Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- Selected Works (6)
- Air Force Institute of Technology (5)
- Claremont Colleges (5)
- Portland State University (5)
- Illinois Math and Science Academy (4)
-
- Prairie View A&M University (4)
- University of Nevada, Las Vegas (4)
- California State University, San Bernardino (3)
- City University of New York (CUNY) (2)
- Illinois State University (2)
- Old Dominion University (2)
- Rose-Hulman Institute of Technology (2)
- Technological University Dublin (2)
- University of South Florida (2)
- Wright State University (2)
- Bard College (1)
- Cedarville University (1)
- Embry-Riddle Aeronautical University (1)
- George Fox University (1)
- Georgia Southern University (1)
- Gettysburg College (1)
- Johnson County Community College (1)
- Louisiana State University (1)
- Montclair State University (1)
- New Jersey Institute of Technology (1)
- Rollins College (1)
- Southern Methodist University (1)
- Stephen F. Austin State University (1)
- University of Tennessee at Chattanooga (1)
- University of Tennessee, Knoxville (1)
- Publication Year
- Publication
-
- Theses and Dissertations (7)
- Aaron Hoffman (5)
- Applications and Applied Mathematics: An International Journal (AAM) (4)
- Differential Equations (4)
- Mathematics and Statistics Faculty Publications and Presentations (4)
-
- UNLV Theses, Dissertations, Professional Papers, and Capstones (4)
- All HMC Faculty Publications and Research (3)
- Dissertations, Theses, and Capstone Projects (2)
- Electronic Theses and Dissertations (2)
- Mathematics & Statistics Theses & Dissertations (2)
- Numeracy (2)
- Rose-Hulman Undergraduate Mathematics Journal (2)
- Spora: A Journal of Biomathematics (2)
- Theses Digitization Project (2)
- Academic Posters Collection (1)
- Articles (1)
- Bradley Minch (1)
- CODEE Journal (1)
- Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works (1)
- Doctoral Dissertations (1)
- Electronic Theses, Projects, and Dissertations (1)
- Electronic Thesis and Dissertation Repository (1)
- Faculty Publications - Department of Mathematics (1)
- Honors Program Theses (1)
- Honors Theses (1)
- Journal of Humanistic Mathematics (1)
- LSU Doctoral Dissertations (1)
- Mathematics Research (1)
- Mathematics and Statistics Faculty Publications (1)
- Publications (1)
- Publication Type
- File Type
Articles 1 - 30 of 68
Full-Text Articles in Physical Sciences and Mathematics
Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince
Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince
Numeracy
This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of …
(R1987) Hermite Wavelets Method For System Of Linear Differential Equations, Inderdeep Singh, Manbir Kaur
(R1987) Hermite Wavelets Method For System Of Linear Differential Equations, Inderdeep Singh, Manbir Kaur
Applications and Applied Mathematics: An International Journal (AAM)
In this research paper, we present an accurate technique for solving the system of linear differential equations. Such equations often arise as a result of modeling in many systems and applications of engineering and science. The proposed scheme is based on Hermite wavelets basis functions and operational matrices of integration. The demonstrated scheme is simple as it converts the problem into algebraic matrix equation. To validate the applicability and efficacy of the developed scheme, some illustrative examples are also considered. The results so obtained with the help of the present proposed numerical technique by using Hermite wavelets are observed to …
Application Of The Two-Variable Model To Simulate A Multisensory Reaction-Time Task, Rebecca Brady, John Butler
Application Of The Two-Variable Model To Simulate A Multisensory Reaction-Time Task, Rebecca Brady, John Butler
Academic Posters Collection
To navigate the world in an efficient manner, the brain seamlessly integrates signals received across multiple sensory modalities. Behavioral studies have suggested that multisensory processing is a winner-take-all sensory response mechanism to some optimal combination of sensory signals. In addition, multiple sensory cues are not always beneficial with some studies showing maladaptive multisensory processing as an identifier of older adults prone to falls from age matched healthy controls.
A stalwart of modelling sensory decision-making is the work by (Wong &Wang, 2006) but to date almost all of this research has been focused on unisensory tasks. We extend the reduced two-variable …
On The Spatial Modelling Of Biological Invasions, Tedi Ramaj
On The Spatial Modelling Of Biological Invasions, Tedi Ramaj
Electronic Thesis and Dissertation Repository
We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …
Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox
Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox
University Honors Theses
A diffusion-convection equation is a partial differential equation featuring two important physical processes. In this paper, we establish the theory of solving a 1D diffusion-convection equation, subject to homogeneous Dirichlet, Robin, or Neumann boundary conditions and a general initial condition. Firstly, we transform the diffusion-convection equation into a pure diffusion equation. Secondly, using a separation of variables technique, we obtain a general solution formula for each boundary type case, subject to transformed boundary and initial conditions. While eigenvalues in the cases of Dirichlet and Neumann boundary conditions can be constructed easily, the Robin boundary condition necessitates solving a transcendental algebraic …
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Rose-Hulman Undergraduate Mathematics Journal
For the SCUDEM V 2020 virtual challenge, we received an outstanding distinction for modeling a bird perched on a bicycle wheel utilizing the appropriate physical equations of rotational motion. Our model includes both theoretical calculations and numerical results from applying the Heaviside function for the swing motion of the bird. We provide a discussion on: our model and its numerical results, the overall limitations and future work of the model we constructed, and the experience we had participating in SCUDEM V 2020.
