Mathematics Commons^™

Math Across The Curriculum, Kelsey Mason

Masters Essays

No abstract provided.

Stochastic Approximation And Applications To Networked Systems, Thu Thi Le Nguyen

Wayne State University Dissertations

This dissertation focuses on a class of SA algorithms with applications to networked systems and is based on the published works that have been done jointly during my Ph.D. training. The networked systems are fundamentally characterized by interaction among control, communications, and computing, with applications in a vast array of emerging technologies such as smart grids, intelligent transportation systems, social networks, smart city, to name just a few. Networked systems encounter many environment uncertainties that are inherently stochastic. Besides the aforementioned advantages, the framework of SA can also accommodate multiple random processes and diversified system dynamics, even random and distributed …

A Mathematical Modeling Of Infrared Neural Stimulation, Cesil S. Alex

Undergraduate Journal of Mathematical Modeling: One + Two

Electrical stimulation is the gold standard for artificial neural stimulation. The greatest disadvantage with electrical stimulation is that it scatters in space and it is difficult to achieve specific point stimulation. Recently, infrared stimulation attracted attention to address this issue. Infrared stimulation works on the principle of heating the tissue, exploiting the energy of infrared lasers to heat the cellular aqueous solution that helps transfer the energy to the cell membrane without direct contact, and provides a discrete localization of stimulation as it does not spread in space like electric fields. In the present study, a heat transfer model for …

Calculating The Area Within The Orbit Of Arrokoth, Aurielle Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The area within the orbit of the Kuiper Belt object (KBO) Arrokoth (or 2014MU₆₉) is approximated using the corresponding ellipse. The fact that the Sun lies at a focus of the ellipse is of interest. Attention is made to the known deviations of orbits from their models. It is at least of interest that the ellipse model is still essentially valid. Theoretically, if there were only the Sun and Arrokoth in the Universe, the orbit would be precisely described by the ellipse model.

Finding The Growth Rate Of A Tumor, Christine Staat

Undergraduate Journal of Mathematical Modeling: One + Two

The Gompertz method is used to analyze the growing glioblastoma data and estimate how accurate the results of growth over time are. The Gompertz curve is expressed as V(t) = αe^-βe-γt. The data from the tumor is graphed in Excel along with the values from the Gompertz equation. Excel solver is used to assist in determining the constant values of α, β, and γ. The data of the tumor is overall very close to the outcome of the Gompertz model following a sigmoidal “S” curve.

Optimization Of Handicap Ramp, Tyler Schilling

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to minimize the cost of building a handicap ramp. This is done by introducing an equation that represents the total cost of the construction, including labor and materials. Variables are then defined in terms of block length l, allowing for an equation with one variable to be graphed and derived. This equation then undergoes the first derivative test to find a value of l that would create a minimum output for cost. This value is then compared to the physical constraints of the project allowing for a realistic minimum cost to be found. …

Probabilistic Machine Learning Using Bayesian Inference, Mayank Pandey

Undergraduate Journal of Mathematical Modeling: One + Two

Machine Learning is a branch of AI (Artificial Intelligence) which expands on the idea of a computational system extending its knowledge about set methodical behaviors from the data that is fed to it to essentially develop analytical skills that can help in identifying patterns and making decisions with little to no participation of a real human being. Computer algorithms help in gaining experience to improve the facility over time for use by both consumers and corporations. In today’s technologically advanced world, Machine Learning has given us self-driving cars, speech recognition software, and AI agents like Siri and Google assistant. This …

Calculating Ambu Bag Dimensions For Use In Portable Ventilators, Camden Smith

Undergraduate Journal of Mathematical Modeling: One + Two

Based on the design of non-portable ventilators, this project examines and analyzes the primary individual component used within a motorized AMBU bag ventilator - the AMBU bag. Calculations are conducted to assess the minimum volume for an AMBU bag to provide sufficient oxygen for average total lung capacity. It allows to determine the feasibility and effectiveness of an electrical, portable AMBU bag ventilator under the reduced size requirements. A calculus-based formula, known as the Disk Method, is utilized for these calculations. It is shown that the Disk method can be reversed to find a shape of an AMBU bag given …

The Famous Coin Change Problem And Its Possible New Applications, Quang Vu

Undergraduate Journal of Mathematical Modeling: One + Two

The classical problem “Coin change” in Computer Science has become a key problem to a number of subsequent problems in different areas: finance, algorithm study, sports, etc. Mathematicians have been paying attention to only two possible outcomes of the problem: the most time/resource efficient solution and the total number of solutions. However, solutions among the “normal solutions” can be beneficial in certain situations, if carefully considered with math and economic phenomena in the past. Our work describes some of such possible beneficial solutions that are worth paying attention to and its application in finance and fiscal policy. Now it is …

The Relationship Between Suicide Rates And Mental Health Provider Ratio, Christian Bates

Undergraduate Journal of Mathematical Modeling: One + Two

This project is an analysis of the relationship between suicide rates and mental health provider ratio within the United States. Data from 2018 are collected for each state regarding its suicide rate, mental health provider ratio, and percent of population unable to receive treatment for mental health problems. An initial analysis is made using suicide rates and mental health provider ratio, with no correlation being found. A second analysis is conducted, using multiple linear regression with the percent of individuals within each state who were unable to access treatment for their mental health problems being the confounding variable. Controlling for …

Role Of Paleomagnetism In The Construction Of Earth’S Geographic Past, Stephanie Robinson

Undergraduate Journal of Mathematical Modeling: One + Two

Rocks have the ability to preserve magnetic information used in determining past geographic formations. The purpose of this report is to determine the past location of a site from a given data set’s magnetic information and the calculations found through their application to paleomagnetism. Magnetic information includes the rock sample’s location and concentration of trace magnetic particles which were used to find declination and inclination on site. The sample’s paleolatitude and paleolongitude are calculated using trigonometric equations that are derived using calculus. After a statistical analysis, these results are compared to the present day’s magnetic poles to determine the past …

Calculating Resonance Angle For Surface Plasmon Resonance Activation On Different Metals, Dang Nguyen

Undergraduate Journal of Mathematical Modeling: One + Two

Surface plasmon resonance (SPR) is the technique that has been used in many fields including biomedical science, optic, biosensing, photothermal plasmon and medicine. With the help of Kretschmann configuration, the setup allows to excite the electrons located around the metal which results in electron oscillation, also known as the plasmonic effect. However, SPR requires many factors in order to be activated. This paper approaches and analyzes two crucial features, the incident angle of incoming light and the effect of permittivity that different metals have in order to determine the sufficient value for the plasmon to exist. Different metals including gold, …

A Trace Bound For Integer-Diagonal Positive Semidefinite Matrices, Lon Mitchell

USF St. Petersburg Campus Faculty Publications

We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r-1.

Simultaneous Zeros Of A System Of Two Quadratic Forms, Nandita Sahajpal

Theses and Dissertations--Mathematics

In this dissertation we investigate the existence of a nontrivial solution to a system of two quadratic forms over local fields and global fields. We specifically study a system of two quadratic forms over an arbitrary number field. The questions that are of particular interest are:

1. How many variables are necessary to guarantee a nontrivial zero to a system of two quadratic forms over a global field or a local field? In other words, what is the u-invariant of a pair of quadratic forms over any global or local field?
2. What is the relation between u-invariants of a …

Prosthetic Leg Model, Dang Nguyen

Undergraduate Journal of Mathematical Modeling: One + Two

The main goal of this paper is to introduce an imitated prosthetic leg model by analyzing the applied forces. Even though the model is based on the idea of a prosthetic leg, it is also applicable to people without disabilities. The same concept of the model can be seen in the circus, where a person maintains a balanced state while on an incredible height without falling. When all the applying forces in the system are calculated, the design achieves the ideal state which allows it to function most effectively. One of the essential factors applied to the imitated prosthetic leg …

An Exploration Of Wind Energy, Bianca De Haan

Undergraduate Journal of Mathematical Modeling: One + Two

Wind energy is renewable energy extrapolated from the wind that has the potential to revolutionize our power supply in the near future as fossil fuels become outdated. Wind turbines capture the energy as the wind spins the blades of the turbine, transforming wind energy into mechanical energy and then into electrical energy through a generator. One of the techniques utilized to understand wind energy is to manipulate various variables in the formula for wind power. These variables such as the power coefficient, wind velocity, number and length of blades are explored to find its optimal value. The variable of turbine …

Hyperelastic Bone Involving The Washer Method, Kristin Jones

Undergraduate Journal of Mathematical Modeling: One + Two

The research conducted focuses on 3D printing and its application in medical equipment. A recent breakthrough in modern material science was made with the creation of hyperelastic bone. This exploration looks at how hyperelastic bone is created, the cost comparison to older tools, and the possible design for hyperelastic bone. Detailed calculations and descriptions are also included to explain the reasoning behind the work conducted.

Locating The Center Of Mass Of Various Simplified Car Designs For The Problem Of Flipping Over An Incline, Sullivan Musgrove

Undergraduate Journal of Mathematical Modeling: One + Two

The center of mass of a given system is referred to as a position that is the average of all of its components. I am given two cases in which I need to find the center of mass for the problem of flipping over an incline. To solve the problem given, I utilize many equations that are derived to find the center of mass of both cases and then test each system when it is encountered with three different inclines increasing by fifteen degrees increments. The tests prove that the probability that a system will flip on an incline is …

Measuring The Rate Of Heat Loss Across Selected Building Materials, Genesis Zambrano

Undergraduate Journal of Mathematical Modeling: One + Two

The rate of heat loss is analyzed for three materials: glass, brick and wood. To do this, the initial and final temperatures are set to 75℉ and 100℉, respectively, and the dimensions of each material are chosen to be 5ft by 5ft with a thickness of 2 inches. The objective of this paper is to see which material is best for insulating heat, thus enhancing the thermal performance of a building. Results from this study suggest that glass and brick have a higher rate of heat loss (high thermal conductance values and low thermal resistance values) compared to wood and …

A Cool Brisk Walk Through Discrete Mathematics, Stephen Davies

Computer Science Articles

A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!

