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On The Second Stiefel-Whitney Class Of Scaled Trace Forms Of Central Simple Algebras., Rosali Brusamarello
On The Second Stiefel-Whitney Class Of Scaled Trace Forms Of Central Simple Algebras., Rosali Brusamarello
LSU Historical Dissertations and Theses
In this work we compute the second Stiefel-Whitney class $w\sb2$ of the scaled trace form $Q\sb{A,a}(x)={\bf tr}\sb{A/k}(ax\sp2),$ where A is a central simple algebra over a perfect field k of characteristic different from two, $a\in A$ is a fixed element, and ${\bf tr}\sb{A/k}$ is the reduced trace. The first three chapters provide background material about quadratic forms, central simple algebras, group cohomology, and representations of linear algebraic groups. The fourth chapter presents two known results about the second Stiefel-Whitney class of trace forms: Serre's formula for the case of etale algebras and Saltman's formula for the case of central simple …
On The Value Functions Of Some Singular Optimal Control Problems., Jesus Alberto Pascal
On The Value Functions Of Some Singular Optimal Control Problems., Jesus Alberto Pascal
LSU Historical Dissertations and Theses
Infinite horizon singular optimal control problems with control taking values in a closed cone U in Rn lead to a dynamic programming equation of the form: maxF2x,v, v',v'' ,F1x,v,v' =0, forall x∈Q, where Q , the state space of the control problem, is some nonempty connected open subset of Rn , and F1, F2 are continuous real-valued functions on QxR2 and QxR3 respectively, with the coercivity assumption for F 2, that is, the function r&rarrr;F2x,u,p,r is nonincreasing on R . A major concern is to determine how smooth the value function v is across the free boundary of the problem. …
Maximal Circuits In Matroids., Pou-Lin Wu
Maximal Circuits In Matroids., Pou-Lin Wu
LSU Historical Dissertations and Theses
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of size c and a largest cocircuit of size c*, then M has at most 2c+c*-1 elements. A question of Oxley that has attracted considerable recent attention is whether there is an upper bound on the size of M that is polynomial in terms of c and c*. In particular, Bonin, McNulty, and Reid conjectured that 12cc* is such a bound. In Chapter 1, we prove this conjecture for an connected graphic and cographic matroids. In Chapter 2, we give a constructive description of …
Spikes In Matroid Theory., Zhaoyang Wu
Spikes In Matroid Theory., Zhaoyang Wu
LSU Historical Dissertations and Theses
For an integer $n\ge 3,$ a rank-n matroid is called an n-spike if it consists of n three-point lines through a common point t such that, for all k in $(1, 2,\..., n - 1),$ the union of every set of k of these Lines has rank $k + 1.$ The point t is called the tip of the n-spike. Ding, Oporowski, Oxley, and Vertigan proved that, for all $n\ge 3,$ there is an integer $N(n)$ such that every 3-connected matroid with at least $N(n)$ elements has a minor isomorphic to a wheel or whirl of rank $n,\ M(K\sb{3,n})$ or …