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Weierstrass Pairs And Minimum Distance Of Goppa Codes., Gretchen L. Matthews
Weierstrass Pairs And Minimum Distance Of Goppa Codes., Gretchen L. Matthews
LSU Historical Dissertations and Theses
We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code that has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this to increase the lower bound on the minimum distance of certain codes defined using a linear combination of the two points. In particular, we obtain some two-point codes on a Hermitian curve that have better parameters than the one-point code on this curve with the same …
Structure And Minors In Graphs And Matroids., Galen Ellsworth Turner Iii
Structure And Minors In Graphs And Matroids., Galen Ellsworth Turner Iii
LSU Historical Dissertations and Theses
This dissertation establishes a number of theorems related to the structure of graphs and, more generally, matroids. In Chapter 2, we prove that a 3-connected graph G that has a triangle in which every single-edge contraction is 3-connected has a minor that uses the triangle and is isomorphic to K5 or the octahedron. We subsequently extend this result to the more general context of matroids. In Chapter 3, we specifically consider the triangle-rounded property that emerges in the results of Chapter 2. In particular, Asano, Nishizeki, and Seymour showed that whenever a 3-connected matroid M has a four-point-line-minor, and T …
On Harmonic Analysis For White Noise Distribution Theory., Aurel Iulian Stan
On Harmonic Analysis For White Noise Distribution Theory., Aurel Iulian Stan
LSU Historical Dissertations and Theses
This thesis is composed of two parts, each part treating a different problem from the theory of Harmonic Analysis. In the first part we present an inequality in White Noise Analysis similar to the classical Heisenberg Inequality for functions in L2Rn . To do this we replace the finite dimensional space R n and its Lebesgue measure by the infinite dimensional space E' , which is the dual of a nuclear space E , and its Gaussian measure. Choosing an arbitrary element eta in E , we may define the multiplication operator Q&d5;h , which is the sum between the …
Integral Kernel Operators In The Cochran -Kuo -Sengupta Space., John Joseph Whitaker
Integral Kernel Operators In The Cochran -Kuo -Sengupta Space., John Joseph Whitaker
LSU Historical Dissertations and Theses
This dissertation contains several results about integral kernel operators in white noise analysis. The results found here apply to the space of test functions and generalized functions that were constructed in the paper of Cochran, Kuo, and Sengupta, based on a sequence of numbers &cubl0;an&cubr0; infinityn=0. . We shall prove results about existence, restrictions, and extensions of integral kernel operators based on the conditions on &cubl0;an&cubr0; infinityn=0. contained in the paper of Kubo, Kuo, and Sengupta. Also, we shall prove an analytic property and growth condition of the symbol of a continuous operator in CKS space. Our results are similar …
Inequalities Between Pythagoras Numbers And Algebraic Ranks In Witt Rings Of Fields., Sidney Taylor Hawkins
Inequalities Between Pythagoras Numbers And Algebraic Ranks In Witt Rings Of Fields., Sidney Taylor Hawkins
LSU Historical Dissertations and Theses
This dissertation establishes new lower bounds for the algebraic ranks of certain Witt classes of quadratic forms. Let K denote a field of characteristic different from 2 and let q be a quadratic form over K. The form q is said to be algebraic when q is Witt equivalent to the trace form qL∣K of some finite algebraic field extension L∣K . When q is algebraic, the algebraic rank of q is defined to be the degree of the minimal extension L∣K whose trace form is Witt equivalent to q. It is an important, unsolved problem to find reasonable bounds …
The Applications Of The Method Of Quasi Reversibility To Some Ill-Posed Problems For The Heat Equation., Xueping Ru
The Applications Of The Method Of Quasi Reversibility To Some Ill-Posed Problems For The Heat Equation., Xueping Ru
LSU Historical Dissertations and Theses
In this work, we study the Cauchy problem for the heat equation, as well as the inverse heat conduction problem, both of which are ill-posed problems in the sense of Hadamard. The first chapter provides the background material about the previous investigations on the ill-posed Cauchy problem for the heat equation and the inverse heat conduction problem by other mathematicians. The method of Quasi-Reversibility is also introduced. In the second chapter we apply the method of Quasi-Reversibility to the Cauchy problem for the heat equation and obtain a formal approximate solution. We prove that the convergence of the approximate solution …
General Riemann Integrals And Their Computation Via Domain., Bin Lu
General Riemann Integrals And Their Computation Via Domain., Bin Lu
LSU Historical Dissertations and Theses
In this work we extend the domain-theoretic approach of the generalized Riemann integral introduced by A. Edalat in 1995. We begin by laying down a related theory of general Riemann integration for bounded real-valued functions on an arbitrary set X with a finitely additive measure on an algebra of subsets of X. Based on the theory developed we obtain a formula to calculate integral of a bounded function in terms of the regular Riemann integral. By classical extension theorems on set functions we can further extend this generalized Riemann integral to more general set functions such as valuations on lattices …
Totally Ordered Monoids., Gretchen Wilke Whipple
Totally Ordered Monoids., Gretchen Wilke Whipple
LSU Historical Dissertations and Theses
In this work, we explore properties of totally ordered commutative monoids---we call them tomonoids. We build on the work in [E]. Our goal is to obtain results that will be useful for studying totally ordered rings with nilpotents. Chapter 1 presents background information. In Chapter 2, we present some criteria for determining when a tomonoid is a quotient of a totally ordered free monoid by a convex congruence. In Chapter 3, we show that every positive tomonoid of rank 2 is a convex Rees quotient of a subtomonoid of a totally ordered abelian group. In Chapter 4, we provide a …