498 research outputs found
The Ore condition, affiliated operators, and the lamplighter group
Let G be the wreath product of Z and Z/2, the so called lamplighter group and
k a commutative ring. We show that kG does not have a classical ring of
quotients (i.e. does not satisfy the Ore condition). This answers a Kourovka
notebook problem. Assume that kG is contained in a ring R in which the element
1-x is invertible, with x a generator of Z considered as subset of G. Then R is
not flat over kG. If k is the field of complex numbers, this applies in
particular to the algebra UG of unbounded operators affiliated to the group von
Neumann algebra of G. We present two proofs of these results. The second one is
due to Warren Dicks, who, having seen our argument, found a much simpler and
more elementary proof, which at the same time yielded a more general result
than we had originally proved. Nevertheless, we present both proofs here, in
the hope that the original arguments might be of use in some other context not
yet known to us.Comment: LaTex2e, 7 pages. Added a new proof of the main result (due to Warren
Dicks) which is shorter, easier and more elementary, and at the same time
yields a slightly more general result. Additionally: misprints removed. to
appear in Proceedings of "Higher dimensional manifold theory", Conference at
ICTP Trieste 200
The anomalous accretion disk of the Cataclysmic Variable RW Sextantis
Synthetic spectra covering the wavelength range 900\AA~to 3000\AA~provide an
accurate fit, established by a analysis, to a combined
observed spectrum of RW Sextantis. Two separately calibrated distances to the
system establish the synthetic spectrum comparison on an absolute flux basis
but with two alternative scaling factors, requiring alternative values of
for final models. Based on comparisons for a range of
values, the observed spectrum does not follow the standard model. Rather than
the exponent 0.25 in the expression for the radial temperature profile, a value
close to 0.125 produces a synthetic spectrum with an accurate fit to the
combined spectrum. A study of time-series spectra shows that a proposed
warped or tilted disk is not supported by the data; an alternative proposal is
that an observed non-axisymmetric wind results from an interaction with the
mass transfer stream debris.Comment: 56 pages, 15 figures, 11 tables. Accepted for The Astrophysical
Journa
On a conjecture of Atiyah
In this note we explain how the computation of the spectrum of the
lamplighter group from \cite{Grigorchuk-Zuk(2000)} yields a counterexample to a
strong version of the Atiyah conjectures about the range of -Betti numbers
of closed manifolds.Comment: 8 pages, A4 pape
The anomalous accretion disk of the Cataclysmic Variable RW Sextantis
Synthetic spectra covering the wavelength range 900\AA~to 3000\AA~provide an
accurate fit, established by a analysis, to a combined
observed spectrum of RW Sextantis. Two separately calibrated distances to the
system establish the synthetic spectrum comparison on an absolute flux basis
but with two alternative scaling factors, requiring alternative values of
for final models. Based on comparisons for a range of
values, the observed spectrum does not follow the standard model. Rather than
the exponent 0.25 in the expression for the radial temperature profile, a value
close to 0.125 produces a synthetic spectrum with an accurate fit to the
combined spectrum. A study of time-series spectra shows that a proposed
warped or tilted disk is not supported by the data; an alternative proposal is
that an observed non-axisymmetric wind results from an interaction with the
mass transfer stream debris.Comment: 56 pages, 15 figures, 11 tables. Accepted for The Astrophysical
Journa
On Turing dynamical systems and the Atiyah problem
Main theorems of the article concern the problem of M. Atiyah on possible
values of l^2-Betti numbers. It is shown that all non-negative real numbers are
l^2-Betti numbers, and that "many" (for example all non-negative algebraic)
real numbers are l^2-Betti numbers of simply connected manifolds with respect
to a free cocompact action. Also an explicit example is constructed which leads
to a simply connected manifold with a transcendental l^2-Betti number with
respect to an action of the threefold direct product of the lamplighter group
Z/2 wr Z. The main new idea is embedding Turing machines into integral group
rings. The main tool developed generalizes known techniques of spectral
computations for certain random walk operators to arbitrary operators in
groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio
GALEX and Optical Light Curves of WX LMi, SDSSJ103100.5+202832.2 and SDSSJ121209.31+013627.7
{\it GALEX} near ultraviolet (NUV) and far-ultraviolet (FUV) light curves of
three extremely low accretion rate polars show distinct modulations in their UV
light curves. While these three systems have a range of magnetic fields from 13
to 70 MG, and of late type secondaries (including a likely brown dwarf in
SDSSJ121209.31+013627.7), the accretion rates are similar, and the UV
observations imply some mechanism is operating to create enhanced emission
zones on the white dwarf. The UV variations match in phase to the two magnetic
poles viewed in the optical in WX LMi and to the single poles evident in the
optical in SDSSJ1212109.31+013627.7 and SDSSJ103100.55+202832.2. Simple spot
models of the UV light curves show that if hot spots are responsible for the UV
variations, the temperatures are on the order of 10,000-14,000K. For the single
pole systems, the size of the FUV spot must be smaller than the NUV and in all
cases, the geometry is likely more complicated than a simple circular spot.Comment: 29 pages, 4 tables, 10 figures, Astrophysical Journal, accepte
MR Cygni revisited
New analysis tools and additional unanalyzed observations justify a reanalysis of MR Cygni. The reanalysis applied successively more restrictive physical models, each with an optimization program. The final model assigned separate first and second order limb darkening coefficients, from model atmospheres, to individual grid points. Proper operation of the optimization procedure was tested on simulated observational data, produced by light synthesis with assigned system parameters, and modulated by simulated observational error. The iterative solution converged to a weakly-determined mass ratio of 0.75. Assuming the B3 primary component is on the main sequence, the HR diagram location of the secondary from the light ratio (ordinate) and adjusted T sub eff (abscissa) was calculated. The derived mass ratio, together with a main-sequence mass for the B3 component, implies a main-sequence secondary spectral type of B4. The photometrically-determined secondary radii agree with this spectral type, in marginal disagreement with the B7 type from the HR diagram analysis. The individual masses, derived from the radial velocity curve of the primary component, the photometrically-determined i, and alternative values of derived mass ratio are seriously discrepant with main sequence objects. The imputed physical status of the system is in disagreement with representations that have appeared in the literature
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