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Articles 61 - 90 of 255
Full-Text Articles in Mathematics
Transpose Symmetry Groups Of Noninvertible Polynomials, Nathan Cordner, Dr. Tyler Jarvis
Transpose Symmetry Groups Of Noninvertible Polynomials, Nathan Cordner, Dr. Tyler Jarvis
Journal of Undergraduate Research
Introduction Mirror symmetry is an area of mathematical research that stems from theoretical physics, particularly from string theory. Solutions of problems in mirror symmetry yield not only interesting mathematical results, but also have important theoretical implications for high energy particle physics.
Byu Computational Number Theory Research Group David Cardon, Darrin Doud, Paul Jenkins, And Pace Nielsen, Pace Nielsen
Byu Computational Number Theory Research Group David Cardon, Darrin Doud, Paul Jenkins, And Pace Nielsen, Pace Nielsen
Journal of Undergraduate Research
In the years 2013-2014 we held a weekly seminar in which every supported student gave presentations at least once (but usually twice or more) per semester. This gave the students opportunities to learn and develop presentations skills, which will help them later in their careers. It also gave them opportunities to work together in a tight-knit group setting. This learning was augmented by regular, one-on-one weekly meetings with their advisors. Many of the students wrote professional research papers published in peer-reviewed journals, presented their research at conferences, and many won prestigious university and even national awards.
Leveraging Mosts (Mathematically Significant Pedagogical Opportunities To Build On Student Thinking), Keith R. Leatham, Blake E. Peterson
Leveraging Mosts (Mathematically Significant Pedagogical Opportunities To Build On Student Thinking), Keith R. Leatham, Blake E. Peterson
Journal of Undergraduate Research
Phase 1, Goal 1: Purposefully create a data set of videotapes and transcripts of secondary classroom mathematics discourse that reflects the student mathematical thinking that can occur in diverse classrooms.
Computational Modeling Of Wave Propagation In Metamaterials, Shue-Sum Chow
Computational Modeling Of Wave Propagation In Metamaterials, Shue-Sum Chow
Journal of Undergraduate Research
The project is concerned with the study of wave propagation in metamaterials. We recall the work plan described in the original proposal and provide an evaluation of the academic objectives.
Defining The Transpose Group In Landau-Ginzburg Mirror Symmetry, Lisa Bendall, Dr. Tyler Jarvis
Defining The Transpose Group In Landau-Ginzburg Mirror Symmetry, Lisa Bendall, Dr. Tyler Jarvis
Journal of Undergraduate Research
Introduction. Mirror symmetry is a phenomenon first observed in theoretical physics, which has garnered interest among mathematicians. The Landau-Ginzburg mirror symmetry conjecture proposes two algebraic structures which are isomorphic, or in some sense “mirror” each other. These structures are built from polynomials and corresponding symmetry groups.
The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
Theses and Dissertations
The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region in the covering space that is guaranteed to contain T. We will then provide an algorithm for solving the n-point Steiner problem on such a surface.
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
Theses and Dissertations
Understanding cell motion facilitates the understanding of many biological processes such as wound healing and cancer growth. Constructing mathematical models that replicate amoeboid cell motion can help us understand and make predictions about real-world cell movement. We review a force-based model of cell motion that considers a cell as a nucleus and several adhesion sites connected to the nucleus by springs. In this model, the cell moves as the adhesion sites attach to and detach from a substrate. This model is then reformulated as a random process that tracks the attachment characteristic (attached or detached) of each adhesion site, the …
The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen
The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen
Theses and Dissertations
Conner and Spencer used ultrafilters to construct homomorphisms between fundamental groups that could not be induced by continuous functions between the underlying spaces. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This led us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We …
A Covering System With Minimum Modulus 42, Tyler Owens
A Covering System With Minimum Modulus 42, Tyler Owens
Theses and Dissertations
We construct a covering system whose minimum modulus is 42. This improves the previous record of 40 by P. Nielsen.
