Mathematical Reasoning And The Inductive Process: An Examination Of The Law Of Quadratic Reciprocity,
2016
California State University - San Bernardino
Mathematical Reasoning And The Inductive Process: An Examination Of The Law Of Quadratic Reciprocity, Nitish Mittal
Electronic Theses, Projects, and Dissertations
This project investigates the development of four different proofs of the law of quadratic reciprocity, in order to study the critical reasoning process that drives discovery in mathematics. We begin with an examination of the first proof of this law given by Gauss. We then describe Gauss’ fourth proof of this law based on Gauss sums, followed by a look at Eisenstein’s geometric simplification of Gauss’ third proof. Finally, we finish with an examination of one of the modern proofs of this theorem published in 1991 by Rousseau. Through this investigation we aim to analyze the different strategies used in …
Realizing Tournaments As Models For K-Majority Voting,
2016
California State University - San Bernardino
Realizing Tournaments As Models For K-Majority Voting, Gina Marie Cheney
Electronic Theses, Projects, and Dissertations
A k-majority tournament is a directed graph that models a k-majority voting scenario, which is realized by 2k - 1 rankings, called linear orderings, of the vertices in the tournament. Every k-majority voting scenario can be modeled by a tournament, but not every tournament is a model for a k-majority voting scenario. In this thesis we show that all acyclic tournaments can be realized as 2-majority tournaments. Further, we develop methods to realize certain quadratic residue tournaments as k-majority tournaments. Thus, each tournament within these classes of tournaments is a model for a k …
Upset Paths And 2-Majority Tournaments,
2016
California State University, San Bernardino
Upset Paths And 2-Majority Tournaments, Rana Ali Alshaikh
Electronic Theses, Projects, and Dissertations
In 2005, Alon, et al. proved that tournaments arising from majority voting scenarios have minimum dominating sets that are bounded by a constant that depends only on the notion of what is meant by a majority. Moreover, they proved that when a majority means that Candidate A beats Candidate B when Candidate A is ranked above Candidate B by at least two out of three voters, the tournament used to model this voting scenario has a minimum dominating set of size at most three. This result gives 2-majority tournaments some significance among all tournaments and motivates us to investigate when …
The Kauffman Bracket And Genus Of Alternating Links,
2016
California State University, San Bernardino
The Kauffman Bracket And Genus Of Alternating Links, Bryan M. Nguyen
Electronic Theses, Projects, and Dissertations
Giving a knot, there are three rules to help us finding the Kauffman bracket polynomial. Choosing knot’s orientation, then applying the Seifert algorithm to find the Euler characteristic and genus of its surface. Finally finding the relationship of the Kauffman bracket polynomial and the genus of the alternating links is the main goal of this paper.
Chromatic Connectivity Of Graphs,
2016
Western Michigan University
Mathematics Without Apologies: Portrait Of A Problematic Vocation (Book Review),
2016
Dordt College
Mathematics Without Apologies: Portrait Of A Problematic Vocation (Book Review), Calvin Jongsma
Faculty Work Comprehensive List
Reviewed Title: Mathematics Without Apologies: Portrait of a Problematic Vocation by Michael Harris. Princeton, NJ: Princeton University Press, 2015. 438 pages. ISBN: 9780691154237.
