Mathematics Commons^™

Preparing For The Future: The Effects Of Financial Literacy On Financial Planning For Young Professionals, Tanay Singh

Senior Theses

Purpose – Many people between the age of 20 and 34 have not considered planning financially for the future in any significant capacity and in doing so, they limit their potential savings. The purpose of this study is to examine what financial expectations are for people in the early stages of their career and determine if improving financial literacy and revealing financial realities helps to produce more accurate or realistic expectations. Ultimately, the goal is to better prepare participants in the study for the working world and increased responsibilities outside of the college/university environment by getting them to start thinking …

Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel, S. D. Purohit, N. Jolly, M. K. Bansal, Jagdev Singh, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Recently, several authors have investigated Chebyshev type inequalities for numerous fractional integral operators. Being motivated by the work done by earlier researchers and their numerous applications in probability, transform theory, numerical quadrature, statistical problems and its significance in fractional boundary value problems. We aim to evaluate Chebyshev type inequalities involving fractional integral operator containing multi-index Mittag-Leffler function in the kernel. Admissible connections of the results mentioned in this article to those associated with previously established familiar fractional integral operators have been pointed out.

Ruscheweyh-Goyal Derivative Of Fractional Order, Its Properties Pertaining To Pre-Starlike Type Functions And Applications, Ritu Agarwal, G. S. Paliwal

Applications and Applied Mathematics: An International Journal (AAM)

The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve …

Circada: Shiny Apps For Exploration Of Experimental And Synthetic Circadian Time Series With An Educational Emphasis, Lisa Cenek, Liubou Klindziuk, Cindy Lopez, Eleanor Mccartney, Blanca Martin Burgos, Selma Tir, Mary E. Harrington, Tanya L. Leise

Psychology: Faculty Publications

Circadian rhythms are daily oscillations in physiology and behavior that can be assessed by recording body temperature, locomotor activity, or bioluminescent reporters, among other measures. These different types of data can vary greatly in waveform, noise characteristics, typical sampling rate, and length of recording. We developed 2 Shiny apps for exploration of these data, enabling visualization and analysis of circadian parameters such as period and phase. Methods include the discrete wavelet transform, sine fitting, the Lomb-Scargle periodogram, autocorrelation, and maximum entropy spectral analysis, giving a sense of how well each method works on each type of data. The apps also …

Decompositions Of Complete Uniform Multipartite Hypergraphs, Patrick Ward

Honors Projects

In recent years, researchers have studied the existence of complete uniform hypergraphs into small-order hypergraphs. In particular, results on small 3-uniform graphs including loose 3, 4, and 5 cycles have been studied, as well as 4-uniform loose cycles of length 3. As part of these studies, decompositions of multipartite hypergraphs were constructed. In this paper, we extend this work to higher uniformity and order as well as expand the class of hypergraphs.

On The Mersenne Prime Numbers, Julia Vanlandingham

Undergraduate Honors Thesis Projects

The prime numbers have been an important field of research for thousands of years and are intertwined with most other fields of mathematics. One topic that has piqued the interest of mathematicians young and old is the Mersenne prime numbers, which have applications in many mathematics and computer science fields. The Mersenne primes get a lot of attention because there is not much known about them. However, we do have a very simple primality test for Mersenne numbers, which is why the largest currently known primes are Mersenne primes. These primes are also very closely related to another class of …

Mathematical And Physical Description Of Conical Intersections, Nicholas Dewey

Honors Projects

Conical intersections (CIs) are points of degeneracy between two or more potential energy surfaces. Due to the intersection point, it is much easier for molecules to transition their electronic, vibrational, and rotational energies between surfaces. Therefore, CIs are critical to the study of excited states, particularly in the context of photochemistry. However, they are difficult to study because they interfere with traditional thermodynamics and deviate from the Born-Oppenheimer approximation. The purpose of this review is to explain why that is the case by exploring the foundation for the mathematics and physics behind CIs. Also included is an application of how …

Alexander Polynomials Of 3-Braid Knots, Marwa Emad Alrefai

Mathematical Sciences Theses

A knot is an embedding of a circle S¹ into the three-dimensional sphere S³. A component link is an embedding of n disjoint circles Ⅱᵢ^ⁿ =₁ S¹ into S³. The main objective of knot theory is to classify knots and links up to natural deformations called isotopies. While there is no simple algorithm that helps decide whether two given knots (or links) are equivalent, various topological invariants have been developed to help distinguish between non-equivalent knots and links. The Alexander polynomial ∆_L(t) is one of the oldest such tools. It …

Ground States And Gibbs Measures Of Λ-Model On Cayley Tree Of Order Two, Rauda Humaid Mohammed Al Shamsi

Mathematical Sciences Theses

Abstract

Statistical mechanics deals with the average properties of a mechanical system. Some examples are; the water in a kettle, the atmosphere inside a room and the number of atoms in a magnet bar. These kinds of systems are made up of a large number of components, usually molecules. The observer has restricted power to consider all the components. All that can be done is to specify a few average quantities of the system such as its density, pressure or temperature. The main objective of statistical mechanics is to predict the relationship between the observable macroscopic properties of the system, …

Searching Games: A Bound For The Responder, Jose Garcia

Student Scholars Day Oral Presentations

A searching game with two unknowns and a lie involves two players, the responder and the questioner. Before the start of the game, the two parties predetermine an amount of numbers n to consider, and how many questions k the questioner can ask before the game ends with a victory (or loss) for the responder. The responder thinks of two secret numbers. The questioner asks questions of the form "How many of your two numbers are in the subset Q of the set {0,...,n-1}?", in an attempt to search and find what the two secret numbers are. If the questioner …

Automated Conjecture Making: Domination On Planar Graphs, Jose Garcia

Student Scholars Day Posters

A planar graph G = (V,E) is a graph that can be embedded in the plane, i.e. it can be drawn in the plane so that no edges intersect except at the vertices. A subset S of vertices in a graph G is called a dominating set if every vertex v ∈ V is either an element of S or is adjacent to an element of S. The domination number of a graph G is the smallest cardinality of a dominating set; we denote the domination number as γ(G). Automated conjecture making is the process of having a computer generate …

Structure-Activity Relationship Of Novel Diphenyl Ureas Targeting Mycobacterium, Piper Burghduf

Student Scholars Day Posters

In 2017, the World Health Organization reported that 10 million people were infected with tuberculosis, 1.6 million of whom died. Tuberculosis is caused by a bacterium called Mycobacterium tuberculosis, which primarily infects an individual’s lungs. Unfortunately, failure to adhere to the long and arduous drug regimen has contributed to the emergence of antibiotic-resistant strains of M. tuberculosis. Therefore, the need for novel antibiotics is imperative to saving millions of lives. Our lab has recently developed a family of diphenyl ureas that exhibited increased antimicrobial activity toward Mycobacterium. Reported herein is the continuation of our previous research involving the synthesis of …

Optimal Control Applied To Cancer Vaccine Protocols, Brady Fritz

Student Scholars Day Posters

This research focused on a mathematical model for the administration of a cancer vaccine. This model involves time delays, making it a more difficult optimal control problem to solve. The mathematical model describes the administration of the vaccine along with certain groups of cells affected over time. The model was programmed into a specialized software called the Sparse Optimization Suite which could output a solution. This solution was then analyzed in order to properly describe it.

Non-Attacking Queen And Rook Placements, Nicholas Layman

Student Scholars Day Posters

In 1848, Max Bezel introduced the problem of placing 8 queens on an 8 × 8 chess board so that none of the queens could attack each other. One generalization of this — the placement of n non-attacking queens on an n × n chess board — is the famous n-queens problem. A different but similar problem is that of placing non-attacking rooks on a generalized chess board which has connections to restricted permutations and has more general solutions known as compared to its queen counterpart. In this presentation, we investigate the intersection of these two problems — placing n …

Class Of Integrals Involving Generalized Hypergeometric Function, D. L. Suthar, Teklay Hailay, Hafte Amsalu, Jagdev Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we establish some definite integrals involving generalized hypergeometric function, product of algebraic functions, Jacobi function, Legendre function and general class of polynomials. Certain special cases of the main results are also pointed out.

Math 120bc – Precalculus, Virginia Thompson

Open Educational Resources

Students will explore advanced topics in algebra, functions and graphs, inverse functions, composite functions, polynomial and rational functions, trigonometry, exponential and logarithmic functions.

Local-Global Principles For Diophantine Equations, Benjamin Barham

Senior Honors Theses

The real number field, denoted ℝ, is the most well-known extension field of ℚ, the field of rational numbers, but it is not the only one. For each prime p, there exists an extension field ℚ_p of ℚ, and these fields, known as the p-adic fields, have some properties substantially different from ℝ. In this paper, we construct the p-adic numbers from the ground up and discuss the local-global principle, which concerns connections between solutions of equations found in ℚ and in ℚ_p. We state the Hasse-Minkowski theorem, which addresses a type …

The Global Existence Of Small Self-Interacting Scalar Field Propagating In The Contracting Universe, Anahit Galstian, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lamaˆitre-Robertson-Walker model of the contracting universe. For the Klein- Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution.

Analysis Of The Healthcare Mers-Cov Outbreak In King Abdulaziz Medical Center, Riyadh, Saudi Arabia, June–August 2015 Using A Seir Ward Transmission Model, Tamer Oraby, Michael G. Tyshenko, Hanan H. Balkhy, Yasar Tasnif, Adriana Quiroz-Gaspar, Zeinab Mohamed, Ayesha Araya, Susie Elsaadany, Eman Al-Mazroa, Mohammed A. Alhelail, Yaseen M. Arabi, Mustafa Al-Zoughool

School of Mathematical & Statistical Sciences Faculty Publications

Middle East respiratory syndrome coronavirus (MERS-CoV) is an emerging zoonotic coronavirus that has a tendency to cause significant healthcare outbreaks among patients with serious comorbidities. We analyzed hospital data from the MERS-CoV outbreak in King Abdulaziz Medical Center, Riyadh, Saudi Arabia, June–August 2015 using the susceptible-exposed-infectious-recovered (SEIR) ward transmission model. The SEIR compartmental model considers several areas within the hospital where transmission occurred. We use a system of ordinary differential equations that incorporates the following units: emergency department (ED), out-patient clinic, intensive care unit, and hospital wards, where each area has its own carrying capacity and distinguishes the transmission by …

Diameter Of 3-Colorable Graphs And Some Remarks On The Midrange Crossing Constant, Inne Singgih

Theses and Dissertations

The first part of this dissertation discussing the problem of bounding the diameter of a graph in terms of its order and minimum degree. The initial problem was solved independently by several authors between 1965 − 1989. They proved that for fixed δ ≥ 2 and large n, diam(G) ≤ 3n+ O(1). In 1989, Erdős, Pach, Pollack, and Tuza conjectured that the upper bound on the diameter can be improved if G does not contain a large complete subgraph K_k.

Let r, δ ≥ 2 be fixed integers and let G be a connected graph with n vertices …

Counting Number Fields By Discriminant, Harsh Mehta

Theses and Dissertations

The central topic of this dissertation is counting number fields ordered by discriminant. We fix a base field k and let Nd(k,G;X) be the number of extensions N/k up to isomorphism with Nk/Q(dN/k) ≤ X, [N : k] = d and the Galois closure of N/k is equal to G.

We establish two main results in this work. In the first result we establish upper bounds for N_|G| (k,G;X) in the case that G is a finite group with an abelian normal subgroup. Further, we establish upper bounds for the case N _|F| (k,G;X) where G is a Frobenius …

Rationality Questions And The Derived Category, Alicia Lamarche

Theses and Dissertations

This document is roughly divided into four chapters. The first outlines basic preliminary material, definitions, and foundational theorems required throughout the text. The second chapter, which is joint work with Dr. Matthew Ballard, gives an example of a family of Fano arithmetic toric varieties in which the derived category is able to detect the existence of k-rational points. More succinctly, we show that if X is a generalized del Pezzo variety defined over a field k, then X contains a k-rational point (and is in fact k-rational, that is, birational to Pnk ) if and only if Db(X) admits a …

Connections Between Extremal Combinatorics, Probabilistic Methods, Ricci Curvature Of Graphs, And Linear Algebra, Zhiyu Wang

Theses and Dissertations

This thesis studies some problems in extremal and probabilistic combinatorics, Ricci curvature of graphs, spectral hypergraph theory and the interplay between these areas. The first main focus of this thesis is to investigate several Ramsey-type problems on graphs, hypergraphs and sequences using probabilistic, combinatorial, algorithmic and spectral techniques:

• The size-Ramsey number Rˆ(G, r) is defined as the minimum number of edges in a hypergraph H such that every r-edge-coloring of H contains a monochromatic copy of G in H. We improved a result of Dudek, La Fleur, Mubayi and Rödl [ J. Graph Theory 2017 ] on the size-Ramsey number …

An Ensemble-Based Projection Method And Its Numerical Investigation, Shuai Yuan

Theses and Dissertations

In many cases, partial differential equation (PDE) models involve a set of parameters whose values may vary over a wide range in application problems, such as optimization, control and uncertainty quantification. Performing multiple numerical simulations in large-scale settings often leads to tremendous demands on computational resources. Thus, the ensemble method has been developed for accelerating a sequence of numerical simulations. In this work we first consider numerical solutions of Navier-Stokes equations under different conditions and introduce the ensemblebased projection method to reduce the computational cost. In particular, we incorporate a sparse grad-div stabilization into the method as a nonzero penalty …

Finite Axiomatisability In Nilpotent Varieties, Joshua Thomas Grice

Theses and Dissertations

Study of general algebraic systems has long been concerned with finite basis results that prove finite axiomatisability of certain classes of general algebras. In the 1970’s, Bjarni Jónsson speculated that a variety generated by a finite algebra might be finitely based provided the variety has a finite residual bound (that is, a finite bound on the cardinality of subdirectly irreducible algebras in the variety). As such, most finite basis results since then have had the hypothesis of a finite residual bound. However, Jónsson also speculated that it might be sufficient to replace the finite residual bound with the weaker hypothesis …

Distance Related Graph Invariants In Triangulations And Quadrangulations Of The Sphere, Trevor Vincent Olsen

Theses and Dissertations

The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. I provide asymptotic upper bounds and sharp lower bounds for the Wiener index of simple triangulations and quadrangulations with given connectivity. Additionally, I make conjectures for the extremal triangulations and quadrangulations which maximize the Wiener index based on computational evidence. If σ(v) denotes the arithmetic mean of the distances from v to all other vertices of G, then the remoteness and proximity of G are defined as the largest and smallest value of σ(v) over all vertices v of G, respectively. …

Windows And Generalized Drinfeld Kernels, Robert R. Vandermolen

Theses and Dissertations

We develop a generalization of a construction of Drinfeld, first inspired by the Qconstruction of Ballard, Diemer, and Favero. We use this construction to provide kernels for Grassmann flops over an arbitrary field of characteristic zero. In the case of Grassmann flops this generalization recovers the kernel for a Fourier-Mukai functor on the derived category of the associated global quotient stack studied by Buchweitz, Leuschke, and Van den Bergh. We show an idempotent property for this kernel, which after restriction, induces a derived equivalence over any twisted form of a Grassmann flop.

Two Inquiries Related To The Digits Of Prime Numbers, Jeremiah T. Southwick

Theses and Dissertations

This dissertation considers two different topics. In the first part of the dissertation, we show that a positive proportion of the primes have the property that if any one of their digits in base 10, including their infinitely many leading 0 digits, is replaced by a different digit, then the resulting number is composite. We show that the same result holds for bases b 2 {2, 3, · · · , 8, 9, 11, 31}.

In the second part of the dissertation, we show for an integer b ≥ 5 that if a polynomial ƒ( x) with non-negative coefficients …

Space-Efficient Prime Knot 7-Mosaics, Aaron Heap, Natalie Lacourt

Mathematics

The concepts of tile number and space-efficiency for knot mosaics were first explored by Heap and Knowles in 2018, where they determined the possible tile numbers and space-efficient layouts for every prime knot with mosaic number 6 or less. In this paper, we extend those results to prime knots with mosaic number 7. Specifically, we find the possible values for the number of non-blank tiles used in a space-efficient 7   7 mosaic of a prime knot are 27, 29, 31, 32, 34, 36, 37, 39, and 41. We also provide the possible layouts for the mosaics that lead to these …

Analysis Of An Ode Model For Sea Turtle Populations With Temperature-Dependent Sex Determination, Lindsey A. Ukishima

Student Publications

The sex of green sea turtles is determined by the temperature at which the eggs are incubated. Recent studies have shown that the sex ratios of sea turtle populations have changed over recent years, likely due to climate change, which has produced a more female-biased population. This paper finds the nonzero equilibrium point of the novel system developed by Herrera et a. (2019) and attempts to determine the stability of the population at that point.