Purity of the Ideal of Continuous Functions with Compact Support

&#60;P&#62;Let C(X) be the ring of all continuous real valued functions defined on a completely regular T1-space. Let CK(X) be the ideal of functions with compact support. Purity of CK(X) is studied and characterized through the subspace XL, the set of all points in X with compact neighborhoods (nbhd). It is proved that CK(X) is pure if and only if XL=&#8746;f&#8712;CK supp f. if CK(X) and CK(Y) are pure ideals, then CK(X) is isomorphic to CK(Y) if and only if XL is homeomorphic to YL. It is proved that CK(X) is pure and XL is basically disconnected if and only if for every f &#8712;CK(X), the ideal (f ) is a projective C(X)-module. Finally it is proved that if CK(X) is pure, then XL is an F'-space if and only if every principal ideal of CK(X) is a flat C(X)-module. Concrete examples exemplifying the concepts studied are given.</p

RV Knorr Cruise KN200-4, 13 Apr-03 May 2011. RAPID Mooring Cruise

This report describes the mooring operations conducted during RV Knorr cruise KN200-4 between 13 April and 3 May 2011. These mooring operations were completed as part of the United Kingdom Natural Environment Research Council (NERC) funded RAPID-WATCH Programme to monitor the Atlantic Meridional Overturning Circulation (MOC) at 26.5°N. The primary purpose on this cruise for the UK team was to service the RAPID Western Boundary moorings while the US teams worked on the Western Boundary Time Series project and the RAPID-MOCHA Western Boundary moorings. Cruise KN200-4 was from Port Everglades, Florida to Port Everglades, Florida and covered the Western Boundary moorings deployed on RB0901 and OC459. This cruise was the ninth annual refurbishment of the Western Boundary section of an array of moorings deployed across the Atlantic in order to continuously observe the MOC. This array will be further refined and refurbished during subsequent years. The instruments deployed on the array consist of a variety of current meters, bottom pressure recorders, and CTD loggers, which, combined with time series measurements of the Florida Straits Current and wind stress estimates, will be used to determine the strength and structure of the MOC at 26.5°N. (http://www.noc.soton.ac.uk/rapid

A Numerical Investigation of Unsteady Bubbly Cavitating Nozzle Flows

The effects of unsteady bubble dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. These equations are solved numerically using a Lagrangian finite volume method. Special formulations are used at the boundary cells to allow Eulerian boundary conditions to be specified. Flow regimes studied include those where steady state solutions exist, and those where steady state solutions diverge at the so-called flashing instability. These latter flows consist of unsteady bubbly shock waves travelling downstream in the diverging section of the nozzle. The computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the shock position and throat pressure for flows with bubbly shocks

Robustness of complex networks to node and cluster damage

Copyright @ 2009 Universtiy of WarwickThe goal of this investigation is to assess the robustness of two popular network structures – random networks and scale-free networks – to node and cluster damage. There is no previous work on the latter. For node damage, we remove nodes iteratively and for cluster damage, we first build a network of clusters and then remove the nodes (clusters)

Soma size distinguishes projection neurons from neurokinin 1 receptor-expressing interneurons in lamina I of the rat lumbar spinal dorsal horn

Lamina I of the spinal dorsal horn contains neurons that project to various brain regions, and ∼80% of these projection cells express the neurokinin 1 receptor (NK1r), the main receptor for substance P. Two populations of NK1r-immunoreactive neurons have been identified in lamina I: small weakly immunoreactive cells and large cells with strong immunolabelling [Cheunsuang O and Morris R (2000) Neuroscience 97:335–345]. The main aim of this study was to test the hypothesis that the large cells are projection neurons and that the small cells are interneurons. Projection neurons were identified by injection of tracers into the caudal ventrolateral medulla and lateral parabrachial area, and this was combined with immunostaining for NK1r. We found a bimodal size distribution for NK1r-immunoreactive neurons. The small cells (with somatic cross-sectional areas &lt;200 μm2) showed weak immunoreactivity, while immunostaining intensity was variable among the large cells. Virtually all (99%) of the immunoreactive cells with soma areas &gt;200 μm2 were retrogradely labelled, while only 10% of retrogradely labelled cells were smaller than this. Soma sizes of retrogradely labelled neurons that lacked NK1r did not differ from those of NK1r-expressing projection neurons. It has been suggested that a population of small pyramidal projection neurons that lack NK1r may correspond to cells activated by innocuous cooling, and we therefore assessed the morphology of retrogradely labelled cells that were not NK1r-immunoreactive. Fifteen percent of these were pyramidal, but these did not differ in size from pyramidal NK1r-immunoreactive projection neurons. These results confirm that large NK1r-immunoreactive lamina I neurons are projection cells, and suggest that the small cells are interneurons. Since almost all of the NK1r-immunoreactive cells with soma size &gt;200 μm2 were retrogradely labelled, cells of this type can be identified as projection cells in anatomical studies