Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

California State University, San Bernardino

Discipline
Keyword
Publication Year
Publication
Publication Type

Articles 181 - 210 of 242

Full-Text Articles in Mathematics

Modeling Queueing Systems, Angela Zoi Leontas Jan 2006

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).

Go to article

Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George Jan 2006

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.

Go to article

The Life And Work Of D.H. Hyers, 1913-1997, Brent D. Singleton Jan 2006

The Life And Work Of D.H. Hyers, 1913-1997, Brent D. Singleton

Library Faculty Publications & Presentations

The following is a sketch of the life and work of Donald Holmes Hyers, Professor Emeritus from the University of Southern California. The theorem put forth by Hyers in 1941 concerning linear functional equations has gained a great deal of interest over the past two decades. Hundreds of articles have been written citing his works, many of which have furthered the theorem. This paper contains a brief description of Hyers’ theorem, a biographical essay and an extensive bibliography of Hyers’ work and works citing the Hyers theorem or the D.H. Hyers–S.M. Ulam–Th.M. Rassias theorem or related subjects of almost the …

Go to article

From Measure To Integration, Sara Hernandez Mcloughlin Jan 2006

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.

Go to article

Symmetric Generation Of Finite Homomorphic Images?, Lee Farber Jan 2005

Symmetric Generation Of Finite Homomorphic Images?, Lee Farber

Theses Digitization Project

The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.

Go to article

Symmetrically Generated Groups, Benny Nguyen Jan 2005

Symmetrically Generated Groups, Benny Nguyen

Theses Digitization Project

This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.

Go to article

Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle Jan 2005

Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle

Theses Digitization Project

In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.

Go to article

A Topological Approach To Nonlinear Analysis, Wendy Ann Peske Jan 2005

A Topological Approach To Nonlinear Analysis, Wendy Ann Peske

Theses Digitization Project

A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.

Go to article

Survival Analysis, Mohammad Alif Wardak Jan 2005

Survival Analysis, Mohammad Alif Wardak

Theses Digitization Project

Survival analysis pertains to a statistical approach designed to take into account the amount of time an experimental unit contributes to a study. A Mayo Clinic study of 418 Primary Biliary Cirrhosis patients during a ten year period was used. The Kaplan-Meier Estimator, a non-parametric statistic, and the Cox Proportional Hazard methods were the tools applied. Kaplan-Meier results include total values/censored values.

Go to article

Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt Jan 2005

Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt

Theses Digitization Project

Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.

Go to article

The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau Jan 2005

The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau

Theses Digitization Project

This project centers around finding specific examples of quintic polynomials that were and were not solvable. This helped to devise a method for finding examples of solvable and unsolvable quintics.

Go to article

Symmetric Representation Of Elements Of Sporadic Groups, Elena Yavorska Harris Jan 2005

Symmetric Representation Of Elements Of Sporadic Groups, Elena Yavorska Harris

Theses Digitization Project

Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.

Go to article

Root Subgroups Of The Rank Two Unitary Groups, Matthew Thomas Henes Jan 2005

Root Subgroups Of The Rank Two Unitary Groups, Matthew Thomas Henes

Theses Digitization Project

Discusses certain one-parameter subgroups of the low-rank unitary groups called root subgroups. Unitary groups also have representations of Lie type which means they consist of transformations that act as automorphisms of an underlying Lie algebra, in this case the special linear algebra. Exploring this definition of the unitary groups, we find a correlation, via exponentiation, to the basis elements of Lie algebra.

Go to article

Numbers Of Generators Of Ideals In Local Rings And A Generalized Pascal's Triangle, Lucia Riderer Jan 2005

Numbers Of Generators Of Ideals In Local Rings And A Generalized Pascal's Triangle, Lucia Riderer

Theses Digitization Project

This paper defines generalized binomial coefficients and shows that they can be used to generate generalized Pascal's Triangles and have properties analogous to binomial coefficients. It uses the generalized binomial coefficients to compute the Dilworth number and the Sperner number of certain rings.

Go to article

Various Steiner Systems, Valentin Jean Racataian Jan 2004

Various Steiner Systems, Valentin Jean Racataian

Theses Digitization Project

This project deals with the automorphism group G of a Steiner system S (3, 4, 10). S₁₀, the symmetrical group of degree 10, acts transitively on T, the set of all Steiner systems with parameters 3, 4, 10. The purpose of this project is to study the action of S₁₀ on cosets of G. This will be achieved by means of a graph of S₁₀ on T x T. The orbits of S₁₀ on T x T are in one-one correspondence with the orbits of G, the stabilizer of an S [e] T on T.

Go to article

The Use Of Divergent Series In History, Alina Birca Jan 2004

The Use Of Divergent Series In History, Alina Birca

Theses Digitization Project

In this thesis the author presents a history of non-convergent series which, in the past, played an important role in mathematics. Euler's formula, Stirling's series and Poincare's theory are examined to show the development of asymptotic series, a subdivision of divergent series.

Go to article

The Riemann Zeta Function, Ernesto Oscar Reyes Jan 2004

The Riemann Zeta Function, Ernesto Oscar Reyes

Theses Digitization Project

The Riemann Zeta Function has a deep connection with the distribution of primes. This expository thesis will explain the techniques used in proving the properties of the Rieman Zeta Function, its analytic continuation to the complex plane, and the functional equation that the the Riemann Zeta Function satisfies.

Go to article

Homomorphic Images Of Semi-Direct Products, Lamies Joureus Nazzal Jan 2004

Homomorphic Images Of Semi-Direct Products, Lamies Joureus Nazzal

Theses Digitization Project

The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.

Go to article

Symmetric Representations Of Elements Of Finite Groups, Abeir Mikhail Kasouha Jan 2004

Symmetric Representations Of Elements Of Finite Groups, Abeir Mikhail Kasouha

Theses Digitization Project

This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

Go to article

Hyperbolic Transformations On Cubics In H², Frank S. Marfai Jan 2003

Hyperbolic Transformations On Cubics In H², Frank S. Marfai

Theses Digitization Project

The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).

Go to article

Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren Jan 2003

Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren

Theses Digitization Project

The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.

Go to article

The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha Jan 2003

The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha

Theses Digitization Project

Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained.

Go to article

The Euler Line In Non-Euclidean Geometry, Elena Strzheletska Jan 2003

The Euler Line In Non-Euclidean Geometry, Elena Strzheletska

Theses Digitization Project

The main purpose of this thesis is to explore the conditions of the existence and properties of the Euler line of a triangle in the hyperbolic plane. Poincaré's conformal disk model and Hermitian matrices were used in the analysis.ʹ

Go to article

1p Spaces, Anh Tuyet Tran Jan 2002

1p Spaces, Anh Tuyet Tran

Theses Digitization Project

In this paper we will study the 1p spaces. We will begin with definitions and different examples of 1p spaces. In particular, we will prove Holder's and Minkowski's inequalities for 1p sequence.

Go to article

Renewal Theory For Uniform Random Variables, Steven Robert Spencer Jan 2002

Renewal Theory For Uniform Random Variables, Steven Robert Spencer

Theses Digitization Project

This project will focus on finding formulas for E[N(t)] using one of the classical problems in the discipline first, and then extending the scope of the problem to include overall times greater than the time t in the original problem. The expected values in these cases will be found using the uniform and exponential distributions of random variables.

Go to article

The Cyclic Cutwidth Of Mesh Cubes, Dwayne William Clarke Jan 2002

The Cyclic Cutwidth Of Mesh Cubes, Dwayne William Clarke

Theses Digitization Project

This project's purpose was to understand the workings of a new theorem introduced in a professional paper on the cutwidth of meshes and then use this knowledge to apply it to the search for the cyclic cutwidth of the n-cube.

Go to article

Fundamental Theorem Of Algebra, Paul Shibalovich Jan 2002

Fundamental Theorem Of Algebra, Paul Shibalovich

Theses Digitization Project

The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.

Go to article

Egyptian Fractions, Jodi Ann Hanley Jan 2002

Egyptian Fractions, Jodi Ann Hanley

Theses Digitization Project

Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception, by the Egyptians, of 2/3. Egyptian fractions have actually played an important part in mathematics history with its primary roots in number theory. This paper will trace the history of Egyptian fractions by starting at the time of the Egyptians, working our way to Fibonacci, a geologist named Farey, continued fractions, Diophantine equations, and unsolved problems in number theory.

Go to article

Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun Jan 2000

Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun

Theses Digitization Project

No abstract provided.

Go to article

Solutions To The Chinese Postman Problem, Kenneth Peter Cramm Jan 2000

Solutions To The Chinese Postman Problem, Kenneth Peter Cramm

Theses Digitization Project

Considering the Chinese Postman Problem, in which a mailman must deliver mail to houses in a neighborhood. The mailman must cover each side of the street that has houses, at least once. The focus of this paper is our attempt to discover the optimal path, or the least number of times each street is walked. The integration of algorithms from graph theory and operations research form the method used to explain solutions to the Chinese Postman Problem.

Go to article

First Prev Next Last