1,494 research outputs found
A control theorem for -adic automorphic forms and Teitelbaum's -invariant
In this article, we describe an efficient method for computing Teitelbaum's
-adic -invariant. These invariants are realized as the
eigenvalues of the -operator acting on a space of harmonic
cocycles on the Bruhat-Tits tree , which is computable by the
methods of Franc and Masdeu described in \cite{fm}. The main difficulty in
computing the -operator is the efficient computation of the
-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 -adic automorphic forms of arbitrary even weight.
Moreover, we give computational evidence for relations between slopes of
-invariants of different levels and weights for .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 2Ă—2 and 2Ă—2 Ă—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.
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