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The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant 2015 East Tennessee State University

The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant

Electronic Theses and Dissertations

In this thesis, we explore the effect of restricting the coefficients of polynomials on the bounds for the number of zeros in a given region. The results presented herein build on a body of work, culminating in the generalization of bounds among three classes of polynomials. The hypotheses of monotonicity on each class of polynomials were further subdivided into sections concerning r reversals among the moduli, real parts, and both real and imaginary parts of the coefficients.


Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai 2015 East Tennessee State University

Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

Electronic Theses and Dissertations

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial ...


Mathematics In Contemporary Society Chapter 1, Patrick J. Wallach 2015 Queensborough Community College

Mathematics In Contemporary Society Chapter 1, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook will be posted in weekly installments.


Geometric Constructions From An Algebraic Perspective, Betzabe Bojorquez 2015 California State University-San Bernardino

Geometric Constructions From An Algebraic Perspective, Betzabe Bojorquez

Electronic Theses, Projects, and Dissertations

Many topics that mathematicians study at times seem so unrelated such as Geometry and Abstract Algebra. These two branches of math would seem unrelated at first glance. I will try to bridge Geometry and Abstract Algebra just a bit with the following topics. We can be sure that after we construct our basic parallel and perpendicular lines, bisected angles, regular polygons, and other basic geometric figures, we are actually constructing what in geometry is simply stated and accepted, because it will be proven using abstract algebra. Also we will look at many classic problems in Geometry that are not possible ...


Hilbert Spaces And Fourier Series, Terri Joan Harris Mrs. 2015 California State University - San Bernardino

Hilbert Spaces And Fourier Series, Terri Joan Harris Mrs.

Electronic Theses, Projects, and Dissertations

I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.


Problems In The Theory Of Extremal Graphs And Hypergraphs, Cory T. Palmer 2015 University of Montana - Missoula

Problems In The Theory Of Extremal Graphs And Hypergraphs, Cory T. Palmer

University Grant Program Reports

Objective: Investigate the tree packing conjecture from graph theory and extremal numbers for hypergraphs.


On Dedekind’S “Über Die Permutationen Des Körpers Aller Algebraischen Zahlen", Joseph JP Arsenault Jr 2015 University of Maine - Main

On Dedekind’S “Über Die Permutationen Des Körpers Aller Algebraischen Zahlen", Joseph Jp Arsenault Jr

Electronic Theses and Dissertations

We provide an analytic read-through of Richard Dedekind's 1901 article “Über die Permutationen des Körpers aller algebraischen Zahlen," describing the principal results concerning infinite Galois theory from both Dedekind's point of view and a modern perspective, noting an apparently uncorrected error in the supplement to the article in the Collected Works. As there is no published English-language translation of the article, we provide an annotated original translation.


A Study Of Green’S Relations On Algebraic Semigroups, Allen O'Hara 2015 The University of Western Ontario

A Study Of Green’S Relations On Algebraic Semigroups, Allen O'Hara

Electronic Thesis and Dissertation Repository

The purpose of this work is to enhance the understanding regular algebraic semigroups by considering the structural influence of Green's relations. There will be three chief topics of discussion.

  • Green's relations and the Adherence order on reductive monoids
  • Renner’s conjecture on regular irreducible semigroups with zero
  • a Green’s relation inspired construction of regular algebraic semigroups

Primarily, we will explore the combinatorial and geometric nature of reductive monoids with zero. Such monoids have a decomposition in terms of a Borel subgroup, called the Bruhat decomposition, which produces a finite monoid, R, the Renner monoid. We will explore ...


Pseudo Schur Complements, Pseudo Principal Pivot Transforms And Their Inheritance Properties, K. C. Sivakumar, Ravindran G., Kavita Bisht 2015 Indian Institute of Technology - Madras

Pseudo Schur Complements, Pseudo Principal Pivot Transforms And Their Inheritance Properties, K. C. Sivakumar, Ravindran G., Kavita Bisht

Electronic Journal of Linear Algebra

Extensions of the Schur complement and the principal pivot transform, where the usual inverses are replaced by the Moore-Penrose inverse, are revisited. These are called the pseudo Schur complement and the pseudo principal pivot transform, respectively. First, a generalization of the characterization of a block matrix to be an M-matrix is extended to the nonnegativity of the Moore-Penrose inverse. A comprehensive treatment of the fundamental properties of the extended notion of the principal pivot transform is presented. Inheritance properties with respect to certain matrix classes are derived, thereby generalizing some of the existing results. Finally, a thorough discussion on the ...


Fourier Inequalities In Lorentz And Lebesgue Spaces, Javad Rastegari Koopaei 2015 The University of Western Ontario

Fourier Inequalities In Lorentz And Lebesgue Spaces, Javad Rastegari Koopaei

Electronic Thesis and Dissertation Repository

Mapping properties of the Fourier transform between weighted Lebesgue and Lorentz spaces are studied. These are generalizations to Hausdorff-Young and Pitt’s inequalities. The boundedness of the Fourier transform on $R^n$ as a map between Lorentz spaces leads to weighted Lebesgue inequalities for the Fourier transform on $R^n$ .

A major part of the work is on Fourier coefficients. Several different sufficient conditions and necessary conditions for the boundedness of Fourier transform on unit circle, viewed as a map between Lorentz $\Lambda$ and $\Gamma$ spaces are established. For a large range of Lorentz indices, necessary and sufficient conditions for ...


Signless Laplacian Spectral Characterization Of Some Joins, Xiaogang Liu, Pengli Lu 2015 Northwestern Polytechnical University-Xi'an and University of Melbourne

Signless Laplacian Spectral Characterization Of Some Joins, Xiaogang Liu, Pengli Lu

Electronic Journal of Linear Algebra

The join of two disjoint graphs G and H, denoted by G ∨ H, is the graph obtained by joining each vertex of G to each vertex of H. In this paper, the signless Laplacian characteristic polynomial of the join of two graphs is first formulated. And then, a lower bound for the i-th largest signless Laplacian eigenvalue of a graph is given. Finally, it is proved that G ∨ K_m, where G is an (n − 2)-regular graph on n vertices, and K_n ∨ K_2 except for n = 3, are determined by their signless Laplacian spectra.


Combinatorial Polynomial Identity Theory, Mayada Khalil Shahada 2015 The University of Western Ontario

Combinatorial Polynomial Identity Theory, Mayada Khalil Shahada

Electronic Thesis and Dissertation Repository

This dissertation consists of two parts. Part I examines certain Burnside-type conditions on the multiplicative semigroup of an (associative unital) algebra $A$.

A semigroup $S$ is called $n$-collapsing if, for every $a_1,\ldots, a_n \in S$, there exist functions $f\neq g$ on the set $\{1,2,\ldots,n\}$ such that \begin{center} $s_{f(1)}\cdots s_{f(n)} = s_{g(1)}\cdots s_{g(n)}$. \end{center} If $f$ and $g$ can be chosen independently of the choice of $s_1,\ldots,s_n$, then $S$ satisfies a semigroup identity. A semigroup $S$ is called $n$-rewritable if $f ...


Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi 2015 The University of Western Ontario

Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi

Electronic Thesis and Dissertation Repository

This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.

In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties ...


Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica 2015 University of Southern Mississippi

Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica

Dissertations

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits ...


Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor) 2015 University of California, Berkeley

Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)

Idaho Conference on Undergraduate Research

With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an ...


Lorentz Invariant Spacelike Surfaces Of Constant Mean Curvature In Anti-De Sitter 3-Space, Jamie Patrick Lambert 2015 University of Southern Mississippi

Lorentz Invariant Spacelike Surfaces Of Constant Mean Curvature In Anti-De Sitter 3-Space, Jamie Patrick Lambert

Master's Theses

In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space H31(−c2) of constant curvature −c2. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in H31(−c2). I also studied the limit behavior of those constant mean curvature c surfaces in H31(−c2). It turns out that they approach a maximal catenoid in Minkowski 3-space E31 as c 0. The limit maximal catenoid is Lorentz invariant in ...


Dynamic Approach To K-Forcing, Yair Caro, Ryan Pepper 2015 University of Houston - Downtown

Dynamic Approach To K-Forcing, Yair Caro, Ryan Pepper

Theory and Applications of Graphs

The k-forcing number of a graph is a generalization of the zero forcing number. In this note, we give a greedy algorithm to approximate the k-forcing number of a graph. Using this dynamic approach, we give corollaries which improve upon two theorems from a recent paper of Amos, Caro, Davila and Pepper [2], while also answering an open problem posed by Meyer [9].


Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D., 2015 AAR Aerospace Consulting, LLC

Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D.,

International Journal of Aviation, Aeronautics, and Aerospace

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and ...


Smooth Representation Of Functions On Non-Periodic Domains By Means Of The Fourier Continuation Method, Nicholas Rubel, David Bilyeu, Justin Koo 2015 University of Texas at Arlington

Smooth Representation Of Functions On Non-Periodic Domains By Means Of The Fourier Continuation Method, Nicholas Rubel, David Bilyeu, Justin Koo

STAR (STEM Teacher and Researcher) Program Posters

This report examines a new methodology in solving Partial Differential Equations (PDEs) numerically. The report also studies the accuracy of this new method as a PDE solver. This new Fourier Continuation (FC) method is one of a few that avoids the well-known Gibbs Phenomenon, which is the overestimation or underestimation of a function. These estimations are oscillations around a “jump” when a non-periodic function is expressed in terms of sines and cosines. Instead, the FC algorithm creates a smooth, periodic extension of a function over a general domain, as demonstrated by the many examples presented here. The FC algorithm was ...


Graph Centers, Hypergraph Degree Sequences, And Induced-Saturation, Sarah Lynne Behrens 2015 University of Nebraska-Lincoln

Graph Centers, Hypergraph Degree Sequences, And Induced-Saturation, Sarah Lynne Behrens

Dissertations, Theses, and Student Research Papers in Mathematics

The center of a graph is the set of vertices whose distance to other vertices is minimal. The centralizing number of a graph G is the minimum number of additional vertices in any graph H where V(G) is the center of H. Buckley, Miller, and Slater and He and Liu provided infinite families of graphs with each centralizing number. We show the number of graphs with each nonzero centralizing number grows super-exponentially with the number of vertices. We also provide a method of altering graphs without changing the centralizing number and give results about the centralizing number of dense ...


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