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Articles 1 - 12 of 12
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The Structure Of Semisimple Artinian Rings, Ravi Samuel Pandian
The Structure Of Semisimple Artinian Rings, Ravi Samuel Pandian
Theses Digitization Project
Proves two famous theorems attributed to J.H.M. Wedderburn, which concern the structure of noncommutative rings. The two theorems include, (1) how any semisimple Artinian ring is the direct sum of a finite number of simple rings; and, (2) the Wedderburn-Artin Theorem. Proofs in this paper follow those outlined in I.N. Herstein's monograph Noncommutative Rings with examples and details provided by the author.
Hausdorff Dimension, Loren Beth Nemeth
Hausdorff Dimension, Loren Beth Nemeth
Theses Digitization Project
The purpose of this study was to define topological dimension and Hausdorff dimension, Namely metric space theory and measure theory. It was verified that in the sets of elementary geometry, the dimensions agree, while in the case of the fractals, the Hausdorff dimension is strictly larger than the topological dimension.
Freeness Of Hopf Algebras, Christopher David Walker
Freeness Of Hopf Algebras, Christopher David Walker
Theses Digitization Project
The Nichols-Zoeller freeness theorem states that a finite dimensional Hopf algebra is free as a module over any subHopfalgebra. We will prove this theorem, as well as the first significant generalization of this theorem, which was proven three years later. This generalization says that if the Hopf algebra is infinite dimensional, then the Hopf algebra is still free if the subHopfalgebra is finite dimensional and semisimple . We will also look at several other significant generalizations that have since been proven.
Minimal Congestion Trees, Shelly Jean Dawson
Minimal Congestion Trees, Shelly Jean Dawson
Theses Digitization Project
Analyzes the results of M.I. Ostrovskii's theorem of inequalities which estimate the minimal edge congestion for finite simple graphs. Uses the generic results of the theorem to examine and further reduce the parameters of inequalities for specific families of graphs, particularly complete graphs and complete bipartite graphs. Also, explores a possible minimal congestion tree for some grids while forming a conjecture for all grids.
The Evolution Of Equation-Solving: Linear, Quadratic, And Cubic, Annabelle Louise Porter
The Evolution Of Equation-Solving: Linear, Quadratic, And Cubic, Annabelle Louise Porter
Theses Digitization Project
This paper is intended as a professional developmental tool to help secondary algebra teachers understand the concepts underlying the algorithms we use, how these algorithms developed, and why they work. It uses a historical perspective to highlight many of the concepts underlying modern equation solving.
Modeling Queueing Systems, Angela Zoi Leontas
Modeling Queueing Systems, Angela Zoi Leontas
Theses Digitization Project
The thesis introduces the theory of queueing systems and demonstrates its applicability to real life problems. It discusses (1) Markovian property and measures of effectiveness with exponential interarrival and service times; (2) Erlang service times, and a single server; (3) different goodness-of-fit tests that can be used to determine whether the exponential distribution is appropriate for a given set of data. A single server queueing system with exponential interarrival times and Erlang service times is simulated using Visual Basic for Applications (VBA).
From Measure To Integration, Sara Hernandez Mcloughlin
From Measure To Integration, Sara Hernandez Mcloughlin
Theses Digitization Project
The thesis studies the notions of outer measure, Lebesgue measurable sets and Lebesgue measure, in detail. After developing Lebesgue integration over the real line, the Riemann integrable functions are classified as those functions whose set of points of discontinuity has measure zero. The convergence theorems are proven and it is shown how these theorems are valid under less stringent assumptions that are required for the Riemann integral. A detailed analysis of abstract measure theory for general measure spaces is given.
Aspects Of The Jones Polynomial, Alvin Mendoza Sacdalan
Aspects Of The Jones Polynomial, Alvin Mendoza Sacdalan
Theses Digitization Project
A knot invariant called the Jones polynomial will be defined in two ways, as the Kauffman Bracket polynomial and the Tutte polynomial. Three properties of the Jones polynomial are discussed. We also see how mutant knots share the same Jones polynomial.
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Theses Digitization Project
The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best paths.
Gauss-Bonnet Formula, Heather Ann Broersma
Gauss-Bonnet Formula, Heather Ann Broersma
Theses Digitization Project
From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Theses Digitization Project
A 2004 article written by Yixun Lin and Aifeng Yang published in the journal Discrete Math characterized the set of a 3-cutwidth critical graphs by five specified elements. This project extends the idea to 4-cutwidth critical graphs.
Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George
Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George
Theses Digitization Project
The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.