13,124 research outputs found
Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
We consider the problem of finding commuting self-adjoint extensions of the
partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain
C_c^\infty(\Omega) where the self-adjointness is defined relative to
L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is
Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E.
Segal and B. Fuglede, and is difficult in general. In this paper, we provide a
representation-theoretic answer in the special case when \Omega=I\times\Omega_2
and I is an open interval. We then apply the results to the case when \Omega is
a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that
{e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal
basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km,
02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt,
61.44.B
Redshift-distance Survey of Early-type Galaxies: The D_n-sigma Relation
In this paper R-band photometric and velocity dispersion measurements for a
sample of 452 elliptical and S0 galaxies in 28 clusters are used to construct a
template D_n-sigma relation. This template relation is constructed by combining
the data from the 28 clusters, under the assumption that galaxies in different
clusters have similar properties. The photometric and spectroscopic data used
consist of new as well as published measurements, converted to a common system,
as presented in a accompanying paper. The resulting direct relation, corrected
for incompleteness bias, is log{D_n} =1.203 log{sigma} + 1.406; the zero-point
has been defined by requiring distant clusters to be at rest relative to the
CMB. This zero-point is consistent with the value obtained by using the
distance to Virgo as determined by the Cepheid period-luminosity relation. This
new D_n-sigma relation leads to a peculiar velocity of -72 (\pm 189) km/s for
the Coma cluster. The scatter in the distance relation corresponds to a
distance error of about 20%, comparable to the values obtained for the
Fundamental Plane relation. Correlations between the scatter and residuals of
the D_n-sigma relation with other parameters that characterize the cluster
and/or the galaxy stellar population are also analyzed. The direct and inverse
relations presented here have been used in recent studies of the peculiar
velocity field mapped by the ENEAR all-sky sample.Comment: 46 pages, 20 figures, and 7 tables. To appear in AJ, vol. 123, no. 5,
May 200
Redshift-Distance Survey of Early-type Galaxies. I. Sample Selection, Properties and Completeness
This is the first in a series of papers describing the recently completed
all-sky redshift-distance survey of nearby early-type galaxies (ENEAR) carried
out for peculiar velocity analysis. The sample is divided into two parts and
consists of 1607 elliptical and lenticular galaxies with cz < 7000 km/s and
with blue magnitudes brighter than m_B=14.5 (ENEARm), and of galaxies in
clusters (ENEARc). Galaxy distances based on the Dn-sigma and Fundamental Plane
(FP) relations are now available for 1359 and 1107 ENEARm galaxies,
respectively, with roughly 80% based on new data gathered by our group. The
Dn-sigma and FP template distance relations are derived by combining 569 and
431 galaxies in 28 clusters, respectively, of which about 60% are based on our
new measurements. The ENEARm redshift-distance survey extends the earlier work
of the 7S and the recent Tully-Fisher surveys sampling a comparable volume. In
subsequent papers of this series we intend to use the ENEAR sample by itself or
in combination with the SFI Tully-Fisher survey to analyze the properties of
the local peculiar velocity field and to test how sensitive the results are to
different sampling and to the distance indicators. We also anticipate that the
homogeneous database assembled will be used for a variety of other applications
and serve as a benchmark for similar studies at high-redshift.Comment: 43 pages, 15 figures, submitted to the Astronomical Journa
Superconductivity and Cobalt Oxidation State in Metastable Na(x)CoO(2-delta)*yH2O (x ~ 1/3; y ~ 4x)
We report the synthesis and superconducting properties of a metastable form
of the known superconductor NaxCoO2*yH2O (x ~ 1/3, y ~ 4x). Instead of using
the conventional bromine-acetonitrile mixture for sodium deintercalation, we
use an aqueous bromine solution. Using this method, we oxidize the sample to a
point that the sodium cobaltate becomes unstable, leading to formation of other
