalized to a case of the forced modified oscillator. The propagators for two models of the relativistic oscillator are also found. An expansion formula of a plane wave in terms of the hyperspherical harmonics and solution of certain infinite system of ordinary differential equations are derived as a by-product.Comment: 29 pages, 4 figure

Echinuria uncinata (Rudolphi) (Nematoda, Acuariidae) in Netta peposaca (Vieillot) (Aves, Anatidae) in South America

This is the first report of a species of Echinuria Soloviev, 1912, on anatid hosts in South America, causing granulomas. It is also the first detailed description and record of a species of Echinuria, for South America in the Rosy-billed Pochard, Netta peposaca (Vieillot, 1816). Fifty-two rosy-billed pochards were examined for helminths in the Municipalities of Santa Vitória do Palmar (locality of Fazenda Sossego) and (locality of Ponta da Antena), State of Rio Grande do Sul, Brazil, and Alvear, Province of Corrientes, northern Argentina. Samples were obtained from 2003 to 2004. After the catch each bird was immediately frozen with dry ice. Prior to necropsy birds were sexed, weighted, measured, and the state of maturity (juvenile or adult) determined, based on the presence or absence of a bursa of Fabricius. The granulomas with the nematodes were found in the proximal esophagus at the junction with the proventriculus. Two birds had one (fistulated) and two granulomas, respectively. One of the birds was from the wintering grounds along the coastal region in the State of Rio Grande do Sul, southern Brazil. The other, from one of the breeding grounds in northern Argentina, was captured before the trip to the wintering grounds along the migratory flyway. Prevalence was 3.8% while the mean intensity of infection was 7.2. Morphometry of males and females and the comparison with previous descriptions and illustrations allowed the identification of the present specimens as E. uncinata.<br>Este é o primeiro registro de uma espécie do gênero Echinuria Soloviev, 1912, em hospedeiros anatídeos na América do Sul, causando granulomas. É, também, a primeira descrição detalhada e o primeiro registro de Echinuria uncinata (Rudolphi, 1819) Soloviev, 1912, para a América do Sul, e o primeiro registro de um nematóide acuarióideo em Netta peposaca (Vieillot, 1816). Cinqüenta e dois marrecões foram examinados para helmintos nas localidades de Fazenda Sossego e Ponta da Antena, Município de Santa Vitória do Palmar, Estado do Rio Grande do Sul, região Sul do Brasil e Alvear, Província de Corrientes, região Norte da Argentina. As amostras foram obtidas no período de 2003 a 2004. Imediatamente após o abate, cada ave foi congelada em gelo seco. As aves foram separadas por sexo, pesadas e medidas. O estado de maturidade de cada ave foi avaliado (juvenil ou adulto) com base na presença ou ausência da bolsa de Fabricius. Os granulomas, contendo os nematóides, estavam situados na base do esôfago quase junto à junção com o proventrículo. Duas aves estavam positivas, com um (fistulado) e dois granulomas, respectivamente. Uma das aves era proveniente do Brasil (pólo de invernia na planície costeira do Estado do Rio Grande do Sul). A outra da região Norte da Argentina, capturada em um dos pólos de nidificação, antes de empreender sua viagem em direção à costa brasileira ao longo de sua rota de migração. A prevalência da infecção foi de 3,8% e a intensidade média de infecção de 7,2. A morfometria de machos e de fêmeas permitiu a identificação dos espécimes como E. uncinata