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Spora: A Journal of Biomathematics
Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year-1 reduces hepatitis B by over 90%, …
Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
UNLV Theses, Dissertations, Professional Papers, and Capstones
Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …
Mathematical Modeling Of A Variable Mass Rocket’S Dynamics Using The Differential Transform Method, Ashwyn Sam
Mathematical Modeling Of A Variable Mass Rocket’S Dynamics Using The Differential Transform Method, Ashwyn Sam
Honors Theses
In this paper, the mathematical modelling of a rocket with varying mass is investigated to construct a function that can describe the velocity and position of the rocket as a function of time. This research is geared more towards small scale rockets where the nonlinear drag term is of great interest to the underlying dynamics of the rocket. A simple force balance on the rocket using Newton’s second law of motion yields a Riccati differential equation for which the solution yields the velocity of the rocket at any given time. This solution can then be integrated with respect to time …
Analysis Of An Ode Model For Sea Turtle Populations With Temperature-Dependent Sex Determination, Lindsey A. Ukishima
Analysis Of An Ode Model For Sea Turtle Populations With Temperature-Dependent Sex Determination, Lindsey A. Ukishima
Student Publications
The sex of green sea turtles is determined by the temperature at which the eggs are incubated. Recent studies have shown that the sex ratios of sea turtle populations have changed over recent years, likely due to climate change, which has produced a more female-biased population. This paper finds the nonzero equilibrium point of the novel system developed by Herrera et a. (2019) and attempts to determine the stability of the population at that point.
Using Differential Equations To Model Predator-Prey Relations As Part Of Scudem Modeling Challenge, Zachary Fralish, Bernard Tyson Iii, Anthony Stefan
Using Differential Equations To Model Predator-Prey Relations As Part Of Scudem Modeling Challenge, Zachary Fralish, Bernard Tyson Iii, Anthony Stefan
Rose-Hulman Undergraduate Mathematics Journal
Differential equation modeling challenges provide students with an opportunity to improve their mathematical capabilities, critical thinking skills, and communication abilities through researching and presenting on a differential equations model. This article functions to display an archetype summary of an undergraduate student team’s response to a provided prompt. Specifically, the provided mathematical model estimates how certain stimuli from a predator are accumulated to trigger a neural response in a prey. Furthermore, it tracks the propagation of the resultant action potential and the physical flight of the prey from the predator through the analysis of larval zebrafish as a model organism. This …
Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, Pierpaolo Natalini, Paolo E. Ricci
Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, Pierpaolo Natalini, Paolo E. Ricci
Applications and Applied Mathematics: An International Journal (AAM)
The adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials. The particular case of adjoint Appell-Euler and Appell-Bernoulli polynomials of the first kind is analyzed.
Dynamical Modeling In Cell Biology With Ordinary Differential Equations, Renee Marie Dale
Dynamical Modeling In Cell Biology With Ordinary Differential Equations, Renee Marie Dale
LSU Doctoral Dissertations
Dynamical systems have been of interest to biologists and mathematicians alike. Many processes in biology lend themselves to dynamical study. Movement, change, and response to stimuli are dynamical characteristics that define what is 'alive'. A scientific relationship between these two fields is therefore natural. In this thesis, I describe how my PhD research variously related to biological, mathematical, and computational problems in cell biology. In chapter 1 I introduce some of the current problems in the field. In chapter 2, my mathematical model of firefly luciferase in vivo shows the importance of dynamical models to understand systems. Data originally collected …
Stability Analysis For The Equilibria Of A Monkeypox Model, Rachel Elizabeth Tewinkel
Stability Analysis For The Equilibria Of A Monkeypox Model, Rachel Elizabeth Tewinkel
Theses and Dissertations
Monkeypox virus was first identified in 1958 and has since been an ongoing problem in Central and Western Africa. Although the smallpox vaccine provides partial immunity against monkeypox, the number of cases has greatly increased since the eradication of smallpox made its vaccination unnecessary. Although studied by epidemiologists, monkeypox has not been thoroughly studied by mathematicians to the extent of other serious diseases. Currently, to our knowledge, only three mathematical models of monkeypox have been proposed and studied. We present the first of these models, which is related to the second, and discuss the global and local asymptotic stability of …
On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun
On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun
Dissertations, Theses, and Capstone Projects
The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions.
