Applied Mathematics Commons^™

A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. Mcgough, Erin N. Bodine

Spora: A Journal of Biomathematics

The smallpox and poliomyelitis (polio) viruses were, at a time, one of the largest threats to global public health killing millions until global eradication campaigns were put into effect. Vaccination led to the eradication of smallpox and the elimination of polio for most of the world. However, polio continues to persist at endemic levels in Pakistan and Afghanistan. We developed ODE models of smallpox and polio to explore differences in transmission dynamics and determine if the underlying biology has made poliomyelitis more difficult to eradicate. Our model analysis shows there are multiple factors which should allow polio to have a …

A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry

Spora: A Journal of Biomathematics

Rhinoceros populations in Africa are in peril largely due to the high value of their horns and the poaching that ensues. The strategy of legalizing the international trade of rhino horn is receiving increased support among both the people and government officials in Africa. Many in the international conservation community remain opposed to the idea. The legalization strategy is straightforward in theory: legalizing the trade of rhino horn will introduce a large quantity of horn to the market, the increased supply will lead to lower prices for rhino horn, and lower prices will reduce the overall poaching pressure these animals …

The Influence Of Green Building Design On Tourists' Intention To Stay In Eco-Friendly Hotels: A Study On Perceptions And Preferences, Enas Al Sayed Salama Dr., Gehad Nasr Abdelsalam Dr.

Journal of Engineering Research

Green building design involves integrating sustainable and environmentally friendly practices into the construction and operation of buildings, including hotels, with the goal of minimizing the adverse impact on the environment. This paper delves into the pivotal role of green building design and eco-service provision within the context of green hotels. The aim is to investigate the interconnections among tourists' environmental concerns, their perceived significance of green building design, and their intention to choose green hotels.

To enhance the understanding of tourist behavior and its implications for tourism in Egypt, a questionnaire was administered in Sharm El Sheikh, a prominent Egyptian …

Experimental Study Of Bent Glass Curtain Walls., Sarah Said Abd El Kariem, Moustafa El Shami, Mahmoud El Nagar

Journal of Engineering Research

A Bent Laminated Glass is commonly used in the residential and commercial structures, its methodology is not present in the curves and tables at the ASTM E1300. Therefore, it has become a need for architects to use basis for this type of glass. To the best of authors ‘knowledge, no one study the bent laminated glass in details. A variety of safety glass that has lately gained popularity in the construction sector is modern laminated glass. Given that it offers a safe failover capability, it is perfect for the automotive industry. Double-lite glass is produced using two or more …

Market Analysis And Bidding Strategy Of Hybrid Renewable Energy Systems Considering Emissions, Fatma Elzahraa, Mohamed Elnemr, Samir Dawoud

Journal of Engineering Research

The competition in the electricity markets makes it difficult to choose a suitable strategy for maximizing profit while reducing harmful emissions. To have an adequate energy price for consumers while minimizing the harmful emissions to the atmosphere and maximizing profits of all participants in the electricity market needs an aggressive bidding strategy. Developing these bidding strategies with the integration of renewable energy (RE) in the electricity market became important. This research studies various bidding strategies for maximizing profits in the deregulated energy market since participants are keen on developing bidding strategies considering emissions. These bidding strategies will consider the integration …

Effects Of Fuel Equivalence Ratio And Swirl Vane Angles On Premixed Burner Turbulent Flame Combustion Characteristics, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

A turbulent flow field has a major effect on the premixed flame structure and temperature distribution that specifically determines the effectiveness of the burned fuel and the amounts of produced emissions. However, the premixed flame tangential and axial velocity distribution through the flame length help to predict the combustion and emissions attributes of the burned fuel. In this regard, an experimental and analytical investigation on premixed turbulent burners at different equivalence fuel-air ratios with different swirl vane angles has been achieved in the present work to assess the combustion performance and emissions characteristics. A theoretical methodology was carried out to …

Enhancing The Performance Of Conventional Solar Still Using The Nano-Doped Paint (Ndp) Coating, Hagar Alm-Eldin Bastawissi Prof.Dr, Nermin Elgendy Engineer, Ayman R. El-Tohamy

