Digital Commons Network^™

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 …

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 …

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 …

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 …

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 …

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 …

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 …

The Effects Of Applied Technology Instruction On Mathematics And Science Achievement Of Eighth Grade Students, John D. Hammons

OTS Master's Level Projects & Papers

The problem of this study was to evaluate the effectiveness of he Grafton Middle School technology education program's interdisciplinary activities in improving math and science grades of its students.

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Learning And Teaching Mathematics K-7: Book 3, Jack Bana, Brian Farrell, Ron Gleeson, Kevin Jones, Alistair Mcintosh, Paul Swan

Research outputs pre 2011

No abstract provided.

Central Sequences And C*-Algebras, Hemant Pendharkar

Doctoral Dissertations

We study central sequences of C*-algebras. We find connections of the central sequences of a C*-algebra and its representations. More specifically, we prove the following results: (a) Characterization of central sequences in certain C*-subalgebras of C(X, Mn), where X is a compact Hausdorff space. We also state the conditions under which central sequences are trivial/hypercentral. (b) A representation of the C*-algebra is in the point norm closure of the set of all equivalence classes of irreducible representation if and only if it is multiplicity free. (c) For a C*-algebra A, all of whose representations are bounded by some fixed number, …

Topics In Chaotic Secure Communication, Andrew Thomas Parker

Doctoral Dissertations

Results in nonlinear dynamics and chaos during this decade have been applied to problems in secure communications with limited success. Most of these applications have been based on the chaotic synchronization property discovered by Pecora and Carroll in 1989 [37]. Short [44, 45, 48] demonstrated the effectiveness of nonlinear dynamic (NLD) forecasting methods in breaking this class of communication schemes. In response, investigators have proposed enhancements to the basic synchronization technique in an attempt to improve the security properties. In this work two of these newer communication systems will be analyzed using NLD forecasting and other techniques to determine the …

Using Character Varieties: Presentations, Invariants, Divisibility And Determinants, Jeffrey Allan Hall

Doctoral Dissertations

If G is a finitely generated group, then the set of all characters from G into a linear algebraic group is a useful (but not complete) invariant of G . In this thesis, we present some new methods for computing with the variety of SL2C -characters of a finitely presented group. We review the theory of Fricke characters, and introduce a notion of presentation simplicity which uses these results. With this definition, we give a set of GAP routines which facilitate the simplification of group presentations. We provide an explicit canonical basis for an invariant ring associated with a symmetrically …

A Comparison Of Problem-Centered Learning Model And Guided-Practice Model On High-School Students' Mathematics Performance And Attitude, Samer G. Malouf

Master's Theses

Digitized thesis

Pseudospectral Techniques For Non -Smooth Evolutionary Problems, Chris Palmer Guenther

Graduate Theses, Dissertations, and Problem Reports (ETD)

A pseudospectral approach is used to solve non-smooth evolutionary problems using Fourier collocation and Chebyshev collocation. It is well known that pseudospectral methods for smooth problems can offer superior accuracy over finite difference and finite element methods.;This paper explores the use of pseudospectral methods for non-smooth evolutionary problems in the area of hyperbolic heat transfer. Boundary and initial conditions are considered which cause instantaneous jumps, in the temperature and flux, prior to the propagation of a thermal wave into the medium. There is a considerable amount of literature that has investigated hyperbolic heat transfer under similar conditions, the common problems …

Outline And Nearly Outline Triple Systems Of Even Index, Michael Neill Ferencak

Graduate Theses, Dissertations, and Problem Reports (ETD)

The main result of this work describes a completely novel structural result for (v, 3, lambda)-designs in the case when lambda is even. Such designs are known as triple systems. Given a finite collection of n elements, a triple system of order n and index lambda is a collection of subsets of size three chosen from the given set with the property that each distinct pair of elements from the set occurs in exactly lambda of the triples. It is well known for what values of n and lambda such systems exist. A partial triple system of order n and …

Generalized Edge Connectivity In Graphs, Kamal P. Hennayake

Graduate Theses, Dissertations, and Problem Reports (ETD)

The edge-connectivity l of a connected graph is the minimum number of edges whose deletion produces a graph with two components. For an integer l > 1, the l-edge connectivity of a graph with | V| ≥ l, denoted by l l, is the smallest number of edges whose removal results in a graph with l components. The strength of G, denoted by l&d1; (G), is the maximum value of l (H), where H runs over all subgraphs of G. In this dissertation we study lower bounds of l l and optimal graphs that reach the lower bound. Former results in …

De-Emphasizing Grade-Level Identities: A Case Study Of Mathematics Instruction In An Intermediate Elementary Multiage Classroom, Kevin Oconnor

Dissertations

This is an interpretive study that investigates the nature of the issues, dilemmas, and successes of planning and implementing a mathematics program with minimal reference to grade-level designations in a multiage classroom setting of fourth—and fifth-grade students.

