Mathematics Commons^™

Volatilization Of Benzene In A River, Eric Dunlop

Undergraduate Journal of Mathematical Modeling: One + Two

Benzene is a volatile organic compound: when it contaminates a river, some of the substance will evaporate as it flows through. We examine the volumetric flow rate to find how volatilization affects the concentration levels of benzene as the substance flows through several consecutive sections of a river, using a specific example to illustrate the general method.

Adiabatic Flame Temperature For Combustion Of Methane Ii, Rebeca Pupo

Undergraduate Journal of Mathematical Modeling: One + Two

We calculate the adiabatic flame temperature of a mixture of methane and oxygen in the presence of a diluent gas then determine the mole fractions of methane without respect to nitrogen and solve for the moles of oxygen present. Knowing the moles of methane and oxygen, allows us to calculate the moles of nitrogen present at four constant mole fractions of nitrogen, and the adiabatic flame temperature is determined from the energy released by the reaction. Lastly, we produce several graphs to compare the adiabatic flame temperatures at different mole fractions of nitrogen.

Diffusion Of Vitamin B12 Across A Mesoporous Metal Organic Framework, Veronica Valencia

Undergraduate Journal of Mathematical Modeling: One + Two

We measure the rate of uptake and the rate of release of a Vitamin B12 solution (dissolved in water) at 2 different temperatures (room temperature and 37°C) by the mesoporous metal organic framework TbMOF-100 at 1-hour intervals using a spectrophotometer. Using the Beer-Lambert law, we calculate the concentration of the stock solution based on the absorbance values obtained with the spectrophotometer. These values allow for the quantification of the initial rate of uptake and the rate of uptake at a random incubation time of the Vitamin B12 by the TbMOF-100. We also calculate the value of the coefficient of diffusion …

Finding The Area Of A Major League Baseball Field, Jacob Courchaine

Undergraduate Journal of Mathematical Modeling: One + Two

Using a Major League Baseball (MLB) baseball field template for guidelines, we estimate the cost of building the largest possible field accepted under MLB standards. This includes finding the areas of both the clay and grassy regions and determining how many bags of clay and fertilizer are required to cover the field.

Towards Interference-Immune And Channel-Aware Multicarrier Schemes: Filters, Lattices, And Interference Issues, Alphan Sahin

USF Tampa Graduate Theses and Dissertations

In this dissertation, multicarrier schemes are reviewed within the framework of Gabor Systems. Their fundamental elements; what to transmit, i.e., symbols, how to transmit, i.e., filters or pulse shape, and where/when to transmit, i.e., lattices are investigated extensively. The relations between different types of multicarrier schemes are discussed.

Within the framework of Gabor systems, a new windowing approach, edge windowing, is developed to address the out-of-band (OOB) radiation problem of orthogonal frequency division multiplexing (OFDM) based multicarrier schemes. To the best of our knowledge, for the first time, the diversity on the range of the users is exploited to suppress …

Study Of Dieldrin In Coralville Reservoir, Jeremy Smith

Undergraduate Journal of Mathematical Modeling: One + Two

Using existing experimental data taken over a period of roughly 12 years that documents the concentrations of dieldrin levels in the environment and fatty tissue of the fish, we construct a model of the total dieldrin concentration decline. Comparisons between the experimental data and speculative data can be made using calculus and elements of statistics in order to better understand the movement of dieldrin in the reservoir. Because of the potentially harmful exposure effects of dieldrin to humans as well as the environment, it is important to be able to predict when stability has been restored to the ecosystem.

Boolean Partition Algebras, Joseph Anthony Van Name

USF Tampa Graduate Theses and Dissertations

A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean

algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces

is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness

of non-Archimedean uniform spaces can be formulated in terms of Boolean partition algebras.

Analytic Functions With Real Boundary Values In Smirnov Classes EP, Lisa De Castro

USF Tampa Graduate Theses and Dissertations

This thesis concerns the classes of analytic functions on bounded, n-connected domains known as the Smirnov classes E^p, where p > 0. Functions in these classes satisfy a certain growth condition and have a relationship to the more well known classes of functions known as the Hardy classes H^p. In this thesis I will show how the geometry of a given domain will determine the existence of non-constant analytic functions in Smirnov classes that possess real boundary values. This is a phenomenon that does not occur among functions in the Hardy classes.

The preliminary and background information …

Topological Degree And Variational Inequality Theories For Pseudomonotone Perturbations Of Maximal Monotone Operators, Teffera Mekonnen Asfaw

USF Tampa Graduate Theses and Dissertations

Let X be a real reflexive locally uniformly convex

Banach space with locally uniformly convex dual space X^*

. Let G be a

bounded open subset of X. Let T:X⊃ D(T)⇒ 2X^*

be maximal

monotone and S: X ⇒ 2X^*

be bounded

pseudomonotone and such that 0 notin cl((T+S)(D(T)∩partG)). Chapter 1 gives general introduction and mathematical prerequisites. In

Chapter 2 we develop a homotopy invariance and uniqueness results for the degree theory constructed by Zhang and Chen for multivalued (S₊) perturbations of

maximal monotone operators. Chapter 3 is devoted to the construction of a new …

Modeling State Transitions With Automata, Egor Dolzhenko

USF Tampa Graduate Theses and Dissertations

Models based on various types of automata are ubiquitous in modern science. These models allow reasoning about deep theoretical questions and provide a basis for the development of efficient algorithms to solve related computational problems. This work discusses several types of automata used in such models, including cellular automata and mandatory results automata.

The first part of this work is dedicated to cellular automata. These automata form an important class of discrete dynamical systems widely used to model physical, biological, and chemical processes. Here we discuss a way to study the dynamics of one-dimensional cellular automata through the theory of …

A Study Of Permutation Polynomials Over Finite Fields, Neranga Fernando

USF Tampa Graduate Theses and Dissertations

Let p be a prime and q = p^k. The polynomial g_n,q isin F_p[x] defined by the functional equation Sigma_{a isin Fq} (x+a)ⁿ = g_n,q(x^q- x) gives rise to many permutation polynomials over finite fields. We are interested in triples (n,e;q) for which g_n,q is a permutation polynomial of F_q^e. In Chapters 2, 3, and 4 of this dissertation, we present many new families of permutation polynomials in the form of g_n,q. The permutation behavior of g_n,q is becoming increasingly more …

Optimization In Non-Parametric Survival Analysis And Climate Change Modeling, Iuliana Teodorescu

USF Tampa Graduate Theses and Dissertations

Many of the open problems of current interest in probability and statistics involve complicated data

sets that do not satisfy the strong assumptions of being independent and identically distributed. Often,

the samples are known only empirically, and making assumptions about underlying parametric

distributions is not warranted by the insufficient information available. Under such circumstances,

the usual Fisher or parametric Bayes approaches cannot be used to model the data or make predictions.

However, this situation is quite often encountered in some of the main challenges facing statistical,

data-driven studies of climate change, clinical studies, or financial markets, to name a few. …

Nonlinear Techniques For Stochastic Systems Of Differential Equations, Tadesse G. Zerihun

USF Tampa Graduate Theses and Dissertations

Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematically develop mathematical tools to undertake the mathematical frame-work to investigate a complex nonlinear nonstationary stochastic systems of differential …

On Algorithmic Fractional Packings Of Hypergraphs, Jill Dizona

USF Tampa Graduate Theses and Dissertations

Let F₀ be a fixed k-uniform hypergraph, and let H be a given k-uniform hypergraph on n vertices. An F₀-packing of H is a family F of edge-disjoint copies of F₀ which are subhypergraphs in H. Let n_F0(H) denote the maximum size |F| of an F₀-packing F of H. It is well-known that computing n_F0(H) is NP-hard for nearly any choice of F₀.

