Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd

It was proved earlier that there are 6 isomorphism classes of hyperplanes in the dual polar space (5,q)$,$ even, which arise from its Grassmann-embedding. In the present paper, we extend these results to the case that $is odd. Specifically, we determine the orbits of the full automorphism group of (5,q)$, $odd, on the projective points (or equivalently, the hyperplanes) of the projective space (13,q)$ which affords the universal embedding of (5,q)$

Development of a Space Vehicle Electromagnetic Interference/compatibility Specification. Volume 3 - System Specification

This specification represents a new approach to controlling electromagnetic interference. In this approach the system integration contractor will be responsible for the development of discrete specification limits to be utilized on the program to which this specification is applied. The specification limits imposed upon subsystem contractors will be developed by the use of a computer program, available from the procuring agency, which is designed to consider the total system electromagnetic environment in the computation of these limits. The integration contractor will be required to mathematically model those circuits which represent required emitters and receptors of electromagnetic energy on the space vehicle. There are contained herein, a list of available computer models into which must be inserted particular parameters of the spacecraft subsystems. These functional models, when inserted into the computer program, will develop discrete specification limits based upon the requirements of the particular system modelled

Relativistic Mean Field calculations of nuclear properties in early stages of stellar collapse

We use the Relativistic Mean Field (RMF) method to calculate properties of neutron rich, usually deformed nuclei, important for equation of state calculations and which have significant abundance in the early stages of stellar collapse. We compare the results of our microscopic calculations with existing cold nuclear equations of state based on macroscopic liquid drop model and the FRLDM model.Comment: 4 pages , Latex, 4 figures, uses espcrc1.sty. To appear in Nucl. Phys. A, proceedings of "Nuclei in the Cosmos 1996" 4th International Symposium on Nuclear Astrophysics. e-mail contact: [email protected]

The generating rank of the unitary and symplectic Grassmannians

We prove that the Grassmannian of totally isotropic $k$-spaces of the polar space associated to the unitary group $\mathsf{SU}_{2n}(\mathbb{F})$ ($n\in \mathbb{N}$) has generating rank ${2n\choose k}$ when $\mathbb{F}\ne \mathbb{F}_4$. We also reprove the main result of Blok [Blok2007], namely that the Grassmannian of totally isotropic $k$-spaces associated to the symplectic group $\mathsf{Sp}_{2n}(\mathbb{F})$ has generating rank ${2n\choose k}-{2n\choose k-2}$, when $\rm{Char}(\mathbb{F})\ne 2$

The generating rank of the unitary and symplectic Grassmannians

AbstractWe prove that the Grassmannian of totally isotropic k-spaces of the polar space associated to the unitary group SU2n(F) (n∈N) has generating rank (2nk) when F≠F4. We also reprove the main result of Blok (2007) [3], namely that the Grassmannian of totally isotropic k-spaces associated to the symplectic group Sp2n(F) has generating rank (2nk)−(2nk−2), when Char(F)≠2

Likeness in Henri Cartier-Bresson's Photo-portraits

After the invention of photography, modern theoreticians were hopeful that photography's faithfulness to nature would resolve painterly deficiencies by providing a more recognizable and convincing reproduction. Paradoxically, the advent of photography did not improve upon painting's failures, but exhibited an inherent problem. In particular, aspects of temporality hindered photography's ability to reproduce a convincing likeness. Concerning this issue, Gombrich opines that it could be "[…] true to say that we never see [in reality] what the instantaneous photograph reveals, for we gather up successions of movements, and never see static configurations as such."1 Because the constant motion of the eyes as well as the ephemeral nature of existence limits perception, I am studying the techniques used to convey aspects of "likeness" in the celebrity photo-portraits by Henri Cartier-Bresson. To establish what stylistic choices contribute to a recognizable portrait, I will analyze Bresson's photographical methods which he delineated in "The Decisive Moment." Bresson's concept of the decisive moment, far from falling within modernist accounts of photography's medium specificity, actually traces back to a much older discussion, one concerned with unearthing relations between photographs and paintings. As examples of this discussion, I look to ideas expressed by late nineteenth-century photographer-scientist Francis Galton and police officer Alphonse Bertillon. These theorists ascertained that photographs are not representative of a sum-total or synthetic image which humans perceive, but are indicative of an imperceptible instant. While Bresson's conception of photographic likeness relates to ideas espoused by Francis Galton, I also prove that Bresson's work is distinct from Galton's as it relates to human typicality. Whereas Galton's ideas concerning likeness relate to a need to arrive at ideal types, a comparison of Bresson's work with broader developments in the history of the concept of objectivity and image making reveals the ways in which Bresson's conception of typicality is distinct from that of Galton.1 Ernst Hans Gombrich, The Image and the Eye: Further studies in the psychology of pictorial representation. Ithaca, New York: Cornell University Press, 1982, p. 50

