Mathematics Commons^™

Methods In Discrete Mathematics To Study Dna Rearrangement Processes, Lina Fajardo Gómez

USF Tampa Graduate Theses and Dissertations

In this work, we introduce novel tools to study DNA recombination pathways and measure their complexity. Genome rearrangement in some ciliate species can be modeled by subword pattern deletions in double-occurrence words (DOWs), words where each symbol appears exactly twice. The iterated deletions can be represented by a graph whose vertices are DOWs connected by an edge if one word can be obtained from the other through a pattern deletion. On this graph, called the “word graph”, we build a complex comprised of cells defined by Cartesian products of simplicial digraphs where we define a boundary operator and compute homology …

Data-Driven Analytical Predictive Modeling For Pancreatic Cancer, Financial & Social Systems, Aditya Chakraborty

USF Tampa Graduate Theses and Dissertations

Pancreatic cancer is one of the most deathly disease and becoming an increasingly commoncause of cancer mortality. It continues giving rise to massive challenges to clinicians and cancer researchers. The combined five-year survival rate for pancreatic cancer is extremely low, about 5 to 10 percent, owing to the fact that a large number of the patients are diagnosed at stage IV when the disease has metastasized. Our study investigates if there exists any statistical significant difference between the median survival times and also the survival probabilities of male and female pancreatic cancer patients at different cancer stages, and irrespective of …

On Simultaneous Similarity Of D-Tuples Of Commuting Square Matrices, Corey Connelly

USF Tampa Graduate Theses and Dissertations

It has been shown by B. Shekhtman that when any d-tuple A of pairwise commuting N × N matrices with complex entries is cyclic, then A is simultaneously similar to the d-tuple of commuting N × N matrices B if and only if B is cyclic, and the sets of polynomials in d variables which annihilate A and B are equivalent.

This thesis offers a further generalization of this result, demonstrating the necessary and sufficient conditions for the simultaneous similarity of n-cyclic d-tuples of commuting square complex-valued matrices.

Stability Analysis Of Delay-Driven Coupled Cantilevers Using The Lambert W-Function, Daniel Siebel-Cortopassi

USF Tampa Graduate Theses and Dissertations

A coupled delay-feedback system of two cantilevers can yield greater sensitivity than that of asingle cantilever system, with potential applications in atomic force microscopy. The Lambert W-function analysis concept for delay differential equations is used to more accurately model the behavior of specific configurations of these cantilever systems. We also use this analysis concept to find parameters which yield stability for greater parameter ranges, of the delay differential equations. The Q factor, or quality factor, is the ratio of energy stored in the system, to the energy lost per fixed oscillation/movement cycle. Having stability of the cantilevers corresponds to the …

A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman

USF Tampa Graduate Theses and Dissertations

The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and …

Advances And Applications Of Optimal Polynomial Approximants, Raymond Centner

USF Tampa Graduate Theses and Dissertations

The history of optimal polynomial approximants (OPAs) dates back to the engineering literature of the 1970s. Here, these polynomials were studied in the context of the Hardy space H^2(X), where X denotes the open unit disk D or the bidisk D^2. Under certain conditions, it was thought that these polynomials had all of their zeros outside the closure of X. Hence, it was suggested that these polynomials could be used to design a stable digital filter. In recent mathematics literature, OPAs have been studied in many different function spaces. In these settings, numerous papers have been devoted to studying the …

Application Of The Riemann-Hilbert Method To Soliton Solutions Of A Nonlocal Reverse-Spacetime Sasa-Satsuma Equation And A Higher-Order Reverse-Time Nls-Type Equation, Ahmed Ahmed

USF Tampa Graduate Theses and Dissertations

For many years, the study of integrable systems has been one of the most fascinating branches of mathematics and has been thought to be an interesting area for both mathematicians and physicists alike.Many natural phenomena can be predicted by using integrable systems, particularly by studying their different solutions, as well as analyzing and exploring their properties and structures. They are commonly found in nonlinear optics, plasmas, ocean and water waves, gravitational fields, and fluid dynamics. Typical examples of integrable systems include the Korteweg-de Vries (KdV) equation, the nonlinear Schrödinger (NLS) equation, and the Kadomtsev-Petviashvili (KP) equation. Solitons are intrinsic solutions …

Symbolic Computation Of Lump Solutions To A Combined (2+1)-Dimensional Nonlinear Evolution Equation, Jingwei He

USF Tampa Graduate Theses and Dissertations

This thesis aims to consider a (2+1)-dimensional nonlinear evolution equation and its lump solutions. Byusing symbolic computation, two classes of lump solutions are presented. And for two specific chosen examples, we will show three-dimensional plots and density plots to exhibit dynamical features of the lump solution, which are made by Maple plot tools.

Educating Consumers And Producers Of Data: Review Of Making Sense Of Numbers By Jane E. Miller (2022), Andrew J. Miller

Numeracy

Author Jane E. Miller has brought her considerable experience writing and teaching about numerate communication to a new textbook, Making Sense of Numbers. Miller uses clear prose, timely and authentic examples, and thought-provoking exercises to educate the next generation of consumers and producers of data, students in introductory quantitative reasoning, research methods, or data analysis courses. While the textbook does not fit the mold of a "typical" quantitative literacy course, creative instructors may find ways to use it in innovative quantitative literacy, data literacy, or introductory data science courses.

The Distribution Of Energies, Dung Tien Do

Undergraduate Journal of Mathematical Modeling: One + Two

The application of calculus is of great importance in physics. It is used to calculate energy, acceleration, velocity, and much more. In this paper, to calculate the internal energy of an ideal gas (gas molecules) we will use Maxwell-Boltzmann statistical distribution based entirely on calculus. The technique represents the mathematical concept that depends on integration and substitution in calculus to solve a problem.

The Effects Of Effluent Discharge Into The Santa Fé River, João Vito Bezerra Dragone

Undergraduate Journal of Mathematical Modeling: One + Two

The discharge of effluents into rivers is something that has occurred a lot throughout our history, rivers like the Mississippi River and the Tiete River (São Paulo, Brazil) have been targets for many years. Therefore, in this paper I choose to show, through hard data and some assumptions, the impact of sewage dumping in water bodies, in this case the Santa Fé River, Florida and the reason why we should avoid dumping these effluents into the rivers.

The Use Of Calculus To Determine Efficient Fertilizer Levels For Crop Production, Cole Loadholtz

Undergraduate Journal of Mathematical Modeling: One + Two

For this project, I wanted to incorporate calculus into agriculture and environmental science methods. More in detail, the problem used asked for the maximum levels of nitrogen (N) and phosphorus (P) that would be best for a current crop yield. This allowed incorporating partial derivatives, and critical points to find the maximum values for the equation. The results show that in order to demonstrate maximum crop yield production, the levels of nitrogen (N) and phosphorus (P) were to be both at 2, with the correct corresponding units. The drawback from this problem is that although the problem showed effective nitrogen …

Converting Velocity Pressure Into Cubic Feet Per Minute (Cfm), Darrian Robinette

Undergraduate Journal of Mathematical Modeling: One + Two

Almost every building in the United States has a HVAC (Heating, ventilation, and air conditioning) system that relies on balancing Velocity Pressure and calculated CFM to properly control the atmosphere in a building. This is ensured and tested by Field Engineers whose job it is to maintain the efficiency and proper output of these HVAC systems. These systems are used to improve indoor air quality, control moisture and condensation, and contaminants while satisfying comfort needs of occupants. Just with any mechanical system, HVAC systems function efficiently with multiple formulas derived from calculus and physics. Every building is equipped with a …

Volume And Cost Of Longboard Using Aircrete, Mira Stimac

Undergraduate Journal of Mathematical Modeling: One + Two

This project utilizes integral calculus to find the volume of a longboard-style surfboard. The cost for using AirCrete as the material for the longboard will then be calculated. Due to the longboard's shape, the longboard is divided into four sections, and the volume of each is found. The final volume for the longboard with the measurements provided is approximately 3821 cubic inches. The cost of making the longboard out of AirCrete was then calculated by using ratios. The final cost for the longboard is $4.70.

