Daniel Frohardt

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Corollary 1.2 Let G be an almost simple classical group with natural module V of dimension n. If G is linear, assume that G does not contain a graph automorphism. Let 2 ≤ k < n − 1, and let K be the stabilizer of a nondegenerate or totally singular k-space of V . Let P be the stabilizer of a singular 1-space of V . Then the permutation module 1P is a(More)
We provide estimates for the xed point ratios in the permutation representations of a nite classical group over a eld of order q on k-subspaces of its natural n-dimensional module. For suuciently large n each element must either have a negligible ratio or act linearly with a large eigenspace. We obtain an asymptotic estimate in the latter case, which in(More)
Let X be a compact, connected Riemann surface of genus g, and let ρ : X → P (C) be a covering map of degree N . Then the monodromy group Mon(X, ρ) acts transitively on the fibre of a generic point. Such a group has genus g. We are concerned with the following question. Given an abstract finite group G and a non-negative integer g, does G arise as a(More)
TWO-TIME-SCALE SYSTEMS IN CONTINUOUS TIME WITH REGIME<lb>SWITCHING AND THEIR APPLICATIONS<lb>by<lb>YOUSEF TALAFHA<lb>December 2013 Advisor: Dr. Gang George Yin<lb>Major: Mathematics<lb>Degree: Doctor of Philosophy This dissertation focuses on two-time-scale stochastic systems represented by switching<lb>diffusions. In the model, a continuous-time Markov(More)
As in [Gur], we define the genus of a finite permutation group G to be the minimal genus of a Riemann surface X such that G ∼= Mon(X,φ) where φ : X → P (C) is a covering of the extended complex plane by X. It is known that if G has a nonabelian composition factor S such that S is not an alternating group, then the genus of G must be bounded below by a(More)
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