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Theses and Dissertations
Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of …
Transposing Noninvertible Polynomials, Nathan Cordner
Transposing Noninvertible Polynomials, Nathan Cordner
Library Research Grants
In the class of invertible polynomials, the notion of dual polynomials W and WT, as well as dual groups G and GT is well-understood. In this paper we investigate finding dual pairs W and WT for noninvertible polynomials. We find that in many instances, our intuition that stems from invertible polynomials does not extend to the noninvertible case.
Connecting Galois Representations With Cohomology, Joseph Allen Adams
Connecting Galois Representations With Cohomology, Joseph Allen Adams
Theses and Dissertations
In this paper, we examine the conjecture of Avner Ash, Darrin Doud, David Pollack, and Warren Sinnott relating Galois representations to the mod p cohomology of congruence subgroups of the general linear group of n dimensions over the integers. We present computational evidence for this conjecture (the ADPS Conjecture) for the case n = 3 by finding Galois representations which appear to correspond to cohomology eigenclasses predicted by the ADPS Conjecture for the prime p, level N, and quadratic nebentype. The examples include representations which appear to be attached to cohomology eigenclasses which arise from D8, S3, A5, and S5 …
Hecke Eigenvalues And Arithmetic Cohomology, William Leonard Cocke
Hecke Eigenvalues And Arithmetic Cohomology, William Leonard Cocke
Theses and Dissertations
We provide algorithms and documention to compute the cohomology of congruence subgroups of the special linear group over the integers when n=3 using the well-rounded retract and the Voronoi decomposition. We define the Sharbly complex and how one acts on a k-sharbly by the Hecke operators. Since the norm of a sharbly is not preserved by the Hecke operators we also examine the reduction techniques described by Gunnells and present our implementation of said techniques for n=3.
Hölder Extensions For Non-Standard Fractal Koch Curves, Joshua Taylor Fetbrandt
Hölder Extensions For Non-Standard Fractal Koch Curves, Joshua Taylor Fetbrandt
Theses and Dissertations
Let K be a non-standard fractal Koch curve with contraction factor α. Assume α is of the form α = 2+1/m for some m ∈ N and that K is embedded in a larger domain Ω. Further suppose that u is any Hölder continuous function on K. Then for each such m ∈ N and iteration n ≥ 0, we construct a bounded linear operator Πn which extends u from the prefractal Koch curve Kn into the whole of Ω. Unfortunately, our sequence of extension functions Πnu are not bounded in norm in the limit because the upper bound is …
Convolutions And Convex Combinations Of Harmonic Mappings Of The Disk, Zachary M. Boyd
Convolutions And Convex Combinations Of Harmonic Mappings Of The Disk, Zachary M. Boyd
Theses and Dissertations
Let f_1, f_2 be univalent harmonic mappings of some planar domain D into the complex plane C. This thesis contains results concerning conditions under which the convolution f_1 ∗ f_2 or the convex combination tf_1 + (1 − t)f_2 is univalent. This is a long-standing problem, and I provide several partial solutions. I also include applications to minimal surfaces.
A New Public-Key Cryptosystem, Christopher James Hettinger
A New Public-Key Cryptosystem, Christopher James Hettinger
Theses and Dissertations
Public key cryptosystems offer important advantages over symmetric methods, but the most important such systems rely on the difficulty of integer factorization (or the related discrete logarithm problem). Advances in quantum computing threaten to render such systems useless. In addition, public-key systems tend to be slower than symmetric systems because of their use of number-theoretic algorithms. I propose a new public key system which may be secure against both classical and quantum attacks, while remaining simple and very fast. The system's action is best described in terms of linear algebra, while its security is more naturally explained in the context …
Algebraic And Combinatorial Properties Of Schur Rings Over Cyclic Groups, Andrew F. Misseldine
Algebraic And Combinatorial Properties Of Schur Rings Over Cyclic Groups, Andrew F. Misseldine
Theses and Dissertations
In this dissertation, we explore the nature of Schur rings over finite cyclic groups, both algebraically and combinatorially. We provide a survey of many fundamental properties and constructions of Schur rings over arbitrary finite groups. After specializing to the case of cyclic groups, we provide an extensive treatment of the idempotents of Schur rings and a description for the complete set of primitive idempotents. We also use Galois theory to provide a classification theorem of Schur rings over cyclic groups similar to a theorem of Leung and Man and use this classification to provide a formula for the number of …
Quasigroup Structures Arising From Partial Latin Squares, William Cocke, Dr. Rodney Forcade
Quasigroup Structures Arising From Partial Latin Squares, William Cocke, Dr. Rodney Forcade
Journal of Undergraduate Research
Latin squares represent one of the oldest elements of modern algebra, despite being over- shadowed by the structurally superior subclass of nite groups. Every nite group generates a Latin square, an n by n grid wherein n distinct element appear exactly once in each row and column. This grid is a Latin square
Up Congruences Of Modular Functions Modulo Powers Of Primes, Michael Griffin, Dr. Paul Jenkins
Up Congruences Of Modular Functions Modulo Powers Of Primes, Michael Griffin, Dr. Paul Jenkins
Journal of Undergraduate Research
Modular forms are constructs of complex analysis that possess many intricate connections to widely-separated branches of mathematics. In the most well-known application of these functions, Andrew Wiles established a connection between the Fourier coefficients of modular forms and elliptic curves–objects of analytic geometry–in order to prove Fermat’s Last Theorem, a classical number theory problem that had resisted proof for more than 350 years. Modular forms have also found applications ranging from cryptography to the million-dollar Birch and Swinerton-Dyer conjecture.
Investigation Of Investor-Manager Conflict In Mutual Funds Using Dynamic Models, Jeremiah Bejarano, Dr. Jeffrey Humpherys
Investigation Of Investor-Manager Conflict In Mutual Funds Using Dynamic Models, Jeremiah Bejarano, Dr. Jeffrey Humpherys
Journal of Undergraduate Research
In this project, my goal was to analyze the relation between marketshare incentives and risk taking in the hedge fund industry. Using the techniques of stochastic optimal control or dynamic programming, as applied in the typical Continuous-Time Consumption and Portfolio Choice model, I worked to develop a mathematical model to explore the effects of management fees and performance bonuses as well as the effects of changing market share on the fund manager’s implicit aversion towards high-risk portfolios. My continuing hypothesis is that due to fundamental differences between the investors and managers incentives, (essentially profit maximization vs. commission maximization) a fund …
A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson
A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson
Theses and Dissertations
The hyperbolic volume of a knot complement is a topological knot invariant. Futer, Kalfagianni, and Purcell have estimated the volumes of Montesinos link complements for Montesinos links with at least three positive tangles. Here we extend their results to all hyperbolic Montesinos links.
The Minimum Rank Of Schemes On Graphs, William Nelson Sexton
The Minimum Rank Of Schemes On Graphs, William Nelson Sexton
Theses and Dissertations
Let G be an undirected graph on n vertices and let S(G) be the class of all real-valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let V = {1, 2, . . . , n} be the vertex set of G. A scheme on G is a function f : V → {0, 1}. Given a scheme f on G, there is an associated class of matrices Sf (G) = {A ∈ S(G)|aii = 0 if and only if f(i) = 0}. A scheme f is said …
Representations Associated To The Group Matrix, Joseph Aaron Keller
Representations Associated To The Group Matrix, Joseph Aaron Keller
Theses and Dissertations
For a finite group G = {g_0 = 1, g_1,. . ., g_{n-1}} , we can associate independent variables x_0, x_1, . . ., x_{n-1} where x_i = x_{g_i}. There is a natural action of Aut(G) on C[x_0, . . . ,x_{n-})]. Let C_1, . . . , C_r be the conjugacy classes of G. If C = {g_{i_1}, g_{i_2}, . . . , g_{i_u }} is a conjugacy class, then let x(C) = x_{i_1} + x_{i_2} + . . . + x_{i_u}. Let ρG be the representation of Aut(G) on C[x_0, . . . , x_(n-1)]/〈x(C_1), . . . …
Combinatorial Approach To Computation Of Jones Polynomial Of A Torus Link, N. Nemirovskaya
Combinatorial Approach To Computation Of Jones Polynomial Of A Torus Link, N. Nemirovskaya
Journal of Undergraduate Research
First of all I would like to thank the Office of Research and Creative Activities for choosing me as one of the recipients of the Research and Creative Activities scholarship. This scholarship allowed me to spend more time working on the proposed project.
