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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
On Properties Of Linear Control Systems On Lie Groups, Fabiana Cardetti
On Properties Of Linear Control Systems On Lie Groups, Fabiana Cardetti
LSU Doctoral Dissertations
In this work we study controllability properties of linear control systems on Lie groups as introduced by Ayala and Tirao in [AT99]. A linear control system _x0006_Σ Lie group G is defined by x' = X(x) + Σkj=1 ujYj(x), where the drift vector field X is an infinitesimal automorphism, uj are piecewise constant functions, and the control vectors Yj are left-invariant vector fields. Properties for the flow of the infinitesimal automorphism X and for the reachable set defined by _x0006_Σ are presented in Chapter 3. Under a condition similar to the Kalman …
A Monotone Follower Control Problem With A Nonconvex Functional And Some Related Problems, Jamiiru Luttamaguzi
A Monotone Follower Control Problem With A Nonconvex Functional And Some Related Problems, Jamiiru Luttamaguzi
LSU Doctoral Dissertations
A generalized one-dimensional monotone follower control problem with a nonconvex functional is considered. The controls are assumed to be nonnegative progressively measurable processes. The verification theorem for this problem is presented. A specific monotone follower control problem with a nonconvex functional is then considered in which the diffusion term is constant. The optimal control for this problem, which is explicitly given, can be viewed as tracking a standard Wiener process by a non anticipating process starting at 0. For some parameters values, the value function for this monotone follower control problem is shown to be C2 and for other …
Racks, Quandles And Virtual Knots, Victor Samuel Nelson
Racks, Quandles And Virtual Knots, Victor Samuel Nelson
LSU Doctoral Dissertations
We begin with a brief survey of the theory of virtual knots, which was announced in 1996 by Kauffman. This leads naturally to the subject of quandles and quandle homology, which we also briefly introduce. Chapter 2 contains a proof in terms of Gauss diagrams that the forbidden moves unknot virtual knots. This chapter includes material which has appeared in the Journal of Knot Theory and its Ramifications and is reprinted here by permission of World Scientific Publishing. In chapter 3 (cowritten with my advisor R.A.Litherland) we confirm a conjecture of J.S.Carter et.al. that the long exact sequence in rack …
Exotic Integral Witt Equivalence Of Algebraic Number Fields, Changheon Kang
Exotic Integral Witt Equivalence Of Algebraic Number Fields, Changheon Kang
LSU Doctoral Dissertations
Two algebraic number fields K and L are said to be exotically integrally Witt equivalent if there is a ring isomorphism W(OK) ~ W(OL) between the Witt rings of the number rings OK and OL of K and L, respectively. This dissertation studies exotic integral Witt equivalence for totally complex number fields and gives necessary and sufficient conditions for exotic integral equivalence in two special classes of totally complex number fields.
On The Stabilization And Regularization Of Rational Approximation Schemes For Semigroups, Simone Flory
On The Stabilization And Regularization Of Rational Approximation Schemes For Semigroups, Simone Flory
LSU Doctoral Dissertations
In this work we discuss consistency, stability and convergence of rational approximation methods for strongly continuous semigroups on Banach spaces. The Lax-Chernoff theorem shows that in this setting consistency and stability assumptions are necessary to obtain strong uniform convergence of approximation methods. We investigate rational approximation methods for strongly continuous semigroups and their consistency properties, with special emphasis on A-stable methods and Padé-type approximations. In particular, we discuss the stability and convergence properties of these schemes, including the stability of the well-known and widely used Backward-Euler and Crank-Nicolson Schemes. Furthermore, we modify stabilization techniques developed by Hansbo, Larsson, Luskin, Rannacher, …
Group Automorphisms And The Decomposition Of Plancherel Measures, David Slay
Group Automorphisms And The Decomposition Of Plancherel Measures, David Slay
LSU Doctoral Dissertations
In this paper, a natural action of the automorphisms of a group on the space of irreducible unitary representations is used to decompose the Plancherel measure on the dual space as an integral of measures on homogeneous spaces. Explicit decompositions are obtained for the cases of free 2 and 3-step nilpotent Lie groups. These results are obtained using direct integral decompositions, induced representations, the Mackey Machine, and measure theory on homogeneous spaces.
Explicit Multiplicative Relations Between Gauss Sums, Brian J. Murray
Explicit Multiplicative Relations Between Gauss Sums, Brian J. Murray
LSU Doctoral Dissertations
H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes.