Physical Sciences and Mathematics Commons^™

Bright Light Therapy And Depression: Assessing Suitability Using Entrainment Maps, Charles A. Mainwaring

Theses

Bright Light Therapy has been shown to be efficacious to mood disorders including Major Depression. Researchers use the Jewett-Forger-Kronauer model of the circadian rhythm with the Unified Model of melatonin including a mathematical term implementing feedback from the melatonin system into the circadian system to quantify the effects of bright light. Early investigations into intrinsic period, light sensitivity, and the circadian pacemaker's sensitivity to blood melatonin concentration may be indicators of subsets of patients with long intrinsic periods exhibiting symptoms of depression.

A Survey On Online Matching And Ad Allocation, Ryan Lee

Theses

One of the classical problems in graph theory is matching. Given an undirected graph, find a matching which is a set of edges without common vertices. In 1990s, Richard Karp, Umesh Vazirani, and Vijay Vazirani would be the first computer scientists to use matchings for online algorithms [8]. In our domain, an online algorithm operates in the online setting where a bipartite graph is given. On one side of the graph there is a set of advertisers and on the other side we have a set of impressions. During the online phase, multiple impressions will arrive and the objective of …

Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti

Theses

In this study, we established a connection between the Chebyshev polynomial of the first kind and the Jones polynomial of generalized weaving knots of type W(3,n,m).
Through our analysis, we demonstrated that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices which allowed us to find an explicit formula for the Alexander polynomial of weaving knots of typeW(3,n).
In addition to confirming Fox’s trapezoidal conjecture, we also discussed the zeroes of the Alexander Polynomial of weaving knots of type W(3,n) as they relate to Hoste’s conjecture. In addition, …

The Reproducing Kernel Method For Solving Integro-Differential And Volterra Integral Equations, Khulood Gamal Qaid

Theses

Integro-differential equations are a class of mathematical equations that involve both derivatives and integrals. They have applications in a wide range of fields, including physics, engineering, finance, and biology such as the spread of diseases, population dynamics, and the behavior of financial markets. The study of these equations requires advanced mathematical techniques, including functional analysis, approximation methods, and numerical analysis. They are a rich area of research with many open questions and challenges.
In this thesis, we will develop and implement the reproducing kernel method to solve a class of integro-differential and Volterra integral equations. We discuss both cases when …

Valuation Of Asian Options In A High Volatility Market With Jumps, Zeeshan Khalid

Theses

The evaluation of financial derivatives represents a central part of financial risk management. There are many types of derivatives among other path-dependent options. In this study, we aim at valuing Asian options. They are path dependent and have several benefits. For instance, their values are habitually lower than European options. Also, an Asian option on a commodity drops the risk value close to maturity. Though, the disadvantage is that they are in general difficult to value since the distribution of the payoff is usually unknown. It is agreed in the literature that a stochastic process with a jumps model for …

A Support Theorem For A Wave Equation, Aysha Khaled Alshamsi

Theses

It is well known that the fundamental solution to the classical wave equation Δ𝑢 (𝑥, 𝑡) − ∂_𝑡𝑡𝑢(𝑥,𝑡) = 0 is supported on the light cone {(𝑥, 𝑡) ∈ ℝ^𝑛× ℝ : ||𝑥|| = |𝑡|} if and only if the dimension 𝑛 is odd and ≥ 3. Because we are living in a 3-dimensional world we can hear each other clearly; One has a pure propagator without residual waves. In this thesis we consider the wave equation

2||𝑥||Δ_𝑘𝑢_𝑘(𝑥, 𝑡) − ∂_𝑡𝑡𝑢(𝑥,𝑡) = 0, (𝑥, 𝑡) ∈ ℝ^𝑛 × ℝ …

Mathematical Models For Thalassemia, Hamda Mohammed Al Dhaheri

Theses

Thalassemia is a genetic blood disorder caused by gene mutation or deletion in a blood protein called hemoglobin. Treatment of thalassemia requires a life-long blood transfusion and removal of excessive iron in the blood stream, which usually causes a big pressure on health care systems. Various forms of thalassemia control measures have been used to reduce the prevalence of thalassemia major. This has resulted in a substantial reduction in the prevalence of thalassemia. However, the thalassemia carrier population remains high, which could lead to an increase in the thalassemia major population through carrier-to-carrier marriages. Thus, we developed two mathematical models …

On The Projections Of Commutative C*-Algebras, Alaa Ahmad Hamdan

Theses

Gelfand and Naimark proved that the Banach algebra of continuous complex-valued functions on a compact space Ω is the only example of commutative unital C*-algebras. We study the C*-algebra C(Ω) and its main elements, such as projections. Also, we discuss the mapping between projections, which preserves orthogonality (orthoisomorphism). A bijective θ between projections induces a bijective Θ between the Boolean algebra of clopen subsets of X. Then, we give main properties of such Θ. For a compact subset X of ℝ, we classify the projections of C(X) by introducing the similar relation on P(C(X)). We introduce an …

Valuation Of Options In A High Volatile Regime Switching Market, Tasnim Mazen Sharif Alhamad

Theses

Financial modeling by Stochastic Differential Equations-SDEs with regime-switching has been utilized to allow moving from one economic state to another. The aim of this thesis is to tackle the pricing of European options under a regime-switching model where the volatility is augmented. Regime-switching models are more realistic since they encompass the effect of an external event on the underlying asset prices. But they are challenging, considering in addition increased volatility in the model will for sure make the option pricing problem more complicated and its solution may not exist analytically. Numerical methods for finance could be very helpful in this …

Numerical Methods For Locating Zeros Of Polynomial Systems Using Resultant, Ayade Salah Abdelmalk

Theses

In this thesis, we modify two methods for locating zeros of polynomial systems which are one dimensional path following and Lanczos method. Both approaches are based on calculating the resultant matrix corresponding to each variable in the system. These methods are stable and preserving the spareness of these matrices. These methods are developed to avoid using the zeros of the multiresultant of each variable which are condition problems. Theoretical and numerical results will be given to show the efficiency of these methods. Finally, algorithms for the Mathematica codes are given.

Mathematical Modeling Of Seir Model With Generalized Incidence Function And The Extension To Covid-19 Model, Shymaa Mohammad Dadoa

Theses

The COVID-19 pandemic had shown the importance of the SEIR model in predicting the outcome of the disease spread and to find the best strategies to contain the pandemic. As this type of model has a limited number of compartments, many other models were derived from the SEIR model to cover, to the maximum, the complex dynamics of the disease spread. These extensions of the SEIR model bring natural validity questions: How can we validate these models? and how far/close are these extended models from giving us real insights into the pandemic?

This thesis investigates the SEIR epidemic model and …

Artificial Neural Network Concepts And Examples, Harcharan Kabbay

Theses

Artificial Neural Networks have gained much media attention in the last few years. Every day, numer- ous articles on Artificial Intelligence, Machine Learning, and Deep Learning exist. Both academics and business are becoming increasingly interested in deep learning. Deep learning has innumerable uses, in- cluding autonomous driving, computer vision, robotics, security and surveillance, and natural language processing. The recent development and focus have primarily been made possible by the convergence of related research efforts and the introduction of APIs like Keras. The availability of high-speed compute resources such as GPUs and TPUs has also been instrumental in developing deep learning …

Properties Of Certain Connected Graphs Related To Their Edge Metric Dimension, Sanabel Mahmoud Y. Bisharat

Theses

Metric dimension, resolving sets and edge metric dimension are very important invariants for the resolvability of graphs that have been studied and investigated intensively in the literature over the last decades. Their immense utilization in network topology, master mind games, robot navigation and representation of chemical compounds make their study very attractive. This thesis is concerned with the graph-theoretic properties of certain families of connected graphs related to their edge metric dimension. The main objective of this thesis is to study the comparison of metric dimension ver-sus edge metric dimension of certain families of graphs. The study investigates the relationship …

On The Generalized Hardy-Littlewood Maximal Operator, Namarig Hashim Hassan

Theses

No abstract provided.

Numerical And Theoretical Investigations Of Fractional Differential Equations, Sara Rafiq Al Fahel

Theses

Fractional calculus has been recently received huge attention from Mathematicians and engineers due to its importance in many real-life applications such as: fluid mechanics, electromagnetic, acoustics, chemistry, biology, physics and material sciences. In this thesis, we present numerical algorithms for solving fractional IVPs and system of fractional IVPs where two types of fractional derivatives are used: Caputo-Fabrizio, and Atangana-Baleanu-Caputo derivatives. These algorithms are developed based on modified Adams-Bashforth method. In addition, we discuss the theoretical solution of special class of fractional IVPs. Several examples are discussed to illustrate the efficiency and accuracy of the present schemes.

