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Articles 211 - 232 of 232
Full-Text Articles in Applied Mathematics
A Risk-Averse Strategy For Blackjack Using Fractional Dynamic Programming, Ryan A. Dutsch
A Risk-Averse Strategy For Blackjack Using Fractional Dynamic Programming, Ryan A. Dutsch
LSU Master's Theses
We present how blackjack is related to a discrete-time control problem, rather than a zero-sum game. Using the compiler Visual C++, we write a program for a strategy for blackjack, but instead of maximizing the expected value, we use a risk-averse approach. We briefly describe how this risk-averse strategy is solved by using a special type of dynamic programming called fractional dynamic programming.
On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb
On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb
LSU Doctoral Dissertations
The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact …
Splitter Theorems For 3- And 4-Regular Graphs, Jinko Kanno
Splitter Theorems For 3- And 4-Regular Graphs, Jinko Kanno
LSU Doctoral Dissertations
Let g be a class of graphs and ≤ be a graph containment relation. A splitter theorem for g under ≤ is a result that claims the existence of a set O of graph operations such that if G and H are in g and H≤G with G≠H, then there is a decreasing sequence of graphs from G to H, say G=G0≥G1≥G2...Gt=H, all intermediate graphs are in g, and each Gi can be obtained from Gi-1 by applying a single …
Book Embeddings Of Graphs, Robin Leigh Blankenship
Book Embeddings Of Graphs, Robin Leigh Blankenship
LSU Doctoral Dissertations
We use a structural theorem of Robertson and Seymour to show that for every minor-closed class of graphs, other than the class of all graphs, there is a number k such that every member of the class can be embedded in a book with k pages. Book embeddings of graphs with relation to surfaces, vertex extensions, clique-sums and r-rings are combined into a single book embedding of a graph in the minor-closed class. The effects of subdividing a complete graph and a complete bipartite graph with respect to book thickness are studied. We prove that if n ≥ 3, …
Equations Of Parametric Surfaces With Base Points Via Syzygies, Haohao Wang
Equations Of Parametric Surfaces With Base Points Via Syzygies, Haohao Wang
LSU Doctoral Dissertations
Suppose $S$ is a parametrized surface in complex projective 3-space $mathbf{P}^3$ given as the image of $phi: mathbf{P}^1 imes mathbf{P}^1 o mathbf{P}^3$. The implicitization problem is to compute an implicit equation $F=0$ of $S$ using the parametrization $phi$. An algorithm using syzygies exists for computing $F$ if $phi$ has no base points, i.e. $phi$ is everywhere defined. This work is an extension of this algorithm to the case of a surface with multiple base points of total multiplicity k. We accomplish this in three chapters. In Chapter 2, we develop the concept and properties of Castelnuovo-Mumford regularity in biprojective spaces. …
Gauss' Method Of Least Squares: An Historically-Based Introduction, Belinda B. Brand
Gauss' Method Of Least Squares: An Historically-Based Introduction, Belinda B. Brand
LSU Master's Theses
This work presents Gauss' justification of the method of least squares, following the treatment given by Gauss himself in "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae," where the main idea is to show that the least squares estimate is the unbiased linear estimate of minimum variance. (Actually, we present Gauss' argument both in his terminology and translated into matrix terminology.) We show how this contrasts with Gauss' earlier justfication in "Theoria Motus Corporum Coelestium" which was based on the assumption of a normal distribution of errors, and yielded the estimate of maximum likelihood. We present as a background the development from …
The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris
The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris
LSU Doctoral Dissertations
In this work, we study the structure of the Kauffman bracket skein module of the quaternionic manifold over the field of rational functions. We begin with a brief survey of manifolds whose Kauffman bracket skein modules are known, and proceed in Chapter 2 by recalling the facts from Temperley-Lieb recoupling theory that we use in the proofs. In Chapter 3, using recoupling theory and with Mathematica's assistance, we index an infinite presentation of the skein module, and conjecture that it is five-dimensional. In Chapter 4, using a new set of relations, we prove that the skein module is indeed spanned …
A Parametrization Approach For Solving The Hamilton-Jacobi-Equation And Application To The A2 Toda Lattice, Mohammad Dikko Aliyu
A Parametrization Approach For Solving The Hamilton-Jacobi-Equation And Application To The A2 Toda Lattice, Mohammad Dikko Aliyu
LSU Master's Theses
Hamilton-Jacobi (HJ)-theory is an extension of Lagrangian mechanics and concerns itself with a directed search for a coordinate transformation in which the equations of motion can be easily integrated. The equations of motion of a given mechanical system can often be simplified considerably by a suitable transformation of variables such that all the new position and momemtum coordinates are constants. A particular type of transformation is chosen in such a way that the new equations of motion retain the same form as in the former coordinates; such a transformation is called canonical or contact and can greatly simplify the solution …
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.
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.
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 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 …
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 …
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 …
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, …
Discrete Mathematics Topics In The Secondary School Curriculum, Aimee Beth Boyd
Discrete Mathematics Topics In The Secondary School Curriculum, Aimee Beth Boyd
LSU Master's Theses
This thesis discusses two topics of discrete mathematics in a manner suitable for presentation at a secondary-school level. The introduction outlines the benefits of including discrete mathematics in the secondary-school curriculum. The two chapters which follow include detailed treatment of the two selected topics: the Traveling Salesman Problem and RSA encryption. The discussion of the Traveling Salesman Problem consists of introduction to the problem through several real-life scenarios, followed by a discussion of various methods for solving the problem. We discuss exact and approximate algorithms together with their computational complexity and practical limitations. The discussion of RSA encryption begins with …
Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri
Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri
LSU Doctoral Dissertations
We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …
Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi
Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi
LSU Doctoral Dissertations
This dissertation makes a contribution to the study of Witt rings of quadratic forms over number fields. To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. The situation is particularly nice when this number is 0; often it is not 0. Earlier investigations have established lower bounds for this number. In this dissertation an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered …
Period Relations For Picard Integrals Defined On A Special Class Of Kaehler Manifolds., Joseph Clement Wilson
Period Relations For Picard Integrals Defined On A Special Class Of Kaehler Manifolds., Joseph Clement Wilson
LSU Historical Dissertations and Theses
No abstract provided.
A Necessary And Sufficient Condition That A Set Be Homeomorphic To A Plane Region Bounded By A Finite Number Of Nonintersecting Circles., Robert Lloyd Broussard
A Necessary And Sufficient Condition That A Set Be Homeomorphic To A Plane Region Bounded By A Finite Number Of Nonintersecting Circles., Robert Lloyd Broussard
LSU Historical Dissertations and Theses
No abstract provided.
The Field Of Values Of A Matrix., John Cecil Currie
The Field Of Values Of A Matrix., John Cecil Currie
LSU Historical Dissertations and Theses
No abstract provided.
Foundations Of Differential Geometry., Frank Atkinson Rickey
Foundations Of Differential Geometry., Frank Atkinson Rickey
LSU Historical Dissertations and Theses
No abstract provided.