Digital Commons Network^™

On The Superabundance Of Singular Varieties In Positive Characteristic, Jake Kettinger

Department of Mathematics: Dissertations, Theses, and Student Research

The geproci property is a recent development in the world of geometry. We call a set of points Z\subseq\P_k^3 an (a,b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P to a plane is a complete intersection of curves of degrees a and b. Examples known as grids have been known since 2011. Previously, the study of the geproci property has taken place within the characteristic 0 setting; prior to the work in this thesis, a procedure has been known for creating an (a,b)-geproci half-grid for 4\leq a\leq b, but it was not …

Partitions Of R^N With Maximal Seclusion And Their Applications To Reproducible Computation, Jason Vander Woude

Department of Mathematics: Dissertations, Theses, and Student Research

We introduce and investigate a natural problem regarding unit cube tilings/partitions of Euclidean space and also consider broad generalizations of this problem. The problem fits well within a historical context of similar problems and also has applications to the study of reproducibility in randomized computation.

Given $k\in\mathbb{N}$ and $\epsilon\in(0,\infty)$, we define a $(k,\epsilon)$-secluded unit cube partition of $\mathbb{R}^{d}$ to be a unit cube partition of $\mathbb{R}^{d}$ such that for every point $\vec{p}\in\R^d$, the closed $\ell_{\infty}$ $\epsilon$-ball around $\vec{p}$ intersects at most $k$ cubes. The problem is to construct such partitions for each dimension $d$ with the primary goal of minimizing …

The Future Is Now In Twisted Coil Polymer Actuators (Tcpa), Ryan Ronquillo

Electronic Theses and Dissertations

This thesis aimed to fabricate and test twisted coiled polymer actuators (TCPA) to understand the mechanical and thermal aspects of this artificial muscle fiber. The purpose of this thesis was to find a linear relationship using the LVDT sensor, fabricating TCPA fibers, and interpreting the data. The project tested whether nylon/polymer could be used as a better artificial muscle fiber.

This research accomplished three goals: (1) designing and fabricating a system capable of creating supercoiled muscle fibers consistently, (2) calibrating the Linear Variable Differential Transformer (LVDT) and Core, and (3) analyzing/interpreting the data of the Twisted Coiled Polymer Actuators (TCPA) …

Gordian Distance And Complete Alexander Neighbors, Ana Wright

Department of Mathematics: Dissertations, Theses, and Student Research

We call a knot K a complete Alexander neighbor if every possible Alexander polynomial is realized by a knot one crossing change away from K. It is unknown whether there exists a complete Alexander neighbor with nontrivial Alexander polynomial. We eliminate infinite families of knots with nontrivial Alexander polynomial from having this property and discuss possible strategies for unresolved cases.

Additionally, we use a condition on determinants of knots one crossing change away from unknotting number one knots to improve KnotInfo’s unknotting number data on 11 and 12 crossing knots. Lickorish introduced an obstruction to unknotting number one, which proves …

Formula 101 Using 2022 Formula One Season Data To Understand The Race Results, Christopher Garcia, Oliver Lopez

Student Scholar Symposium Abstracts and Posters

The reason why I am interested in Formula One is that my friend showed me what Formula One was all about. It became interesting to see the action of the sport, including the battles the drivers have during the race and how fast they go through a corner. Also, when qualifying comes around, they push their car to the absolute limit to gain a few seconds off their opponents. The drivers only in the top 10 receive points from the winner getting 25 points, the last driver in the top 10 getting 1 point, and those below the top ten …

Fractal Newton Methods, Ali Akgül, David E. Grow

Mathematics and Statistics Faculty Research & Creative Works

We introduce fractal Newton methods for solving (Formula presented.) that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.

