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2020

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Articles 511 - 540 of 1327

Full-Text Articles in Mathematics

A Different Approach To Endpoint Weak-Type Estimates For Calder̟N-Zygmund Operators, Cody B. Stockdale May 2020

A Different Approach To Endpoint Weak-Type Estimates For Calder̟N-Zygmund Operators, Cody B. Stockdale

Arts & Sciences Graduate Student Theses and Dissertations

The aim of this thesis is to investigate weak-type inequalities for linear and multilinear Calderón-Zygmund operators in Euclidean and weighted settings using the Calderón- Zygmund decomposition and ideas inspired by Nazarov, Treil, and Volberg. In the linear setting, a new simple proof of the classical weak-type (1; 1) property is given with motivation For multilinear Calderón-Zygmund operators, the Nazarov-Treil-Volberg ideas lead to a new proof of the weak-type (1,. . . ,1; 1/m) estimate. Connecting the weighted and multilinear settings, a weighted weak-type estimate for multilinear Calderón-Zygmund operators is proved. Two proofs for the weighted multilinear inequality are presented – …

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Laurent Series Expansion And Its Applications, Anna Sobczyk May 2020

Laurent Series Expansion And Its Applications, Anna Sobczyk

University Honors Theses

The Laurent expansion is a well-known topic in complex analysis for its application in obtaining residues of complex functions around their singularities. Computing the Laurent series of a function around its singularities turns out to be an efficient way to determine the residue of the function as well as to compute the integral of the function along any closed curves around its singularities. Based on the theory of the Laurent series, this paper provides several working examples where the Laurent series of a function is determined and then used to calculate the integral of the function along any closed curve …

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Bayesian Posterior Inference And Lan For L̩Vy Models Under High-Frequency Data, Qi Wang May 2020

Bayesian Posterior Inference And Lan For L̩Vy Models Under High-Frequency Data, Qi Wang

Arts & Sciences Graduate Student Theses and Dissertations

Parameter estimation and inference for L̩vy models under high-frequency data has been an exciting and important task in the field of financial mathematics and has been found practically useful when analyzing real financial data. One feature of L̩vy models is the allowance of jumps to model the abrupt changes sometimes observed in the market. In this thesis, we discuss some problems related to the statistical inference of L̩vy models based on high-frequency data emphasizing on the presence of the jumps. The first problem we consider focuses on the estimation of the volatility, which is critical to measure and control the …

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Operator Noncommutative Function Theory And Partial Matrix And Operator Convexity, Mark E. Mancuso May 2020

Operator Noncommutative Function Theory And Partial Matrix And Operator Convexity, Mark E. Mancuso

Arts & Sciences Graduate Student Theses and Dissertations

No abstract provided.

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A Study On Lexicographic Shellable Posets, Tiansi Li May 2020

A Study On Lexicographic Shellable Posets, Tiansi Li

Arts & Sciences Graduate Student Theses and Dissertations

In this thesis, I will discuss the relations and differences between EL-shellable and CL-shellable posets. I will present examples of EL-shellable posets that are previously known to be CL-shellable, including rank-selected subposets of EL- shellable posets such as the Smirnov words posets, and comodernistic lattices. I will show that EL-shellability is equivalent to root-independent recursive atom ordering, and present two examples of CL-shellable posets that are not EL- shellable, one of which is a graded poset and the other is ungraded. In the end, I will briefly discuss how I think might fully characterize CL-shellable posets that are not EL-shellable.

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Computation Of Knudsen Diffusivity In Domains With Boundary Micro-Structure, Luis Alberto Garcia German May 2020

Computation Of Knudsen Diffusivity In Domains With Boundary Micro-Structure, Luis Alberto Garcia German

Arts & Sciences Graduate Student Theses and Dissertations

We develop an analytical framework and numerical methods for the determination of the coefficient of self-diffusivity for the transport of a rarefied gas in channels, in the limit of large Knudsen number. We provide an effective method for determining the influence of channel surface micro-structure on the value of diffusivity. We also show how characteristic numbers of the system, namely geometric parameters of the micro-structure, the spectral gap of a Markov transition operator defined for a given micro-structure, and the tangential momentum accommodation coefficient of a commonly used model of surface scattering, are related. Examples of micro-structures are investigated regarding …

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Multilevel Asymptotic Parallel-In-Time Techniques For Temporally Oscillatory Pdes, Nicholas Abel May 2020

Multilevel Asymptotic Parallel-In-Time Techniques For Temporally Oscillatory Pdes, Nicholas Abel

Mathematics & Statistics ETDs

As the clock speeds of individual processors level off and the amount of parallel resources continue to increase rapidly, further exploitation of parallelism is necessary to improve compute times. For time-dependent differential equations, the serial computation of time-stepping presents a bottleneck, but parallel-in-time integration methods offer a way to compute the solution in parallel along the time domain. Parallel-in-time methods have been successful in achieving speedup when computing solutions for parabolic problems; however, for problems with large hyperbolic terms and no strong diffusivity, parallel-in-time methods have traditionally struggled to offer speedup. While work has been done to understand why parallel-in-time …

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"Tracker Software And Matchbox Car Jumps”, Kelly W. Remijan May 2020

"Tracker Software And Matchbox Car Jumps”, Kelly W. Remijan

Teacher Resources

No abstract provided.

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Strategies And Algorithms Of Sudoku, Callie Weaver May 2020

Strategies And Algorithms Of Sudoku, Callie Weaver

Mathematics Senior Capstone Papers

This paper discusses different strategies for the game of Sudoku and how those strategies relate to other problem solving techniques while also attempting to use those other techniques in a way that improves the strategies for Sudoku. This includes a thorough analysis of the general algorithm and an algorithm that is formed by the Occupancy Theorem and Preemptive Sets. This paper also compares these algorithms that directly relate to Sudoku with algorithms to similar combinatorial problems such as the Traveling Salesman problem and more. With the study of game theory becoming more popular, these strategies have also been shown to …

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Fostering Student Engagement Through A Real-World, Collaborative Project Across Disciplines And Institutions, Laura Mebert, Roy Barnes, Jacqueline Dalley, Leszek Gawarecki, Farnaz Ghazi Nezami, Gregory Shafer, Jill Slater, Erin Yezbick May 2020

Fostering Student Engagement Through A Real-World, Collaborative Project Across Disciplines And Institutions, Laura Mebert, Roy Barnes, Jacqueline Dalley, Leszek Gawarecki, Farnaz Ghazi Nezami, Gregory Shafer, Jill Slater, Erin Yezbick

Mathematics Publications

Ample research has identified several features of a learning experience likely to enhance student learning, including collaboration, open-ended exploration, and problem-based learning in real-life scenarios. Missing is a model of how instructors might combine these elements into a single project that works flexibly across disciplines and institutions. This article fills this gap by offering such a model and reporting on its effectiveness in fostering student engagement. It describes a project that instructors at four colleges and universities in Flint, Michigan (USA) piloted during the height of the Flint water crisis. The project asked students to apply class content to the …

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Domination Number Of Annulus Triangulations, Toshiki Abe, Junki Higa, Shin-Ichi Tokunaga May 2020

Domination Number Of Annulus Triangulations, Toshiki Abe, Junki Higa, Shin-Ichi Tokunaga

Theory & Applications of Graphs

An annulus triangulation G is a 2-connected plane graph with two disjoint faces f1 and f2 such that every face other than f1 and f2 are triangular, and that every vertex of G is contained in the boundary cycle of f1 or f2. In this paper, we prove that every annulus triangulation G with t vertices of degree 2 has a dominating set with cardinality at most ⌊ \frac{|V(G)|+t+1}{4} ⌋ if G is not isomorphic to the octahedron. In particular, this bound is best possible.

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"Human Cannonball Stunts And Quadratic Functions”, Kelly W. Remijan May 2020

"Human Cannonball Stunts And Quadratic Functions”, Kelly W. Remijan

Teacher Resources

No abstract provided.

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The Theory Of Cryptography In Bitcoin, Can Hong May 2020

The Theory Of Cryptography In Bitcoin, Can Hong

Mathematics Senior Capstone Papers

Bitcoin is a well known virtual currency, or cryptocurrency. It was created by a group of people using the name Satoshi Nakamoto in 2008. Currently, many people are utilizing Bitcoin for personal gains and transactions. To keep transactions secure requires techniques from modern cryptography. In this paper, we explain certain aspects of the cryptography of Bitcoin. We are going to discuss two components of the cryptography of Bitcoin—hash functions and signatures. We will describe what the hash function and signature are, give some examples of hash functions, and discuss certain criteria that good hash functions should satisfy.

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Periodic Points And Sharkovsky’S Theorem, Luke J. Seaton May 2020

Periodic Points And Sharkovsky’S Theorem, Luke J. Seaton

Mathematics Senior Capstone Papers

The number of periodic points of a function depends on the context. The number of complex periodic points and rational periodic points have been shown to be infinite and finite, respectively, if f is a polynomial of degree at least 2. However, the number of real periodic points can be either finite or infinite. Sharkovskys Theorem states that if p is left of q in the “Sharkovsky ordering” and the continuous function f has a point of period p, then f also has a point of period q. This statement becomes very powerful when considering a function that has points …

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Leveraging Model Flexibility And Deep Structure: Non-Parametric And Deep Models For Computer Vision Processes With Applications To Deep Model Compression, Anthony D. Rhodes May 2020

