Nonlinear Dynamics Of Mountain Pine Beetle Populations: Discussion Of Forestry Policy, A Survey Of Existing Mathematical Models, And Code Base Demonstration,
2024
Colorado School of Mines
Nonlinear Dynamics Of Mountain Pine Beetle Populations: Discussion Of Forestry Policy, A Survey Of Existing Mathematical Models, And Code Base Demonstration, Scott A. Strong, Maya Maes-Johnson
CODEE Journal
This article presents existing mathematical models associated with mountain pine beetle populations in lodgepole pine forests, whose reproductive cycle requires the destruction of colonized host trees, decreasing timber availability/quality, and providing fuel sources for wildfires. With the existence of a positive-feedback loop with environmental warming, the need for intervention and management is clear. However, the legislative responses to the focusing events from our 2000-2010 North American epidemics are characterized as under-leveraged. While the reasons for this are multifaceted, increasing the capacity of STEM-informed individuals to take part in quantitative modeling of the underlying ecosystem generates awareness and provides pathways connecting …
Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change,
2024
Bryn Mawr College
Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay
CODEE Journal
How does mathematics connect with the search for solutions to the climate emergency? One simple connection, which can be explored in an introductory differential equations course, can be found by analyzing the energy generated by solar panels or wind turbines. The power generated by these devices is typically recorded at standard time intervals producing a data set which gives a discrete approximation to the power function $P(t)$. Using numerical techniques such as Euler’s method, one can determine the energy generated. Here we describe how we introduce the topic of solar power, apply Euler’s method to determine the energy generated, and …
Applying The Sir Model: Can Students Advise The Mayor Of A Small Community?,
2024
University of Wollongong
Applying The Sir Model: Can Students Advise The Mayor Of A Small Community?, Carrin Goosen, Mark I. Nelson, Mahime Watanabe
CODEE Journal
This is an account of a modelling scenario that uses the sir epidemic model. It was used in a third year applied mathematics subject. All students were enrolled in a mathematics degree of some type. Students are presented with the results of a test carried out on 100 individuals in a community containing 3000 people. From this they determined the number of infectious and recovered individuals in the population. Given the per capita recovery rate and making a suitable assumption about the number of infectious individuals at the start of the epidemic, they then estimate the infectious contact rate and …
Ode Models Of Wealth Concentration And Taxation,
2024
Tufts University and American University of Armenia
Ode Models Of Wealth Concentration And Taxation, Bruce Boghosian, Christoph Borgers
CODEE Journal
We refer to an individual holding a non-negligible fraction of the country’s total wealth as an oligarch. We explain how a model due to Boghosian et al. can be used to explore the effects of taxation on the emergence of oligarchs. The model suggests that oligarchs will emerge when wealth taxation is below a certain threshold, not when it is above the threshold. The underlying mechanism is a transcritical bifurcation. The model also suggests that taxation of income and capital gains alone cannot prevent the emergence of oligarchs. We suggest several opportunities for students to explore modifications of the model.
To Open Or Not To Open: Developing A Covid-19 Model Specific To Small Residential Campuses,
2024
Scripps College
To Open Or Not To Open: Developing A Covid-19 Model Specific To Small Residential Campuses, Christina Joy Edholm, Maryann Hohn, Nicole Lee Falicov, Emily Lee, Lily Natasha Wartman, Ami Radunskaya
CODEE Journal
In May 2020, administrators of residential colleges struggled with the decision of whether or not to open their campuses in the Fall semester of 2020. To help guide this decision, we formulated an ODE model capturing the dynamics of the spread of COVID-19 on a residential campus. In order to provide as much information as possible for administrators, the model accounts for the different behaviors, susceptibility, and risks in the various sub-populations that make up the campus community. In particular, we start with a traditional SEIR model and add compartments representing relevant variables, such as quarantine compartments and a hospitalized …
Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina,
2024
Brown University
Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum
CODEE Journal
Common mechanistic models include Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models. These models in their basic forms have generally failed to capture the nature of the COVID-19 pandemic's multiple waves and do not take into account public policies such as social distancing, mask mandates, and the ``Stay-at-Home'' orders implemented in early 2020. While the Susceptible-Vaccinated-Infected-Recovered-Deceased (SVIRD) model only adds two more compartments to the SIR model, the inclusion of time-dependent parameters allows for the model to better capture the first two waves of the COVID-19 pandemic when surveillance testing was common practice for a large portion of the population. We find …
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations,
2024
Gonzaga University
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist
CODEE Journal
In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.