products if not controlled. This compound has the same structure as the
reported superconductor, yet it exhibits a systematic variation of the
superconducting transition temperature (Tc) as a function of time. Immediately
after synthesis, this compound is not a superconductor, even though it contains
appropriate amounts of sodium and water. The samples become superconducting
with low Tc values after ~ 90 h. Tc continually increases until it reaches a
maximum value (4.5 K) after about 260 h. Then Tc drops drastically, becoming
non-superconducting approximately 100 h later. Corresponding time-dependent
neutron powder diffraction data shows that the changes in superconductivity
exhibited by the metastable cobaltate correspond to slow formation of oxygen
vacancies in the CoO2 layers. In effect, the formation of these defects
continually reduces the cobalt oxidation state causing the sample to evolve
through its superconducting life cycle. Thus, the dome-shaped superconducting
phase diagram is mapped as a function of cobalt oxidation state using a single
sample. The width of this dome based on the formal oxidation state of cobalt is
very narrow - approximately 0.1 valence units wide. Interestingly, the maximum
Tc in NaxCoO2*yH2O occurs when the cobalt oxidation state is near 3.5. Thus, we
speculate that the maximum Tc occurs near the charge ordered insulating state
that correlates with the average cobalt oxidation state of 3.5.Comment: 22 pages, 9 figures, 1 tabl
Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension
Let be a local ring, and let and be finitely generated
-modules such that has finite complete intersection dimension. In this
paper we define and study, under certain conditions, a pairing using the
modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand
diference. We exploit this pairing to examine the number of consecutive
vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all
. Our results recover and improve on most of the known bounds in the
literature, especially when has dimension at most two
The Star Formation Epoch of the Most Massive Early-Type Galaxies
We present new Keck spectroscopy of early-type galaxies in three galaxy
clusters at z~0.5. We focus on the fundamental plane (FP) relation, and combine
the kinematics with structural parameters determined from HST images. The
galaxies obey clear FP relations, which are offset from the FP of the nearby
Coma cluster due to passive evolution of the stellar populations. The z~0.5
data are combined with published data for 11 additional clusters at
0.18<z<1.28, to determine the evolution of the mean M/L(B) ratio of cluster
galaxies with masses M>10^11 M_sun, as implied by the FP. We find
dlog(M/L(B))/dz = -0.555+-0.042, stronger evolution than was previously
inferred from smaller samples. The observed evolution depends on the
luminosity-weighted mean age of the stars in the galaxies, the initial mass
function (IMF), selection effects due to progenitor bias, and other parameters.
Assuming a normal IMF but allowing for various other sources of uncertainty we
find z* = 2.01+-0.20 for the luminosity-weighted mean star formation epoch. The
main uncertainty is the slope of the IMF in the range 1-2 Solar masses: we find
z* = 4.0 for a top-heavy IMF with slope x=0. The M/L(B) ratios of the cluster
galaxies are compared to those of recently published samples of field
early-type galaxies at 0.32<z<1.14. Assuming that progenitor bias and the IMF
do not depend on environment we find that the present-day age of stars in
massive field galaxies is 4.1 +- 2.0 % (~0.4 Gyr) less than that of stars in
massive cluster galaxies, consistent with most, but not all, previous studies
of local and distant early-type galaxies. This relatively small age difference
is surprising in the context of expectations from ``standard'' hierarchical
galaxy formation models. [ABRIDGED]Comment: Accepted for publication in ApJ. Minor corrections to match published
versio
Tuning of magnetic and electronic states by control of oxygen content in lanthanum strontium cobaltites
We report on the magnetic, resistive, and structural studies of perovskite
LaSrCoO. By using the relation of synthesis
temperature and oxygen partial pressure to oxygen stoichiometry obtained from
thermogravimetric analysis, we have synthesized a series of samples with
precisely controlled . These samples show three structural
phases at , , , and two-phase
behavior for other oxygen contents. The stoichiometric material with