Monitoring Drug Concentration In Emergency Medicine, Andrew Woods

Undergraduate Journal of Mathematical Modeling: One + Two

The careful monitoring of a drug’s concentration in the body of a patient is of the utmost importance in modern medicine. Many of the lifesaving medications that are administered in an emergency medicine environment have a narrow window of efficacy. This effective concentration is in an ever-changing state, as the body processes and eliminates exogenous compounds that are introduced to maintain homeostasis. To ensure the proper treatment and/or management of ailments, special attention must be given to the concentration of a given drug in the body as time progresses. These changing concentrations can be evaluated and tracked using the mathematical …

Internal Combustion Engines: Modeling Internal Temperature As A Function Of Time, Garrett Fandrich

Undergraduate Journal of Mathematical Modeling: One + Two

Just like any thermodynamic system, combustion engines must be cooled to eliminate friction due to heat. Without proper cooling, internal components, such as connecting rods, rod bearings, and pistons can be severely damaged due to thermal expansion, leading to severe damage to the engine block or outright catastrophic failure. Modern engines are cooled using coolant, which flows through internal passageways within the engine block to pull heat away from the system. The use of coolant and external components, such as a water pump, radiator, and thermostat allow an engine to efficiently warm to standard operating temperature and remain at said …

Application Of Calculus In The Elastic Curve (Deflection), Ryan Hillock

Undergraduate Journal of Mathematical Modeling: One + Two

Beams are extremely important structure members that are used in nearly every application where significant loads need to be supported. In mechanical and civil engineering being able to appropriately design beams to withstand the expected-to-be loads is a foundational skill. Proper beam design is what keeps large machines from failing and buildings from collapsing. One important aspect of beam design to consider is the deflection of the beam due to the applied loads. It is often useful to determine the deflection along any given point in the beam in order to make sure the loaded beam does not displace any …

An Introduction To Calling Bullshit: Learning To Think Outside The Black Box, Jevin D. West, Carl T. Bergstrom

Numeracy

Bergstrom, Carl T. and Jevin D. West. 2020. Calling Bullshit: The Art of Skepticism in a Data-Driven World. (New York: Random House) 336 pp. ISBN 978-0525509202.

While statistical methods receive greater attention, the art of critically evaluating information in everyday life more commonly depends on thinking outside the black box of the algorithm. In this piece we introduce readers to our book and associated online teaching materials—for readers who want to more capably call “bullshit” or to teach their students to do the same.

Riemann-Hilbert Problems For Nonlocal Reverse-Time Nonlinear Second-Order And Fourth-Order Akns Systems Of Multiple Components And Exact Soliton Solutions, Alle Adjiri

USF Tampa Graduate Theses and Dissertations

We first investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann-Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix. Secondly, we present the inverse scattering transform for solving a class of eight-component AKNS integrable equations obtained by a specific reduction associated with a block matrix spectral problem. The inverse scattering transform based on Riemann-Hilbert problems is presented along with a jump matrix taken to …

Long-Time Asymptotics For Mkdv Type Reduced Equations Of The Akns Hierarchy In Weighted L2 Sobolev Spaces, Fudong Wang

USF Tampa Graduate Theses and Dissertations

The long-time asymptotics of nonlinear integrable partial differential equations is one of the important research areas in the field of integrable systems. The main tool to analyze the long-time behaviors is the so-called nonlinear steepest descent method, or Deift-Zhou's method, which was born in 1993. To apply Deift-Zhou's method, one first uses the inverse scattering transform to formulate the nonlinear PDEs in terms of an oscillatory 2 by 2 matrix Riemann-Hilbert problem (RHP). After about 15 years of development, a generalized version of Deift-Zhou's method, the ∂—steepest method, came out. The ∂—steepest descent method is a useful method for analyzing …

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Looking Back At Quantitative Reasoning, William Briggs

Numeracy

A teacher looks back on three decades of teaching, pondering, and writing about quantitative reasoning (QR) and shares a few lessons learned. The skills that we teach in QR courses are more important than ever in providing students with a sense of civic virtue: the ability to be engaged and informed citizens in an increasingly complex and quantitative world.