Modeling Aircraft Takeoffs,
2024
Sewanee University
Modeling Aircraft Takeoffs, Catherine Cavagnaro
CODEE Journal
Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter …
Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model,
2024
Ball State University
Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier
CODEE Journal
A Sand Tank Groundwater Model is a tabletop physical model constructed of plexiglass and filled with sand that is typically used to illustrate how groundwater water flows through an aquifer, how water wells work, and the effects of contaminants introduced into an aquifer. Mathematically groundwater flow through an aquifer can be modeled with the heat equation. We will show how a Sand Tank Groundwater Model can be used to simulate groundwater flow through an aquifer with a no flow boundary condition.
Integrating External Controls By Regression Calibration For Genome-Wide Association Study,
2024
Michigan Technological University
Integrating External Controls By Regression Calibration For Genome-Wide Association Study, Lirong Zhu, Shijia Yan, Xuewei Cao, Shuanglin Zhang, Qiuying Sha
Michigan Tech Publications
Genome-wide association studies (GWAS) have successfully revealed many disease-associated genetic variants. For a case-control study, the adequate power of an association test can be achieved with a large sample size, although genotyping large samples is expensive. A cost-effective strategy to boost power is to integrate external control samples with publicly available genotyped data. However, the naive integration of external controls may inflate the type I error rates if ignoring the systematic differences (batch effect) between studies, such as the differences in sequencing platforms, genotype-calling procedures, population stratification, and so forth. To account for the batch effect, we propose an approach …
Time Scale Theory On Stability Of Explicit And Implicit Discrete Epidemic Models: Applications To Swine Flu Outbreak,
2024
Missouri University of Science and Technology
Time Scale Theory On Stability Of Explicit And Implicit Discrete Epidemic Models: Applications To Swine Flu Outbreak, Gülşah Yeni, Elvan Akın, Naveen K. Vaidya
Mathematics and Statistics Faculty Research & Creative Works
Time scales theory has been in use since the 1980s with many applications. Only very recently, it has been used to describe within-host and between-hosts dynamics of infectious diseases. In this study, we present explicit and implicit discrete epidemic models motivated by the time scales modeling approach. We use these models to formulate the basic reproduction number, which determines whether an outbreak occurs, or the disease dies out. We discuss the stability of the disease-free and endemic equilibrium points using the linearization method and Lyapunov function. Furthermore, we apply our models to swine flu outbreak data to demonstrate that the …
On A Multivalued Prescribed Mean Curvature Problem And Inclusions Defined On Dual Spaces,
2024
Missouri University of Science and Technology
On A Multivalued Prescribed Mean Curvature Problem And Inclusions Defined On Dual Spaces, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
This article addresses two main objectives. First, it establishes a functional analytic framework and presents existence results for a quasilinear inclusion describing a prescribed mean curvature problem with homogeneous Dirichlet boundary conditions, involving a multivalued lower order term. The formulation of the problem is done in the space of functions with bounded variation. The second objective is to introduce a general existence theory for inclusions defined on nonreflexive Banach spaces, which is specifically applicable to the aforementioned prescribed mean curvature problem. This problem can be formulated as a multivalued variational inequality in the space of functions with bounded variation, which, …
Pre-Calculus: Thinking Deeply About Simple Things,
2024
Georgia College
Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter
Graduate Research Showcase
“Pre-Calculus: Thinking Deeply About Simple Things” is a research-based creative endeavor focused on designing a high-school pre-calculus course. This course aims to foster deep, meaningful thinking, as well as an appreciation of the values of diversity, equity, and inclusion in the math classroom. The course leverages students’ funds of knowledge to employ culturally responsive teaching methods to connect mathematical concepts to the students’ backgrounds, interests, and real-life situations. This course also integrates social-emotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problem-based learning, the course …
Lipschitz Stability For Impulsive Riemann–Liouville Fractional Differential Equations,
2024
Missouri University of Science and Technology
Lipschitz Stability For Impulsive Riemann–Liouville Fractional Differential Equations, Martin Bohner, Snezhana Hristova
Mathematics and Statistics Faculty Research & Creative Works
