1,107 research outputs found
Endotrivial Modules for the General Linear Group in a Nondefining Characteristic
Suppose that is a finite group such that , and that is a central subgroup of .
Let be the abelian group of equivalence classes of endotrivial
-modules, where is an algebraically closed field of
characteristic~ not dividing . We show that the torsion free rank of
is at most one, and we determine in the case that the Sylow
-subgroup of is abelian and nontrivial. The proofs for the torsion
subgroup of use the theory of Young modules for
and a new method due to Balmer for computing the
kernel of restrictions in the group of endotrivial modules
Excited Baryon Decay Widths in Large N_c QCD
We study excited baryon decay widths in large N_c QCD. It was suggested
previously that some spin-flavor mixed-symmetric baryon states have strong
couplings of O(N_c^{-1/2}) to nucleons [implying narrow widths of O(1/N_c)], as
opposed to the generic expectation based on Witten's counting rules of an
O(N_c^0) coupling. The calculation obtaining these narrow widths was performed
in the context of a simple quark-shell model. This paper addresses the question
of whether the existence of such narrow states is a general property of large
N_c QCD. We show that a general large N_c QCD analysis does not predict such
narrow states; rather they are a consequence of the extreme simplicity of the
quark model.Comment: 9 page
Complete Analysis of Baryon Magnetic Moments in 1/N_c
We generate a complete basis of magnetic moment operators for the N_c = 3
ground-state baryons in the 1/N_c expansion, and compute and tabulate all
associated matrix elements. We then compare to previous results derived in the
literature and predict additional relations among baryon magnetic moments
holding to subleading order in 1/N_c and flavor SU(3) breaking. Finally, we
predict all unknown diagonal and transition magnetic moments to <= 0.15 mu_N
accuracy, and suggest possible experimental measurements to improve the
analysis even further.Comment: 28 pages (including 11 tables), ReVTeX. One reference and grant
acknowledgment adde
Generating Optimized Trajectories for Robotic Spray Painting
In the manufacturing industry, spray painting is often an important part of the manufacturing process. Especially in the automotive industry, the perceived quality of the final product is closely linked to the exactness and smoothness of the painting process. For complex products or low batch size production, manual spray painting is often used. But in large scale production with a high degree of automation, the painting is usually performed by industrial robots. There is a need to improve and simplify the generation of robot trajectories used in industrial paint booths. A novel method for spray paint optimization is presented, which can be used to smooth out a generated initial trajectory and minimize paint thickness deviations from a target thickness. The smoothed out trajectory is found by solving, using an interior point solver, a continuous non-linear optimization problem. A two-dimensional reference function of the applied paint thickness is selected by fitting a spline function to experimental data. This applicator footprint profile is then projected to the geometry and used as a paint deposition model. After generating an initial trajectory, the position and duration of each trajectory segment are used as optimization variables. The primary goal of the optimization is to obtain a paint applicator trajectory, which would closely match a target paint thickness when executed. The algorithm has been shown to produce satisfactory results on both a simple 2-dimensional test example, and a non-trivial industrial case of painting a tractor fender. The resulting trajectory is also proven feasible to be executed by an industrial robot
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