Finitely Generated Modules Over A Principal Ideal Domain, Mariam Mutawa Meshaab Shemal Al-Dhaheri

Theses

This thesis covers the main theory of modules: modules, submodules, cosets, quotient modules, homomorphisms, ideals, direct sums, and some related topics. Using these notions, a theorem on the structure of finitely generated modules over domains of principal ideals is proved. As an application of this theorem, the theory of the structure of normal forms of matrices over various fields is presented.

Reproducing Kernel Method For Solving Fuzzy Initial Value Problems, Qamar Kamel Dallashi

Theses

In this thesis, numerical solution of the fuzzy initial value problem will be investigated based on the reproducing kernel method. Problems of this type are either difficult to solve or impossible, in some cases, since they will produce a complicated optimized problem. To overcome this challenge, reproducing kernel method will be modified to solve this type of problems. Theoretical and numerical results will be presented to show the efficiency of the proposed method.

Flow Of Quantum Genetic Lotka-Volterra Algebras On M2(ℂ), Sondos Muhammed Syam

Theses

In this thesis, a class of flow quantum Lotka-Volterra genetic algebras (FQLVG-A) is investigated and its structure is studied. Moreover, the necessary and sufficient conditions for the associativity and alternatively of FQGLV-A are derived. In addition, idempotent elements in FQGLV-A are found. Also, derivations of a class of FQLVG-A are described. Also, the automorphisms of a class of FQLVG-A and their positivity are examined.

Stationary Probability Distributions Of Stochastic Gradient Descent And The Success And Failure Of The Diffusion Approximation, William Joseph Mccann

Theses

In this thesis, Stochastic Gradient Descent (SGD), an optimization method originally popular due to its computational efficiency, is analyzed using Markov chain methods. We compute both numerically, and in some cases analytically, the stationary probability distributions (invariant measures) for the SGD Markov operator over all step sizes or learning rates. The stationary probability distributions provide insight into how the long-time behavior of SGD samples the objective function minimum.

A key focus of this thesis is to provide a systematic study in one dimension comparing the exact SGD stationary distributions to the Fokker-Planck diffusion approximation equations —which are commonly used in …

Streaming Down The Stern-Brocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), Marcus L. Shell

Theses

This paper explores and elaborates on a method of solving Pell’s equation as introduced by Norman Wildberger. In the first chapters of the paper, foundational topics are introduced in expository style including an explanation of Pell’s equation. An explanation of continued fractions and their ability to express quadratic irrationals is provided as well as a connection to the Stern-Brocot tree and a convenient means of representation for each in terms of 2×2 matrices with integer elements. This representation will provide a useful way of navigating the Stern-Brocot tree computationally and permit us a means of computing continued fractions without the …

Sum Of Squares With Q-Series, Gosper’S Q- Trigonometry, An New Identities Via An Extended Bailey Transform, Zina Al Houchan

Theses

This report is concerned about q-series and some of their applications. Firstly, Jacobi’s q-series proof for Legendre’s theorem on sums of four squares will be presented. By way of comparison, the classical approach of this result will be also discussed. Secondly, Gosper’s q-trigonometry will be introduced using Jacobi’s theta functions and the theory of elliptic functions shall be employed to confirm one of Gosper’s conjectures. As an application, a proof for Fermat’s theorem on the sums of squares will be provided. Thirdly, an extended version of Bailey’s transform will be established and as a consequence, a variety of new q-series …

The Q-Gauss Product, Q-Trigonometry Via Landen-Like Identities, And Positive Alternating Q-Series, Sarah Abo Touk

Theses

The object of this report is q-series and their relationship with certain special functions. Firstly, Jackson’s q-analogue of the Euler gamma function is introduced and a q-analogue for a famous formula of Gauss on products of the gamma function will be presented. Secondly, Jacobi’s theta functions will be discussed in details and new Landenlike half argument formulas will be established. As an application, q-trigonometric formulas shall be derived and a new proof for a well-known q-series relation of Jacobi will be given. Thirdly, an extended Bailey transform will be presented and a variety of new q-series will be deduced as …

Controllability And Observability Of Blood Glucose Levels And The Impact Of Covid-19 On Diabetic Patients, Mahra Salem Nasser Abdulla Alblooshi

