770 research outputs found
Note on cubature formulae and designs obtained from group orbits
In 1960, Sobolev proved that for a finite reflection group G, a G-invariant
cubature formula is of degree t if and only if it is exact for all G-invariant
polynomials of degree at most t. In this paper, we find some observations on
invariant cubature formulas and Euclidean designs in connection with the
Sobolev theorem. First, we give an alternative proof of theorems by Xu (1998)
on necessary and sufficient conditions for the existence of cubature formulas
with some strong symmetry. The new proof is shorter and simpler compared to the
original one by Xu, and moreover gives a general interpretation of the
analytically-written conditions of Xu's theorems. Second, we extend a theorem
by Neumaier and Seidel (1988) on Euclidean designs to invariant Euclidean
designs, and thereby classify tight Euclidean designs obtained from unions of
the orbits of the corner vectors. This result generalizes a theorem of Bajnok
(2007) which classifies tight Euclidean designs invariant under the Weyl group
of type B to other finite reflection groups.Comment: 18 pages, no figur
The Planetary Nebulae Spectrograph: the green light for Galaxy Kinematics
Planetary nebulae are now well established as probes of galaxy dynamics and
as standard candles in distance determinations. Motivated by the need to
improve the efficiency of planetary nebulae searches and the speed with which
their radial velocities are determined, a dedicated instrument - the Planetary
Nebulae Spectrograph or PN.S - has been designed and commissioned at the 4.2m
William Herschel Telescope. The high optical efficiency of the spectrograph
results in the detection of typically ~ 150 PN in galaxies at the distance of
the Virgo cluster in one night of observations. In the same observation the
radial velocities are obtained with an accuracy of ~ 20 km/sComment: Accepted by PASP, to appear November 2002; the figures have been
degraded for archival purpose
Graphic Statics and Symmetry
Reciprocal diagrams are a geometric construction dating back to Maxwell and Cremona in which a self-stressed plane framework with a planar graph is paired with another self-stressed reciprocal framework on the dual graph. Either one of the reciprocal frameworks is the form diagram of a self-stressable structure and the other is the force diagram of the corresponding axial forces. This geometric technique offers insights into the self-stresses and infinitesimal motions (mechanisms) of both frameworks in the reciprocal pair. For a symmetric framework with a fully-symmetric self-stress, we obtain an equi-symmetric reciprocal pair of plane frameworks, as well as the associated symmetric discrete dual Airy stress function polyhedra. In this paper we exploit symmetry to refine the Maxwell–Cremona correspondence by considering the decomposition of the self-stress and motion spaces into invariant subspaces corresponding to the irreducible representations of the symmetry group. As such, the familiar relationship for the number of self-stresses of a framework, , and the number of mechanisms of the reciprocal, , is reworked into a symmetry adapted version which provides greater insights into the properties of the reciprocal framework pair. We also show how the quotient graph of a symmetric framework and its reciprocal can be used to efficiently detect infinitesimal motions, self-stresses and polyhedral liftings of different symmetry types. This allows for symmetry-adapted simplified structural analyses of symmetric structures
Hexagonal extensions of toroidal maps and hypermaps
The rank 3 concept of a hypermap has recently been generalized to a higher rank structure in which hypermaps can be seen as “hyperfaces” but very few examples can be found in literature. We study finite rank 4 structures obtained by hexagonal extensions of toroidal hypermaps. Many new examples are produced that are regular or chiral, even when the extensions are polytopal. We also construct a new infinite family of finite nonlinear hexagonal extensions of the tetrahedron.The authors would like to thank two anonymous referees for their numerous helpful and insightful comments. This research was supported by a Marsden grant (UOA1218) of the Royal Society of New Zealand, by NSERC and by the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.publishe
Human factors in space telepresence
The problems of interfacing a human with a teleoperation system, for work in space are discussed. Much of the information presented here is the result of experience gained by the M.I.T. Space Systems Laboratory during the past two years of work on the ARAMIS (Automation, Robotics, and Machine Intelligence Systems) project. Many factors impact the design of the man-machine interface for a teleoperator. The effects of each are described in turn. An annotated bibliography gives the key references that were used. No conclusions are presented as a best design, since much depends on the particular application desired, and the relevant technology is swiftly changing
Spacecraft design project: Low Earth orbit communications satellite
This is the final product of the spacecraft design project completed to fulfill the academic requirements of the Spacecraft Design and Integration 2 course (AE-4871) taught at the U.S. Naval Postgraduate School. The Spacecraft Design and Integration 2 course is intended to provide students detailed design experience in selection and design of both satellite system and subsystem components, and their location and integration into a final spacecraft configuration. The design team pursued a design to support a Low Earth Orbiting (LEO) communications system (GLOBALSTAR) currently under development by the Loral Cellular Systems Corporation. Each of the 14 team members was assigned both primary and secondary duties in program management or system design. Hardware selection, spacecraft component design, analysis, and integration were accomplished within the constraints imposed by the 11 week academic schedule and the available design facilities
Handbook of space environmental effects on solar cell power systems
Space environmental effects on solar cell power systems for earth satellite
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