Review Of Social Workers Count: Numbers And Social Issues By Michael Anthony Lewis, Michael T. Catalano

Numeracy

Lewis, Michael Anthony. 2017. Social Workers Count: Numbers and Social Issues. 2019. New York: Oxford University Press. 223 pp. ISBN 978-019046713-5

The numeracy movement, although largely birthed within the mathematics community, is an outside-the-box endeavor which has always sought to break down or at least transgress traditional disciplinary boundaries. Michael Anthony Lewis’s book is a testament that this effort is succeeding. Lewis is a social worker and sociologist with an impressive resume, author of Economics for Social Workers, co-editor of The Ethics and Economics of the Basic Income Guarantee, and member of the faculty at the Silberman School …

The Dangers Of Lift On Parked Planes: General Aviation Airport Safety, Robert Malloy

Undergraduate Journal of Mathematical Modeling: One + Two

The focus of this paper is to investigate proper aircraft management for safety on an airfield. This is accomplished by looking at lift caused by powerful winds to the aircrafts stored on an airfield, and the tension it places on the rope that secures them. This work could be used to determine when aircrafts are in high-risk and need to be stored either in hangars or moved to other airports prior to storms. The calculations used to determine these conclusions are also explored in the paper.

Area Of Irregular Shaped Roof, Omar Alkhawaldeh

Undergraduate Journal of Mathematical Modeling: One + Two

This project makes use of calculus, specifically integration, to find the exact area of a roof garden to minimize the cost of material used in flooring it. Since the roof is of irregular shape, it is divided into four sections, the integral of each section is taken, and a relationship between the integrals is generated. Positive results are found, and the data reveal that the area of the grass floor is 175.3 m² while the area of the wooden floor is 23.4 m² with the total price being 2472 US dollars.

Calculating Probable Theoretical Offspring Genotype In Fruit Flies, Megan Keller

Undergraduate Journal of Mathematical Modeling: One + Two

Being able to calculate an offspring's theoretical genotype is critical in genetic sciences. We calculate the theoretical genotype and phenotype of fruit fly offspring. Using the product rule, we determine the probability for each trait and then for each genotype. In conclusion, we calculate 64 different genotypes that are supposed to be possible, but only 8 phenotypes are possible.

Mathematical Reconstruction Of A Traffic Crash, Benjamin Covert

Undergraduate Journal of Mathematical Modeling: One + Two

The objective is to find the impact speeds of two motor vehicles involved in a traffic crash. The calculations take into account the approach (pre-collision) and departure (post collision) angles, as well as weights and post collision speeds of both vehicles. The data is provided by Timothy Sleyzack who investigated this traffic collision. The conclusions confirm the validity of the use of Conservation of Linear Momentum in the field of traffic crash reconstruction.

Emergency Communications Deficiency Locator, Austin Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The Bi-Directional Amplifier (BDA) is the newest edition to Life Safety in the state of Florida. The Florida Fire Prevention Code (NFPA 1) section 11.10.1 states that “In all new and existing buildings, minimum radio signal strength for fire department communications shall be maintained at a level determined by the authority having jurisdiction (Committee NFPA 1: Fire Code 2018). That authority having jurisdiction for our local Tampa Bay area is the Hillsborough County Fire Rescue department and they have posted their own requirements along with the Florida Senate for emergency communication standards. All existing “Hi-rise” buildings, 75 feet tall …

Evaluating The Improvement In Dna Fingerprinting, Dani Dray

Undergraduate Journal of Mathematical Modeling: One + Two

DNA fingerprinting is a forensic technique used to create patterns that are unique to a person’s DNA. Previously, these fingerprints were made from 13 different segments of DNA, but today they are made from the 20 ones. The fundamental principle of counting is used to determine how much of an improvement was made after adding the 7 additional DNA segments. It is found that this addition greatly reduces the likelihood of two people having the same exact fingerprint, therefore improving the accuracy and reliability of DNA fingerprinting.

Predicting The Cost Of Dental Care Using A Probability Model, Nadine Wehbe

Undergraduate Journal of Mathematical Modeling: One + Two

This paper uses survey data to present a probability model that allows dental offices to predict patient costs. The quantitative model is useful for developing and accepting capitation rates. It accounts for whether the care is initial care or maintenance care, the type of dental care (such as operative, prosthetics, or periodontics), and different age groups, all of which affect the cost of dental treatment.