Machine Learning For Disease Prediction,
2016
Brigham Young University
Machine Learning For Disease Prediction, Abraham Jacob Frandsen
Theses and Dissertations
Millions of people in the United States alone suffer from undiagnosed or late-diagnosed chronic diseases such as Chronic Kidney Disease and Type II Diabetes. Catching these diseases earlier facilitates preventive healthcare interventions, which in turn can lead to tremendous cost savings and improved health outcomes. We develop algorithms for predicting disease occurrence by drawing from ideas and techniques in the field of machine learning. We explore standard classification methods such as logistic regression and random forest, as well as more sophisticated sequence models, including recurrent neural networks. We focus especially on the use of medical code data for disease prediction, …
The Evolution Of Cryptology,
2016
California State University - San Bernardino
The Evolution Of Cryptology, Gwendolyn Rae Souza
Electronic Theses, Projects, and Dissertations
We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of …
Ádám's Conjecture And Arc Reversal Problems,
2016
California State University - San Bernardino
Ádám's Conjecture And Arc Reversal Problems, Claudio D. Salas
Electronic Theses, Projects, and Dissertations
A. Ádám conjectured that for any non-acyclic digraph D, there exists an arc whose reversal reduces the total number of cycles in D. In this thesis we characterize and identify structure common to all digraphs for which Ádám's conjecture holds. We investigate quasi-acyclic digraphs and verify that Ádám's conjecture holds for such digraphs. We develop the notions of arc-cycle transversals and reversal sets to classify and quantify this structure. It is known that Ádám's conjecture does not hold for certain infinite families of digraphs. We provide constructions for such counterexamples to Ádám's conjecture. Finally, we address a conjecture …
Weakly Holomorphic Modular Forms In Prime Power Levels Of Genus Zero,
2016
Brigham Young University
Weakly Holomorphic Modular Forms In Prime Power Levels Of Genus Zero, David Joshua Thornton
Theses and Dissertations
Let N ∈ {8,9,16,25} and let M#0(N) be the space of level N weakly holomorphic modular functions with poles only at the cusp at infinity. We explicitly construct a canonical basis for M#0(N) indexed by the order of the pole at infinity and show that many of the coefficients of the elements of these bases are divisible by high powers of the prime dividing the level N. Additionally, we show that these basis elements satisfy an interesting duality property. We also give an argument that extends level 1 results …
Periodic Points And Surfaces Given By Trace Maps,
2016
Brigham Young University
Periodic Points And Surfaces Given By Trace Maps, Kevin Gregory Johnston
Theses and Dissertations
In this thesis, we consider the properties of diffeomorphisms of R3 called trace maps. We begin by introducing the definition of the trace map. The group B3 acts by trace maps on R3. The first two chapters deal with the action of a specific element of B3,called αn. In particular, we study the fixed points of αn lying on a topological subspace contained in R3, called T . We investigate the duality of the fixed points of the action ofαn, which will be defined later in the thesis.Chapter 3 involves the study of the fixed points of an element called …
Schur Rings Over Projective Special Linear Groups,
2016
Brigham Young University
Schur Rings Over Projective Special Linear Groups, David R. Wagner
Theses and Dissertations
This thesis presents an introduction to Schur rings (S-rings) and their various properties. Special attention is given to S-rings that are commutative. A number of original results are proved, including a complete classification of the central S-rings over the simple groups PSL(2,q), where q is any prime power. A discussion is made of the counting of symmetric S-rings over cyclic groups of prime power order. An appendix is included that gives all S-rings over the symmetric group over 4 elements with basic structural properties, along with code that can be used, for groups of comparatively small order, to enumerate all …
Existence Of A Periodic Brake Orbit In The Fully Symmetricplanar Four Body Problem,
2016
Brigham Young University - Provo
Existence Of A Periodic Brake Orbit In The Fully Symmetricplanar Four Body Problem, Ammon Si-Yuen Lam
Theses and Dissertations
We investigate the existence of a symmetric singular periodic brake orbit in the equal mass, fully symmetric planar four body problem. Using regularized coordinates, we remove the singularity of binary collision for each symmetric pair. We use topological and symmetry tools in our investigation.
Essays On Inequality, Polarization And Contests.,
2016
Indian Statistical Institute
Essays On Inequality, Polarization And Contests., Bhargav Bhattacharya Dr.
Doctoral Theses
No abstract provided.
On Solutions For Linear And Nonlinear Schrödinger Equations With Variable Coefficients: A Computational Approach,
2016
The University of Texas Rio Grande Valley
On Solutions For Linear And Nonlinear Schrödinger Equations With Variable Coefficients: A Computational Approach, Gabriel Amador, Kiara Colon, Nathalie Luna, Gerardo Mercado, Enrique Pereira, Erwin Suazo
School of Mathematical & Statistical Sciences Faculty Publications
In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them to the standard NLS models. Consequently, we can construct bright-, dark- and Peregrine-type soliton solutions for NLS with variable coefficients. As an important application of solutions for the Riccati equation with parameters, by means of computer algebra systems, it is shown that the parameters change the dynamics of the solutions. Finally, we test numerical approximations for the …
The Contributions Of Anatol Rapoport To Game Theory,
2016
Western University
The Contributions Of Anatol Rapoport To Game Theory, Erika Simpson
Political Science Publications
Game theory is used to rationally and dispassionately examine the strategic behaviour of nations, especially superpower behaviour. This article explains how basic game theory - at its simplest level - was used by Anatol Rapoport to generate ideas about how to enhance world peace. Rapoport was at the forefront of the game theoreticians who sought to conceptualize strategies that could promote international cooperation. Accordingly, the basic logic of game theory is explained using the game models of ‘Chicken’ and ‘Prisoner’s Dilemma’. These models were used by Rapoport in his books and lectures in simple and complex ways. Then Rapoport’s revolutionary …
Partitions Of Finite Frames,
2016
Rowan University
Partitions Of Finite Frames, James Michael Rosado
Theses and Dissertations
An open question stated by Marcus, Spielman, and Srivastava [10] asks "whether one can design an efficient algorithm to find the partitions guaranteed by Corollary 1.5." This corollary states that given a set of vectors in C whose outer products sum to the identity there exists a partition of these vectors such that norms of the outer-product sums of each subset satisfy an inequality bound. Here particular types of vector sets called finite frames are analyzed and constructed to satisfy the inequality described in Corollary 1.5. In this thesis, rigorous proofs and formulations of outer-product norms are utilized to find …
An Investigation Of Minimal Surfaces In So(3),
2016
Rose-Hulman Institute of Technology
An Investigation Of Minimal Surfaces In So(3), Luke Bohn
Rose-Hulman Undergraduate Research Publications
Classical minimal surface theory can be thought of as dealing with the shapes of soap films stretched across wires in Euclidean space R3. This article will examine such structures in an abstract three-dimensional space, the Lie Group SO(3). This is the space of possible rotations in R3, where each rotation is expressed as three angles: two to indicate the axis of rotation and one to indicate the amount of rotation. The properties of the space SO(3) may result in minimal surfaces that behave differently than they do in R3.
Nonlinear Harmonic Modes Of Steel Strings On An Electric Guitar,
2016
Linfield College
Nonlinear Harmonic Modes Of Steel Strings On An Electric Guitar, Joel Wenrich
Senior Theses
Steel strings used on electric and acoustic guitars are non-ideal oscillators that can produce imperfect intonation. According to theory, this intonation should be a function of the bending stiffness of the string, which is related to the dimensions of length and thickness of the string. To test this theory, solid steel strings of three different linear densities were analyzed using an oscilloscope and a Fast Fourier Transform function. We found that strings exhibited more drastic nonlinear harmonic behavior as their effective length was shortened and as linear density increased.
Hydrodynamic Theories For Flows Of Active Liquid Crystals And The Generalized Onsager Principle,
2016
UNC Chapel Hill
Hydrodynamic Theories For Flows Of Active Liquid Crystals And The Generalized Onsager Principle, Xiaogang Yang, Jun Li, M. Gregory Forest, Qi Wang
Faculty Publications
We articulate and apply the generalized Onsager principle to derive transport equations for active liquid crystals in a fixed domain as well as in a free surface domain adjacent to a passive fluid matrix. The Onsager principle ensures fundamental variational structure of the models as well as dissipative properties of the passive component in the models, irrespective of the choice of scale (kinetic to continuum) and of the physical potentials. Many popular models for passive and active liquid crystals in a fixed domain subject to consistent boundary conditions at solid walls, as well as active liquid crystals in a free …