Fully Decoupled Energy-Stable Numerical Schemes For Two-Phase Coupled Porous Media And Free Flow With Different Densities And Viscosities, Yali Gao, Xiaoming He, Tao Lin, Yanping Lin

Mathematics and Statistics Faculty Research & Creative Works

In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn-Hilliard-Darcy system with different densities/viscosities describing the porous media flow in matrix, a Cahn-illiard-Navier-Stokes system with different densities/viscosities describing the free fluid in conduit, and seven interface conditions coupling the flows in the matrix and the conduit. Based on the separate Cahn-Hilliard equations in the porous media region and the free flow region, a weak formulation is proposed to incorporate the …

An Integer Garch Model For A Poisson Process With Time-Varying Zero-Inflation, Isuru Panduka Ratnayake, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

A serially dependent Poisson process with time-varying zero-inflation is proposed. Such formulations have the potential to model count data time series arising from phenomena such as infectious diseases that ebb and flow over time. The model assumes that the intensity of the Poisson process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation and allows the zero-inflation parameter to vary over time and be governed by a deterministic function or by an exogenous variable. Both the expectation maximization (EM) and the maximum likelihood estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter …

Effects Of Factors On The Market Price Of The Shares Using Design Of Experiment, Amir Ahmad Dar, Mohammad Shahfaraz Khan, Imran Azad, Tanveer Ahmad Tarray, N. Anuradha, Qaiser Farroq Dar

Applied Mathematics & Information Sciences

When the cost of capital, dividends and the price of the share at the beginning is known, Modigliani and Miller’s model can be used to estimate the price of the share at the end of the period. A design of experiment (Taguchi’s orthogonal array) is used in order to investigate the impact of three parameters on the price of the share at the end of the period. The main aim of this research article is to find which parameter is more significant on the price of the share at the end of the period. Taguchi’s methodology of design of the …

Why Inverse Layers In Pavement? Why Zipper Fracking? Why Interleaving In Education? A General Explanation, Edgar Daniel Rodriguez Velasquez, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, if we split our efforts into two disconnected chunks, we get better results: a pavement is stronger if instead of a single strengthening layer, we place two parts of this layer separated by no-so-strong layers; teaching is more effective if instead of concentrating a topic in a single time interval, we split it into two parts separated in time, etc. In this paper, we provide a general explanation for all these phenomena.

Gradient Estimates And The Fundamental Solution For Higher-Order Elliptic Systems With Lower-Order Terms, Ariel E. Barton, Michael J. Duffy Jr.

Mathematical Sciences Faculty Publications and Presentations

We establish the Caccioppoli inequality, a reverse Hölder inequality in the spirit of the classic estimate of Meyers, and construct the fundamental solution for linear elliptic differential equations of order 2m with certain lower order terms.

Long-Time Stability For An Imex Discretization Of The 1d Fujita Equation, Victoria Luongo

Honors College Theses

We study an efficient time-stepping scheme for the 1D Fujita equation that is implicit for the linear terms but explicit for the nonlinear terms. We analyze the long-time stability of the scheme for varying parameter values, which reveal parameter value regimes in which the method is stable. We provide numerical results that illustrate the theory and show the analytically derived stability conditions are sufficient to achieve long-time stability results.

Fast -- Asymptotically Optimal -- Methods For Determining The Optimal Number Of Features, Saied Tizpaz-Niari, Luc Longpré, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In machine learning -- and in data processing in general -- it is very important to select the proper number of features. If we select too few, we miss important information and do not get good results, but if we select too many, this will include many irrelevant ones that only bring noise and thus again worsen the results. The usual method of selecting the proper number of features is to add features one by one until the quality stops improving and starts deteriorating again. This method works, but it often takes too much time. In this paper, we propose …

Listening For Common Ground In High School And Early Collegiate Mathematics, Gail Burrill, Henry Cohn, Yvonne Lai, Dev P. Sinha, Ji Y. Son, Katherine F. Stevenson

Department of Mathematics: Faculty Publications

Solutions to pressing and complex social challenges require that we reach for common ground. Only through cooperation among people with a broad range of backgrounds and expertise can progress be made on issues as challenging as improving student success in mathematics. In this spirit, the AMS Committee on Education held a forum in May 2022 entitled The Evolving Curriculum in High School and Early Undergraduate Mathematical Sciences Education.¹ This article is a report on that forum by the authors listed above, who were among the organizers and presenters.

Let’S Make Patterns!: Symmetric Rubik’S Cube Permutations, Danny Anderson

Theses/Capstones/Creative Projects

Rubik’s cubes are well-known for having several different patterns, or permutations, that can be made from them. Meanwhile, cubes generally display a wide variety of symmetries. Naturally, these ideas can be combined to form a notion of "symmetric Rubik's cube patterns." The goal of this paper is to find an algorithm that can produce all of the permutations that display symmetries.

A Study In The Freeness Of Finitely Generated Anp-Modules Upon Restriction To Principal Subalgebras, Luke Manford Flattery

Mathematics Dissertations - Archive

We are interested in quantitative information on the freeness of modules over a truncated polynomial ring when restricting to subalgebras generated by a linear form. After investigating the structure of the truncated polynomial ring, subalgebras generated by a linear form, and corresponding vector spaces, we construct a generic representation and discuss its connection to a certain affine space. We quantify the abundance of freeness of modules using a certain variety called the rank variety. For any possible dimension we construct a module whose rank variety has that dimension. Finally, we define another variety, called the module variety, and show that …

Mechanism Of Hairpin Vortex Formation By Liutex, Yifei Yu

Mathematics Dissertations - Archive

Turbulence is still a mystery for human after more than one century’s development of fluid dynamics. Hairpin vortex formation is regarded as an essential process for a laminar flow transition to the turbulent flow. A new correct third generation vortex identification method, Liutex, was proposed in 2018, which can represent local rotation direction and reveal the local angular speed correctly. Using this powerful tool, the mechanism of hairpin vortex formation is re-examined. This dissertation (1) explains the mechanism of hairpin vortex formation by solving Orr-Sommerfeld equation using Chebyshev spectrum method (2) observes the DNS result of flat plate boundary layer …

Likelihood Inference For Flexible Cure Models With Interval Censored Data, Jodi Treszoks

Mathematics Dissertations - Archive

Models for survival data with a surviving fraction, known as cure rate models, play a vital role in survival analysis. Due to the improvement of intervening methodologies, some subjects are seen to be immune permanently. While cure rate models have been studied extensively in the recent literature with a standard assumption of right-censored data, in many applied settings, such as recidivism studies or medical studies where the event of interest is not immediately harmful, continuous observation of a subject is impracticable. We call lifetime data generated with discrete follow-up times as interval-censored. In this thesis, we extend several existing cure …

Intrinsic Tame Filling Functions And Other Refinements Of Diameter Functions, Andrew Quaisley

Department of Mathematics: Dissertations, Theses, and Student Research

Tame filling functions are quasi-isometry invariants that are refinements of the diameter function of a group. Although tame filling functions were defined in part to provide a proper refinement of the diameter function, we show that every finite presentation of a group has an intrinsic tame filling function that is equivalent to its intrinsic diameter function. We then introduce some alternative filling functions—based on concepts similar to those used to define intrinsic tame filling functions—that are potential proper refinements of the intrinsic diameter function.

Adviser: Susan Hermiller and Mark Brittenham

The Full Degree Spanning Tree Problem, Sarah Acquaviva

Theses, Dissertations and Culminating Projects

Given a graph G, we study the problem of finding a spanning tree T that maximizes the number of vertices of full degree; that is, the number of vertices whose degree in T equals its degree in G. We prove a few general bounds and then analyze this parameter on various classes of graphs including grid graphs, hypercubes, and random regular graphs. We also explore a related problem that focuses on maximizing the number of leaves in a spanning tree of a graph.

Curriculum Connectivity In Montclair State University’S Undergraduate Mathematics Program, Ana G. Da Silva Jesus

Theses, Dissertations and Culminating Projects

According to Piaget’s cognitive development theory and the constructivism learning theory of education, real learning occurs when students establish long term connections between disciplines by either adapting or redefining previously acquired knowledge. These ideologies have important teaching and learning implications that directly influence curriculum development and the design of a course of study. This thesis explores the interconnectedness of the subjects required for the successful completion of an undergraduate math program at Montclair State University. More specifically, it models students’ unique connections through a learning network and investigates the correlation between the interconnectivity of subjects and students’ overall performance. Results …

The Hilbert Sequence And Its Associated Jacobi Matrix, Caleb Beckler

Honors Theses

In this project, we investigate positive definite sequences and their associated Jacobi matrices in Hilbert space. We set out to determine the Jacobi matrix associated to the Hilbert sequence by methods described in Akhiezer’s book The Classical Moment Problem. Using methods in Teschl’s book Jacobi Operators and Completely Integrable Nonlinear Lattice, we determine the essential spectrum of the corresponding Jacobi matrix.

Cohen-Macaulay Properties Of Closed Neighborhood Ideals, Jackson Leaman

All Theses

This thesis investigates Cohen-Macaulay properties of squarefree monomial ideals, which is an important line of inquiry in the field of combinatorial commutative algebra. A famous example of this is Villareal’s edge ideal [11]: given a finite simple graph G with vertices x1, . . . , xn, the edge ideal of G is generated by all the monomials of the form xixj where xi and xj are adjacent in G. Villareal’s characterization of Cohen-Macaulay edge ideals associated to trees is an often-cited result in the literature. This was extended to chordal and bipartite graphs by Herzog, Hibi, and Zheng in …

A Frobenius-Schur Extension For Real Projective Representation, Levi Gagnon‐Ririe

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many problems in physics have explicit mathematical descriptions. This thesis aims to provide the mathematical tools for a particular problem in physics, that of Quantum Mechanical symmetries. In essence, we extend the known mathematics to a more general setting and provide a wider view of Real projective representation theory. The work done in this thesis contributes to the subfield of mathematics known as representation theory and to the subfield of physics concerned with time reversal symmetry.

Examining Model Complexity's Effects When Predicting Continuous Measures From Ordinal Labels, Mckade S. Thomas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many real world problems require the prediction of ordinal variables where the values are a set of categories with an ordering to them. However, in many of these cases the categorical nature of the ordinal data is not a desirable outcome. As such, regression models treat ordinal variables as continuous and do not bind their predictions to discrete categories. Prior research has found that these models are capable of learning useful information between the discrete levels of the ordinal labels they are trained on, but complex models may learn ordinal labels too closely, missing the information between levels. In this …

Uconn Baseball Batting Order Optimization, Gavin Rublewski, Gavin Rublewski

Honors Scholar Theses

Challenging conventional wisdom is at the very core of baseball analytics. Using data and statistical analysis, the sets of rules by which coaches make decisions can be justified, or possibly refuted. One of those sets of rules relates to the construction of a batting order. Through data collection, data adjustment, the construction of a baseball simulator, and the use of a Monte Carlo Simulation, I have assessed thousands of possible batting orders to determine the roster-specific strategies that lead to optimal run production for the 2023 UConn baseball team. This paper details a repeatable process in which basic player statistics …

Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin

Electronic Theses and Dissertations

The well known Eneström-Kakeya Theorem states that: for P(z)=∑_i=0ⁿ a_i zⁱ, a polynomial of degree n with real coefficients satisfying 0 ≤ a₀ ≤ a₁ ≤ ⋯≤ a_n, all zeros of P(z) lie in |z|≤1 in the complex plane. In this thesis, we will find inner and outer bounds in which the zeros of complex and quaternionic polynomials lie. We will do this by imposing restrictions on the real and imaginary parts, and on the moduli, of the complex and quaternionic coefficients. We also apply similar restrictions on complex polynomials with …

Prefix-Rewriting: The Falsification By Fellow Traveler Property And Practical Computation, Ash Declerk

Department of Mathematics: Dissertations, Theses, and Student Research

The word problem is one of the fundamental areas of research in infinite group theory, and rewriting systems (including finite convergent rewriting systems, automatic structures, and autostackable structures) are key approaches to working on the word problem. In this dissertation, we discuss two approaches to creating bounded regular convergent prefix-rewriting systems.

Groups with the falsification by fellow traveler property are known to have solvable word problem, but they are not known to be automatic or to have finite convergent rewriting systems. We show that groups with this geometric property are geodesically autostackable. As a key part of proving this, we …

Tribute To Gene Chase, Calvin Jongsma

Faculty Work Comprehensive List

Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.

Solving Boundary Value And Initial Boundary Value Problems Of Partial Differential Equations Using Meshless Methods, Adam Johnson

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation, the methods of fundamental solutions (MFS) and the methods of particular solutions (MPS) are used to solve the boundary value problems of the Poisson and Helmholtz equations, where the particular solutions of the Poisson and Helmholtz equations in [13, 14] are used. Then the initial boundary value problems of the diffusion and wave equations are discretized into a sequence of boundary value problems of the Helmholtz equation by using either the Laplace transform or time difference methods along the lines of [8]. The Helmholtz problems are solved consequently in an iterative manner which leads to the solution …