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Articles 301 - 330 of 848
Full-Text Articles in Applied Mathematics
The Interplay Between Costly Reproduction And Unpredictable Environments Shapes The Stability Of Cooperative Breeding, Glenn Steven Young
The Interplay Between Costly Reproduction And Unpredictable Environments Shapes The Stability Of Cooperative Breeding, Glenn Steven Young
Biology and Medicine Through Mathematics Conference
No abstract provided.
A Novel Chebyshev Wavelet Method For Solving Fractional-Order Optimal Control Problems, Ghodsieh Ghanbari
A Novel Chebyshev Wavelet Method For Solving Fractional-Order Optimal Control Problems, Ghodsieh Ghanbari
Theses and Dissertations
This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison …
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
Theses and Dissertations
The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …
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%, …
Predicting Box Office Revenues Using Differential Equation Models, Brenden David
Predicting Box Office Revenues Using Differential Equation Models, Brenden David
Mathematics Senior Capstone Papers
The growing popularity of the internet has increased exponentially in the past few decades. This sudden increase in popularity allows for users to gain access to more information than was thought possible in the past, including access to box-office movie revenues of previously released movies. Since we now have access to thousands of movie’s box office revenues, we can analyze some sort of trend within specific genres of movies. With these trends we develop a differential equations model that will predict the box office revenues of a movie that is in its early stages of the box office. This model …
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Spora: A Journal of Biomathematics
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R0 to changes in sociological parameter values.
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes
CODEE Journal
Starting with a toy climate model from the literature, we employ a system of two nonlinear differential equations to model the reciprocal effects of the average temperature and the percentage of glacial volume on Earth. In the literature, this model is used to demonstrate the potential for a stable periodic orbit over a long time span in the form of an attracting limit cycle. In the roughly twenty five years since this model appeared in the literature, the effects of global warming and human-impacted climate change have become much more well known and apparent. We demonstrate modification of initial conditions …
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Spora: A Journal of Biomathematics
Radiation therapy remains as one of the main cancer treatment modalities. Typical regimens for radiotherapy comprise a constant dose administered on weekdays, and no radiation on weekends. In this paper, we examine adaptive dosages of radiation treatment strategies for heterogeneous tumors using a dynamical system model that consist of radiation-resistant and parental populations with unique interactive properties, namely, PC3 and DU145 prostate cancer cell lines. We show that stronger doses of radiation given in longer time intervals, while keeping the overall dosage the same, are effective in PC3 cell lines, but not in DU145 cell lines. In addition, we tested …
Numerical Treatment For Special Type Of Mixed Linear Delay Volterra Integro-Differential Equations, Atheer J. Kadhim
Numerical Treatment For Special Type Of Mixed Linear Delay Volterra Integro-Differential Equations, Atheer J. Kadhim
Emirates Journal for Engineering Research
The idea of research is a representation of the nonlinear pseudo-random generators using state-space equations that is not based on the usual description as shift register synthesis but in terms of matrices. Different types of nonlinear pseudo-random generators with their algorithms have been applied in order to investigate the output pseudo-random sequences. Moreover, two examples are given for conciliated the results of this representation.
Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan
Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan
CMC Senior Theses
When it comes to women in professional hierarchies, it is important to recognize the lack of representation at the higher levels. By modeling these situations we hope to draw attention to the issues currently plaguing professional atmospheres. In a paper by Clifton et. al. (2019), they model the fraction of women at any level in a professional hierarchy using the parameters of hiring gender bias and internal homophily on behalf of the applicant. This thesis will focus on a key theory in Clifton et. al.’s analysis and explain its role in the model, specifically bifrucation analysis. In order to analyze …
New Techniques In Celestial Mechanics, Ali Abdulrasool Abdulhussein
New Techniques In Celestial Mechanics, Ali Abdulrasool Abdulhussein
Graduate Theses, Dissertations, and Problem Reports (ETD)
It is shown that for the classical system of the N body problem ( Newtonian Motion), if the motion of the N particles starts from a planar initial motion at t=t_{0}, then the motion of the N particles continues to be planar for every t\in[t_{0},t_{1}], assuming that no collisions occur between the N particles. Same argument is shown about the linear motion, namely, for the classical system of the N body problem, if the motion of the N particles starts from a linear initial motion at t=t_{0}, then the motion of the N particles continues to be linear for every …
Structure-Dependent Characterizations Of Multistationarity In Mass-Action Reaction Networks, Galyna Voitiuk
Structure-Dependent Characterizations Of Multistationarity In Mass-Action Reaction Networks, Galyna Voitiuk
Graduate Theses, Dissertations, and Problem Reports (ETD)
This project explores a topic in Chemical Reaction Network Theory. We analyze networks with one dimensional stoichiometric subspace using mass-action kinetics. For these types of networks, we study how the capacity for multiple positive equilibria and multiple positive nondegenerate equilibria can be determined using Euclidian embedded graphs. Our work adds to the catalog of the class of reaction networks with one-dimensional stoichiometric subspace answering in the affirmative a conjecture posed by Joshi and Shiu: Conjecture 0.1 (Question 6.1 [26]). A reaction network with one-dimensional stoichiometric subspace and more than one source complex has the capacity for multistationarity if and only …
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Theses and Dissertations
Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …
Stroke Clustering And Fitting In Vector Art, Khandokar Shakib
Stroke Clustering And Fitting In Vector Art, Khandokar Shakib
Senior Independent Study Theses
Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.
The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood
The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood
Theses and Dissertations (Comprehensive)
The motion of objects in the sky has captured the attention of scientists and mathematicians since classical times. The problem of determining their motion has been dubbed the Kepler problem, and has since been generalized into an abstract problem of dynamical systems. In particular, the question of whether a classical system produces closed and bounded orbits is of importance even to modern mathematical physics, since these systems can often be analysed by hand. The aforementioned question was originally studied by Bertrand in the context of celestial mechanics, and is therefore referred to as the Bertrand problem. We investigate the qualitative …
Scientific Breakdown Of A Ferromagnetic Nanofluid In Hemodynamics: Enhanced Therapeutic Approach, M. M. Bhatti, Sara Abdelsalam
Scientific Breakdown Of A Ferromagnetic Nanofluid In Hemodynamics: Enhanced Therapeutic Approach, M. M. Bhatti, Sara Abdelsalam
Basic Science Engineering
In this article, we examine the mechanism of cobalt and tantalum nanoparticles through a hybrid fluid model. The nanofluid is propagating through an anisotropically tapered artery with three different configurations; converging, diverging and non-tapered. To examine the rheology of the blood we have incorporated a Williamson fluid model which reveals both Newtonian and non-Newtonian effects. Mathematical and physical formulations are derived using the Lubrication approach for continuity, momentum and energy equations. The impact of magnetic field, porosity and viscous dissipation are also taken into the proposed formulation. A perturbation approach is used to determine the solutions of the formulated nonlinear …
Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt
Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt
Departmental Honors & Graduate Capstone Projects
In this research project, we used numerical methods to investigate trends in the susceptible, exposed, infectious, quarantined, recovered, closed cases and insusceptible populations for the COVID-19 pandemic in 2021. We used the SEIQR model containing seven ordinary differential equations, based on the SIR model for epidemics. An analytical solution was derived from a simplified version of the model, created by making various assumptions about the original model. Numerical solutions were generated for the first 100 days of 2021 using algorithms based on Euler's Method, Runge-Kutta Method, and Multistep Methods. Our goal is to show that numerical methods can help us …
(R1497) On The Invariant Subspaces Of The Fractional Integral Operator, Mehmet Gürdal, Anar Adiloglu Nabiev, Meral Ayyıldız
(R1497) On The Invariant Subspaces Of The Fractional Integral Operator, Mehmet Gürdal, Anar Adiloglu Nabiev, Meral Ayyıldız
Applications and Applied Mathematics: An International Journal (AAM)
In operator theory, there is an important problem called the invariant subspace problem. This important problem of mathematics has been clear for more than half a century. However the solution seems to be nowhere in sight. With this motivation, we investigate the invariant subspaces of the fractional integral operator in the Banach space with certain conditions in this paper. Also by using the Duhamel product method, unicellularity of the fractional integral operator on some space is obtained and the description of the invariant subspaces is given.
(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez
(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez
Applications and Applied Mathematics: An International Journal (AAM)
In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number …
(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat
(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat
Applications and Applied Mathematics: An International Journal (AAM)
The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …
(R1523) Abundant Natural Resources, Ethnic Diversity And Inclusive Growth In Sub-Saharan Africa: A Mathematical Approach, Juliet I. Adenuga, Kazeem B. Ajide, Anthonia T. Odeleye, Abayomi A. Ayoade
(R1523) Abundant Natural Resources, Ethnic Diversity And Inclusive Growth In Sub-Saharan Africa: A Mathematical Approach, Juliet I. Adenuga, Kazeem B. Ajide, Anthonia T. Odeleye, Abayomi A. Ayoade
Applications and Applied Mathematics: An International Journal (AAM)
The sub-Saharan African region is blessed with abundant natural resources and diverse ethnic groups, yet the region is dominated by the largest number of poor people worldwide due to inequitable distribution of national income. Existing statistics forecast decay in the quality of lives over the years compared to the continent of Asia that shares similar history with the region. In this paper, a-five dimensional first-order nonlinear ordinary differential equations was formulated to give insight into various factors that shaped dynamics of inclusive growth in sub-Saharan Africa. The validity test was performed based on ample mathematical theorems and the model was …
(R1524) The Existence And Uniqueness Of Solution For Fractional Newel-Whitehead-Segel Equation Within Caputo-Fabrizio Fractional Operator, Ali Khalouta
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.
(R1412) Stability And Bifurcation Of A Cholera Epidemic Model With Saturated Recovery Rate, Huda Abdul-Satar, Raid K. Naji
(R1412) Stability And Bifurcation Of A Cholera Epidemic Model With Saturated Recovery Rate, Huda Abdul-Satar, Raid K. Naji
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound …
Optimal Control Techniques In Addiction Modeling, Leigh Pearcy, William Christopher Strickland, Suzanne Lenhart
Optimal Control Techniques In Addiction Modeling, Leigh Pearcy, William Christopher Strickland, Suzanne Lenhart
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Ecological Dynamics On Large Metapopulation Graphs, Daniel Cooney
Ecological Dynamics On Large Metapopulation Graphs, Daniel Cooney
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Impact Of Fungicide Treatment On The Dynamics Of Cocoa Black Pod Disease, Bismark Oduro
The Impact Of Fungicide Treatment On The Dynamics Of Cocoa Black Pod Disease, Bismark Oduro
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling, Analysis And Simulation Of Covid-19 Interaction Dynamics Between Local Community In Saudi Arabia And Visiting Sub-Population, Manal Badgaish, Padmanabhan Seshaiyer
Modeling, Analysis And Simulation Of Covid-19 Interaction Dynamics Between Local Community In Saudi Arabia And Visiting Sub-Population, Manal Badgaish, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Estimation Of Parameters Of Epidemiological Models Under A Non-Parametric Approach And Its Application For Covid-19 In Bogotá D.C., Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Soledad Torres
Estimation Of Parameters Of Epidemiological Models Under A Non-Parametric Approach And Its Application For Covid-19 In Bogotá D.C., Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Soledad Torres
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba
Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Estimation Analysis For The Seir Model With Stochastic Perturbation For The Covid-19 Outbreak In Bogotá, Viswanathan Arunachalam, Andres Rios-Gutierrez
Estimation Analysis For The Seir Model With Stochastic Perturbation For The Covid-19 Outbreak In Bogotá, Viswanathan Arunachalam, Andres Rios-Gutierrez
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.