A geometric study of the dispersionless Boussinesq type equation

We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney-Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in . The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators that send conservation laws and symmetries to each other but are neither Hamiltonian, nor symplectic. These operators give rise to a noncommutative infinite-dimensional algebra of recursion operators

The N=2 supersymmetric unconstrained matrix GNLS hierarchies

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of N=2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N=2 superfields, it reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2 unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2 supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.Comment: 11 pages, LaTex, misprints correcte

On symmetries and cohomological invariants of equations possessing flat representations

We study the equation E_fc of flat connections in a fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion to arbitrary PDE and prove that flat representations of an equation E are in 1-1 correspondence with morphisms f: E\to E_fc, where E and E_fc are treated as submanifolds of infinite jet spaces. We show that flat representations include several known types of zero-curvature formulations of PDE. In particular, the Lax pairs of the self-dual Yang-Mills equations and their reductions are of this type. With each flat representation we associate a complex C_f of vector-valued differential forms such that its first cohomology describes infinitesimal deformations of the flat structure, which are responsible, in particular, for parameters in Backlund transformations. In addition, each higher infinitesimal symmetry S of E defines a 1-cocycle c_S of C_f. Symmetries with exact c_S form a subalgebra reflecting some geometric properties of E and f. We show that the complex corresponding to E_fc itself is 0-acyclic and 1-acyclic (independently of the bundle topology), which means that higher symmetries of E_fc are exhausted by generalized gauge ones, and compute the bracket on 0-cochains induced by commutation of symmetries.Comment: 30 page

Small food stores and availability of nutritious foods: a comparison of database and in-store measures, Northern California, 2009.

IntroductionSmall food stores are prevalent in urban neighborhoods, but the availability of nutritious food at such stores is not well known. The objective of this study was to determine whether data from 3 sources would yield a single, homogenous, healthful food store category that can be used to accurately characterize community nutrition environments for public health research.MethodsWe conducted in-store surveys in 2009 on store type and the availability of nutritious food in a sample of nonchain food stores (n = 102) in 6 predominantly urban counties in Northern California (Alameda, Contra Costa, Marin, Sacramento, San Francisco, and Santa Clara). We compared survey results with commercial database information and neighborhood sociodemographic data by using independent sample t tests and classification and regression trees.ResultsSampled small food stores yielded a heterogeneous group of stores in terms of store type and nutritious food options. Most stores were identified as convenience (54%) or specialty stores (22%); others were small grocery stores (19%) and large grocery stores (5%). Convenience and specialty stores were smaller and carried fewer nutritious and fresh food items. The availability of nutritious food and produce was better in stores in neighborhoods that had a higher percentage of white residents and a lower population density but did not differ significantly by neighborhood income.ConclusionCommercial databases alone may not adequately categorize small food stores and the availability of nutritious foods. Alternative measures are needed to more accurately inform research and policies that seek to address disparities in diet-related health conditions

Feasibility of electrostatic microparticle propulsion

This paper discusses the feasibility of electrostatic space propulsion which uses microparticles as propellant. It is shown that particle charging in a plasma is not sufficient for electrostatic acceleration. Moreover, it appears technically difficult to extract charged particles out of a plasma for subsequent acceleration without them being discharged. Two novel thruster concepts are proposed. In the first one, particles with low secondary electron emission are charged using energetic electrons in the order of magnitude of 100eV. The second concept charges the particles by contact with needle electrodes at high electrostatic potential (∼20kV). Both methods allow the maximum possible charges on microparticles. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

Development of a Detector Control System for the ATLAS Pixel Detector

The innermost part of the ATLAS experiment will be a pixel detector containing around 1750 individual detector modules. A detector control system (DCS) is required to handle thousands of I/O channels with varying characteristics. The main building blocks of the pixel DCS are the cooling system, the power supplies and the thermal interlock system, responsible for the ultimate safety of the pixel sensors. The ATLAS Embedded Local Monitor Board (ELMB), a multi purpose front end I/O system with a CAN interface, is foreseen for several monitoring and control tasks. The Supervisory, Control And Data Acquisition (SCADA) system will use PVSS, a commercial software product chosen for the CERN LHC experiments. We report on the status of the different building blocks of the ATLAS pixel DCS.Comment: 3 pages, 2 figures, ICALEPCS 200

On Waylen's regular axisymmetric similarity solutions

We review the similarity solutions proposed by Waylen for a regular time-dependent axisymmetric vacuum space-time, and show that the key equation introduced to solve the invariant surface conditions is related by a Baecklund transform to a restriction on the similarity variables. We further show that the vacuum space-times produced via this path automatically possess a (possibly homothetic) Killing vector, which may be time-like.Comment: 8 pages, LaTeX2

Border ownership selectivity in human early visual cortex and its modulation by attention

Natural images are usually cluttered because objects occlude one another. A critical aspect of recognizing these visual objects is to identify the borders between image regions that belong to different objects. However, the neural coding of border ownership in human visual cortex is largely unknown. In this study, we designed two simple but compelling stimuli in which a slight change of contextual information could induce a dramatic change of border ownership. Using functional MRI adaptation, we found that border ownership selectivity in V2 was robust and reliable across subjects, and it was largely dependent on attention. Our study provides the first human evidence that V2 is a critical area for the processing of border ownership and that this processing depends on the modulation from higher-level cortical areas. Copyright © 2009 Society for Neuroscience