1,171 research outputs found
Maximally Frobenius-destabilized vector bundles over smooth algebraic curves
Vector bundles in positive characteristics have a tendency to be destabilized
after pulling back by the Frobenius morphism. In this paper, we closely examine
vector bundles over curves that are, in an appropriate sense, maximally
destabilized by the Frobenius morphism. Then we prove that such bundles of rank
2 exist over any curve in characteristic 3, and are unique up to twisting by a
line bundle. We also give an application of such bundles to the study of ample
vector bundles, which is valid in all characteristics.Comment: 17 pages, corrected an error in section
Metaplectic group schemes
Given a reductive group scheme , we give a linear algebraic description of
reduced \'etale -cocycles on its classifying stack . These
cocycles form a -groupoid, which we interpret as parameters of metaplectic
covers of . We use our linear algebraic description to define the Langlands
dual of a metaplectic cover.Comment: 50 page
A CNC machine guiderail wear in-process monitoring system
This research investigates and establishes a system for monitoring the guiderail wear on medium size CNC machines. The system possesses the function of measuring the wear state on guiderails in an in-process way, which is more functional and efficient than the traditional method.
In this research, two different types of sensors for monitoring each particular friction wear feature have been implemented. Calculations to complete designing of a physical experimental rig and the realisation of in-process monitoring are also discussed in detail.
The first type sensor adopted in the experiment is the accelerometer, used for monitoring the vibration caused by the wear on bearings and the increasing roughness on the guiderail surface. The second sensor is the capacitance probe mounted on the table and against a straight edge, searching the deviation signal of the moving table while rolling on the guiderail surface with wear.
The novelty of this thesis covering an in-process monitoring approach has been tested based on a physical experimental rig. The data calculation illustrates how the noise and other disturbances are filtered and data analysed to determine the state of wear. This system utilises an indirect solution to wear monitoring with less cost while delivering convincing reliability according to the experiment result. The thesis shows the possibility to acquire CNC machine guiderail wear data through an in-process monitoring system
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