Theses

Diabetes is a metabolic disorder that is characterized by high blood glucose concentrations resulting from insulin deficiency in case of type 1 or insulin inefficiency in case of type 2. While no cure for diabetes exists, the artificial pancreas is a possible way to manage diabetes, especially for type 1 diabetics. Where an artificial pancreas is a closed-loop control system with an integrated mathematical model. This control system imitates the function of a healthy pancreas. The first part of this thesis is concerned with the control system of an artificial pancreas that is based on Bergman’s minimal model of glucose-insulin …

Ovals And Niho Bent Functions In Small Dimensions, Rasha M. E. Shat

Theses

In this thesis hyperovals and ovals are considered in the projective plane PG(2,q), q = 2^m even. Traditionally these objects are studied algebraically via o-polynomials. In our work, a different approach is used by means of g-functions. These functions also provide a natural description of Niho bent functions. Using g-functions, all ovals and Niho bent functions are listed up to equivalency for dimensions m ≤ 6.

Predicting Carcass Cut Yields In Cattle From Digitalimages Using Artificial Intelligence, Darragh Matthews

Theses

Beef carcass classification in Europe is predicated on the EUROP grid for both fatness and conformation. Although this system performs well for grouping visually similar carcasses, it cannot be used to accurately predict meat yields from these groups, especially when considered on an individual cut level. Deep Learning (DL) has proven to be a successful tool for many image classification problems but has yet to be fully proven in a regression scenario using carcass images. Here we have trained DL models to predict carcass cut yields and compared predictions to more standard machine learning (ML) methods. Three approaches were undertaken …

Analysis Of Gameplay Strategies In Hearthstone: A Data Science Approach, Connor W. Watson

Theses

In recent years, games have been a popular test bed for AI research, and the presence of Collectible Card Games (CCGs) in that space is still increasing. One such CCG for both competitive/casual play and AI research is Hearthstone, a two-player adversarial game where players seeks to implement one of several gameplay strategies to defeat their opponent and decrease all of their Health points to zero. Although some open source simulators exist, some of their methodologies for simulated agents create opponents with a relatively low skill level. Using evolutionary algorithms, this thesis seeks to evolve agents with a higher skill …

Mathematical Modeling Of Corona Virus In The United Arab Emirates, Alya Saif Ahmad Alshehhi

Theses

The Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is a viral in-fectious disease that can be transmitted to humans through interaction with infected ani-mals or humans. The Middle East respiratory syndrome (MERS) is still one of the main public health concerns in the Gulf region including United Arab Emirates. The fact that diseases have been imported into other parts of the world show the possibility of has a MERS pandemic. In this work, we are aiming to study a mathematical model of the MERS transmission among the UAE population and camels. The goal is to determine what are the paths of …

Efficient Reduced Bias Genetic Algorithm For Generic Community Detection Objectives, Aditya Karnam Gururaj Rao

Theses

The problem of community structure identification has been an extensively investigated area for biology, physics, social sciences, and computer science in recent years for studying the properties of networks representing complex relationships. Most traditional methods, such as K-means and hierarchical clustering, are based on the assumption that communities have spherical configurations. Lately, Genetic Algorithms (GA) are being utilized for efficient community detection without imposing sphericity. GAs are machine learning methods which mimic natural selection and scale with the complexity of the network. However, traditional GA approaches employ a representation method that dramatically increases the solution space to be searched by …

Series Solutions Of Multi-Layer Boundary Value Problems, Amr Saad Hassan Bolbol

Theses

It is well known that differential equations (DEs) play an important role in many sciences. They are mathematical representations of many physical systems. By studying such DEs, one gains many important insights about the physical system. Solutions of DEs provide information on the physical system behavior. As many physical systems are nonlinear in nature, this naturally gives rise to nonlinear differential equations (NLDEs). Such NLDEs are, in most cases, hard or sometimes impossible to solve analytically. In such situations, we resort to numerical techniques to approximate the solutions. The purpose of this thesis is to consider nonlinear multi-layer boundary value …

Finite Semifields And Their Applications, Shamsa Ali Rashed Al Saedi

Theses

This thesis is concerned with finite semi fields. The objective of this thesis is to give a full description of Knuth orbits of known commutative semi fields. We also describe planar functions corresponding to commutative semi fields. Results are presented by tables. Nuclei of semi fields are studied. Finally we consider applications of semi fields, planar functions and spreads to construction of mutually unbiased bases.