39,752 research outputs found
Counting lifts of Brauer characters
In this paper we examine the behavior of lifts of Brauer characters in
p-solvable groups where p is an odd prime. In the main result, we show that if
\phi \in IBrp(G) is a Brauer character of a solvable group such that \phi has
an abelian vertex subgroup Q, then the number of lifts of \phi in Irr(G) is at
most |Q|. In order to accomplish this, we develop several results about lifts
of Brauer characters in p-solvable groups that were previously only known to be
true in the case of groups of odd order.Comment: A different proof of Theorem 1 is in the paper "The number of lifts
of Brauer characters with a normal vertex" by J.P. Cossey, M.L.Lewis, and G.
Navarro. Hence, we do not expect to try to publish this note. We feel that
the proof in this paper is of independent interes
Lifts and vertex pairs in solvable groups
Suppose is a -solvable group, where is odd. We explore the
connection between lifts of Brauer characters of and certain local objects
in , called vertex pairs. We show that if is a lift, then the vertex
pairs of form a single conjugacy class. We use this to prove a
sufficient condition for a given pair to be a vertex pair of a lift and to
study the behavior of lifts with respect to normal subgroups
Factors affecting the location of payday lending and traditional banking services in North Carolina
Payday lending is a relatively new and fast growing segment of the “fringe banking” industry. This paper offers a comparative, descriptive analysis of the location patterns of traditional banks and payday lenders. Utilizing a dataset at the Zip Code Tabulation Area level in North Carolina, we perform negative binomial regressions and find evidence supporting some, but not all common assertions about the location patterns of both types of institutions. A key finding is that after controlling for many covariates, race is still a powerful predictor of the locations of both banks and payday lenders.payday lending, fringe banking, location analysis
On the Groenewold-Van Hove problem for R^{2n}
We discuss the Groenewold-Van Hove problem for R^{2n}, and completely solve
it when n = 1. We rigorously show that there exists an obstruction to
quantizing the Poisson algebra of polynomials on R^{2n}, thereby filling a gap
in Groenewold's original proof without introducing extra hypotheses. Moreover,
when n = 1 we determine the largest Lie subalgebras of polynomials which can be
unambiguously quantized, and explicitly construct all their possible
quantizations.Comment: 15 pages, Latex. Error in the proof of Prop. 3 corrected; minor
rewritin
Length requirements for numerical-relativity waveforms
One way to produce complete inspiral-merger-ringdown gravitational waveforms
from black-hole-binary systems is to connect post-Newtonian (PN) and
numerical-relativity (NR) results to create "hybrid" waveforms. Hybrid
waveforms are central to the construction of some phenomenological models for
GW search templates, and for tests of GW search pipelines. The dominant error
source in hybrid waveforms arises from the PN contribution, and can be reduced
by increasing the number of NR GW cycles that are included in the hybrid.
Hybrid waveforms are considered sufficiently accurate for GW detection if their
mismatch error is below 3% (i.e., a fitting factor about 0.97). We address the
question of the length requirements of NR waveforms such that the final hybrid
waveforms meet this requirement, considering nonspinning binaries with q =
M_2/M_1 \in [1,4] and equal-mass binaries with \chi = S_i/M_i^2 \in [-0.5,0.5].
We conclude that for the cases we study simulations must contain between three
(in the equal-mass nonspinning case) and ten (the \chi = 0.5 case) orbits
before merger, but there is also evidence that these are the regions of
parameter space for which the least number of cycles will be needed.Comment: Corrected some typo
- …