Mathematics Commons^™

Design Of A Rainwater Catchment System, Neil Cammardella

Undergraduate Journal of Mathematical Modeling: One + Two

Certain dimensions of a rainwater catchment and storage system were optimized using climatological and sociological data. Using only daily demand and average daily rain fall data, the following dimensions were optimized: 1) The horizontal roof area needed to collect the daily demand of water, 2) The tank size needed to store all the water collected during a heavy rain event, 3) When full, how long the tank will be able to provide water without rain, and 4) The diameter of the outlet flow orifice. With these calculations, we can design a rainwater catchment system that can capture the daily demand …

Optimal Operation Of A Concentrator, Katrina Stine

Undergraduate Journal of Mathematical Modeling: One + Two

Concentrators are used in the industrial world to remove water from a chemical or substance by heating the liquid until the water evaporates thereby concentrating the remaining substance. The goal of this project is to find the optimum cycle time, number of cycles per year, and the heating element area that would minimize the total annual cost and hours of operation of an industrial concentrator. It was found that the specified concentrator would achieve a minimum total cost of $48,720.50 per year and take 993.8 hours to meet the production goal of evaporating one million kilograms of water.

Average Light Intensity Inside A Photobioreactor, Herby Jean

Undergraduate Journal of Mathematical Modeling: One + Two

For energy production, microalgae are one of the few alternatives with high potential. Similar to plants, algae require energy acquired from light sources to grow. This project uses calculus to determine the light intensity inside of a photobioreactor filled with algae. Under preset conditions along with estimated values, we applied Lambert-Beer's law to formulate an equation to calculate how much light intensity escapes a photobioreactor and determine the average light intensity that was present inside the reactor.

The Effects Of Age On Short-Term Memory Loss Due To Proactive Interference, Alisha Berkauzer

Undergraduate Journal of Mathematical Modeling: One + Two

This project focused on how proactive interference affects the short-term memory of people based on their age. The goal was to find the prime age for learning information and storing it in one's memory. Seven people from ages fifteen to forty were tested individually, using a set color pattern, in order to see how well each individual could remember the different color patterns as difficulty of the pattern increased. The obtained data was fitted by the polynomial regression. The “fitted” curve shows that as age increases, the individual's performance in memorizing the more difficult patterns decreases. Also, the peaked level …

Going Ballistic: Bullet Trajectories, Amanda Wade

Undergraduate Journal of Mathematical Modeling: One + Two

This project seeks to answer at what angle does a gun marksman have to aim in order to hit the center of a target one meter off the ground and 1000 meters away? We begin by modeling the bullet's trajectory using Euler's method with the help of a Microsoft Excel spreadsheet solver, and then systematically search for the angle corresponding to the center of the target. It was found that a marksman shooting a target 1000 meters away and 1 meter off the ground has to aim the rifle 0.436° above horizontal to hit the center.

A Mathematical Model For Swine Flu 2009 With Vaccination, Irfan Turk

Mathematics Theses - Archive

H1N1 influenza is one of the deadliest diseases in human's history. Swine Flu 2009 is the same virus and it was named in 2009. Vaccination is of the most common ways to control a disease. We offer a new vaccination model with recommendations from the US Centers for Disease Control and Prevention (CDC). The entire population is divided into 4 different age groups: one group with no vaccination, one group with 2 doses of vaccination, and two groups with 1 dose of vaccination. We establish that higher levels of vaccination lead to greater savings of life. We also consider the …

Some Problems Of Integral Geometry In Advanced Imaging, Rim Gouia

Mathematics Dissertations - Archive

During the past decade, our society has become dependent on advanced mathematics for many of our daily needs. Mathematics is at the heart of the 21st century technologies and more specifically the emerging imaging technologies from thermoacoustic tomography (TAT) and ultrasound computed tomography (UCT) to non-destructive testing (NDT). All of these applications reconstruct the internal structure of an object from external measurements without damaging the entity under investigation. The basic mathematical idea common to such reconstruction problems is often based upon Radon integral transform.The Radon integral transform Rf puts into correspondence to agiven function f its integrals over certain subsets. …

On The Existence Of Totally Reflexive Modules, Kristen Ann Beck

Mathematics Dissertations - Archive

In this manuscript, we investigate the existence of non-free totally reflexive modules over two classes of commutative local (Noetherian) rings.First, we demonstrate existence over a class of local rings which are defined by a Gorenstein homomorphism. Among the corollaries to this result, we recover a theorem of Avramov, Gasharov, and Peeva (1997) concerning the existence of non-free totally reflexive modules over local rings with embedded deformations. We also give a general construction for a class of local rings which satisfy the hypotheses of our theorem, and we show it is able to produce rings without embedded deformations.The second focus of …

Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension, Manizheh Nafari

Mathematics Dissertations - Archive

M. Artin, W. Schelter, J. Tate, and M. Van den Bergh introduced the notion of non-commutative regular algebras, and classified regular algebras of global dimension 3 on degree-one generators by using geometry (i.e., point schemes) in the late 1980s. Recently, T. Cassidy and M. Vancliff generalized the notion of a graded Clifford algebra and called it a graded skew Clifford algebra.In this thesis, we prove that all classes of quadratic regular algebras of global dimension 3 contain graded skew Clifford algebras or Ore extensions of graded skew Clifford algebras of global dimension 2. We also prove that some regular algebras …

Travelling Distance Of A Skimboard, Michael Rzonca

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project was to determine the optimum conditions to maximize the distance travelled on a skimboard. Given the differential equation that governs the changes in velocity of the skimboard, we were able to integrate and find an expression for the distance travelled by the skimboard. Using this expression we substitute different values for variables, such as angle of attack and resistance caused by the surface area of the rider, to explore the effect on the total distance travelled by the skimboard.

Roller Coasters Need Calculus Too!, Christina Marshall

Undergraduate Journal of Mathematical Modeling: One + Two

Using the specifications of the given launch roller coaster, we were able to determine the position vector of the roller coaster as a function of time. After determining the position function, we took the derivative of this function to calculate the velocity of the coaster as a function of time. From this calculated velocity vector, we were able to determine the time required for the coaster to reach its maximum height. We substitute this time value back into the position function to determine the maximum height the launch roller coaster can obtain.

Adiabatic Flame Temperature For Combustion Of Methane, Rebeca Pupo

Undergraduate Journal of Mathematical Modeling: One + Two

This project calculated the adiabatic flame temperature of a combustion reaction of pure methane and oxygen, assuming that all of the heat liberated by the combustion reaction goes into heating the resulting mixture. Mole fractions of methane to oxygen were computed from 0.05 to 0.95, in increments of 0.05, and then an integral was computed was computed with respect to temperature using the moles of product produced or leftover moles of reactants from the starting mole fraction times the specific heat of each respective gas. The highest adiabatic flame temperature evaluated, occurred at a mole fraction of 0.35.

Model For Facial Cooling, Jacalyn Sampson

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to estimate the ambient temperature and the wind speed that cause painful sensation in a cheek. Our findings confirm that the higher the wind speed, the less cold air is required to cause cheek pain.

Quantum Measures And Integrals, S. Gudder

Mathematics Preprint Series

We show that quantum measures and integrals appear naturally in any L2-Hilbert space H. We begin by defining a decoherence operator D(A, B) and it’s associated q-measure operator µ(A) = D(A, A) on H. We show that these operators have certain positivity, additivity and continuity properties. If ρ is a state on H, then Dρ(A, B) = tr [ρD(A, B)] and µρ(A) = Dρ(A, A) have the usual properties of a decoherence functional and q-measure, respectively. The quantization of a random variable f is defined to be a certain self-adjoint operator fb on H. Continuity and additivity properties of the …

The Linear Quadratic Tracker On Time Scales, Martin Bohner, Nick Wintz

Faculty Scholarship

In this work, we study a natural extension of the Linear Quadratic Regulator (LQR) on time scales. Here, we unify and extend the Linear Quadratic Tracker (LQT). We seek to find an affine optimal control that minimizes a cost functional associated with a completely observable linear system. We then find an affine optimal control for the fixed final state case in terms of the current state. Finally we include an example in disturbance/rejection modelling. A numerical example is also included.