is a cubic ferromagnetic metal with the Curie temperature K. The increase of to 0.15 is followed by a linear decrease of
to 160 K and a metal-insulator transition near the
boundary of the cubic structure range. Further increase of results in
formation of a tetragonal phase for
and a brownmillerite phase for . At low
temperatures, these are weak ferromagnetic insulators (canted antiferromagnets)
with magnetic transitions at and 120 K, respectively. At
higher temperatures, the phase is -type
antiferromagnetic between 230 K and 360 K. Low temperature magnetic
properties of this system for can be described in terms of a
mixture of Co ions in the low-spin state and Co ions in the
intermediate-spin state and a possible spin transition of Co to the
intermediate-spin state above . For , there appears to
be a combination of Co and Co ions, both in the high-spin state
with dominating antiferromagnetic interactions.Comment: RevTeX, 9 pages, 7 figures, to be published in Physical Review
The Fundamental Plane of Gravitational Lens Galaxies and The Evolution of Early-Type Galaxies in Low Density Environments
Most gravitational lenses are early-type galaxies in relatively low density
environments -- a ``field'' rather than a ``cluster'' population. We show that
field early-type galaxies with 0 < z < 1, as represented by the lens galaxies,
lie on the same fundamental plane as those in rich clusters at similar
redshifts. We then use the fundamental plane to measure the combined
evolutionary and K-corrections for early-type galaxies in the V, I and H bands.
Only for passively evolving stellar populations formed at z > 2 (H_0=65 km/s
Mpc, Omega_0=0.3, Lambda_0=0.7) can the lens galaxies be matched to the local
fundamental plane. The high formation epoch and the lack of significant
differences between the field and cluster populations contradict many current
models of the formation history of early-type galaxies. Lens galaxy colors and
the fundamental plane provide good photometric redshift estimates with an
empirical accuracy of -0.03 +/- 0.11 for the 17 lenses with known redshifts. A
mass model dominated by dark matter is more consistent with the data than
either an isotropic or radially anisotropic constant M/L mass model, and a
radially anisotropic model is better than an isotropic model.Comment: 36 pages, 9 figures, 6 tables. ApJ in press. Final version contains
more observational dat
The Assembly History of Field Spheroidals: Evolution of Mass-to-light Ratios and Signatures of Recent Star Formation
We present a comprehensive catalog of high signal-to-noise spectra obtained
with the DEIMOS spectrograph on the Keck II telescope for a sample of
F850LP<22.43 (AB) field spheroidal (E+S0s; 163) and bulge dominated disk (61)
galaxies in the redshift range 0.2<z<1.2. We examine the zero point, tilt and
scatter of the Fundamental Plane (FP) as a function of redshift and
morphological properties, carefully accounting for luminosity-dependent biases
via Montecarlo simulations. The evolution of the overall FP can be represented
by a mean change in effective mass-to-light ratio given by <d \log (M/L_{\rm
B})/dz>=-0.72^{+0.07}_{-0.05}\pm0.04. However, this evolution depends
significantly on the dynamical mass, being slower for larger masses as reported
in a previous letter. In addition, we separately show the intrinsic scatter of
the FP increases with redshift as d(rms(M/L_{\rm B}))/dz=0.040\pm0.015.
Although these trends are consistent with single burst populations which formed
at for high mass spheroidals and z_{f}~1.2 for lower mass systems, a
more realistic picture is that most of the stellar mass formed in all systems
at z>2 with subsequent activity continuing to lower redshifts (z<1.2). The
fraction of stellar mass formed at recent times depend strongly on galactic
mass, ranging from <1% for masses above 10^{11.5} M_{\odot} to 20-40% below
10^{11} M_{\odot}. Independent support for recent activity is provided by
spectroscopic ([\ion{O}{2}] emission, H\delta) and photometric (blue cores and
broad-band colors) diagnostics. Via the analysis of a large sample with many
independent diagnostics, we are able to reconcile previously disparate
interpretations of the assembly history of field spheroidals. [Abridged]Comment: 26 pages including 24 figures, submitted to ApJ. Complete and compact
version with full resolution images available at
http://www.astro.ucla.edu/~ttreu/ms.pd
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