Applied Mathematics Commons^™

On Nonlinear Contractions In New Extended 𝒃-Metric Spaces, Hassen Aydi, Abdelbasset Felhi, Tayyab Kamran, Erdal Karapınar, Muhammad U. Ali

Applications and Applied Mathematics: An International Journal (AAM)

Very recently, the notion of extended 𝑏-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended 𝑏-metric space is given.

Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.

Electronic Theses, Projects, and Dissertations

Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.

The Martingale Approach To Financial Mathematics, Jordan M. Rowley

Master's Theses

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …

Analyzing The Structural Properties Of Pulmonary Arterial Networks, Megan J. Chambers

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Spraying Strategies For Controlling Re-Infestation By Chagas Disease Vectors, Bismark Oduro, Winfried Just, Mario Grijalva

Biology and Medicine Through Mathematics Conference

No abstract provided.

Do Metabolic Networks Follow A Power Law? A Psamm Analysis, Ryan Geib, Lubos Thoma, Ying Zhang

Senior Honors Projects

Inspired by the landmark paper “Emergence of Scaling in Random Networks” by Barabási and Albert, the field of network science has focused heavily on the power law distribution in recent years. This distribution has been used to model everything from the popularity of sites on the World Wide Web to the number of citations received on a scientific paper. The feature of this distribution is highlighted by the fact that many nodes (websites or papers) have few connections (internet links or citations) while few “hubs” are connected to many nodes. These properties lead to two very important observed effects: the …

Combinatorial Optimization: Introductory Problems And Methods, Erin Brownell

Honors Scholar Theses

This paper will cover some topics of combinatorial optimization, the study of finding the best possible arrangement of a set of discrete objects. These topics include the shortest path problem and network flows, which can be extended to solve more complex problems. We will also briefly cover some basics of graph theory and solving linear programming problems to give context to the reader.

Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the …

The Mathematical Modeling Of Ballet, Kendall Gibson

Mathematics Senior Capstone Papers

This project aims to analyze the connections between ballet and mathematics. Specifically, this project focuses on analyzing the three-dimensional surfaces created as a dancer performs ballet choreography. The primary goal is to use a Vicon motion capture system in conjunction with MATLAB to model the three-dimensional lines and surfaces created by a dancer’s legs as she performs specific ballet movements. The movements used for this experiment were a pique turn and a rond de jambe. The data was collected using sensors to create objects in Vicon to record the position of the ankle, knee, and hip of the working leg …

An Imputation Approach To Developing Alternative Futures Of Country Conflict, Zachary J. Kane

Theses and Dissertations

Understanding what causes countries to be in a state of violent conflict is of vital importance to developing realistic national strategies on both a regional and global scale. Given these causes, it is important to understand the effects of missing data, how to impute that data, and the interrelation between data elements. Utilizing both open source data and previously generated equations that predict a country’s likelihood to transition conflict statuses, this research projects data into the future and predicts each nations’ subsequent conflict statuses. Future data is populated using a novel approach inspired by stochastic regression imputation. The replicated future …

Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee

UNLV Gaming Research & Review Journal

There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. Is there a systematic way to derive such a hand-rank table? We show that there is indeed, and it involves finding the exact optimal …

Neural Machine Translation, Quinn M. Lanners, Thomas Laurent

Honors Thesis

Neural Machine Translation is the primary algorithm used in industry to perform machine translation. This state-of-the-art algorithm is an application of deep learning in which massive datasets of translated sentences are used to train a model capable of translating between any two languages. The architecture behind neural machine translation is composed of two recurrent neural networks used together in tandem to create an Encoder Decoder structure. Attention mechanisms have recently been developed to further increase the accuracy of these models. In this senior thesis, the various parts of Neural Machine Translation are explored towards the eventual creation of a tutorial …

Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

UNO Student Research and Creative Activity Fair

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet …

Parametric Natura Morta, Maria C. Mannone

The Transdisciplinary STEAM+ Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

Stair Climbing Hand Truck, James Mcpherson

All Undergraduate Projects

Abstract

Getting a heavy object up a flight of stairs usually requires a team of two or more people. Even with a team of people, the task is often still difficult, dangerous, and possibly insurmountable by one person. This problem is especially prevalent in for those who are moving into apartment complexes. Most apartment complexes have many buildings with two or more floors of living quarters, and elevators are often missing. This project sought to offer a solution to this problem. The solution in question; a motorized hand-truck with 2, trigonal planar pinwheels in place of the stock wheels. The …

An Overview Of Computational Mathematical Physics: A Deep Dive On Gauge Theories, Andre Simoneau

CMC Senior Theses

Over the course of a college mathematics degree, students are inevitably exposed to elementary physics. The derivation of the equations of motion are the classic examples of applications of derivatives and integrals. These equations of motion are easy to understand, however they can be expressed in other ways that students aren't often exposed to. Using the Lagrangian and the Hamiltonian, we can capture the same governing dynamics of Newtonian mechanics with equations that emphasize physical quantities other than position, velocity, and acceleration like Newton's equations do. Building o of these alternate interpretations of mechanics and understanding gauge transformations, we begin …

Determination Of Optimal Parameter Estimates For Medical Interventions In Human Metabolism And Inflammation, Marcella Torres

Theses and Dissertations

In this work we have developed three ordinary differential equation models of biological systems: body mass change in response to exercise, immune system response to a general inflammatory stimulus, and the immune system response in atherosclerosis. The purpose of developing such computational tools is to test hypotheses about the underlying biological processes that drive system outcomes as well as possible real medical interventions. Therefore, we focus our analysis on understanding key interactions between model parameters and outcomes to deepen our understanding of these complex processes as a means to developing effective treatments in obesity, sarcopenia, and inflammatory diseases.

We develop …

Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, Jessica S. Lugo

Murray State Theses and Dissertations

Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules.

The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost …

Understanding The Ntru Cryptosystem, Benjamin Clark

Williams Honors College, Honors Research Projects

In this paper, we will examine the NTRU Public Key Cryptosystem. The NTRU cryptosystem was created by Joseph Silverman, Jeffery Hoffstein, and Jill Pipher in 1996. This system uses truncated polynomial rings to encrypt and decrypt data. It was recently released into the public domain in 2013. This paper will describe how this cryptosystem works and give a basic understanding on how to encrypt and decrypt using this system.

Credit Risk Analysis Using Machine Learning And Neural Networks, Dhruv Dhanesh Thanawala

Dissertations, Master's Theses and Master's Reports

A key activity within the banking industry is to extend credit to customers, hence,

credit risk analysis is critical for nancial risk management. There are various methods

used to perform credit risk analysis. In this project, we analyze German and

Australian nancial data from UC Irvine Machine Learning repository, reproducing

results previously published in literature. Further, using the same dataset and various

machine learning algorithms, we attempt to create better models by tuning available

parameters, however, our results are at best comparable to published results.

In this report, we have explained the algorithms and mathematical framework that

goes behind developing …

Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.

Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Extreme Climate Events And The Ecological Dynamics Of Plant-Herbivore Interactions, David C. Elzinga, Christopher A. Klausmeier, William C. Wetzel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Vaccination Strategies And Herd Immunity Thresholds In Small World Models, Emily Mcclung, Sam Rivas, Emma Soriano

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Intercropping In Semi-Arid India: An Analysis Of Risks And Trade Offs, Jack Pringle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding Sexual Violence Against Women, Maria Martinez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Sensitivity For In Vitro Anthrax Studies, Yareley Gonzalez, Maria Macias-Bedolla, Megan O. Powell

Spora: A Journal of Biomathematics

Studies done on interactions between spores and macrophages done in vitro show inconsistent results based on experimental protocol and inhibit meaningful extrapolation to in vivo. In this study, we perform a sensitivity analysis of a model representing in vitro studies of interactions between anthrax spores and macrophages to help address the effects of these inconsistencies. We perform both local and global analyses using Latin hypercube sampling and partial rank correlation coefficients. Our analysis indicates the amount of intracellular bacteria over time is most sensitive to the killing of intracellular bacteria by the macrophages and replication of the bacteria inside …