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Cone Extended b-Metric Space Over Banach Algebra

Thesis Info

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Author

Umair Ahmed Butt

Department

Department of Mathematics

Program

MS

Institute

Capital University of Science & Technology

Institute Type

Private

City

Islamabad

Country

Pakistan

Thesis Completing Year

2019

Subject

Mathematics

Language

English

Link

https://thesis.cust.edu.pk/UploadedFiles/MMT181009.pdf

Added

2021-02-17 19:49:13

Modified

2023-01-06 19:20:37

ARI ID

1676709506416

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I/We begin by the Blessed Name of Allah

The Immensely Merciful to all, The Infinitely Compassionate to everyone.

21:01
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21:02
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21:03
Their hearts are preoccupied with trivial things.
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21:04
He - The Prophet – said:
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21:05
No way!
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Ever since man has stepped on earth and tried to implement a collective social life pattern, then onwards the idea of the establishment of state has come into existence. History has witnessed diverse governance patterns as per indigenous values and ideologies. At the time of advent of Islam, there was monarchy and kingship that prevailed beyond the deserts of Arabia that sustained on royal descendants, whereas, in Arabia rulers would be selected upon their competence and acumen for ruler ship. When Islam came, religious angle was included too however, the various modes of interpretation became a bone of contention later on. In this research article, a review of oriental and occidental thought patterns have been reviewed. Similarly it has been tried to assess how diverse and divergent these two points of view remained.

Numerical Approximation of Classical and Relativistic Magnetohydrodynamics

A wide range of phenomena related to solar physics, astrophysics and laboratory plasmas contain many features of magnetohydrodynamics (MHD). This thesis presents the numerical studies of classical and relativistic MHD models. In classical MHD, the two dimensional ideal MHD and the shallow water MHD equations are numerically investigated. The third model is a one-dimensional special relativistic MHD (SRMHD) system. These MHD systems are formed by coupling the Maxwell''s equations with the hydrodynamics equations. The simulation of relativistic MHD flows is more difficult due to flow near the speed of light and because of nonlinear relations between conserved and primitive variables. The proposed numerical methods include the space-time conservation element and solution element (CE/SE) method and the kinetic flux vector splitting (KFVS) scheme. In CE/SE solver, the conservation elements are used for calculating the flow variables only, while a central differencing procedure is used to approximate the derivatives of flow variables. The KFVS scheme is based on the direct splitting of macroscopic flux functions of the system. The MUSCL-type reconstruction technique is used to achieve the second order accuracy of the KFVS method. For the designed MHD codes, the projection method is used to satisfy the divergence-free constraint associated with the magnetic field. For validation and comparison, the central scheme is applied to the investigated models. The case studies of ideal MHD include the MHD Kelvin- Helmholtz instability, the MHD rotor problem, the MHD shock interaction with clouds, the blast wave problem and the very famous Orszag-Tang MHD turbulence problem. In the SRMHD case, the one-dimensional relativistic Riemann problems, the interaction of shock fronts, and the relativistic blast wave problems are studied. In all test cases, the suggested computational techniques produced accurate results efficiently.