Mathematics In Rural Mexico: Motivations And Barriers For Adult Women Learners, Janel Wilson Williams, Dr. Jacqualine Taylor Voyles
Mathematics In Rural Mexico: Motivations And Barriers For Adult Women Learners, Janel Wilson Williams, Dr. Jacqualine Taylor Voyles
Journal of Undergraduate Research
Math educators have long realized that women in general have shied away from involvement in the mathematical world. Current research in the mathematics education field studies the motivations and barriers women have to studying math. My research extends this topic to a small village in Mexico: La Estancia. By studying factors that encourage or discourage adult Mexican women from studying math in rural settings, important influences can be identified. The identification of these elements can lead to the development of important intervention programs targeted at minimizing negative influences while capitalizing on and strengthening the existing positive influences.
Pre-Service University Math Education Programs In Japan, Vonn R. Christenson, Dr. Blake Peterson
Pre-Service University Math Education Programs In Japan, Vonn R. Christenson, Dr. Blake Peterson
Journal of Undergraduate Research
For years the United States has lagged behind the international community in mathematical performance at the elementary and secondary education levels. In the Third International Mathematics and Science Study (TIMSS), differences between the teaching style in Japan and the United States were studied, identified and recorded. Through this study, it was discovered that students in the United States “encounter mathematics that is at a lower level, is somewhat superficial, and is not as fully or coherently developed” as the mathematics in Japan.i
Solving Laplace’S Equation On A Personal Computer, Michael Higley, Dr. Peter Bates
Solving Laplace’S Equation On A Personal Computer, Michael Higley, Dr. Peter Bates
Journal of Undergraduate Research
Laplace’s equation is a differential equations that describes many physical properties in steady state systems. It can be used to describe heat distributions, displacements in elastic media, or electrostatic fields. My interest is in solving an electrostatics problem where the domain—the area in which the equation has physical meaning—is irregular enough that the only way to solve the problem is to use some sort of numerical approximation.
Ratios Of Positive Definite Matrices, Dena Plant, Dr. Wayne Barrett
Ratios Of Positive Definite Matrices, Dena Plant, Dr. Wayne Barrett
Journal of Undergraduate Research
As our research began we focused on proving the hypothesis that for a 4 x 4 Positive Definite matrix A, the ratio
Length Minimizing Network For N Points On The K-Torus, W. Lauritz Petersen, Dr. Denise Halverson
Length Minimizing Network For N Points On The K-Torus, W. Lauritz Petersen, Dr. Denise Halverson
Journal of Undergraduate Research
Our project consisted of several components with the end goal being: given n points on the ktorus (a donut with k number of holes), what would the shortest path network be to connect all the n points (network meaning a network of paths connecting each of the n-points).
Optimal Energy Recovery In Finite Time For Linearly Dissipative Systems, Mark Meilstrup, Dr. Scott Glasgow
Optimal Energy Recovery In Finite Time For Linearly Dissipative Systems, Mark Meilstrup, Dr. Scott Glasgow
Journal of Undergraduate Research
Many physical processes involve the loss or dissipation of energy. For example, when pushing a box across the floor, some of the energy that is spent will be lost to frictional forces. Our research is concerned with the study of the energy which is lost, and also the energy which is recoverable, in the more complex setting of a linearly dissipative optical system. We consider some electromagnetic pulse, such as a laser beam, entering and interacting with an absorbing medium, such as glass or some gas. When the pulse exits the medium, some of the energy has been absorbed, and …