4,306 research outputs found
The Classification of -Modules with Partial Decomposition Bases in
Ulm's Theorem presents invariants that classify countable abelian torsion
groups up to isomorphism. Barwise and Eklof extended this result to the
classification of arbitrary abelian torsion groups up to -equivalence. In this paper, we extend this classification to a class
of mixed -modules which includes all Warfield modules and is
closed under -equivalence. The defining property of these
modules is the existence of what we call a partial decomposition basis, a
generalization of the concept of decomposition basis. We prove a complete
classification theorem in using invariants deduced from the
classical Ulm and Warfield invariants
Photogrammetry and ballistic analysis of a high-flying projectile in the STS-124 space shuttle launch
A method combining photogrammetry with ballistic analysis is demonstrated to
identify flying debris in a rocket launch environment. Debris traveling near
the STS-124 Space Shuttle was captured on cameras viewing the launch pad within
the first few seconds after launch. One particular piece of debris caught the
attention of investigators studying the release of flame trench fire bricks
because its high trajectory could indicate a flight risk to the Space Shuttle.
Digitized images from two pad perimeter high-speed 16-mm film cameras were
processed using photogrammetry software based on a multi-parameter optimization
technique. Reference points in the image were found from 3D CAD models of the
launch pad and from surveyed points on the pad. The three-dimensional reference
points were matched to the equivalent two-dimensional camera projections by
optimizing the camera model parameters using a gradient search optimization
technique. Using this method of solving the triangulation problem, the xyz
position of the object's path relative to the reference point coordinate system
was found for every set of synchronized images. This trajectory was then
compared to a predicted trajectory while performing regression analysis on the
ballistic coefficient and other parameters. This identified, with a high degree
of confidence, the object's material density and thus its probable origin
within the launch pad environment. Future extensions of this methodology may
make it possible to diagnose the underlying causes of debris-releasing events
in near-real time, thus improving flight safety.Comment: 26 pages, 11 figures, 3 table
The emergence of classical behavior in magnetic adatoms
A wide class of nanomagnets shows striking quantum behavior, known as quantum
spin tunneling (QST): instead of two degenerate ground states with opposite
magnetizations, a bonding-antibonding pair forms, resulting in a splitting of
the ground state doublet with wave functions linear combination of two
classically opposite magnetic states, leading to the quenching of their
magnetic moment. Here we study how QST is destroyed and classical behavior
emerges in the case of magnetic adatoms, as the strength of their coupling,
either to the substrate or to each other, is increased. Both spin-substrate and
spin-spin coupling renormalize the QST splitting to zero allowing the
environmental decoherence to eliminate superpositions between classical states,
leading to the emergence of spontaneous magnetization.Comment: 5 pages, 4 figure
Splitting of the Identity Component in Locally Compact Abelian Groups
In this paper we are concerned with the splitting of the identity component G0 in an LCA group G. As Pontrjagin duality shows, this splitting is to the splitting of the torsion part tA in a discrete abelian group A, if G is assumed to be compact
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