Leveraging Model Flexibility And Deep Structure: Non-Parametric And Deep Models For Computer Vision Processes With Applications To Deep Model Compression, Anthony D. Rhodes

Dissertations and Theses

My dissertation presents several new algorithms incorporating non-parametric and deep learning approaches for computer vision and related tasks, including object localization, object tracking and model compression. With respect to object localization, I introduce a method to perform active localization by modeling spatial and other relationships between objects in a coherent "visual situation" using a set of probability distributions. I further refine this approach with the Multipole Density Estimation with Importance Clustering (MIC-Situate) algorithm. Next, I formulate active, "situation" object search as a Bayesian optimization problem using Gaussian Processes. Using my Gaussian Process Context Situation Learning (GP-CL) algorithm, I demonstrate improved …

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Modeling The Global Plastic Pollution In Our Oceans, Anna Fateiger May 2020

Modeling The Global Plastic Pollution In Our Oceans, Anna Fateiger

Honors Program Theses and Projects

Plastic is everywhere—from our plastic bottles and straws to the inside of our phones and the clothes we wear every day. Its widespread use has left a legacy of trash, with large amounts of plastic spilling from landfills into oceans. The accumulation of plastic debris in our oceans has severely affected marine life and has even entered into the human food chain. In this project, we created a mathematical model to estimate global plastic waste-generation and ocean runoff using existing data from 1980 to 2015. Using a dynamic system, we calculated the amount of plastic that ends up in landfills …

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"Car Darts And Parabolas”, Kelly W. Remijan May 2020

"Car Darts And Parabolas”, Kelly W. Remijan

Teacher Resources

No abstract provided.

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"Straw Rockets And Parabolas”, Kelly W. Remijan May 2020

"Straw Rockets And Parabolas”, Kelly W. Remijan

Teacher Resources

No abstract provided.

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"Matchbox Stunts And Simulations”, Kelly W. Remijan May 2020

"Matchbox Stunts And Simulations”, Kelly W. Remijan

Teacher Resources

No abstract provided.

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An In-Depth Look At P-Adic Numbers, Xiaona Zhou May 2020

An In-Depth Look At P-Adic Numbers, Xiaona Zhou

Publications and Research

In this study, we consider $p$-adic numbers. We will also study the $p$-adic norm representation of real number, which is defined as $\mathbb{Q}_p = \{\sum_{j=m}^{\infty }a_j p^j: a_j \in \mathbb{D}_p, m\in\mathbb{Z}, a_m\neq 0\} \cup \{0\}$, where $p$ is a prime number. We explore properties of the $p$-adics by using examples. In particular, we will show that $\sqrt{6},i \in \mathbb{Q}_5$ and $\sqrt{2} \in \mathbb{Q}_7 $. $p$-adic numbers have a wide range of applicationsnin fields such as string theory, quantum mechanics, and transportation in porous disordered media in geology.

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A Statistical Analysis Of The Unm Facets Design Identity & Beliefs Survey Data, Clarissa A. Sorensen-Unruh May 2020

A Statistical Analysis Of The Unm Facets Design Identity & Beliefs Survey Data, Clarissa A. Sorensen-Unruh

Mathematics & Statistics ETDs

The NSF-funded FACETS (Formation of Accomplished Chemical Engineers for Transforming Society, NSF Award 1623105) grant aims to transform the undergraduate engineering experience in the Department of Chemical and Biological Engineering at the University of New Mexico to address attrition within engineering majors, especially among underserved populations (Brainard & Carlin, 1998). The UNM FACETS Design Identity & Beliefs survey, an assessment tool used as part of the research of the grant, generated the dataset used in this study. I performed several different statistical analyses on the dataset, including confirmatory factor analysis (CFA), principal component analysis (PCA), and cluster analysis. The …

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Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu May 2020

Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu

UCARE: Research Products

In recent years nonlocal models have been successfully introduced in a variety of applications, such as dynamic fracture, nonlocal diffusion, flocking, and image processing. Thus, the development of a nonlocal calculus theory, together with the study of nonlocal operators has become the focus of many theoretical investigations. Our work focuses on a Helmholtz decomposition in the nonlocal (integral) framework. In the classical (differential) setting the Helmholtz decomposition states that we can decompose a three dimensional vector field as a sum of an irrotational function and a solenoidal function. We will define new nonlocal gradient and curl operators that allow us …

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Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber May 2020

Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber

Graduate Student Portfolios, Professional Papers, and Capstone Projects

Over the course of a year, I investigated reformative approaches to the teaching of calculus. My research revealed the substantial findings of two educators, Michael Oehrtman and Pat Thompson, and inspired me to design a course based upon two key ideas, covariation and approximation metaphors. Over a period of six weeks, I taught a course tailored around these ideas and documented student responses to both classroom activities and quizzes. Responses were organized intonarratives, covariation, rates of change, limits, and delta notation. Covariation with respect to rates of change was found to be incredibly complex, and students would often see it …