In this thesis, we consider the special case when F₀ is a linear hypergraph, that is, when no two edges …

Wronskian, Grammian And Pfaffian Solutions To Nonlinear Partial Differential Equations, Alrazi Abdeljabbar

USF Tampa Graduate Theses and Dissertations

It is significantly important to search for exact soliton solutions to nonlinear partial differential equations (PDEs) of mathematical physics. Transforming nonlinear PDEs into bilinear forms using the Hirota differential operators enables us to apply the Wronskian and Pfaffian techniques to search for exact solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation with not only constant coefficients but also variable coefficients under a certain constraint

(u_t + α ₁(t)u_xxy + 3α ₂(t)u_xu_y)_x +α ₃ (t)u_ty -α ₄(t)u_zz + α ₅(t)(u_x + α ₃(t)u_y) = …

Pfaffian And Wronskian Solutions To Generalized Integrable Nonlinear Partial Differential Equations, Magdy Asaad

USF Tampa Graduate Theses and Dissertations

The aim of this work is to use the Pfaffian technique, along with the Hirota bilinear method to construct different classes of exact solutions to various of generalized integrable nonlinear partial differential equations. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

The derivation and solutions of integrable nonlinear partial differential equations in two spatial dimensions have been …

Team-Teaching Experiences Of A Mathematician And A Mathematics Teacher Educator: An Interpretative Phenomenological Case Study, Sarah K. Bleiler

USF Tampa Graduate Theses and Dissertations

In recent years, experts and organizations involved in mathematics education have emphasized the importance of collaboration between mathematicians and mathematics teacher educators as a means of improving the professional preparation of mathematics teachers. While several such collaborative endeavors have been documented in the extant literature, most research reports have focused on the products, rather than the process, of collaboration. The purpose of this interpretative phenomenological case study is to gain an understanding of the lived experiences of a mathematician and a mathematics teacher educator as they engaged in a team-teaching collaboration within the context of prospective secondary mathematics teacher preparation. …

Self-Assembly Of Self-Similar Structures By Active Tiles, Daria Karpenko

USF Tampa Graduate Theses and Dissertations

The natural capacity of DNA for molecular self-assembly has already been exploited to create DNA based tiles which can self-assemble into nano-scale arrays and carry out nano-scale computation. Thus far, however, all such self-assembly has been passive, in the sense that the binding capacities of a tile are never altered throughout the assembly. The idea of active tiles, tiles that can send signals to each other and activate latent binding sites, has been proposed but never incorporated into a formal model. Here, I present an extension of the existent abstract tile assembly model by defining an active tile assembly and …

Incorporating Quantitative Reasoning In Common Core Courses: Mathematics For The Ghost Map, John R. Jungck

Numeracy

How can mathematics be integrated into multi-section interdisciplinary courses to enhance thematic understandings and shared common readings? As an example, four forms of quantitative reasoning are used to understand and critique one such common reading: Steven Berlin Johnson’s "The Ghost Map: The Story of London's Most Terrifying Epidemic - and How it Changed Science, Cities and the Modern World" (Riverhead Books, 2006). Geometry, statistics, modeling, and networks are featured in this essay as the means of depicting, understanding, elaborating, and critiquing the public health issues raised in Johnson’s book. Specific pedagogical examples and resources are included to illustrate applications and …

Parts Of The Whole: Learn More, Learn Better, Dorothy Wallace

Numeracy

Building on previous columns in Numeracy, this column analyzes various teaching techniques in terms of their ability to build cognitive schema, extend existing schema, reinforce learning, move mean understanding of a group of students, and reduce variance in understanding of a group. We offer a pedagogical cycle as an example of how to address multiple learning goals using common teaching methods.

If Only Math Majors Could Write..., Bernard L. Madison

Numeracy

This text of the opening plenary address to the 2011 Summit of the Appalachian College Association and the meeting of the National Numeracy Network makes an argument that quantitative reasoning and writing should be taught together. The argument is set up by noting that humanists have historically banished quantitative issues from their study of the liberal arts and that science, engineering, and mathematics education suffers from lack of approaches to learning that promote complex, deeper understanding, most notably integrative and reflective learning. Therefore, everyone would profit from combining writing and quantitative reasoning. Five more specific reasons are discussed, drawing evidence …

Period Life Tables: A Resource For Quantitative Literacy, Thomas J. Pfaff, Stanley Seltzer

Numeracy

A period life table provides an estimate of the probability that a person will die at a particular age. Using data available online, we examine tables of expected years to live for males and females against age for three populations: the United States in 2007, the U.S. at the turn of the twentieth century, and the Roman Empire. Scatter plots of males and females for each population show how life expectancy increases with age (e.g., U.S. 2007: 50 year-old female > 40 year-old female > 45 year-old male). The three data sets allow historical comparisons (e.g., of gender disparity, larger now; of …

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Numeracy

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students.

Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

Quantitative Literacy Interventions At University Of Cape Town: Effects Of Separation From Academic Disciplines, Vera Frith

Numeracy

The aim of the Numeracy Centre at the University of Cape Town is to develop students’ quantitative literacy (QL) in a manner consistent with their programmes of study and intended roles in the community. Our theoretical perspective on the nature of QL is in line with that of the New Literacies Studies and sees academic QL as practices in different academic disciplinary contexts. This means that for us the ideal curriculum structure for developing QL would fully integrate it into the teaching of the disciplines. This is in practice not achievable in most cases, especially since many students do not …

Numeracy, Financial Literacy, And Financial Decision-Making, Annamaria Lusardi

Numeracy

Financial decisions, be they related to asset building or debt management, require the capacity to do calculations, including some complex ones. But how numerate are individuals, in particular when it comes to calculations related to financial decisions? Studies and surveys implemented in both the United States and in other countries that are described in this paper show the level of numeracy among the population to be very low. Moreover, lack of numeracy is not only widespread but is particularly severe among some demographic groups, such as women, the elderly, and those with low educational attainment. This has potential consequences for …

The Joy Of Quantitative Reasoning, Caren Diefenderfer

Numeracy

One of the advantages of focusing on quantitative reasoning is that it spans a wide variety of topics. As incoming president of the National Numeracy Network, I would like to take the opportunity of this editorial to tell my story of intellectual reward from finding common purpose in quantitative reasoning with colleagues from disciplines outside of mathematics. The story starts with an NSF-funded faculty development project (DUE-9952807) to further a QR across-the-curriculum program and the finding from that program that merging authentic context with mathematics brings interaction and collaboration. That joy in learning from and working with colleagues in other …

Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald

Undergraduate Journal of Mathematical Modeling: One + Two

In this project we model volumetric flow rate through a parabolic ceramic water filter (CWF) to determine how quickly it can process water while still improving its quality. The volumetric flow rate is dependent upon the pore size of the filter, the surface area, and the height of water in the filter (hydraulic head). We derive differential equations governing this flow from the conservation of mass principle and Darcy's Law and find the flow rate with respect to time. We then use methods of calculus to find optimal specifications for the filter. This work is related to the research conducted …

The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project was to determine the area-to-depth relationship in Lake Behnke, which acts as the principal stormwater drainage basin for the University of South Florida campus in Tampa, Florida. Data previously collected in a stormwater management study by Jeffery Earhart illustrated a linear correlation between the lake's area and depth; however, that study was conducted in 1998, and this present work serves to double check that correlation. We analyzed a bathymetric map of Lake Behnke that displayed several contour lines indicating depth and approximated the area inside each closed curve with a contour integral. The resulting relationship …

Overfishing Of The Common Snook, Allison Ashcroft

Undergraduate Journal of Mathematical Modeling: One + Two

The chief aim of this project is to determine if the populations of the common snook, Centropomus Undecimalis, in the Atlantic and Gulf coast are being affected by overfishing. This is established by evaluating the intrinsic rate of change for these populations and their carrying capacities. It turns out that the carrying capacity for the population of the Atlantic coast is approximately one million snook and its intrinsic rate is 0.00621, while the carrying capacity of the Gulf coast's population is 2.9 million snook and its intrinsic rate is 0.00165. The decline of both populations is most likely due …

Complexity Of Mitochondrial Genome Sequences, Brandon Toun

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project is to compare the complexities of different species' mitochondrial genome sequences. Using an implementation of Deflate compression algorithm from Java standard library, we were able to compress mitochondrial genomes of nine different species. The complexity of each sequence is estimated as a ratio of the original sequence length to the length of the compressed sequence. In addition, we show how a notion of topological entropy from symbolic dynamics can be used as another complexity measure of nucleotide sequences.