2,401 research outputs found
Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type
The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by
F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of
functions that satisfy the Dirichlet boundary conditions and whose derivatives
are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into
manifolds of codimension 1 in X. If f''0, the set C_j is shown to be
non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the
range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure
Interpreting the eH Stretching Region, Through Infrared Partial Deuteration Studies
Information derived from a study of \u27isolated\u27 CH stretching
frequencies, measured in partially deuterated organic and organemetallic compounds, is reviewed. This includes CH bond lengths and dissociation energies, and HCH angles in methyl groups, Excellent agreement is found between CH bond length differences predicted from VCH\u27s values and those calculated by ab initio methods. V\u27sCH data also agree with the results of high overtone, local mode studies in distinguishing differences in CH bond strengths. The former however are based on spectra which are easier to assign
to specific bonds. They also enable one to understand the spectra
of normal, undeuterated molecules in the CH stretching region,
through \u27energy factored force field\u27 calculations. Reference is made to situations involvlng free internal rotation of methyl groups, and to studies of other \u27isolated\u27 MH bonds (M = N, Si, Ge, Sn)
A novel search for gravitationally lensed radio sources in wide-field VLBI imaging from the mJIVE-20 survey
We present a novel pilot search for gravitational lenses in the mJIVE-20
survey, which observed radio sources selected from FIRST with the
VLBA at an angular resolution of 5 mas. We have taken the visibility data for
an initial sources that were detected by the mJIVE-20 observations and
re-mapped them to make wide-field images, selecting fourteen sources that had
multiple components separated by mas, with a flux-ratio of
: and a surface brightness consistent with gravitational lensing.
Two of these candidates are re-discoveries of gravitational lenses found as
part of CLASS. The remaining twelve candidates were then re-observed at 1.4 GHz
and then simultaneously at 4.1 and 7.1 GHz with the VLBA to measure the
spectral index and surface brightness of the individual components as a
function of frequency. Ten were rejected as core-jet or core-hotspot(s)
systems, with surface brightness distributions and/or spectral indices
inconsistent with gravitational lensing, and one was rejected after lens
modelling demonstrated that the candidate lensed images failed the parity test.
The final lens candidate has an image configuration that is consistent with a
simple lens mass model, although further observations are required to confirm
the lensing nature. Given the two confirmed gravitational lenses in the
mJIVE-20 sample, we find a robust lensing-rate of :() for a
statistical sample of 635 radio sources detected on mas-scales, which is
consistent with that found for CLASS.Comment: 31 pages, 22 figures; accepted for publication in MNRA
Mass along the Line of Sight to the Gravitational Lens B1608+656: Galaxy Groups and Implications for H_0
We report the discovery of four groups of galaxies along the line of sight to the B1608+656 gravitational lens system. One group is at the redshift of the primary lensing galaxy (z = 0.631) and appears to have a low mass, with eight spectroscopically confirmed members and an estimated velocity dispersion of 150 ± 60 km s^(-1). The three other groups are in the foreground of the lens. These groups contain ~10 confirmed members each and are located at redshifts of 0.265, 0.426, and 0.52. Two of the three additional groups are centered roughly on the lens system, while the third is centered ~1' south of the lens. We investigate the effect of each of the four groups on the gravitational lensing potential of the B1608+656 system, with a particular focus on the implications for the value of H_0 derived from this system. We find that each group provides an external convergence of ~0.005-0.060, depending on the assumptions made in the calculation. For the B1608+656 system, the stellar velocity dispersion of the lensing galaxy has been measured, thus breaking the mass sheet degeneracy due to the group that is physically associated with the lens. The effect of the other groups along the line of sight can be folded into the overall uncertainties due to large-scale structure (LSS) along the line of sight. Because B1608+656 appears to lie along an overdense line of sight, the LSS will cause the measurement of H_0 to be biased high for this system. This effect could be 5% or greater
2-D constrained Navier-Stokes equation and intermediate asymptotics
We introduce a modified version of the two-dimensional Navier-Stokes
equation, preserving energy and momentum of inertia, which is motivated by the
occurrence of different dissipation time scales and related to the gradient
flow structure of the 2-D Navier-Stokes equation. The hope is to understand
intermediate asymptotics. The analysis we present here is purely formal. A
rigorous study of this equation will be done in a forthcoming paper
The Cosmic Lens All-Sky Survey parent population - I. Sample selection and number counts
We present the selection of the Jodrell Bank Flat-spectrum (JBF) radio source
sample, which is designed to reduce the uncertainties in the Cosmic Lens
All-Sky Survey (CLASS) gravitational lensing statistics arising from the lack
of knowledge about the parent population luminosity function. From observations
at 4.86 GHz with the Very Large Array, we have selected a sample of 117
flat-spectrum radio sources with flux densities greater than 5 mJy. These
sources were selected in a similar manner to the CLASS complete sample and are
therefore representative of the parent population at low flux densities. The
vast majority (~90 per cent) of the JBF sample are found to be compact on the
arcsecond scales probed here and show little evidence of any extended radio jet
emission. Using the JBF and CLASS complete samples we find the differential
number counts slope of the parent population above and below the CLASS 30 mJy
flux density limit to be -2.07+/-0.02 and -1.96+/-0.12, respectively.Comment: 10 pages, 4 figures, accepted for publication in MNRA
Economy of Albany, Carbon, and Sweetwater counties, Wyoming, The: description and analysis
Submitted to U.S. Dept. of Interior, Bureau of Land Management, Colorado State Office, Denver, Colorado.Bibliography: pages 74-76.Contract no. YA-510-PH8-57
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