10,041 research outputs found
Construction of Parseval wavelets from redundant filter systems
We consider wavelets in L^2(R^d) which have generalized multiresolutions.
This means that the initial resolution subspace V_0 in L^2(R^d) is not singly
generated. As a result, the representation of the integer lattice Z^d
restricted to V_0 has a nontrivial multiplicity function. We show how the
corresponding analysis and synthesis for these wavelets can be understood in
terms of unitary-matrix-valued functions on a torus acting on a certain vector
bundle. Specifically, we show how the wavelet functions on R^d can be
constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos
in Sections 1 and 4, v3 adds a number of references on GMRA theory and
wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and
two more reference
Harmonic analysis of iterated function systems with overlap
In this paper we extend previous work on IFSs without overlap. Our method
involves systems of operators generalizing the more familiar Cuntz relations
from operator algebra theory, and from subband filter operators in signal
processing.Comment: 37 page
Forming Galaxies with MOND
Beginning with a simple model for the growth of structure, I consider the
dissipationless evolution of a MOND-dominated region in an expanding Universe
by means of a spherically symmetric N-body code. I demonstrate that the final
virialized objects resemble elliptical galaxies with well-defined relationships
between the mass, radius, and velocity dispersion. These calculations suggest
that, in the context of MOND, massive elliptical galaxies may be formed early
(z > 10) as a result of monolithic dissipationless collapse. Then I reconsider
the classic argument that a galaxy of stars results from cooling and
fragmentation of a gas cloud on a time scale shorter than that of dynamical
collapse. Qualitatively, the results are similar to that of the traditional
picture; moreover, the existence, in MOND, of a density-temperature relation
for virialized, near isothermal objects as well as a mass-temperature relation
implies that there is a definite limit to the mass of a gas cloud where this
condition can be met-- an upper limit corresponding to that of presently
observed massive galaxies.Comment: 9 pages, 9 figures, revised in response to comments of referee. Table
added, extended discussion, accepted MNRA
Saddle-point van Hove singularity and the phase diagram of high-Tc cuprates
We examine the generic phase behavior of high-Tc cuprate superconductors in
terms a universal van Hove singularity in the strongly overdoped region. Using
a rigid ARPES-derived dispersion we solve the BCS gap equation and show that
the pairing interaction or pairing energy cutoff must be a rapidly declining
function of doping. This result is prejudicial to a phonon-based pairing
interaction and more consistent with a magnetic or magnetically enhanced
interaction.Comment: 5 pages, 2 figures, submitted to Physical Review
Negative thermal expansion of MgB in the superconducting state and anomalous behavior of the bulk Gr\"uneisen function
The thermal expansion coefficient of MgB is revealed to change
from positive to negative on cooling through the superconducting transition
temperature . The Gr\"uneisen function also becomes negative at
followed by a dramatic increase to large positive values at low temperature.
The results suggest anomalous coupling between superconducting electrons and
low-energy phonons.Comment: 5 figures. submitted to Phys. Rev. Let
The Mystery Deepens: Spitzer Observations of Cool White Dwarfs
We present 4.5m and 8m photometric observations of 18 cool white
dwarfs obtained with the Spitzer Space Telescope. Our observations demonstrate
that four white dwarfs with T_eff< 6000 K show slightly depressed mid-infrared
fluxes relative to white dwarf models. In addition, another white dwarf with a
peculiar optical and near-infrared spectral energy distribution (LHS 1126) is
found to display significant flux deficits in Spitzer observations. These
mid-infrared flux deficits are not predicted by the current white dwarf models
including collision induced absorption due to molecular hydrogen. We postulate
that either the collision induced absorption calculations are incomplete or
there are other unrecognized physical processes occuring in cool white dwarf
atmospheres. The spectral energy distribution of LHS 1126 surprisingly fits a
Rayleigh-Jeans spectrum in the infrared, mimicking a hot white dwarf with
effective temperature well in excess of 10 K. This implies that the source
of this flux deficit is probably not molecular absorption but some other
process.Comment: 17 pages, 4 figures, ApJ in press, 10 May 200
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