Mathematics Commons^™

Spectral Analysis And Synthesis For Radial Sections Of Homogenous Vector Bundles On Certain Noncompath Riemannian Symmetric Spaces., Sanjoy Pusti Dr.

Doctoral Theses

We consider two classical theorems of real analysis which deals with translation invariant subspaces of integrable and smooth functions on R respectively. The first one is a theorem of Norbert Wiener [63] which states that if the Fourier transform of a function f ∈ L 1 (R) has no real zeros then the finite linear combinations of translations f(x − a) of f with complex coefficients form a dense subspace in L 1 (R), equivalently, span{g ∗ f | g ∈ L 1 (R)} is dense in L 1 (R). This theorem is well known as the Wiener-Tauberian Theorem (WTT). …

Homogeneous Operators In The Cowen-Douglas Class., Subrata Shyam Roy Dr.

Doctoral Theses

Although, we have used techniques developed in the paper of Cowen-Douglas [18, 20], a systematic account of Hilbert space operators using a variety of tools from several different areas of mathematics is given in the book [26]. This book provides, what the authors call, a sheaf model for a large class of commuting Hilbert space operators. It is likely that these ideas will play a significant role in the future development of the topics discussed here.

The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas

Theses Digitization Project

This project is an expository survey of the Universal Coefficient Theorem for Cohomology. Algebraic preliminaries, homology, and cohomology are discussed prior to the proof of the theorem.

The Fundamental Group And Van Kampen's Theorem, Aaron Christopher Thomas

Theses Digitization Project

This thesis deals with the field of algebraic topology. Basic topological facts are addressed including open and closed sets, continuity, homeomorphisms, and path connectedness as well as discussing Van Kampen's Theorem in detail.

There Are Only Four, Danielle Josette Mccoy

Theses Digitization Project

This paper is an investigation of finite-dimensional normed algebras over the reals from both an abstract and concrete point of view.

Cooperative Learning In The Mathematics Classroom, Janine Regnier

Mathematics Graduate Theses

Student interactions are important which provokes the idea that cooperative learning should be incorporated into classrooms. Research states many benefits for incorporating cooperative learning and are included in the literature review. Cooperative groups were introduced and studied by the author, who ultimately concluded that cooperative learning does have a place in Mathematics classrooms and should be used when the lesson lends itself to a cooperative environment. The study results can be found in this paper following the literature review.

The Classification Of Simple Lie Algebras In Maple, D. Russell Sadler

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Lie algebras are invaluable tools in mathematics and physics as they enable us to study certain geometric objects such as Lie groups and differentiable manifolds. The computer algebra system Maple has several tools in its Lie Algebras package to work with Lie algebras and Lie groups. The purpose of this paper is to supplement the existing software with tools that are essential for the classification of simple Lie algebras over C.

In particular, we use a method to find a Cartan subalgebra of a Lie algebra in polynomial time. From the Cartan subalgebra we can compute the corresponding root system. …

Hands-On Activities And Activities Involving Technology To Help Students Construct Concepts And Gain A Deeper Understanding And Appreciation For Mathematical Concepts Based On The Utah Core Curriculum For Algebra Ii, Brookeann Watterson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Research shows there are several methods that expand students' understanding, appreciation for, and interest in mathematics by following teaching strategies. These strategies include incorporating hands-on activities, technology, discovery learning, cooperative learning, and having activities be applicable to real world contexts. This project focuses specifically on activities based on objectives from the Utah State Core for Algebra II that incorporate such strategies in five units: (I) absolute value, (2) exponential growth /decay and logarithms, (3) trigonometric functions, (4) probability, permutations and combinations, and (5) statistics.

Chinese Remainder Theorem And Its Applications, Jacquelyn Ha Lac

Theses Digitization Project

No abstract provided.

N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …

The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza

MPP Published Research

Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …

Some Necessary Conditions Of Boolean Functions To Resist Algebraic Attacks., Deepak Dalai Dr.

Doctoral Theses

No abstract provided.

Infinite Product Group, Keith G. Penrod

Theses and Dissertations

The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.

Structural Properties Of Formal Polynomial Algebras In Noncommuting Or Nonassociating Indeterminates, Serge C. Ballif

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In order to enlarge the class of equations provided by traditional polynomials over a binary algebra A to a more useful class of equations, we introduce polynomials in noncommuting or nonassociating indeterminates. We discuss algebraic properties of these formal polynomial algebras and their accompanying polynomial function algebras. We present certain basis results for polynomial algebras, which are used to address the question of zero divisors in a polynomial algebra. We give an analog of the remainder theorem and the factor theorem for polynomials. Particular emphasis is placed on showing the difference between polynomials and polynomial functions. We also provide a …

Reality Properties Of Conjugacy Classes In Algebraic Groups., Anupam Kumar Singh Dr.

Doctoral Theses

In this thesis we denote a field by k. We consider fields of characteristic not 2 unless stated otherwise. The notation ¯k and ks denotes an algebraic closure and separable closure of k respectively. The symbols Q, R, C will denote fields of rational, real, complex numbers respectively. The symbol Z will denote the set of integers. We denote by cd(k) the cohomological dimension of k.We use G to denote an algebraic group and G(k) to denote the group of k rational points of G. Sometimes we abuse notation and denote the group of ¯k points of G by G. …

Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.