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From Branches To Fibers - Investigating F-Actin Networks With Biochemistry And Mathematical Modeling, Melissa A. Riddle May 2020

From Branches To Fibers - Investigating F-Actin Networks With Biochemistry And Mathematical Modeling, Melissa A. Riddle

Senior Honors Projects, 2020-current

F-actin networks have different structures throughout the cell depending on their location or mechanical role. For example, at the leading edge of a migrating cell, F-actin is organized in a region called the lamellipodia as a branched network responsible for pushing the membrane outwards. Behind the lamellipodia is a lamellar actin network where focal adhesions and stress fibers originate, and then within the cell cortex, actin is arranged in a gel-like network. Stress fibers are an important organization of F-actin and how they arise from either the branched lamellipodia network or the gel-like cortex network is poorly understood. Our approach …

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Bridge To Bulldogs: A Student And Financial Analysis, Rebekah Moss May 2020

Bridge To Bulldogs: A Student And Financial Analysis, Rebekah Moss

Mathematics Senior Capstone Papers

In this paper, we discuss the statistical analysis of the Bridge to Bulldogs program. The Bridge to Bulldogs program provides prospective students, who do not meet all of the admission requirements, an alternate route of admission to Louisiana Tech University. The program is offered over two consecutive quarters, either summer/fall or fall/winter. During the program, students focus on building their math skills through tutoring and special advising. We compare the Bridge students to other first-time freshman in relation to scores in Freshman level math classes. We also compare composite and Math ACT scores. Finally, we perform a financial analysis, including …

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An Analysis And Comparison Of Knot Polynomials, Hannah Steinhauer May 2020

An Analysis And Comparison Of Knot Polynomials, Hannah Steinhauer

Senior Honors Projects, 2020-current

Knot polynomials are polynomial equations that are assigned to knot projections based on the mathematical properties of the knots. They are also invariants, or properties of knots that do not change under ambient isotopy. In other words, given an invariant α for a knot K, α is the same for any projection of K. We will define these knot polynomials and explain the processes by which one finds them for a given knot projection. We will also compare the relative usefulness of these polynomials.

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Conjugation By Circulant Matrices In Non-Commutative Cryptography, Hannah B. Frederick May 2020

Conjugation By Circulant Matrices In Non-Commutative Cryptography, Hannah B. Frederick

Departmental Honors & Graduate Capstone Projects

We introduce a procedure in which two trusted individuals, Alice and Bob, may share a secret matrix K from the non-abelian general linear group of matrices. In this procedure, the matrix K is concealed from an eavesdropper, Eve, by a sequence of conjugations by elements from a pre-determined abelian subgroup of the general linear group. We demonstrate that the group of invertible circulant matrices is one abelian subgroup that may be able to withstand a brute force attack. To analyze this we need a technique to determine the order of this group, and to do this we make use of …

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Lattice Paths In Diagonals And Dimensions, Freya Bennett May 2020

Lattice Paths In Diagonals And Dimensions, Freya Bennett

Honors Theses

The Lattice Paths of Combinatorics have been used in many applications, normally under the guise of a different name, due to its versatility in surface variety and specificity of answer. The Lattice Path’s of game development, in finding paths around barriers in mazes, is called Path Finder with the A∗ algorithms as its method of solving.

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Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges May 2020

Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges

LSU Doctoral Dissertations

Our main results are asymptotic zero-one laws satisfied by the diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane; the upper boundary is called the shape. For various types of unimodal sequences, we show that, as the number of squares tends to infinity, 100% of shapes are near a certain curve---that is, there is a single limit shape. Similar phenomena have been well-studied for integer partitions, but several technical difficulties arise in the extension of such asymptotic statistical laws to unimodal sequences. We develop a widely applicable method for obtaining these limit …

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The Sir Models, Their Applications, And Approximations Of Their Rates, Christopher Cano May 2020

The Sir Models, Their Applications, And Approximations Of Their Rates, Christopher Cano

Mathematics Senior Capstone Papers

The SIR (Susceptible-Infected-Recovered) models are used to help predict the spread of diseases. The goals of this paper are: elaborating on the methods of approximating the recovery rate, infection rate, and loss of immunity rate, comparing the SIR models with these approximation methods to real world data, and determining the most accurate combination of the approximation methods for each SIR model. There are several SIR models such as the Kermack-McKendrick, SIRS, and SI models that are designed for specific diseases. Understanding the parameters of these models will assist us in maximizing their accuracy. For example, there is no explicit formula …

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