Family, marriage and social change in some Libyan villages.

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Parallel alogorithms for MIMD parallel computers

This thesis mainly covers the design and analysis of asynchronous parallel algorithms that can be run on MIMD (Multiple Instruction Multiple Data) parallel computers, in particular the NEPTUNE system at Loughborough University. Initially the fundamentals of parallel computer architectures are introduced with different parallel architectures being described and compared. The principles of parallel programming and the design of parallel algorithms are also outlined. Also the main characteristics of the 4 processor MIMD NEPTUNE system are presented, and performance indicators, i.e. the speed-up and the efficiency factors are defined for the measurement of parallelism in a given system. Both numerical and non-numerical algorithms are covered in the thesis. In the numerical solution of partial differential equations, a new parallel 9-point block iterative method is developed. Here, the organization of the blocks is done in such a way that each process contains its own group of 9 points on the network, therefore, they can be run in parallel. The parallel implementation of both 9-point and 4- point block iterative methods were programmed using natural and redblack ordering with synchronous and asynchronous approaches. The results obtained for these different implementations were compared and analysed. Next the parallel version of the A.G.E. (Alternating Group Explicit) method is developed in which the explicit nature of the difference equation is revealed and exploited when applied to derive the solution of both linear and non-linear 2-point boundary value problems. Two strategies have been used in the implementation of the parallel A.G.E. method using the synchronous and asynchronous approaches. The results from these implementations were compared. Also for comparison reasons the results obtained from the parallel A.G.E. were compared with the ~ corresponding results obtained from the parallel versions of the Jacobi, Gauss-Seidel and S.O.R. methods. Finally, a computational complexity analysis of the parallel A.G.E. algorithms is included. In the area of non-numeric algorithms, the problems of sorting and searching were studied. The sorting methods which were investigated was the shell and the digit sort methods. with each method different parallel strategies and approaches were used and compared to find the best results which can be obtained on the parallel machine. In the searching methods, the sequential search algorithm in an unordered table and the binary search algorithms were investigated and implemented in parallel with a presentation of the results. Finally, a complexity analysis of these methods is presented. The thesis concludes with a chapter summarizing the main results

Determination Of Delta 13c Values Of Amphetamine And Methamphetamine Using Gas Chromatography/ Combustion/ Isotope Ratio Mass Spectrometry (Gc/C/Irms)

Drug abuse of amphetamine-type stimulants (ATS) has been considered as the most widespread problem around the world and also regarded as a threat to national security. This study is focused on stable carbon isotope analysis by isotope ratio mass spectrometry (IRMS) to develop and validate a method for amphetamine and methamphetamine analysis. The ability to measure isotope distribution in natural abundance with high accuracy and precision has increased the application of gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS) for various applications in recent years. Urine Samples spiked with amphetamine and methamphetamine standards were extracted using liquid–liquid extraction and subsequently, reconstituted with the mobile phase for further purification and separation using High Performance Liquid Chromatography (HPLC). These fractions were collected and analysed using the GC/C/IRMS. GC/C/IRMS showed δ13C value of -24.72 ±0.6‰ and -28.90 ±0.15‰ for amphetamine methamphetamine, respectively. The solid samples of the same amphetamine and methamphetamine standards were also analysed to determine the δ13C of each standard by using the FLASH elemental analyzer isotope ratio mass spectrometry (EA/IRMS); these were then compared with the results obtained from the GC/C/IRMS. EA/IRMS showed comparable results with those obtained with GC/C/IRMS; amphetamine showed the δ13C value of -24.90 ±0.03‰, while methamphetamine showed δ13C result of -28.99 ±0.03‰

Homotopy Perturbation and Elzaki Transform for Solving Nonlinear Partial Differential Equations

In this work, we present a reliable combination of homotopy perturbation method and Elzaki transform to investigate some nonlinear partial differential equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The proposed homotopy perturbation method is applied to the reformulated first and second order initial value problem which leads the solution in terms of transformed variables, and the series solution is obtained by making use of the inverse transformation. The results show the efficiency of this method. Keywords: Homotopy perturbation methods, Elzaki transform nonlinear partial differential equations

Solution of Nonlinear High Order Multi-Point Boundary Value Problems By Semi-Analytic Technique

In this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems

Analytical Solution for Telegraph Equation by Modified of Sumudu Transform "Elzaki Transform"

In this work modified of Sumudu transform [10,11,12] which is called Elzaki transform method ( new integral transform) is considered to solve general linear telegraph equation, this method is a powerful tool for solving differential equations and integral equations [1, 2, 3, 4, 5]. Using modified of Sumudu transform or Elzaki transform, it is possible to find the exact solution of telegraph equation. This method is more efficient and easier to handle as compare to the Sumudu transform method and variational iteration method. To illustrate the ability of the method some examples are provided.   Keywords: modified of Sumudu transform- Elzaki transform - Telegraph equation - Partial Derivative

Solution of Linear and Nonlinear Partial Differential Equations Using Mixture of Elzaki Transform and the Projected Differential Transform Method

The aim of this study is to solve some linear and nonlinear partial differential equations using the new integral transform "Elzaki transform" and projected differential transform method. The nonlinear terms can be handled by using of projected differential transform method; this method is more efficient and easy to handle such partial differential equations in comparison to other methods. The results show the efficiency and validation of this method. Keywords: Elzaki transform, projected differential transform method, nonlinear partial differential equations