Journal of Engineering Research

Nations are throughout the entire globe continuously confronting the problem of potable water shortage. Recently, it has been thought that using solar energy to desalinate brackish water offers a practical answer to the world's water crises. The output of these stills, is meager, and academics haven't done much to boost it in any way. Solar distillers have been proposed as an efficient method to produce potable water. In recent years, saltwater has produced drinking water by various ways. The efficiency of a solar distiller is significantly influenced by various factors, most important factor of them is the absorber surface. In …

Engine Performance And Emissions Improvement Study On Direct Injection Of Diesel/Ammonia Dual Fuel By Adding Cng As Partially Premixed Charge, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi Prof. Dr., Mohammed Osama Elsamadony Dr. Eng., Abdallah Salem Abdalhadi Eng.

Journal of Engineering Research

Researchers have recently moved on in their studies to find a solution to prevent or reduce this problem. There have been directions taken by researchers to solve the problem, including, replacing fossil fuels with environmentally friendly types or by combining two or more types of fuel. This is by modifying fuel injection systems as appears in the PCCI, RCCI, or HCCI systems, or working to integrate the two trends by using new injection systems and burning alternative fuels with fossil fuels. Therefore, the trend has good results on the specific consumption of fuel, raising thermal efficiency, and working to reduce …

Experimental Study On The Impact Of Secondary Air Injection And Different Swirl Van Angles On Premixed Turbulent Flame Propagation And Emission Behaviors, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

The objective of the present paper is to investigate experimentally the flame characteristics utilizing different secondary air inlet direction for different primary air swirl numbers and equivalence fuel-air ratios. In this study, an experimental test rig was carried out to investigate the flame temperature and emission behavior with flame length at the equivalence fuel-air ratios taken0.96, 0.80, 0.70, and 0.60, and swirl vane angles were varied as 20, 30, 45, and 60° to generate different swirl numbers of 0.26, 0.416, 0.71 and 1.23, respectively. In addition to the introduction of secondary air in test combustor, whereas the primary air and …

The Effect Of An Existing Tunnel And A Newly Excavated Tunnel On Ground Loss Beneath Sand Slope-3d Numerical Study, Ashraf Nazir, Ahmed Nasr, Asmaa Saeed

Journal of Engineering Research

Abstract- Most researchers perform their numerical models for tunnels by modeling perfectly horizontal ground surfaces above the tunnels. The prediction of surface settlement of a sandy slope due to the interaction mechanism between the slope and the tunnels is one of the critical problems in urban areas. As a result, in this work, a numerical analysis using PLAXIS 3D TUNNEL has been performed to investigate the effect of tunnel excavation on the deformation of a shallow sandy slope, and empirically by the Herzog method. The study also assesses the influence of parameters on slope deformation that have not been …

Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans

Spora: A Journal of Biomathematics

Compartmental modeling serves as a necessary framework in many fields, especially biomathematics and ecology. This article introduces readers to a user-friendly approach to constructing compartmental models and solving the resulting systems of differential equations to simulate real-world applications. The platform used is Berkeley Madonna, a software package that has an intuitive graphical interface which empowers users—even those with limited mathematical and programming backgrounds—to focus on modeling concepts rather than mathematical or programming intricacies. This makes Berkeley Madonna an ideal platform for students, educators, and researchers.

Training Data Augmentation With Data Distilled By Principal Component Analysis, Nikolay Metodiev Sirakov, Tahsin Shahnewaz, Arie Nakhmmani

Faculty Publications

This work develops a new method for vector data augmentation. The proposed method applies principal component analysis (PCA), determines the eigenvectors of a set of training vectors for a machine learning (ML) method and uses them to generate the distilled vectors. The training and PCA-distilled vectors have the same dimension. The user chooses the number of vectors to be distilled and augmented to the set of training vectors. A statistical approach determines the lowest number of vectors to be distilled such that when augmented to the original vectors, the extended set trains an ML classifier to achieve a required accuracy. …

Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr

CODEE Journal

This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters’ political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our app at https: //centrism.streamlit.app/. Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary …

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.