Hrushovski first proposed an algorithm for computing the differential …
Sir Models: Differential Equations That Support The Common Good, Lorelei Koss
Sir Models: Differential Equations That Support The Common Good, Lorelei Koss
CODEE Journal
This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.
The Effect Of Using A Project-Based Learning (Pbl) Approach To Improve Engineering Students' Understanding Of Statistics, Fionnuala Farrell, Michael Carr
The Effect Of Using A Project-Based Learning (Pbl) Approach To Improve Engineering Students' Understanding Of Statistics, Fionnuala Farrell, Michael Carr
Articles
Over the last number of years we have gradually been introducing a project based learning approach to the teaching of engineering mathematics inDublin Institute of Technology. Several projects are now in existence for the teaching of both second-order differential equations and first order differential equations.We intend to incrementally extend this approach acrossmore of the engineering mathematics curriculum. As part of this ongoing process, practical realworld projects in statistics were incorporated into a second year ordinary degree mathematics module. This paper provides an overview of these projects and their implementation. As a means to measure the success of this initiative, we …
Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag
Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag
Dissertations, Theses, and Capstone Projects
The algebraic framework for capturing properties of solution sets of differential equations was formally introduced by Ritt and Kolchin. As a parallel to the classical Galois groups of polynomial equations, they devised the notion of a differential Galois group for a linear differential equation. Just as solvability of a polynomial equation by radicals is linked to the equation’s Galois group, so too is the ability to express the solution to a linear differential equation in "closed form" linked to the equation’s differential Galois group. It is thus useful even outside of mathematics to be able to compute and represent these …
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Theses and Dissertations
Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows …
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Electronic Theses and Dissertations
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
Senior Projects Spring 2018
Mathematical models are finding increased use in biology, and partuculary in the field of cancer research. In relation to cancer, systems of differential equations have been proven to model tumor growth for many types of cancer while taking into account one or many features of tumor growth. One feature of tumor growth that models must take into account is that tumors do not grow exponentially. One model that embodies this feature is the Gomperts Model of Cell Growth. By fitting this model to long-term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor …
Modeling Public Opinion, Arden Baxter
Modeling Public Opinion, Arden Baxter
Honors Program Theses
The population dynamics of public opinion have many similarities to those of epidemics. For example, models of epidemics and public opinion share characteristics like contact rates, incubation times, and recruitment rates. Generally, epidemic dynamics have been presented through epidemiological models. In this paper we adapt an epidemiological model to demonstrate the population dynamics of public opinion given two opposing viewpoints. We find equilibrium solutions for various cases of the system and examine the local stability. Overall, our system provides sociological insight on the spread and transition of a public opinion.
Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace
Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace
Numeracy
The importance of mathematics to biology is illustrated by search data from Google Scholar. I argue that a pedagogical approach based on student research projects is likely to improve retention and foster critical thinking about mathematical modeling, as well as reinforce quantitative reasoning and the appreciation of calculus as a tool. The usual features of a course (e.g., the instructor, assessment, text, etc.) are shown to have very different purposes in a research-based course.
Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker
Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker
The Research and Scholarship Symposium (2013-2019)
Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.
Steady And Stable: Numerical Investigations Of Nonlinear Partial Differential Equations, R. Corban Harwood
Steady And Stable: Numerical Investigations Of Nonlinear Partial Differential Equations, R. Corban Harwood
Faculty Publications - Department of Mathematics
Excerpt: "Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation."
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Electronic Theses and Dissertations
Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Applications and Applied Mathematics: An International Journal (AAM)
In this article, modified (G'/G )-expansion method is presented to establish the exact complex solutions of the time fractional Gross-Pitaevskii (GP) equation in the sense of the conformable fractional derivative. This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. Based on two transformations, fractional GP equation can be converted into nonlinear ordinary differential equation of integer orders. In the end, we will discuss the solutions of the fractional GP equation with external potentials.
Spontaneous Calcium Release In Cardiac Myocytes: Store Overload And Electrical Dynamics, Amanda M. Alexander, Erin K. Denardo, Eric Frazier Iii, Michael Mccauley, Nicholas Rojina, Zana Coulibaly, Bradford E. Peercy, Leighton T. Izu
Spontaneous Calcium Release In Cardiac Myocytes: Store Overload And Electrical Dynamics, Amanda M. Alexander, Erin K. Denardo, Eric Frazier Iii, Michael Mccauley, Nicholas Rojina, Zana Coulibaly, Bradford E. Peercy, Leighton T. Izu
Spora: A Journal of Biomathematics
Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca2+) mishandling in cardiac muscle cells. We adapt Izu's et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes implemented by Gobbert, and analyzed in Coulibaly et al. to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca2+ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with …
Newton's Law Of Cooling, Caleb J. Emmons
Newton's Law Of Cooling, Caleb J. Emmons
Journal of Humanistic Mathematics
A poem reflecting three different viewpoints on Newton's Law of Cooling.
1. Coffee, Ruth Dover