Initial and impulsive conditions for initial value problems of systems of nonlinear impulsive Riemann–Liouville fractional differential equations are introduced. The case when the lower limit of the fractional derivative is changed at each time point of the impulses is studied. In the case studied, the solution has a singularity at the initial time and at any point of the impulses. This leads to the need to appropriately generalize the classical concept of Lipschitz stability. Two derivative types of Lyapunov functions are utilized in order to deduce sufficient conditions for the new stability concept. Three examples are provided for illustration purpose …
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractional Differential Equations At Resonance,
2024
Missouri University of Science and Technology
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractional Differential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava
Mathematics and Statistics Faculty Research & Creative Works
Using the Coincidence Degree Theory of Mawhin and Constructing Appropriate Operators, We Investigate the Existence of Solutions to Hadamard Fractional Differential Equations (FRDEs) at Resonance
On A Fully Coupled Nonlocal Multipoint Boundary Value Problem For A Dual Hybrid System Of Nonlinear Q -Fractional Differential Equations,
2024
Missouri University of Science and Technology
On A Fully Coupled Nonlocal Multipoint Boundary Value Problem For A Dual Hybrid System Of Nonlinear Q -Fractional Differential Equations, Ahmed Alsaedi, Martin Bohner, Bashir Ahmad, Boshra Alharbi
Mathematics and Statistics Faculty Research & Creative Works
A new class of nonlocal multipoint boundary value problems involving a dual hybrid system of nonlinear Riemann-Liouville-type q-fractional differential equations is studied in this paper. Existence and uniqueness results for the given problem are derived by applying the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle. Examples are presented for illustrating the obtained results. The work established in this paper is a useful contribution to the existing literature on q-fractional differential equations. Some interesting special cases are also discussed.
Critical Point Approaches To Nonlinear Square Root Laplacian Equations,
2024
Missouri University of Science and Technology
Critical Point Approaches To Nonlinear Square Root Laplacian Equations, Martin Bohner, Giuseppe Caristi, Shapour Heidarkhani, Amjad Salari
Mathematics and Statistics Faculty Research & Creative Works
This work is devoted to the study of multiplicity results of solutions for a class of nonlinear equations involving the square root of the Laplacian. Indeed, we will use variational methods for smooth functionals, defined on reflexive Banach spaces, in order to achieve the existence of at least three solutions for the equations. Moreover, assuming that the nonlinear terms are nonnegative, we will prove that the solutions are nonnegative. Finally, by presenting an example, we will ensure the applicability of our results.
Open Diameter Maps On Suspensions,
2024
Missouri University of Science and Technology
Open Diameter Maps On Suspensions, Hussam Abobaker, Włodzimierz J. Charatonik, Robert Paul Roe
Mathematics and Statistics Faculty Research & Creative Works
It is shown that if X is a metric continuum, which admits an open diameter map, then the suspension of X, admits an open diameter map. As a corollary, we have that all spheres admit open diameter maps.
Educators’ Beliefs About Using Academic Acceleration With Gifted Math Students And Others: Barriers And Opportunities,
2024
Marshall University
Educators’ Beliefs About Using Academic Acceleration With Gifted Math Students And Others: Barriers And Opportunities, Jason Gorgia
Theses, Dissertations and Capstones
This study examined the perceptions of educators (i.e., math teachers, administrators, and others) for insight into the absence of acceleration as a common pedagogical strategy in mathematics, despite longstanding research supporting the practice for students gifted in math and the interest frequently articulated by policymakers and educators in boosting American K-12 students’ math achievement. Educators from 48 states responded to scale-based and open-ended questions about math acceleration through an online survey where 713 of 818 respondents were teachers, balanced almost evenly among elementary, middle, and high schools, and among urban, suburban, and rural settings. The responses of teachers and non-teaching …
Computing The Roots Of Twisting Sheaves Over The Projective Line Arising From Monodromy Representations,
2024
Wayne State University
Computing The Roots Of Twisting Sheaves Over The Projective Line Arising From Monodromy Representations, Diego Yepez
Wayne State University Dissertations
Given a monodromy representation of the projective line minus a finite number of points, one can extend the resulting vector bundle with connection map canonically to a vector bundle with logarithmic connection map over all of the projective line. Now, since vector bundles split as twisting sheaves over the projective line, the focus of this work regards knowing the exact decomposition.