The study focused on how one teacher conceptualized, designed, and structured a mathematics curriculum. An analysis of over 60 hours of interviews conducted over six months revealed a teacher who integrated her knowledge of elementary mathematics with her knowledge and practice of teaching and learning theories, mathematical understanding, curriculum perspectives, and classroom management. This integration is explained through a conceptual framework of the …

Generalizations Of Colorability And Connectivity Of Graphs, Xiankun Zhang

Graduate Theses, Dissertations, and Problem Reports (ETD)

Let G = (V, E) be a graph and A a non-trivial Abelian group, and let F( G, A) denote the set of all functions f : E (G) → A. Denote by D an orientation of E( G). Then G is A-colorable if and only if for every f ∈ F(G, A) there exists an A-coloring c: V( G) → A such that for every e = (x, y) ∈ E(G) (assumed to be directed from x to y), c( x)--c(y) ≠ f(e). We define the group chromatic number of c1 (G) to be the minimum number m for …

Development And Validation Of A Modular Hybrid Electric Vehicle Simulation Model, William Frederick Kellermeyer Iii

Graduate Theses, Dissertations, and Problem Reports (ETD)

To attempt to bring rigor and analysis to the design process, accurate simulation programs are crucial. Most hybrid electric vehicle hybrid electric vehicle (HEV) simulation programs are written for very specific component configurations and only allow changes in component sizes. These programs prove helpful only if one designs a component configuration similar to the one already simulated. A modular based program such as the one developed here allows simpler reconfiguration of the components for an accurate simulation of almost any component configuration design. This HEV simulation program allows for simulation of all three types of hybrids, with several engine types …

The Sharp Sobolev Inequality And The Banchoff-Pohl Inequality On Surfaces, Ralph Howard

Faculty Publications

No abstract provided.

Multi-Selectible Continua, Joseph Edward Mcparland

Graduate Theses, Dissertations, and Problem Reports (ETD)

A particular coexistence of multiple continuous selections (a "multi-selection") within a function space for a non-degenerate metric continuum X is investigated for the hyperspaces 2X and C(X). It is demonstrated that (i) multi-selections do not exist for 2X and that (ii) the existence of a multi-selection for C(X) is equivalent to X being a dendrite.

Asymptotic Norming Properties And Related Themes., Sudeshna Basu Dr.

Doctoral Theses

In the first part of this chapter, we explain the main theme of this thesis. The second part consists of some of the notions and results used in subsequent discussions.It is a very familiar fact that a point outside a (bounded) closed convex set in a Banach space can be separated from the latter by a hyperplane. One can ask whether the separation can be effected by disjoint balls. This is a typical example of a ball separation property, study of which has become important in Banach space theory. In this thesis, we study several such properties along with some …

On The Developement Of An Optical Character Recognition(Ocr) System For Printed Bangla Script., Umapada Pal Dr.

Doctoral Theses

This thesis concerns OCR development of machine printed text in an Indian lan- guage, Bangla (Bengali) which is the fourthmost popular language in the world and the secondmost popular language in India.1.1 Optical Character Recognition Optical Character Recognition (OCR) is a process of automatic computer recog- nition of characters in optically scanned and digitized pages of text. OCR is ene of the most fascinating and challenging areas of pattern recognition with various practical applications. It can contribute tremendously to the advancement of an automation process and can improve the interface between man and machine in many applications, including office automation …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Neuro Fuzzy Reasoning For Pattern Classification And Object Recognition., Jayati Ghosh Dr.

Doctoral Theses

In real world, pattern classification and object recognition problems are faced with fuzzi- ness that is connected with diverse facets of cognitive activity of the human being. An origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification and /or recognition procedures. Though a lot of scientific efforts have already been dedicated to pattern recognition problems, especially to classification procedures, still pattern recognition is confronted with a continuous challenge coming from a human being who can perform lot of ex- tremely complex classification tasks by …

On The Geometrisability Of Some Strongly Regular Graphs Related To Polar Spaces., Pratima Panigraphi Dr.

Doctoral Theses

GraphsA graph G = (VE) consists of a finite set V and a subset E of ). (Here () denotes the set of all 2-subsets of V.) Elements of Vare called the vertices and the elements of E are called the edges of the graph. So Vis the vertex set and E is the edge set of the graph G. Two vertices a, y are said to be adjacent if the pair {a, y} is an edge; otherwise they are non-adjacent. If two vertices are adjacent then each is called a neighbour of the other vertex.Sometimes the edges of a …

Static Interconnection Networks And Parallel Algorithms For Efficient Problem Solving., T. Krishnan Dr.

Doctoral Theses

There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.

Wiener Tauberian Theorems On Semisimple Lie Group., Rudra Pada Sarkar Dr.

Doctoral Theses

In their celebrated study of Harmonic analysis on semi-simple Lie groups Ehrenpreis and Mautner [E-M] noticed that the analogue of the claasical Wiener Tauberian theorem resting on the unitary dual does not hold for semisimple Lle groups. A simple proof of this fact due to M. Duflo appears in (H). Ehrenpreis and Mautner went on in (E-M] to formulate the problem on the commutative Banach algebra of the SO2(R)-biinvariant functions in L1(SL2(R))1, and obtained two different versions of the theorem involving, this time, the dual of the Banach algebra which includes, beside the unitary dual of G, a part of …

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …