30,045,452 research outputs found
The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field
Let k be a global field and let k_v be the completion of k with respect to v,
a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected
algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let
G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma)
be its congruence kernel. Lubotzky has shown that C is infinite, confirming an
earlier conjecture of Serre. Here we provide complete solution of the
congruence subgroup problem for \Gamm$ by determining the structure of C. It is
shown that C is a free profinite product, one of whose factors is
\hat{F}_{\omega}, the free profinite group on countably many generators. The
most surprising conclusion from our results is that the structure of C depends
only on the characteristic of k. The structure of C is already known for a
number of special cases. Perhaps the most important of these is the
(non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the
ring of S-integers in k, with S=\{v\}, which plays a central role in the theory
of Drinfeld modules. The proof makes use of a decomposition theorem of
Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated
with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat
Hardness of Exact Distance Queries in Sparse Graphs Through Hub Labeling
A distance labeling scheme is an assignment of bit-labels to the vertices of
an undirected, unweighted graph such that the distance between any pair of
vertices can be decoded solely from their labels. An important class of
distance labeling schemes is that of hub labelings, where a node
stores its distance to the so-called hubs , chosen so that for
any there is belonging to some shortest
path. Notice that for most existing graph classes, the best distance labelling
constructions existing use at some point a hub labeling scheme at least as a
key building block. Our interest lies in hub labelings of sparse graphs, i.e.,
those with , for which we show a lowerbound of
for the average size of the hubsets.
Additionally, we show a hub-labeling construction for sparse graphs of average
size for some , where is the
so-called Ruzsa-Szemer{\'e}di function, linked to structure of induced
matchings in dense graphs. This implies that further improving the lower bound
on hub labeling size to would require a
breakthrough in the study of lower bounds on , which have resisted
substantial improvement in the last 70 years. For general distance labeling of
sparse graphs, we show a lowerbound of , where is the communication complexity of the
Sum-Index problem over . Our results suggest that the best achievable
hub-label size and distance-label size in sparse graphs may be
for some
Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+
We perform amplitude analyses of the decays , , and , and measure CP-violating
parameters and partial branching fractions. The results are based on a data
sample of approximately decays, collected with the
BABAR detector at the PEP-II asymmetric-energy factory at the SLAC National
Accelerator Laboratory. For , we find a direct CP asymmetry
in of , which differs
from zero by . For , we measure the
CP-violating phase .
For , we measure an overall direct CP asymmetry of
. We also perform an angular-moment analysis of
the three channels, and determine that the state can be described
well by the sum of the resonances , , and
.Comment: 35 pages, 68 postscript figures. v3 - minor modifications to agree
with published versio
The assembly of massive galaxies from NIR observations of the Hubble Deep Field South
We use a deep K(AB)<25 galaxy sample in the Hubble Deep Field South to trace
the evolution of the cosmological stellar mass density from z~ 0.5 to z~3. We
find clear evidence for a decrease of the average stellar mass density at high
redshift, 2<z<3.2, that is 15^{+25}_{-5}% of the local value, two times higher
than what observed in the Hubble Deep Field North. To take into account for the
selection effects, we define a homogeneous subsample of galaxies with
10^{10}M_\odot \leq M_* \leq 10^{11}M_\odot: in this sample, the mass density
at z>2 is 20^{+20}_{-5} % of the local value. In the mass--limited subsample at
z>2, the fraction of passively fading galaxies is at most 25%, although they
can contribute up to about 40% of the stellar mass density. On the other hand,
star--forming galaxies at z>2 form stars with an average specific rate at least
~4 x10^{-10} yr, 3 times higher than the z<~1 value. This
implies that UV bright star--forming galaxies are substancial contributors to
the rise of the stellar mass density with cosmic time. Although these results
are globally consistent with --CDM scenarios, the present rendition of
semi analytic models fails to match the stellar mass density produced by more
massive galaxies present at z>2.Comment: Accepted for publication on ApJLetter
SDSS IV MaNGA - Rotation Velocity Lags in the Extraplanar Ionized Gas from MaNGA Observations of Edge-on Galaxies
We present a study of the kinematics of the extraplanar ionized gas around
several dozen galaxies observed by the Mapping of Nearby Galaxies at the Apache
Point Observatory (MaNGA) survey. We considered a sample of 67 edge-on galaxies
out of more than 1400 extragalactic targets observed by MaNGA, in which we
found 25 galaxies (or 37%) with regular lagging of the rotation curve at large
distances from the galactic midplane. We model the observed emission
velocity fields in the galaxies, taking projection effects and a simple model
for the dust extinction into the account. We show that the vertical lag of the
rotation curve is necessary in the modeling, and estimate the lag amplitude in
the galaxies. We find no correlation between the lag and the star formation
rate in the galaxies. At the same time, we report a correlation between the lag
and the galactic stellar mass, central stellar velocity dispersion, and axial
ratio of the light distribution. These correlations suggest a possible higher
ratio of infalling-to-local gas in early-type disk galaxies or a connection
between lags and the possible presence of hot gaseous halos, which may be more
prevalent in more massive galaxies. These results again demonstrate that
observations of extraplanar gas can serve as a potential probe for accretion of
gas.Comment: 13 pages, 11 figures, accepted for publication in Ap
Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set
We report a measurement of the bottom-strange meson mixing phase \beta_s
using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays
in which the quark-flavor content of the bottom-strange meson is identified at
production. This measurement uses the full data set of proton-antiproton
collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment
at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity.
We report confidence regions in the two-dimensional space of \beta_s and the
B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2,
-1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in
agreement with the standard model expectation. Assuming the standard model
value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +-
0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +-
0.009 (syst) ps, which are consistent and competitive with determinations by
other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012
Tau and Charm physics highlights
In tau physics, we are at the frontier between the completion of the LEP
program and the start of analyses from b-factories, which are expected to
produce results in the coming years. Nice results from CLEO are steadily
delivered in the meantime. For charm, impressive progress have been achieved by
fixed target experiments in the search for CP violation and D^0 - \bar D^0
oscillations. First results from b-factories demonstrate the power of these
facilities in such areas. The novel measurement of the D* width by CLEO happens
to be rather different from current expectations. The absence of a charm
factory explains the lack or the very slow progress in the absolute scale
determinations for charm decays.Comment: "Typos corrected and references added
On First-Order Generalized Maxwell Equations
The generalized Maxwell equations including an additional scalar field are
considered in the first-order formalism. The gauge invariance of the Lagrangian
and equations is broken resulting the appearance of a scalar field. We find the
canonical and symmetrical Belinfante energy-momentum tensors. It is shown that
the traces of the energy-momentum tensors are not equal to zero and the
dilatation symmetry is broken in the theory considered. The matrix Hamiltonian
form of equations is obtained after the exclusion of the nondynamical
components. The canonical quantization is performed and the propagator of the
fields is found in the first-order formalism.Comment: 14 pages, corrections in Eq.(38),(39),(59
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