Preliminary observations on the use of a frame trawl in hydroacoustic surveys

Thirteen hauls were made during the hydroacoustic survey of the Ugandan waters of Lake Victoria from 7-19 February 1999. Ten of the hauls were made above the oxycline which was clearly visible as a strong echo on the echogram at between 25 and 35 m depth in most of the sampled areas. The remaining three hauls targeted the oxycline. Approximate equal weights of Rastrineobola argentia and Haplocromine cichlids were caught in total, but with marked differences between hauls. Near the surface R. argentia dominated the catches. In midwater Haplochromines were dominant. At the oxycline Caridina niloticus was abundan

On the Deuring Polynomial for Drinfeld Modules in Legendre Form

We study a family $\psi^{\lambda}$ of $\mathbb F_q[T]$-Drinfeld modules, which is a natural analog of Legendre elliptic curves. We then find a surprising recurrence giving the corresponding Deuring polynomial $H_{p(T)}(\lambda)$ characterising supersingular Legendre Drinfeld modules $\psi^{\lambda}$ in characteristic $p(T)$.Comment: This article supersedes arXiv:1110.607

Good families of Drinfeld modular curves

In this paper we investigate examples of good and optimal Drinfeld modular towers of function fields. Surprisingly, the optimality of these towers has not been investigated in full detail in the literature. We also give an algorithmic approach on how to obtain explicit defining equations for some of these towers and in particular give a new explicit example of an optimal tower over a quadratic finite field

A complete characterization of Galois subfields of the generalized Giulietti--Korchm\'aros function field

We give a complete characterization of all Galois subfields of the generalized Giulietti--Korchm\'aros function fields \mathcal C_n / \fqn for $n\ge 5$. Calculating the genera of the corresponding fixed fields, we find new additions to the list of known genera of maximal function fields

A new tower over cubic finite fields

We present a new explicit tower of function fields (Fn)n≥0 over the finite field with ` = q3 elements, where the limit of the ratios (number of rational places of Fn)/(genus of Fn) is bigger or equal to 2(q2 − 1)/(q + 2). This tower contains as a subtower the tower which was introduced by Bezerra– Garcia–Stichtenoth (see [3]), and in the particular case q = 2 it coincides with the tower of van der Geer–van der Vlugt (see [12]). Many features of the new tower are very similar to those of the optimal wild tower in [8] over the quadratic field Fq2 (whose modularity was shown in [6] by Elkies).

Detection of the radial velocity curve of the B5-A0 supergiant companion star of Cir X-1?

In this Paper we report on phase resolved I-band optical spectroscopic and photometric observations of CirX-1 obtained with the Very Large Telescope. The spectra are dominated by Paschen absorption lines at nearly all orbital phases except near phase zero (coinciding with the X-ray dip) when the absorption lines are filled-in by broad Paschen emission lines. The radial velocity curve of the absorption lines corresponds to an eccentric orbit (e=0.45) whose period and time of periastron passage are consistent with the period and phase predicted by the most recent X-ray dip ephemeris. We found that the I-band magnitude decreases from 17.6 to ~16.8 near phase 0.9-1.0, this brightening coincides in phase with the X-ray dip. Even though it is likely that the absorption line spectrum is associated with the companion star of CirX-1, we cannot exclude the possibility that the spectrum originates in the accretion disc. However, if the spectrum belongs to the companion star, it must be a supergiant of spectral type B5-A0. If we assume that the compact object does not move through the companion star at periastron, the companion star mass is constrained to ~<10 Msun for a 1.4 Msun neutron star, whereas the inclination has to be ~> 13.7 degrees. Alternatively, the measured absorption lines and their radial velocity curve can be associated with the accretion disc surrounding a 1.4 Msun neutron star and its motion around the centre of mass. An absorption line spectrum from an accretion disc is typically found when our line-of-sight passes through the accretion disc rim implying a high inclination. However, from radio observations it was found that the angle between the line-of-sight and the jet axis is smaller than 5 degrees implying that the jet ploughs through the accretion disc in this scenario.Comment: 8 pages, 4 figures, 3 tables, accepted by MNRA

Towers of Function Fields over Non-prime Finite Fields

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara's quantity $A(\ell)$, for $\ell = p^n$ with $p$ prime and $n>3$ odd. We relate the explicit equations to Drinfeld modular varieties