Mathematics Commons^™

A Combinatorial Miscellany: Antipodes, Parking Cars, And Descent Set Powers, Alexander Thomas Happ

Theses and Dissertations--Mathematics

In this dissertation we first introduce an extension of the notion of parking functions to cars of different sizes. We prove a product formula for the number of such sequences and provide a refinement using a multi-parameter extension of the Abel--Rothe polynomial. Next, we study the incidence Hopf algebra on the noncrossing partition lattice. We demonstrate a bijection between the terms in the canceled chain decomposition of its antipode and noncrossing hypertrees. Thirdly, we analyze the sum of the 𝑟th powers of the descent set statistic on permutations and how many small prime factors occur in these numbers. These results …

Model Function Of Women’S 1500m World Record Improvement Over Time, Annie Allmark

Undergraduate Journal of Mathematical Modeling: One + Two

We give an example of simple modeling of the known sport results that can be used for athletes’ self-improvement and estimation of future achievements.

This project compares the women’s 1500-meter world record times to the time elapsed between when they were run. The function of time which describes this comparison is found through graphing the data and interpreting the graphs. Then the obtained model function is compared to the real time data. The conclusions drawn from the result include that the calculated function of time lacks in accuracy as time elapsed increases, but the model could be used to estimate …

Polycrystalline Silicon Solar Module Power Max, Jaynil Patel

Undergraduate Journal of Mathematical Modeling: One + Two

In recent years solar energy has started to make its impact in the sunshine state. The solar panels are made up of photovoltaic cells, which convert the sun’s rays into electricity. One of the ways to improve solar panel efficiency is to increase the power output of a solar collector. The maximum power is calculated by determining the maximum power for voltage and the current. This is done by adding the maximum values for the equation for power and then using differentiation. After the maximum values are found for each hour of the day from sunset to noon, each individual …

Tsunami Waves, Samantha Pennino

Undergraduate Journal of Mathematical Modeling: One + Two

Predicting the travel time of tsunami waves is imperative to the safety and well-being of possibly affected communities since tsunami waves can happen incredibly fast. So, knowing how long an area is until a tsunami approaches dramatically helps with mitigation strategies. As an example we calculate the travel time of a tsunami wave to Somalia and Sri-Lanka that flowed an earthquake in 2004 in the Indian ocean off the coast of Sumatra. This is done by using the velocity from the shallow wave equation of the waves and piecewise integration.

Optimization Of A Water Gas Shift Reaction, Ali Albuloushi

Undergraduate Journal of Mathematical Modeling: One + Two

The optimum flow rate of steam (H₂0) to the reactor for the purpose of producing hydrogen gas for sale is determined.

Trend Analysis And Completion Prediction Of The Section Project, Ronald Jones

Undergraduate Journal of Mathematical Modeling: One + Two

Creating an accurate prediction of the completion timeline of a software development project is complicated and error prone. Developers will gain a natural intuition as to how long a task should take then. However, this prediction can end up being wrong in many cases due to many factors. This paper will attempt to determine a formula which allows a more accurate prediction to be created.

Creating an accurate prediction of the completion timeline of a software development project is complicated and error prone. Developers will gain a natural intuition as to how long a task should take then. However, this …

Minimizing Container Weight, Ibrahim Alomran

Undergraduate Journal of Mathematical Modeling: One + Two

Increased globalization has resulted in increased competition in the shipping industry. Since large carriers control over 70% of the total shipping industry, small carriers are left with only 30% of the market share to compete for. Ultimately, profit margins for small carriers have become very minimal. There is, therefore, need to develop a strategy that will aid in optimizing the profits of carriers. The goal of this paper is to develop a model that will help determine the minimum weight for a particular container design. The validity of the model is important in the sense that minimum container weight will …

Elapsed Time Of Vehicle Acceleration, Jensen Mctighe

Undergraduate Journal of Mathematical Modeling: One + Two

Newton’s Second Law states that force is equal to the mass of an object multiplied by its acceleration. More specifically, force is the mass times the instantaneous change in velocity over time of an object. By rearranging this equation, it can be determined that the time elapsed of the acceleration of an object is equal to the integral of the inverse value of the force relative to change in velocity (dv). In the context of real world application, this method can be used to calculate the time taken for a vehicle to accelerate from its minimum to maximum speed, given …

Design Of Nozzle For High-Powered Solid Rocket Propellant, Jackson Stephenson

Undergraduate Journal of Mathematical Modeling: One + Two

This paper presents a preliminary nozzle design for a high-altitude rocket to be built by SOAR, the Society of Aeronautics and Rocketry. The equations and methods used for analysis came from professional sources via text or informational videos. The equations in focus will look at the temperature/pressure/area-Mach relationships for isentropic flow, pressure expansions in selected materials, and finding other characteristic properties using safe chemical property assumptions using CEARUN. The equations were used under the assumption of an isentropic flow under sea level conditions. If the design and the projected results look promising, they will be implemented soon for machining and …

Organic Agricultural Analysis: Efficiency Of Common Practices, Bradley Biega

Undergraduate Journal of Mathematical Modeling: One + Two

To analyze the efficiency of common watering practices in an organic agriculture setting we use Sweetwater Organic Farm’s conventional methods for irrigation and land allotment as well as some algebra and calculus technique. Sweetwater’s operation is limited to their largest growing field. A mathematical model is built to determine the current efficiency of the rotary head sprinkler system. Then the efficiency of this system is compared to a new drip line system. Several variables like soil porosity, absorption rates, and areas where no plants are located, are taken into consideration. Our results show that the current irrigation in place wastes …

Using The Entropy Rate Balance To Determine The Heat Transfer And Work In An Internally Reversible, Polytropic, Steady State Flow Process, Savannah Griffin

Undergraduate Journal of Mathematical Modeling: One + Two

The entropy rate equation for internally reversible steady state flow process has been used to calculate the heat transfer and work in an internally reversible, polytropic, steady state flow process.

Geochemical Modeling Of Fractional Magma Crystallization, Luke Varner

Undergraduate Journal of Mathematical Modeling: One + Two

Modern day geologists use many different modeling programs such as Geospatial Information Systems in addition to R (programming language) for a wide array of applications such as: projecting collected data for mapping, visualization, and trend prediction. Computational power for these modeling programs is derived from Calculus, Probability, and Statistics. The purpose of this paper is to provide a site-specific geochemical analysis of an igneous rock formation composed of two specific compositions allowing for the predictions of rock formation derived from the resultant geochemical model.

Comparing Two Flywheel-Piston Linkages, Anthony Sanchez

Undergraduate Journal of Mathematical Modeling: One + Two

The main idea of this paper is to compare two different ways of linking a flywheel to a piston: the Scotch Yoke linkage and the Eccentric linkage. The Scotch Yoke linkage is a way to convert the linear motion of a piston into rotational motion by using a flywheel, or vice versa. The Eccentric mechanism, on the other hand, consists of a circular wheel that is fixed to a rotating axle that makes it rotate. We compare two methods by expressing both motions as functions of three variables (R, L and θ) and use these functions to …

The Impact Of Truncating Data On The Predictive Ability For Single-Step Genomic Best Linear Unbiased Prediction, Jeremy T. Howard, Thomas A. Rathje, Caitlyn E. Bruns, Danielle F. Wilson-Wells, Stephen D. Kachman, Matthew L. Spangler

Department of Animal Science: Faculty Publications

Simulated and swine industry data sets were utilized to assess the impact of removing older data on the predictive ability of selection candidate estimated breeding values (EBV) when using single-step genomic best linear unbiased prediction (ssGBLUP). Simulated data included thirty replicates designed to mimic the structure of swine data sets. For the simulated data, varying amounts of data were truncated based on the number of ancestral generations back from the selection candidates. The swine data sets consisted of phenotypic and genotypic records for three traits across two breeds on animals born from 2003 to 2017. Phenotypes and genotypes were iteratively …

Radiosity Integral Equation Model For An Interior Space Illumination Design: Mars Project, Hien Ngo

Mathematics Theses

This research project is focused on finding the true solution of the exterior Dirichlet problem to determine the convergence results for the Spherical Quatrefoil using the Galerkin Method. A mathematical model, based on the Radiosity integral equation will be utilized to investigate the role of incoming light waves for different surfaces with various emissivity and reflectivity functions. Theoretical and computational details of the method will provide sufficient information for designing proper lighting of an interior space inside a habitat that can ultimately be used for future endeavors in Mars exploration.

Invariant Subspaces Of Operators Quasi-Similar To L-Weakly And M-Weaklycompact Operators, Erdal Bayram

Turkish Journal of Mathematics

Let T be an L-weakly compact operator defined on a Banach lattice E without order continuous norm. We prove that the bounded operator S defined on a Banach space X has a nontrivial closed invariant subspace if there exists an operator in the commutant of S that is quasi-similar to T. Additively, some similar and relevant results are extended to a larger classes of operators called super right-commutant. We also show that quasi-similarity need not preserve L-weakly or M-weakly compactness.

On Product And Golden Stuctures And Harmonicity, Sadetti̇n Erdem

Turkish Journal of Mathematics

In this work, almost product and almost golden structures are studied. Conditions for those structures being integrable and parallel are investigated. Moreover, the harmonicity of a map between almost product or almost golden manifolds with pure or hyperbolic metric is discussed under certain conditions.

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

Open Educational Resources

These five units were 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.

We are grateful for the support we received from the Open Educational Research (OER) initiative of the City University of New …

Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

College of Graduate Studies: Theses & Dissertations

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …

Higher Cluster Categories And Qft Dualities, Sebastián Franco, Gregg Musiker

Publications and Research

We introduce a unified mathematical framework that elegantly describes minimally supersymmetry gauge theories in even dimensions, ranging from six dimensions to zero dimensions, and their dualities. This approach combines and extends recent developments on graded quivers with potentials, higher Ginzburg algebras, and higher cluster categories (also known as m-cluster categories). Quiver mutations studied in the context of mathematics precisely correspond to the order-(m + 1) dualities of the gauge theories. Our work indicates that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities.