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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
Q-Series With Applications To Binomial Coefficients, Integer Partitions And Sums Of Squares, Amna Abdul Baset Saif Saif Al Suwaidi
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
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
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
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, …
Mathematical Modeling Of Communicable Imported Diseases Screening In The United Arab Emirates, Lahbib Ben Ahmadi
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 …
Pricing European Option Under A Modified Cev Model, Wafaa Ibrahim Abuzarqa
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 Groups Acting On The Riemann Sphere, Ruba Yousef Wadi
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
Quaternary Affine-Invariant Codes, Badria H Omar Salih
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
On The Geometry Of Fuchsian Groups, Hala Alaqad
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 …
The Pricing Of Asian Options In High Volatile Markets: A Pde Approach, Nabil Kamal Riziq Al Farra
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 …
Existence And Uniqueness Of Solutions For A Class Of Non-Linear Boundary Value Problems Of Fractional Order, Arwa Abdulla Omar Salem Ba Abdulla
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
Mathematical Modeling Of The Imported Malaria In The United Arab Emirates, Fatima Hassan Ali Alawadhi
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
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.
Bifurcation Analysis Of Mutually Coupled Laser Systems, Vincent Brennan
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, …