Physical Sciences and Mathematics Commons^™

Accelerating Multiparametric Mri For Adaptive Radiotherapy, Shraddha Pandey

USF Tampa Graduate Theses and Dissertations

MR guided Radiotherapy (MRgRT) marks an important paradigm shift in the field of radiotherapy. Superior tissue contrast of MRI offers better visualization of the abnormal lesions, as a result precise radiation dose delivery is possible. In case of online treatment planning, MRgRT offers better control of intratumoral motion and quick adaptation to changes in the gross tumor volume. Nonetheless, the MRgRT process flow does suffer from some challenges that limit its clinical usability. The primary aspects of MRgRT workflow are MRI acquisition, tumor delineation, dose map prediction and administering treatment. It is estimated that the acquisition of MRI takes around …

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser

Journal of Practitioner Research

Whole group math talks, or number talks, are a common practice to get students talking about their own understanding of mathematical concepts. The purpose of this study was to implement math talks in small group settings to see what would happen, specifically to students’ conceptual understanding as well their general perceptions of math talks. This study took place in a fourth-grade math classroom, and math talks were implemented with the whole class for a week and then moved to small groups for the remaining three weeks of the study. During the study, a pre-and post-assessment was given, field notes were …

Boundary Behavior Of Analytic Functions And Approximation Theory, Spyros Pasias

USF Tampa Graduate Theses and Dissertations

In this Thesis we deal with problems regarding boundary behavior of analytic functions and approximation theory. We will begin by characterizing the set in which Blaschke products fail to have radial limits but have unrestricted limits on its complement. We will then proceed and solve several cases of an open problem posed in \cite{Da}. The goal of the problem is to unify two known theorems to create a stronger theorem; in particular we want to find necessary and sufficient conditions on sets $E_1\subset E_2$ of the unit circle such that there exists a bounded analytic function that fails to have …

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 …

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 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 …

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.

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 …

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.

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 …

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 …