Physical Sciences and Mathematics Commons^™

Some Algebraic Aspect And Applications Of A Family Of Functions Over Finite Fields, Shaima Ahmed Thabet

Theses

We study two families of functions over finite fields; the Multivalued Threshold

Functions and the Multivariate Polynomials. Recent advances made in our Conception and our understanding of Boolean Threshold Functions and Multivariate Threshold Functions have considerably increased the importance of the role that they Play in our days in areas like cryptography, circuit complexity, learning theory, social choice, quantum complexity, and in many other areas. Theoretical aspects of Bovid and Gauche who gave an algebraic first studied threshold functions Approach of Boolean Threshold Functions using group ring theory. We will present some algebraic properties of Boolean threshold functions. For the …

Q-Series With Applications To Binomial Coefficients, Integer Partitions And Sums Of Squares, Amna Abdul Baset Saif Saif Al Suwaidi

Theses

In this report we shall introduce q-series and we shall discuss some of their applications to the integer partitions, the sums of squares, and the binomial coefficients. We will present the basic theory of q-series including the most famous theorems and rules governing these objects such as the q-binomial theorem and the Jacobi’s triple identity. We shall present the q-binomial coefficients which roughly speaking connect the binomial coefficients to q-series, we will give the most important results on q-binomial coefficients, and we shall provide some of our new results on the divisibility of binomial coefficients. Moreover, we shall give some …

Direct Sums Decompositions: Applications, Wahdan Mohammad Yousef Abuziadeh

Theses

In this thesis we study the behavior of direct sum decomposition's in the category of modules. We present some of the most important "classical" results involving direct sum decomposition's for modules (e.g. Krull-Schmidt theorem, decomposition theorems for finitely generated modules over PID etc.). In the last part of the thesis we obtain new results, namely isomorphic refinement theorems for direct sum decomposition's of regular modules. We also obtain a link between regular modules and the exchange property.

Series Solutions Of Multi-Term Fractional Differential Equations, Yousef Ibrahim Al-Srihin

Theses

In this thesis, we introduce a new series solutions for multi-term fractional differential equations of Caputo’s type. The idea is similar to the well-known Taylor Series method, but we overcome the difficulty of computing iterated fractional derivatives, which do not commuted in general. To illustrate the efficiency of the new algorithm, we apply it for several types of multi-term fractional differential equations and compare the results with the ones obtained by the well-known Adomian decomposition method (ADM).

Geometric Integrators With Application To Hamiltonian Systems, Hebatallah Jamil Al Sakaji

Theses

Geometric numerical integration is a relatively new area of numerical analysis. The aim is to preserve the geometric properties of the flow of a differential equation such as symplecticity or reversibility. A conventional numerical integrator approximates the flow of the continuous-time equations using only the information about the vector field, ignoring the physical laws and the properties of the original trajectory. In this way, small inaccuracies accumulated over long periods of time will significantly diminish the operational lifespan of such discrete solutions. Geometric integrators, on the other hand, are built in a way that preserve the structure of continuous dynamics, …

Pricing European Option Under A Modified Cev Model, Wafaa Ibrahim Abuzarqa

Theses

A financial derivative is an instrument whose payoff is derived from the behavior of another underlying asset. One of the most commonly used derivatives is the option which gives the right to buy or to sell an underlying asset at a pre-specified price at (European) or at and before (American) an expiration date. Finding a fair price of the option is called the option pricing problem and it depends on the underlying asset prices during the period from the initial time to expiration date. Thus, a “good” model for the underlying asset price trajectory is needed. In this work, we …

The Pricing Of Asian Options In High Volatile Markets: A Pde Approach, Nabil Kamal Riziq Al Farra

Theses

Financial derivatives are very important tools in risk management since they decrease uncertainty. Moreover, if used effectively, they can grow the income and save the cost. There are many types of financial derivatives, for instance: futures/forwards, options, and swaps. The present thesis deals with the pricing problem for Asian options. The main aim of the thesis is to generalize the Asian option pricing Partial Differential Equation (PDE) in order to handle post-crash markets where the volatility is high. In other words, we seek to extend the work on the Asian option pricing PDE under the well-known Black-Scholes model to a …

On The Geometry Of Fuchsian Groups, Hala Alaqad

Theses

In this Master thesis we consider the discrete groups with emphasis on the geometry of discrete groups, which lie at the intersection between Hyperbolic Geometry, Topology, Abstract Algebra, and Complex Analysis. Fuchsian groups are discrete subgroups of the group PSL(2,ℝ) of linear fractional transformations of one complex variable, which is isomorphic to a quotient topological group: PSL(2,ℝ)≅SL(2,ℝ)/{±I}. Here SL (2,ℝ) is special linear group and I is the identity. We study discrete groups, in particular, Fuchsian groups. We present the geometric properties of Fuchsian groups such as fundamental domains, compactness, and Dilichlet tessellations. In addition, we also present some algebraic …

Quaternary Affine-Invariant Codes, Badria H Omar Salih

Theses

This thesis concerned with extended cyclic codes. The objective of this thesis is to give a full description of binary and quaternary affine-invariant codes of small dimensions. Extended cyclic codes are studied using group ring methods. Affine-invariant codes are described by their defining sets. Results are presented by enumeration of defining sets. Full description of affine-invariant codes is given for small dimensions

The Groups Acting On The Riemann Sphere, Ruba Yousef Wadi

Theses

In this Master thesis we consider the group actions, with emphasis on the group of general Möbius transformations of one complex valuable acting on the Riemann sphere. We study some invariant subspaces of Riemann sphere under the actions of natural groups of transformations, including the invariant quantities in Hyperbolic Geometry that is a beautiful area of Mathematics. We use analytic and algebraic points of view to describe some group actions on Riemann sphere; in particular, we present the relationships between isometries of hyperbolic plane, Möbius transformations, and groups of matrices. Keywords: Group actions, Riemann sphere, general Möbius transformations, transitivity, hyperbolic

Mathematical Modeling Of Communicable Imported Diseases Screening In The United Arab Emirates, Lahbib Ben Ahmadi

Theses

The United Arab Emirates (UAE), as one of the countries with high numbers of expatriates in the world, is expected to face public health challenges. The reason for this situation is that the majority of those expatriates belong to regions where health issues are usually left behind. This may create the possibility of having imported communicable diseases. However, screening policy should be tested and adapted to protect the population from any imported communicable disease. This study aims at identifying an approach and method to deal with these imported diseases via a set of differential equations. The spread of a communicable …

Mathematical Modeling Of The Imported Malaria In The United Arab Emirates, Fatima Hassan Ali Alawadhi

Theses

Although the UAE was certified to be free of local malaria transmission cases in 2007, the increased number of imported malaria cases in recent years required the attention of the public health professionals. The aim of this work is to study, via mathematical modeling, the impact of imported malaria cases on the population of the UAE. The nature of the health policies in the UAE imposes on us a model that classifies the living population of the UAE in two categories. The local population, who represent the permanent residents that do not have any health requirement for their residency, and …

An Efficient Method For Solving A Discrete Orthogonal Approximation To Fractional Boundary Value Problems, Mwaffag Husein Nahar Sharadga

Theses

In this thesis we developed a numerical method for solving a class of nonlinear fractional boundary value problems using the fractional order Legendre Tau-path following method. Theoretical and numerical analyses are presented. The numerical results showed that this method works properly and efficiently.

Existence And Uniqueness Of Solutions For A Class Of Non-Linear Boundary Value Problems Of Fractional Order, Arwa Abdulla Omar Salem Ba Abdulla

Theses

In this thesis, we extend the maximum principle and the method of upper and lower solutions to study a class of nonlinear fractional boundary value problems with the Caputo fractional derivative 1

Bifurcation Analysis Of Mutually Coupled Laser Systems, Vincent Brennan

Theses

Coupled laser systems have application in everyday modern life, including for example, telecommunications and cryptography. Therefore it is important to gain insight into the dynamic processes at work and theoretical modeling can elucidate such processes. The work presented in this thesis is primarily concerned with aspects such as excitability and phase locking in mutually coupled oscillators. Phase-only delay-coupled oscillator models are introduced to demonstrate excitability and it is subsequently shown that similar processes can occur in a low-dimensional variation of these models. Further, delay differential rate equation models also exhibit excitability and these are explored and contrasted with another, similar, …

Evaluation, Adaptation And Validation Of A Model To Predict Grass Growth In Ireland, Christina Hurtado Uria

Theses

Budgeting grass supply allows producers to minimise the quantity of purchased feed required in the diet of grazing livestock. One tool for managing grass supply could be a mathematical model that can simulate grass growth. The development of such a model would allow better management around the variability of feed supply and help identify feed surpluses and deficits, and therefore increase the accuracy of management decisions. This would be a key feature of profitable milk and meat production systems in the future which will be hugely important as global food demand increases due to population growth. It is forecasted that …

The Geometry Of The Space Of Oriented Geodesics Of Hyperbolic 3-Space, Nikos Georgiou

Theses

In this thesis we construct a Kähler structure (J, Ω, G) on the space L(H³) of oriented geodesics of hyperbolic 3-space H³ and investigate its properties. We prove that (L(H³),J) is biholomorphic to (see thesis pdf), and that the Kähler metric G is of neutral signature, conformally flat and scalar flat.

We establish that the identity component of the isometry group of the metric G on L(H³) is isomorphic to the identity component of the hyperbolic isometry group. We show that the geodesics of G correspond to ruled minimal surfaces in H3, which …

The Evolution Of Cell Colonies In Volvocacean Algae : Investigation By Theoretical Analysis And Computer Simulation., Frank Noe

Theses

This thesis presents a mathematical analysis and computational simulation which is used to investigate the evolution of cell colonies. The evolutionary transition from unicellular to cell colony form is a prerequesite for multicellular life as it exists abundantly on earth. This transition has occured numerous times independently so that we expect a high selective advantage to be associated with it. The photosynthetic green algae order Volvocaceae is an appropriate set of model organisms for the study of the evolution of cell colonies since it comprises living unicellular organisms, cell colonies, and multicellular organisms of different shapes, sizes and levels of …