399 research outputs found
A Discrete Theory of Connections on Principal Bundles
Connections on principal bundles play a fundamental role in expressing the
equations of motion for mechanical systems with symmetry in an intrinsic
fashion. A discrete theory of connections on principal bundles is constructed
by introducing the discrete analogue of the Atiyah sequence, with a connection
corresponding to the choice of a splitting of the short exact sequence.
Equivalent representations of a discrete connection are considered, and an
extension of the pair groupoid composition, that takes into account the
principal bundle structure, is introduced. Computational issues, such as the
order of approximation, are also addressed. Discrete connections provide an
intrinsic method for introducing coordinates on the reduced space for discrete
mechanics, and provide the necessary discrete geometry to introduce more
general discrete symmetry reduction. In addition, discrete analogues of the
Levi-Civita connection, and its curvature, are introduced by using the
machinery of discrete exterior calculus, and discrete connections.Comment: 38 pages, 11 figures. Fixed labels in figure
Do \u27Off-Site\u27 Adult Businesses Have Secondary Effects? Legal Doctrine, Social Theory, and Empirical Evidence
Recent federal court decisions appear to limit the ability of cities to mitigate the ambient crime risks associated with adult entertainment businesses. In one instance, a court has assumed that criminological theories do not apply to “off-site” adult businesses. After developing the legal doctrine of secondary effects, we demonstrate that the prevailing criminological theory applies to all adult business models. To corroborate the theory, we report the results of a before/after quasi-experiment for an off-site adult business. When an off-site adult business opens, ambient crime risk doubles compared to a control area. As theory predicts, moreover, ambient victimization risk is most acute in night-time hours. The theoretical development and empirical results have obvious implications for the evolving legal doctrine of secondary effects
A General Local-to-Global Principle for Convexity of Momentum Maps
We extend the Local-to-Global-Principle used in the proof of convexity
theorems for momentum maps to not necessarily closed maps whose target space
carries a convexity structure which need not be based on a metric. Using a new
factorization of the momentum map, convexity of its image is proved without
local fiber connectedness, and for almost arbitrary spaces of definition.
Geodesics are obtained by straightening rather than shortening of arcs, which
allows a unified treatment and extension of previous convexity results.Comment: 19 pages LaTeX2e, Preprint 2009, see also: Convexity of Momentum
Maps: A Topological Analysis, several parts of the content were presented at
the Young Topologists Meeting 2010 in Copenhagen, Denmark, June 16-20, 2010,
and at Geometry, Mechanics, and Dynamics: A workshop celebrating the 60th
birthday of Tudor Ratiu at CIRM, Luminy, France, July 12-16, 201
The Association of Adult Businesses with Secondary Effects: Legal Doctrine, Social Theory, and Empirical Evidence
In the decade since the U.S. Supreme Court’s decision in Alameda Books v. City of Los Angeles, 535 U.S. 425 (2002), the adult entertainment industry has attacked the legal rationale local governments rely upon as the justification for their regulation of adult businesses: that such businesses are associated with so-called negative secondary effects. These attacks have taken a variety of forms, including: trying to subject the studies of secondary effects relied upon by local governments to the Daubert standard for admission of scientific evidence in federal litigation; producing studies that purport to show no association between adult businesses and negative secondary effects in a given jurisdiction; and claims that distinct business models and/or specific local conditions are not associated with the secondary effects demonstrated in the studies relied on by many local governments. In this Article, we demonstrate that, contrary to the industry’s claims, methodologically appropriate studies confirm criminological theory’s prediction that adult businesses are associated with heightened incidences of crime regardless of jurisdiction, business model or location and thus, such studies should have legal and policy effects supporting regulation of adult businesses
Symplectic Microgeometry II: Generating functions
We adapt the notion of generating functions for lagrangian submanifolds to
symplectic microgeometry. We show that a symplectic micromorphism always admits
a global generating function. As an application, we describe hamiltonian flows
as special symplectic micromorphisms whose local generating functions are the
solutions of Hamilton-Jacobi equations. We obtain a purely categorical
formulation of the temporal evolution in classical mechanics.Comment: 27 pages, 1 figur
The Maslov Gerbe
Let Lag(E) be the grassmannian of lagrangian subspaces of a complex
symplectic vector space E. We construct a Maslov class which generates the
second integral cohomology of Lag(E), and we show that its mod 2 reduction is
the characteristic class of a flat gerbe with structure group Z_2. We explain
the relation of this gerbe to the well-known flat Maslov line bundle with
structure group Z_4 over the real lagrangian grassmannian, whose characteristic
class is the mod 4 reduction of the real Maslov class.Comment: 8 page
Observation of the Cabibbo-suppressed charmed baryon decay Λ_c^+→pφ
We report the observation of the Cabibbo-suppressed decays Λ_c^+→pK^-K^+ and Λ_c^+→pφ using data collected with the CLEO II detector at CESR. The latter mode, observed for the first time with significant statistics, is of interest as a test of color suppression in charm decays. We have determined the branching ratios for these modes relative to Λ_c^+→pK^-π^+ and compared our results with theory
Diagnosing space telescope misalignment and jitter using stellar images
Accurate knowledge of the telescope's point spread function (PSF) is
essential for the weak gravitational lensing measurements that hold great
promise for cosmological constraints. For space telescopes, the PSF may vary
with time due to thermal drifts in the telescope structure, and/or due to
jitter in the spacecraft pointing (ground-based telescopes have additional
sources of variation). We describe and simulate a procedure for using the
images of the stars in each exposure to determine the misalignment and jitter
parameters, and reconstruct the PSF at any point in that exposure's field of
view. The simulation uses the design of the SNAP (http://snap.lbl.gov)
telescope. Stellar-image data in a typical exposure determines secondary-mirror
positions as precisely as . The PSF ellipticities and size, which
are the quantities of interest for weak lensing are determined to and accuracies respectively in each exposure,
sufficient to meet weak-lensing requirements. We show that, for the case of a
space telescope, the PSF estimation errors scale inversely with the square root
of the total number of photons collected from all the usable stars in the
exposure.Comment: 20 pages, 6 figs, submitted to PAS
Searches for New Quarks and Leptons Produced in Z-Boson Decay
We have searched for events with new-particle topologies in 390 hadronic Z decays with the Mark II detector at the SLAC Linear Collider. We place 95%-confidence-level lower limits of 40.7 GeV/c^2 for the top-quark mass, 42.0 GeV/c^2 for the mass of a fourth-generation charge - 1/3 quark, and 41.3 GeV/c^2 for the mass of an unstable Dirac neutral lepton
Measurement of Z Decays into Lepton Pairs
We present measurements by the Mark II experiment of the ratios of the leptonic partial widths of the Z boson to the hadronic partial width. The results are Γ_(ee)/Γ_(had)=0.037_(-0.012^()+0.016),Γ_(µµ)/Γ_(had)=0.053-_(0.015)^(+0.020), and Γ_(ττ)/Γ_(had)=0.066_(-0.017)^(+0.021), in good agreement with the standard-model prediction of 0.048. From the average leptonic width result, Γ_(ll)/Γ_(had)=0.053_(-0.009)^(+0.010), we derive Γ_(had)=1.56_(-0.24)^(+0.28) GeV. We find for the vector coupling constants of the tau and muon v_τ^2=0.31±0.31_(-0.30)^(+0.43) and v_μ^2=0.05±0.30_(-0.23)^(+0.34)
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