Geoids in General Relativity: Geoid Quasilocal Frames

We develop, in the context of general relativity, the notion of a geoid -- a surface of constant "gravitational potential". In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general and operationally useful construction called a quasilocal frame -- that is, a choice of a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume. We study the geometric properties of these geoid quasilocal frames, and construct solutions for them in some simple spacetimes. We then compare these results -- focusing on the computationally tractable scenario of a non-rotating body with a quadrupole perturbation -- against their counterparts in Newtonian gravity (the setting for current applications of the geoid), and we compute general-relativistic corrections to some measurable geometric quantities.Comment: 24 pages, 8 figures; v2: reference added; v3: introduction clarified, reference adde

An Examination of the Benefits of E-Business to Small and Medium Size Businesses

Small and Medium Sized Enterprises (SME) play a significant part in economies throughout the world. In the early developmental stages of e-commerce/e-business many believed that it would enable these SMEs to compete head-to-head with large companies. While much has been done to examine the adoption of e-commerce/e-business, few have addressed the benefit that it is providing these businesses. This study identifies the types of e-commerce that SMEs are using and examines the benefits that are received from this use

Black Holes and Boson Stars with One Killing Field in Arbitrary Odd Dimensions

We extend the recent D=5 results of Dias, Horowitz and Santos by finding asymptotically AdS rotating black hole and boson star solutions with scalar hair in arbitrary odd spacetime dimension. Both the black holes and the boson stars are invariant under a single Killing vector field which co-rotates with the scalar field and, in the black hole case, is tangent to the generator of the horizon. Furthermore, we explicitly construct boson star and small black hole ($r_+ \ll \ell$) solutions perturbatively assuming a small amplitude for the scalar field, resulting in solutions valid for low energies and angular momenta. We find that just as in D=5, the angular momentum is primarily carried by the scalar field in $D>5$, whereas unlike D=5 the energy is also primarily carried by the scalar field in $D>5$; the thermodynamics in D=5 are governed by both the black hole and scalar field whereas in $D>5$ they are governed primarily by the scalar field alone. We focus on cataloguing these solutions for the spacetime dimensions of interest in string theory, namely $D=5,7,9,11$.Comment: 28 pages, 1 table, 2 Appendices. v2: minor typos corrected, references added, small discussion added to section 4. v3: typos corrected, thermodynamic discussion expanded, accepted in PR

Composition and properties of bovine colostrum: a review

International audienceAbstractColostrum is the initial milk secreted by mammals following parturition, the composition and physicochemical properties of which are highly dynamic and variable. The composition and physicochemical properties of colostrum during the initial post-partum period has not been systematically reviewed for many years, although the topic remains of interest both to milk producers and processors. In this article, the current understanding of the composition of colostrum, i.e. carbohydrates, proteins, growth factors, enzymes, enzyme inhibitors, nucleotides and nucleosides, cytokines, fats, vitamins and minerals, is reviewed. In addition, the physicochemical properties, i.e. pH and buffering capacity, colour, density and specific gravity, osmotic pressure, somatic cell count, properties of casein micelles, ethanol stability and rennet coagulation properties are discussed, as well as the effects of heat-treating colostrum

Rigid motion revisited: rigid quasilocal frames

We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a "system" in general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (constant size) and shear-free (constant shape). This definition of a system is anticipated to yield simple, exact geometrical insights into the problem of motion in general relativity. It begins by answering the questions what is in motion (a rigid two-dimensional system boundary), and what motions of this rigid boundary are possible. Nearly a century ago Herglotz and Noether showed that a three-parameter family of timelike worldlines in Minkowski space satisfying Born's 1909 rigidity conditions has only three degrees of freedom instead of the six we are familiar with from Newtonian mechanics. We argue that in fact we can implement Born's notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent papers) - with precisely the expected three translational and three rotational degrees of freedom - provided the system is defined quasilocally as the two-dimensional set of points comprising the boundary of a finite spatial volume, rather than the three-dimensional set of points within the volume.Comment: 10 pages (two column), 24 pages (preprint), 1 figur

HST/STIS Ultraviolet Imaging of Polar Aurora on Ganymede

We report new observations of the spectrum of Ganymede in the spectral range 1160 - 1720 A made with the Space Telescope Imaging Spectrograph (STIS) on HST on 1998 October 30. The observations were undertaken to locate the regions of the atomic oxygen emissions at 1304 and 1356 A, previously observed with the GHRS on HST, that Hall et al. (1998) claimed indicated the presence of polar aurorae on Ganymede. The use of the 2" wide STIS slit, slightly wider than the disk diameter of Ganymede, produced objective spectra with images of the two oxygen emissions clearly separated. The OI emissions appear in both hemispheres, at latitudes above 40 degrees, in accordance with recent Galileo magnetometer data that indicate the presence of an intrinsic magnetic field such that Jovian magnetic field lines are linked to the surface of Ganymede only at high latitudes. Both the brightness and relative north-south intensity of the emissions varied considerably over the four contiguous orbits (5.5 hours) of observation, presumably due to the changing Jovian plasma environment at Ganymede. However, the observed longitudinal non-uniformity in the emission brightness at high latitudes, particularly in the southern hemisphere, and the lack of pronounced limb brightening near the poles are difficult to understand with current models. In addition to observed solar HI Lyman-alpha reflected from the disk, extended Lyman-alpha emission resonantly scattered from a hydrogen exosphere is detected out to beyond two Ganymede radii from the limb, and its brightness is consistent with the Galileo UVS measurements of Barth et al. (1997).Comment: 7 pages, 4 figures, accepted for publication in ApJ, June 1, 200