Mathematics Commons^™

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.

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 …

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.