Physical Sciences and Mathematics Commons^™

(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 …

An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber

Electronic Theses and Dissertations

Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way …

Rigorous Analysis Of An Edge-Based Network Disease Model, Sabrina Mai

Honors Undergraduate Theses

Edge-based network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a disease-free equilibrium for the edge-based network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly used network model by relaxing some assumed conditions and factor in a dependency on initial conditions. We find that this modification still accounts for realistic dynamics of disease spread …

Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, Golibjon Botirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a model where the spin takes values in the set [0,1]^d, and is assigned to the vertexes of the Cayley tree. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some non-linear integral equation. For a concrete form of the Kernel of the integral equation we show the uniqueness of solution.

Mathematical Modelling Of English Coulee: Tanks In Series, Matthew Picklo

Essential Studies UNDergraduate Showcase

In the scope of the College of Arts and Science project: “Coulee Cleanway: Modelling and Analysis of the English Coulee Physiochemical Environment, UND Campus, Grand Forks”, a mathematical model attempting to describe the transportation of dissolved species within the English Coulee was developed based on “Tanks in Series”. By dividing the channel into discrete regions, a governing system of equations derived from conservation of mass equations and well-mixed assumptions is used to describe the spatial and temporal changes in concentration. The resulting system of differential equations was solved by a Runge-Kutta 4 numerical method, which allowed for the addition of …

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Gerald W Young

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Kevin L. Kreider

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Curtis B. Clemons

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Nao Mimoto

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Associated Hypotheses In Linear Models For Unbalanced Data, Carlos J. Soto

Theses and Dissertations

When looking at factorial experiments there are several natural hypotheses that can be tested. In a two-factor or a by b design, the three null hypotheses of greatest interest are the absence of each main effect and the absence of interaction. There are two ways to construct the numerator sum of squares for testing these, namely either adjusted or sequential sums of squares (also known as type I and type III in SAS). Searle has pointed out that, for unbalanced data, a sequential sum of squares for one of these hypotheses is equal (with probability 1) to an adjusted sum …

Sensor Selection And Integration To Improve Video Segmentation In Complex Environments, Adam R. Reckley, Wei-Wem Hsu, Chung-Hao Chen, Gangfeng Ma, E-Wen Huang

Civil & Environmental Engineering Faculty Publications

Background subtraction is often considered to be a required stage of any video surveillance system being used to detect objects in a single frame and/or track objects across multiple frames in a video sequence. Most current state-of-the-art techniques for object detection and tracking utilize some form of background subtraction that involves developing a model of the background at a pixel, region, or frame level and designating any elements that deviate from the background model as foreground. However, most existing approaches are capable of segmenting a number of distinct components but unable to distinguish between the desired object of interest and …

A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam

Applications and Applied Mathematics: An International Journal (AAM)

First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.

Differential Equations: A Universal Language, Bethany Caron

Senior Honors Projects

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.” – David Hilbert Differential equations are equations of one or more variables that involve both functions and their derivatives. These equations have many applications to the everyday “non-math” world, including modeling in engineering, physics, biology, chemistry, and economics. Differential equations are used when a situation arises where one needs to study a continuously changing quantity (expressed as a function) and its rate of change (expressed through its derivatives). The solutions to differential equations are functions that make the original equation hold true, and they can …

Modeling Algae Self-Replenishment, V. S. Manoranjan, Miguel A. Olmos Gomez, R. Corban Harwood

Faculty Publications - Department of Mathematics

This paper presents a sunlight-dependent algae growth model. Driven by the circumstances surrounding Lake Chapala, Mexico, this theoretical model is an endeavor to understand the resilient sustainability of algae that threatens the area’s ecosystem. In this paper, free-floating algae (phytoplankton) are treated as two distinct populations according to their location in the body of water: the vibrant sunlit upper region and the stagnate lower region where photosynthesis is not possible. The numerical solution for the model is analyzed and results are discussed in light of previous studies and the state of Lake Chapala.

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

The Fokker-Planck And Related Equations In Theoretical Population Dynamics, George Derise

Mathematics & Statistics Theses & Dissertations

The population growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics because population growth is basically a random event. There are a large number of chance factors influencing growth that might not be taken into account by deterministic models. The effect of other species (for example, in the chance meeting of a predator), population fluctuations due to weather changes that would alter food …

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

A Logistic System Simulation Model Encompassing Poisson Processes And Normal Or Weibull Life, Willard A. Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis describes a computer simulation model for determining effective spares stock levels for recoverable items at Air Force bases and depots. The simulation model is based on the following fundamental inventory theory; whenever a demand arises, it is satisfied from stock on hand, and the quantity equal to that demand is recorded immediately; when a demand exceeds stock on hand, the excess demand is backordered immediately and when item life expires procurement action is initiated at depot level. The resulting product of the model cam be used as a guide for the optimum distribution of available spares or as …