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.

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 …

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 …

Inhabiting Numbers: Weaving, Polyphony, And Embodied Mathematics, Kristine Barrett

Textile Society of America: Symposium Proceedings

Inhabiting Numbers: Polyphony as Woven Sound explores connections between vocal polyphony and textile practices, specifically weaving and spinning. Rather than consider music and weaving as separate from one another, the following paper presents the ways in which they are deeply intertwined and mutually constitutive forms of cultural expression. The technical modes of thinking produced through repetition inherent in both—particularly as practices utilizing complex mathematical structures—produce ways of thinking unique to each. Through practice, I suggest these technical modes of making transit across different materials and mediums—in both explicit and implicit ways. The music created through the interweaving of multiple voices …

Human System Composite Performance Measures: General Systems Performance Theory Insights, Lawrence Disalvi

Bioengineering Dissertations - Archive

Composite Performance Measures (CPMs) of human performance are widely employed in applications that range from mundane to life-changing, yet they are frequently presented without explanation or reference to theoretical underpinnings. The conceptual soundness of a widely used CPM approach, based on additive combination of constituent components, has been called into question by Kondraske. He argues the relevance of General Systems Performance Theory (GSPT) and performance capacity envelope concepts when applied to multidimensional CPM measures.

To obtain evidence-based answers to assertions regarding CPM types and rationale employed in medical and non-medical contexts, a Systematic Descriptive Review was conducted. Separately, the GSPT-based …

Mathematical Modeling Of Microscale Biology In Polyelectrolyte Brushes, William J. Ceely

CGU Theses & Dissertations

Biological macromolecules including nucleic acids, proteins, and glycosaminoglycans are typically anionic and can span domains of up to hundreds of nanometers and even micron length scales. The structures exist in crowded environments that are dominated by multivalent electrostatic interactions that can be modeled using mean-field continuum approaches that represent underlying molecular nanoscale biophysics. In this thesis, we develop such models for polyelectrolyte brushes using both steady state modified Poisson-Boltzmann models and transient modified Poisson-Nernst-Planck models that incorporate important ion-specific (Hofmeister) effects. The transient model enables observation of the relative physical effects as an initial non-equilibrium state relaxes to the steady …

Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi

Mathematics Dissertations - Archive

In this thesis, we employ optimal control frameworks in two distinct contexts: Human immunodeficiency virus (HIV) and esophageal cancer. For HIV, we introduce a comprehensive data-driven nonlinear optimization framework designed for personalized therapies. This framework utilizes a deterministic in-host nonlinear ordinary differential equation (ODE) model and formulates two optimization problems using individual patient data. The first problem focuses on estimating patient-specific parameters through constrained optimization, while the second problem determines optimal combination therapies to reduce viral load to undetectable levels. Several numerical experiments suggest that our framework can provide a robust and effective optimal dosages with lower toxicity levels to …

Probing The Ising Model’S Thermodynamics Through Restricted Boltzmann Machines, Xiaobei (Emma) Zhang

HMC Senior Theses

This thesis explores the connection between physics and machine learning by using Restricted Boltzmann Machines (RBMs) to study the thermodynamic properties of the Ising model. The Ising model is a simple but realistic model that captures the magnetic behavior of a system, where spins occupy a lattice of sites and different spin configurations correspond to different energies. The model exhibits phase transitions between ferromagnetic and paramagnetic phases as a function of temperature. RBMs are two-layered neural networks that can learn probability distributions over binary spins. The study generates 2D Ising model data at different temperatures using Monte Carlo simulations, including …

Exploring Sigmoidal Bounded Confidence Models With Mean Field Methods, Tian Dong

HMC Senior Theses

Mathematicians use models of opinion dynamics to describe how opinions in a group of people change over time, which can yield insight into mechanisms behind phenomena like polarization and consensus. In these models, mathematicians represent the community as a graph, where nodes represent agents and edges represent possible interactions. Opinion updates are modeled with a system of differential equations (ODEs). Our work focuses on the sigmoidal bounded confidence model (SBCM), where agents update their opinion toward a weighted average of their neighbors' opinions by weighting similar opinions more heavily. Using tools developed in physics (mean-field theory), we derive a continuity …