Doctoral Theses

Cone Linear Complementarity ProblemLet V be a finite dimensional real inner product space and K be a closed convex cone in V. Given a linear transformation L : V → V and a vector q ∈ V the cone linear complementarity problem or linear complementarity problem over K, denoted as LCP(K, L, q), is to find a vector x ∈ K such thatL(x) + q ∈ K+ and hx, L(x) + qi = 0,where h., .i denotes an inner product on V and K is the dual cone of K defined as:K∗ := {y ∈ V : hx, yi ≥ …

Torsion-Free Groups And Modules With The Involution Property, Brendan Goldsmith, C. Meehan, S.L. Wallutis

Articles

An Abelian group or module is said to have the involution property if every endomorphism is the sum of two automorphisms, one of which is an involution. We investigate this property for completely decomposable torsion-free Abelian groups and modules over the ring of -adic integers.

On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth

Mathematics Faculty Publications

A proper short exact sequence in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of …

Quantum Stochastic Dilation Of A Class Of Quantum Dynamical Semigroups And Quantum Random Walks., Lingaraj Sahu Dr.

Doctoral Theses

No abstract provided.

Notes For Mat 7500 – Winter '93, Revised Winter '06, David Handel

Mathematics Faculty Research Publications

These notes developed from a one semester course at Wayne State University, taught several times in the last three decades of the 1900s. The subject matter is analysis on manifolds, consisting of the theory of smooth manifolds, differential forms, integration of forms, the generalized Stokes' Theorem, de Rham cohomology, and some related topics. The course is intended for first or second year graduate students in Mathematics with a background in Advanced Calculus, General Topology, linear algebra (including quotient spaces), and a little elementary group theory (including some familiarity with the symmetric groups). Given the above background, the notes are self-contained. …

Classifying E-Algebras Over Dedekind Domains, Brendan Goldsmith, R. Gobel

Articles

An R-algebra A is said to be a generalized E-algebra if A is isomorphic to the algebra EndR(A). Generalized E-algebras have been extensively investigated. In this work they are classified ‘modulo cotorsion-free modules’ when the underlying ring R is a Dedekind domain.

The Classical Dirichlet Space, William T. Ross

Department of Math & Statistics Faculty Publications

In this survey paper, we will present a selection of results concerning the class of analytic functions f on the open unit disk D := {z ϵ C : │z│ < 1} which have finite Dirichlet integral.

Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr.

Doctoral Theses

In this thesis we study combinatorial aspects of Boolean functions and S-boxes with impor- tant cryptographic properties and construct new functions possesing such properties. These have possible applications in the design of private key (symmetric key) cryptosystems.Symmetric key cryptosystems are broadly divided into two classes.1. Stream Ciphers,2. Block Ciphers.Some recent proposals of stream ciphers are SNOW [37], SCREAM [52], TURING (98], MUGI (117), HBB (102], RABBIT (9), HELIX (38] and some proposals of block ciphers are DES, AES, RC6 [97), MARS (12], SERPENT (6], TWOFISH (104].In stream cipher cryptography a pseudorandom sequence of bits of length cqual to the message …

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.

On Banach Lattice Algebras, Ayşe Uyar

Turkish Journal of Mathematics

In this study, without using the assumption a^{-1} > 0, it is shown that E is lattice - and algebra - isometric isomorphic to the reals R whenever E is a Banach lattice f-algebra with unit e, e = 1, in which for every a > 0 the inverse a^{-1} exists. Subsequently, an alternative proof to a result of Huijsmans is given for Banach lattice algebras.

Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth

Mathematics Faculty Publications

In this note, we prove that in a Hausdorff topological abelian group, the closed subgroup generated by all compact elements is equal to teh closed subgroup generated by all compact elements which are topologically p-torsion for some prime p. In particular, this yields a new, short solution to a question raised by Armacost [A]. Using Pontrjagin duality, we obtain new descriptions of the identity component of a locally compact abelian group.

Fermat's Last Theorem For Rational Exponents, Curtis D. Bennett, A. M. W. Glass, Gábor J. Székely

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

Intersection Properties Of Balls In Banach Spaces And Related Topics., Sudipta Dutta Dr.

Doctoral Theses

In the first part of this chapter, we explain in general terms the background and the main theme of this thesis and provide a chapter-wise summary of its principal results. In the second part, we introduce some notations and preliminaries that will be used in the subsequent chapters.As a prototype of the properties we will study in this thesis, let us call a closed linear subspace Y of a Banach space X a (P)-subspace of X if Y has a certain property P as a subspace of X. If a Banach space X, in its canonical embedding, is a (P)-subspace …

The Effects Of The Cognitive Tutor Algebra On Student Attitudes And Achievement In A 9th Grade Algebra Course, Gary S. Plano

Seton Hall University Dissertations and Theses (ETDs)

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