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

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

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

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 $20 {\rm nm}$. The PSF ellipticities and size, which are the quantities of interest for weak lensing are determined to $4.0 \times 10^{-4}$ and $2.2 \times 10^{-4}$ 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)