Integrable Evolution Equations, Ramesh C. Sharma

Mathematics Dissertations - Archive

Integrable evolution equations are certain nonlinear partial differential equations or semidiscrete nonlinear difference equations that are used to model wave propagation in various media. The goal of this thesis is to present the derivation of integrable evolution equations in a way accessible to nonexperts in the field of integrable systems and to illustrate those derivations by various explicit examples. In the case of nonlinear partial differential equations, both the spacial variable x and temporal variable t are continuous independent variables. In the case of semidiscrete nonlinear difference equations, the spacial variable n is a discrete independent variable and the temporal …

New Methods In Electrical Source Imaging Based On Eeg And Post-Mortem Pathology Data, Julio Cesar Enciso Alva

Mathematics Dissertations - Archive

A central task for Neuroscience is to determine the location of electrical activity of neural origin inside the brain. Electrical signals can be recorded at a high resolution in time but low resolution in space, thus making it difficult to locate their source unambiguously. Electrical Source Imaging (ESI) is a particular framework for neural electrical source location; it is possible by modeling any additional information we may have about the electrical sources. For instance, minimal-norm estimators assume that the most plausible estimation is that with a lower norm. However, these estimators possess a low resolution in space.

In this work, …

A New Proper Orthogonal Decomposition Method With Second Difference Quotients For The Wave Equation, Andrew Calvin Janes

Masters Theses

"Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In \cite {Sarahs}, a new approach to POD with DQs was developed that is more computationally efficient than the standard DQ POD approach and it also retains the guaranteed pointwise in time error bounds of the standard method. In this thesis, we extend the new DQ POD approach from \cite {Sarahs} to the case of second difference quotients (DDQs). Specifically, a new POD method utilizing DDQs and only one snapshot and …

Cryptographic Algorithms, Cryptocurrencies, And A Predictive Model Of Bitcoin Value By Pls Regression, Paul Kenneth O'Connor

Masters Theses

"With the invention of Bitcoin in 2009, as a seemingly timed response to the ongoing financial crisis, the popularity of the cryptocurrency has since continued to grow. Just this year, the Security Exchange Commission approved Bitcoin for exchange traded funds, allowing major investment firms to begin product trading. With this approval, and during this very moment of writing, Bitcoin has entered a bull market and reached a record value of over 72,000 USD. In addition, the Bitcoin halving event in April of 2024 is expected to increase demand even further. It has been anticipated that Bitcoin and other cryptocurrencies will …

Comparative Study Of Crypto Volatility And Price Forecasting Using A Mixture Of Time Series And Machine Learning Models, Abhishek Kafle

Masters Theses

"Forecasting financial product volatility and price is crucial for informed decision-making in investment and risk management. The models considered include GARCH, LSTM, GRU, BiLSTM, and hybrid models that incorporate various combinations of these models. We present a comparative analysis of forecasting volatility and price using the aforementioned models.

We also introduce a user-friendly dashboard for model training and evaluation, enabling users to upload datasets and customize model parameters. The dashboard allows users to select the type of model, specify the dataset range for training, determine the number of epochs, adjust the number of layers for deep …

Bringing Gans To Medieval Times: Manuscript Translation Models, Tonilynn M. Holtz

College of Graduate Studies: Theses & Dissertations

The Generative Adversarial Networks (GAN) recently emerged as a powerful framework for producing new knowledge from existing knowledge. These models aim to learn patterns from input data then use that knowledge to generate output data samples that plausibly appear to belong to the same set as the input data. Medieval manuscripts study has been an important research area in the humanities field for many decades. These rare manuscripts are often times inaccessible to the general public, including students in scholars, and it is of a great interest to provide digital support (including, but not limited to translation and search) for …

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

College of Graduate Studies: Theses & Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …