A control theorem for pp-adic automorphic forms and Teitelbaum's L\mathcal{L}-invariant

In this article, we describe an efficient method for computing Teitelbaum's $p$-adic $\mathcal{L}$-invariant. These invariants are realized as the eigenvalues of the $\mathcal{L}$-operator acting on a space of harmonic cocycles on the Bruhat-Tits tree $\mathcal{T}$, which is computable by the methods of Franc and Masdeu described in \cite{fm}. The main difficulty in computing the $\mathcal{L}$-operator is the efficient computation of the $p$-adic Coleman integrals in its definition. To solve this problem, we use overconvergent methods, first developed by Darmon, Greenberg, Pollack and Stevens. In order to make these methods applicable to our setting, we prove a control theorem for $p$-adic automorphic forms of arbitrary even weight. Moreover, we give computational evidence for relations between slopes of $\mathcal{L}$-invariants of different levels and weights for $p=2$.Comment: 26 page

Eccentric discs in binaries with intermediate mass ratios: Superhumps in the VY Sculptoris stars

We investigate the role of the eccentric disc resonance in systems with mass ratios q greater than 1/4, and demonstrate the effects that changes in the mass flux from the secondary star have upon the disc radius and structure. The addition of material with low specific angular momentum to its outer edge restricts a disc radially. Should the mass flux from the secondary be reduced, it is possible for the disc in a system with mass ratio as large as 1/3 to expand to the 3:1 eccentric inner Lindblad resonance and for superhumps to be excited.Comment: 6 pages with 7 figures, accepted by MNRA

Construction and Application of Log-linear Models to Assess Academic Performance

Log-Linear Models (LLMs) are important techniques used in categorical data analysis. Though there are some available published work about LLMs, the explanation of model building process and the theoretical background are not adequate. Furthermore, research about the application of the LLM theory and the selection procedure of the best model are handful. Therefore, this manuscript aims to fill that vacuum. At first, the construction of LLM and Hierarchical Log-Linear Models (HLLMs), a branch of LLMs are discussed in connection with both 2×2 and 2×2 ×2 contingency tables. Secondly, an application is presented to analyze the collected data set about the academic performance of elementary students. The manuscript also discusses the criteria to select the best model that fits the collected data

The effects of tidally induced disc structure on white dwarf accretion in intermediate polars

We investigate the effects of tidally induced asymmetric disc structure on accretion onto the white dwarf in intermediate polars. Using numerical simulation, we show that it is possible for tidally induced spiral waves to propagate sufficiently far into the disc of an intermediate polar that accretion onto the central white dwarf could be modulated as a result. We suggest that accretion from the resulting asymmetric inner disc may contribute to the observed X-ray and optical periodicities in the light curves of these systems. In contrast to the stream-fed accretion model for these periodicities, the tidal picture predicts that modulation can exist even for systems with weaker magnetic fields where the magnetospheric radius is smaller than the radius of periastron of the mass transfer stream. We also predict that additional periodic components should exist in the emission from low mass ratio intermediate polars displaying superhumps.Comment: 9 pages, 5 figures, accepted for publication in MNRA

WD1953-011 - a magnetic white dwarf with peculiar field structure

We present H-alpha spectra of the magnetic white dwarf star WD1953-011 which confirm the presence of the broad Zeeman components corresponding to a field strength of about 500kG found by Maxted & Marsh (1999). We also find that the line profile is variable over a timescale of a day or less. The core of the H-alpha line also shows a narrow Zeeman triplet corresponding to a field strength of of about 100kG which appears to be almost constant in shape. These observations suggest that the magnetic field on WD1953-011 has a complex structure and that the star has a rotational period of hours or days which causes the observed variability of the spectra. We argue that neither an offset dipole model nor a double-dipole model are sufficient to explain our observations. Instead, we propose a two component model consisting of a high field region of magnetic field strength of about 500kG covering about 10% of the surface area of the star superimposed on an underlying dipolar field of mean field strength of about 70kG. Radial velocity measurements of the narrow Zeeman triplet show that the radial velocity is constant to within a few km/s so this star is unlikely to be a close binary.Comment: Accpeted for publication in MNRAS. 4 pages, 2 figure

Level correlations in integrable systems

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger scales. We apply our results to a rectangle with incommensurate sides and show that they are in excellent agreement with the limiting cases established in the semiclassical theory of level rigidity.Comment: 5 page

The Detection of Cold Dust in Cas A: Evidence for the Formation of Metallic Needles in the Ejecta

Recently, Dunne et al. (2003) obtained 450 and 850 micron SCUBA images of CasA, and reported the detection of 2-4 M_sun of cold, 18K, dust in the remnant. Here we show that their interpretation of the observations faces serious difficulties. Their inferred dust mass is larger than the mass of refractory material in the ejecta of a 10 to 30 M_sun star. The cold dust model faces even more difficulties if the 170 micron observations of the remnant are included in the analysis, decreasing the cold dust temperature to ~ 8K, and increasing its mass to > 20 M_sun. We offer here a more plausible interpretation of their observation, in which the cold dust emission is generated by conducting needles with properties that are completely determined by the combined submillimeter and X-ray observations of the remnant. The needles consist of metallic whiskers with <1% of embedded impurities that may have condensed out of blobs of material that were expelled at high velocities from the inner metal-rich layers of the star in an asymmetric explosion. The needles are collisionally heated by the shocked gas to a temperature of 8K. Taking the destruction of needles into account, a dust mass of only 1E-4 to 1E-3M_sun is needed to account for the observed SCUBA emission. Aligned in the magnetic field, needles may give rise to observable polarized emission. The detection of submillimeter polarization will therefore offer definitive proof for a needle origin for the cold dust emission. Supernovae may still be proven to be important sources of interstellar dust, but the evidence is still inconclusive.Comment: 18 pages including 4 figures. Accepted for publication in the ApJ. Missing reference adde