Complete Bipartite Graph Embeddings On Orientable Surfaces Using Cayley Maps, Madeline Spies

Honors Program Theses

We explored how effective Cayley Maps are at embedding complete bipartite graphs onto orientable surfaces, such as spheres and tori. We embedded the graphs onto surfaces using Cayley Maps with the intent of finding rotations that result in the graphs’ optimal genera. Because there are only three groups that can be used to describe Kp,p, where p is prime, we chose to focus on this specific graph type. This paper explains how we determined the genera when using a Cayley Map, provides general theorems for surface face sizes and the Dihedral Group, and discusses our results for Kp,p up to …

Classification Of The Subalgebras Of The Algebra Of All 2 By 2 Matrices, Justin Luis Bernal

Open Access Theses & Dissertations

Classification of the subalgebras of the familiar algebra of all $n\times n$ real matrices over the real numbers can get quite unwieldy as all subalgebras are of dimension ranging from $1$ to $n^2$. Classification of the subalgebras of the algebra of all $2\times 2$ real matrices over the real numbers is an interesting first start.

Since $\2$ is of dimension $4$ then its possible subalgebras are of dimension $1, 2, 3,$ or $4$. The one-dimensional subalgebra and four-dimensional subalgebra need little to no attention. The two-dimensional and three-dimensional subalgebras however turn out to be of significance.

It turns out there …

Machine Learning Analysis To Characterize Phase Variations In Laser Propagation Through Deep Turbulence, Luis Fernando Rodriguez Sanchez

Open Access Theses & Dissertations

The present Dissertation is focused on the analysis of the atmospheric conditions of a turbulent environmental system and its effects on the diffraction of a laser beam that moves through it. The study is based on the optical communication of two labs placed at the summit of two mountains located in Maui, Hawaii. The emitter system is located at the Mauna Loa mountain and the receiver at the Haleakala. The distance between both mountains is 150 km. The emitter system is at a height of 3.1 km and the receiver at 3.4 km. The maritime environment at the location experiences …

Trigonometry: A Brief Conversation, Carolyn D. King Phd, Tam Evelyn, Fei Ye Phd, Beata Ewa Carvajal

Open Educational Resources

These five units are specifically tailored to foster the mastery of a few selected trigonometry topics that comprise the one credit MA-121 Elementary Trigonometry course. Each unit introduces the topic, provides space for practice, but more importantly, provides opportunities for students to reflect on the work in order to deepen their conceptual understanding.

These units have also been assigned to students of other courses such as pre-calculus and calculus as a review of trigonometric basics essential to those courses. This is the second edition of the materials. Units 4 and 5 have been edited to reflect suggestions from instructors who …

A Historical Activity Adding Irrational Numbers, Cynthia J. Huffman Ph.D.

Faculty Submissions

In this activity, students will follow and then analyze work by mathematician and fencing master Ludolph Van Ceulen (1540-1610) on adding similar radical numbers, like . His method is quite different from the method currently in use in the secondary school curriculum and College Algebra, in that he does not first simplify the square root expressions before adding them. This activity could be used with high school or College Algebra students after they have learned the current method, in order to reinforce their understanding of radicals. The activity would also be appropriate to use with pre-service mathematics teachers or in …

On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank

Faculty Journal Articles

We determine the ranks of string C-group representations of 4-dimensional projective symplectic groups over a finite field, and comment on those of higher-dimensional symplectic and orthogonal groups.

Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank

Faculty Journal Articles

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner similar to those, our sequence facilitates inductive reasoning about, and calculation of the groups of symmetries of a tensor. The new insights these methods afford can be applied to problems ranging from understanding algebraic structures to distinguishing entangled states in particle physics.

Orthogonal Groups In Characteristic 2 Acting On Polytopes Of High Rank, Peter A. Brooksbank, Dimitri Leemans, John T. Ferrara

Faculty Journal Articles

No abstract provided.

Detection And Localization Of Linear Features Based On Image Processing Methods, Sean Cormick Matz

CGU Theses & Dissertations

In this work, the general problem of the detection of features in images is considered. One of the methods, the orientation detection of lines, utilized the Radon transform (sinogram) of an image to detect lines at different angles in an image. The line thickness algorithm was generated by finding a pattern formed by particular lines in an image. The filtering of reconstructed images dealt with the removal of blur and other artifacts that arose in the course of inverting the Radon transform of an image to attempt to obtain the original image.

Fuzzy Logistic Regression For Detecting Differential Dna Methylation Regions, Tarek M. Bubaker Bennaser

Doctoral Dissertations

“Epigenetics is the study of changes in gene activity or function that are not related to a change in the DNA sequence. DNA methylation is one of the main types of epigenetic modifications, that occur when a methyl chemical group attaches to a cytosine on the DNA sequence. Although the sequence does not change, the addition of a methyl group can change the way genes are expressed and produce different phenotypes. DNA methylation is involved in many biological processes and has important implications in the fields of biomedicine and agriculture.

Statistical methods have been developed to compare DNA methylation at …