The Maximum Rectilinear Crossing Number Of The Wheel Graph, Elie Feder

Publications and Research

We find and prove the maximum rectilinear crossing number of the wheel graph. First, we illustrate a picture of the wheel graph with many crossings to prove a lower bound. We then prove that this bound is sharp. The treatment is divided into two cases for n even and n odd.

Existence Of Mild Solutions For Abstract Mixed Type Semilinear Evolution Equations, Hong-Bo Shi, Wan-Tong Li, Hong-Rui Sun

Turkish Journal of Mathematics

This paper is concerned with the existence of global mild solutions and positive mild solutions to initial value problem for a class of mixed type semilinear evolution equations with noncompact semigroup in Banach spaces. The main method is based on a new fixed point theorem with respect to convex-power condensing operator.

Cognitive Constructs In Linear Algebra; Metaphors, Metonymies, Modes, Ruben Carrizales

Open Access Theses & Dissertations

Analysis focused on the presence of different thinking modes, metonymies, and metaphors found on the interview responses to questions related to linear independence, span, and spanning sets of three students, A12, A22 and C3, taking their first linear algebra course at the college level. Findings provide insight into how first year linear algebra students move from one thinking mode to another, and the kind of metonymies and metaphors are used to construct new knowledge. The main purpose of this research was to discover and analyze the presence of the different modes of thinking and metonymy/metaphors- in the reasoning of these …

The Isomorphisms Between The Upper And Lower Triangular Matrix Algebras, Zahi Fawaz

Open Access Theses & Dissertations

Since matrix equations with triangular matrices are easier to solve, the triangular matrices are very important in mathematics. For instance, the LU decomposition gives an algorithm to decompose any invertible matrix A into two triangular factors: a lower triangle matrix L and an upper triangle matrix U. Moreover, the inverse of a triangular matrix is also triangular. Also the product of two lower triangular matrices produces a lower triangular matrix, the same apply for upper triangular matrices. A lot of important notions, such as the determinant, the eigenvalue problem and many others are easy to handle when we are working …

Bayesian Model Selection For Classification With Possibly Large Number Of Groups, Justin Kyle Davis

Electronic Theses and Dissertations

The purpose of the present dissertation is to study model selection techniques which are specifically designed for classification of high-dimensional data with a large number of classes. To the best of our knowledge, this problem has never been studied in depth previously. We assume that the number of components p is much larger than the number of samples n, and that only few of those p components are useful for subsequent classification. In what follows, we introduce two Bayesian models which use two different approaches to the problem: one which discards components which have “almost constant” values (Model 1) and …

Towards Nominal Formal Languages, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto

Engineering Faculty Articles and Research

We introduce formal languages over infinite alphabets where words may contain binders.We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages.

Generic Trace Logics, Christian Kissig, Alexander Kurz

Engineering Faculty Articles and Research

We combine previous work on coalgebraic logic with the coalgebraic traces semantics of Hasuo, Jacobs, and Sokolova.

Four Popular Books On Consumer Debt: A Context For Quantitative Literacy, Andrew J. Miller

Numeracy

The topics of credit cards, mortgages, subprime lending, and fringe banking are rich sources of problems and discussions for classes focused on quantitative literacy. In this theme book review, we look at four recent books on the consumer debt industry: Credit Card Nation, by Robert Manning; Maxed Out, by James Scurlock; Collateral Damaged, by Charles Geisst; and Broke, USA, by Gary Rivlin. Credit Card Nation takes a scholarly look at the history of credit in America with a focus on the genesis and growth of the credit card industry up to the turn of the 20th century. Maxed Out also …

Of Music, Mathematics, And Magic: Why Math Is All Made Up And Why It Works So Well, Gregory A. Leach

Masters Theses

The purpose of my study was to answer the philosophical question of whether mathematics is invented or discovered. This question is an age-old and important one with many implications regarding the understanding of mathematics, logic, science, and truth. Answering this question correctly can inform us not only about the nature of what is known, but even what is possible to know. In the field of mathematics itself, the answer to this question could change the way that mathematics is taught, learned, and implemented in the future. The problem was addressed through research, comparison, and analysis of books and articles where …

Real Number Rado Numbers For The Equation ∑_(I=1)^(M-1)▒X_(I+C=X_M ), Melanie Zinter

The Journal of Undergraduate Research

This paper will examine the type of Ramsey theory concerned with the preservation of solution to specific linear equations under set partition. That is, if a solution to a linear equation exists in the natural numbers, must one also exist within one set of a partition of the natural numbers? To differentiate sets of a partition of the natural numbers from one another, it is convenient to use colors. Then a solution in just one set of a partition of the natural numbers can be referred to as monochromatic solution, or a solution in a single color. [Page 1]

Xenakis' Combination Of Music And Mathematics, Janelle Anderson

The Journal of Undergraduate Research

My interest in using mathematics in music composition stems from the works of the contemporary composer Iannis Xenakis. As a physics and music education major I am able to combine both fields of study for this topic. Although Xenakis wrote many orchestral compositions it is his vocal music that I have concentrated on as I too am a singer. Graphic representation and new music notation are among the methods used to analyze his music. I found that his first choral work was called “Nuits,” which I proceeded to analyze. I also found myself interested in the analysis of a more …

2011-2012 Unlv Mcnair Journal, Cyndy Anang, Sajar Camara, Pamela Cornejo, Carla Antonieta Farcello, Ilse Anahi Garcia, Natiera Magnuson, William L. Mccurdy, Lorena Munoz, Maxym V. Myroshnychenko, Ricardo Rios, Theodore Waldeck, Barbara Wallen, Ana Zuniga, Brenda M. Aguilar, Tiffany Alexandra Alvarez, Daniel N. Erosa, Paige C. Espinosa, Carla Antonieta Farcello, Julienne Jochel Paraiso, Nathaniel Derek Phillipps, Carmen Vallin, Jacent N. Wamala, Ernesto Zamora-Ramos

McNair Journal

Journal articles based on research conducted by undergraduate students in the McNair Scholars Program

Table of Contents

Biography of Dr. Ronald E. McNair

Statements:

Dr. Neal J. Smatresk, UNLV President

Dr. Juanita P. Fain, Vice President of Student Affairs

Dr. William W. Sullivan, Associate Vice President for Retention and Outreach

Mr. Keith Rogers, Deputy Executive Director of the Center for Academic Enrichment and Outreach

McNair Scholars Institute Staff

Mathematics In The Age Of Technology: There Is A Place For Technology In The Mathematics Classroom, Helen Crompton

Teaching & Learning Faculty Publications

In today’s world of ubiquitous computing there are a number of technologies available to K-12 educators for teaching and learning mathematics. However, Koehler and Mishra (2008) have described how teaching and learning with such technologies presents a “wicked problem,” as it can involve a number of variables, independent of each other and contextually bound, that need to be brought together. This article highlights the advantages technology offers for mathematics education and looks at some of the reasons behind the poor uptake, such as teacher beliefs and lack of training. A number of solutions are offered to address these issues, including …

Daemon Decay And Cosmic Inflation, Emil Prodanov

Articles

Quantum tunneling in Reissner--Nordstroem geometry is studied and the tunneling rate is determined. A possible scenario for cosmic inflation, followed by reheating phases and subsequent radiation-domination expansion, is proposed.

Computer Monitored Problem Solving Dialogues, Lisa Dion, Jeremy Jank, Nicole Rutt

Symposium on Research and Creative Expression (SORCE)

This project looks over the shoulder at students collaboratively engaged in a math problem-solving activity. One task we looked at was mechanically classifying the students current activity or knowledge state, of which we have identified 15 different categories. We have produced an automatic classifier that examines student sentences and is 55% accurate in identifying utterances as containing certain bits of knowledge or evidence of certain activities. The classifier was built from a corpus of student-written reports. Treating each sentence as a bag of words, we built vector space models of the word co-occurrence matrix using both non-negative matrix factorization (NMF) …