Comment on "Pulsar Velocities and Neutrino Oscillations"

In a recent Letter, Kusenko and Segre proposed a new mechanism to explain the observed proper motions of pulsars. Their mechanism was based on the asymmetric neutrino emission induced by neutrino oscillations in the protoneutron star magnetic field. In this note I point out that their estimate of the asymmetry in the neutrino emission is incorrect. A proper calculation shows that their mechanism at least requires a magnetic field of 10**16 G in order to produce the observed average pulsar velocity.Comment: 4 pages, RevTe

Electron-positron energy deposition rate from neutrino pair annihilation in the equatorial plane of rapidly rotating neutron and quark stars

The neutrino-antineutrino annihilation into electron-positron pairs near the surface of compact general relativistic stars could play an important role in supernova explosions, neutron star collapse, or for close neutron star binaries near their last stable orbit. General relativistic effects increase the energy deposition rates due to the annihilation process. We investigate the deposition of energy and momentum due to the annihilations of neutrinos and antineutrinos in the equatorial plane of the rapidly rotating neutron and quark stars, respectively. We analyze the influence of general relativistic effects, and we obtain the general relativistic corrections to the energy and momentum deposition rates for arbitrary stationary and axisymmetric space-times. We obtain the energy and momentum deposition rates for several classes of rapidly rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the MIT bag model equation of state and in the CFL (Color-Flavor-Locked) phase, respectively. Compared to the Newtonian calculations, rotation and general relativistic effects increase the total annihilation rate measured by an observer at infinity. The differences in the equations of state for neutron and quark matter also have important effects on the spatial distribution of the energy deposition rate by neutrino-antineutrino annihilation.Comment: 29 pages, 6 figures, accepted for publication in MNRA

Making Black Holes in Supernovae

The possibility of making stellar mass black holes in supernovae that otherwise produce viable Type II and Ib supernova explosions is discussed and estimates given of their number in the Milky Way Galaxy. Observational diagnostics of stellar mass black hole formation are reviewed. While the equation of state sets the critical mass, fall back during the explosion is an equally important (and uncertain) element in determining if a black hole is formed. SN 1987A may or may not harbor a black hole, but if the critical mass for neutron stars is 1.5 - 1.6 M\sun, as Brown and Bethe suggest, it probably does. Observations alone do not yet resolve the issue. Reasons for this state of ambiguity are discussed and suggestions given as to how gamma-ray and x-ray observations in the future might help.Comment: 14 pages, uuencoded gzipped postscript, Accepted Nuclear Physics A, Gerry Brown Festschrift contributio

Spherical collapse of supermassive stars: neutrino emission and gamma-ray bursts

We present the results of numerical simulations of the spherically symmetric gravitational collapse of supermassive stars (SMS). The collapse is studied using a general relativistic hydrodynamics code. The coupled system of Einstein and fluid equations is solved employing observer time coordinates, by foliating the spacetime by means of outgoing null hypersurfaces. The code contains an equation of state which includes effects due to radiation, electrons and baryons, and detailed microphysics to account for electron-positron pairs. In addition energy losses by thermal neutrino emission are included. We are able to follow the collapse of SMS from the onset of instability up to the point of black hole formation. Several SMS with masses in the range $5\times 10^5 M_{\odot}- 10^9 M_{\odot}$ are simulated. In all models an apparent horizon forms initially, enclosing the innermost 25% of the stellar mass. From the computed neutrino luminosities, estimates of the energy deposition by $\nu\bar{\nu}$-annihilation are obtained. Only a small fraction of this energy is deposited near the surface of the star, where, as proposed recently by Fuller & Shi (1998), it could cause the ultrarelativistic flow believed to be responsible for $\gamma$-ray bursts. Our simulations show that for collapsing SMS with masses larger than $5\times 10^5 M_{\odot}$ the energy deposition is at least two orders of magnitude too small to explain the energetics of observed long-duration bursts at cosmological redshifts. In addition, in the absence of rotational effects the energy is deposited in a region containing most of the stellar mass. Therefore relativistic ejection of matter is impossible.Comment: 13 pages, 11 figures, submitted to A&