Signatures of hermitian forms and the Knebusch Trace Formula

Signatures of quadratic forms have been generalized to hermitian forms over algebras with involution. In the literature this is done via Morita theory, which causes sign ambiguities in certain cases. In this paper, a hermitian version of the Knebusch Trace Formula is established and used as a main tool to resolve these ambiguities. The last page is an erratum for the published version. We inadvertently (I) gave an incorrect definition of adjoint involutions; (II) omitted dealing with the case $(H\times H, \widehat{\phantom{m}}\,)$. As $W(H\times H, \widehat{\phantom{m}}\,)= W(R\times R, \widehat{\phantom{m}}\,)=0$, the omission does not affect our reasoning or our results. For the sake of completeness we point out where some small changes should be made in the published version.Comment: This is the final version before publication. The last page is an updated erratum for the published versio

Division, adjoints, and dualities of bilinear maps

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the adjoint category is not a module category but nevertheless it is suitably familiar. The universal properties have geometric perspectives. For example, products are orthogonal sums. The bilinear division maps are the simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes the understanding that the atoms of linear geometries are algebraic objects with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism; hence, nonassociative division rings can be studied within this framework. This also corrects an error in an earlier pre-print; see Remark 2.11

Student and Agency Personnel Perceptions of the Impact of Community Service-Learning

The purpose of this study was to investigate student and agency personnel perceptions of the impact of community service-learning across several different courses at a Midwestern metropolitan university. Eighty-five students and 18 community agency personnel completed the Service-Learning Index. The results of the study indicated that student and agency personnel perceptions of the impact of community service-learning were positive and similar and did not vary across academic disciplines. Perspectives about the service-learning course received the highest ratings from both students and community agency personnel. Recommendations were made to expand the community service-learning program at the university where the study took place

Pfister involutions

The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to a Pfister form. Moreover, cohomological invariants of those algebras with involution are discusse

An Improved Model for Relativistic Solar Proton Acceleration applied to the 2005 January 20 and Earlier Events

This paper presents results on modelling the ground level response of the higher energy protons for the 2005 January 20 ground level enhancement (GLE). This event, known as GLE 69, produced the highest intensity of relativistic solar particles since the famous event on 1956 February 23. The location of recent X-ray and gamma-ray emission (N14 W61) was near to Sun-Earth connecting magnetic field lines, thus providing the opportunity to directly observe the acceleration source from Earth. We restrict our analysis to protons of energy greater than 450 MeV to avoid complications arising from transport processes that can affect the propagation of low energy protons. In light of this revised approach we have reinvestigated two previous GLEs: those of 2000 July 14 (GLE 59) and 2001 April 15 (GLE 60). Within the limitations of the spectral forms employed, we find that from the peak (06:55 UT) to the decline (07:30 UT) phases of GLE 69, neutron monitor observations from 450 MeV to 10 GeV are best fitted by the Gallegos-Cruz & Perez-Peraza stochastic acceleration model. In contrast, the Ellison & Ramaty spectra did not fit the neutron monitor observations as well. This result suggests that for GLE 69, a stochastic process cannot be discounted as a mechanism for relativistic particle acceleration, particularly during the initial stages of this solar event. For GLE 59 we find evidence that more than one acceleration mechanism was present, consistent with both shock and stochastic acceleration processes dominating at different times of the event. For GLE 60 we find that Ellison & Ramaty spectra better represent the neutron monitor observations compared to stochastic acceleration spectra. The results for GLEs 59 and 60 are in agreement with our previous work.Comment: 42 pages, 10 figures, 10 tables, published in ApJ, August 200

SONTRAC: an imaging spectrometer for solar neutrons

An instrument capable of unambiguously determining the energy and direction of incident neutrons has important applications in solar physics-as well as environmental monitoring and medical/radiological sciences. The SONTRAC (SOlar Neutron TRACking) instrument is designed to operate in the neutron energy range of 20-250 MeV. The measurement principle is based on non-relativistic double scatter of neutrons off ambient protons (n-p scattering) within a block of densely packed scintillating fibers. Using this double-scatter mode it is possible to uniquely determine neutron energy and direction on an event-by-event basis. A fully operational science model of such an instrument has been built using 300 μm (250 μm active) scintillating fibers. The science model consists of a 5×5×5 cm cube of orthogonal plastic scintillating fiber layers. Two orthogonal imaging chains, employing image intensifiers and CCD cameras, allow full 3-dimensional reconstruction of scattered proton particle tracks. We report the results of the science model instrument calibration using 35-65 MeV protons. The proton calibration is the first step toward understanding the instrument response to n-p scatter events. Preliminary results give proton energy resolution of 2% (6%) at 67.5 (35) MeV, and angular resolution of 2° (4.5°) at 67.5 (35) MeV. These measurements are being used to validate detailed instrument simulations that will be used to optimize the instrument design and develop quantitative estimates of science return. Based on the proton calibration, neutron energy and angular resolution for a 10×10×10 cm version of SONTRAC is expected to be ~5% an

Development and performance of the Fast Neutron Imaging Telescope for SNM detection

FNIT (the Fast Neutron Imaging Telescope), a detector with both imaging and energy measurement capabilities, sensitive to neutrons in the range 0.8-20 MeV, was initially conceived to study solar neutrons as a candidate design for the Inner Heliosphere Sentinel (IHS) spacecraft of NASA\u27s Solar Sentinels program and successively reconfigured to locate fission neutron sources. By accurately identifying the position of the source with imaging techniques and reconstructing the Watt spectrum of fission neutrons, FNIT can detect samples of special nuclear material (SNM), including heavily shielded and masked ones. The detection principle is based on multiple elastic neutron-proton scatterings in organic scintillators. By reconstructing n-p event locations and sequence and measuring the recoil proton energies, the direction and energy spectrum of the primary neutron flux can be determined and neutron sources identified. We describe the design of the FNIT prototype and present its energy reconstruction and imaging performance, assessed by exposing FNIT to a neutron beam and to a Pu fission neutron source

Service Oriented Robotic Architecture for Space Robotics: Design, Testing, and Lessons Learned

This paper presents the lessons learned from six years of experiments with planetary rover prototypes running the Service Oriented Robotic Architecture (SORA) developed by the Intelligent Robotics Group (IRG) at the NASA Ames Research Center. SORA relies on proven software engineering methods and technologies applied to space robotics. Based on a Service Oriented Architecture and robust middleware, SORA encompasses on-board robot control and a full suite of software tools necessary for remotely operated exploration missions. SORA has been eld tested in numerous scenarios of robotic lunar and planetary exploration. The experiments conducted by IRG with SORA exercise a large set of the constraints encountered in space applications: remote robotic assets, ight relevant science instruments, distributed operations, high network latencies and unreliable or intermittent communication links. In this paper, we present the results of these eld tests in regard to the developed architecture, and discuss its bene ts and limitations

Algebraic lattice constellations: bounds on performance

In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions, minimum product distance, and bounds for full-diversity complex rotated Z[i]/sup n/-lattices for any dimension n, which avoid the need of component interleaving