فقہی اختلافات کے مابین امام شعرانی اور شاہ ولی اللہ کے اسالیب تطبیق

In the Islamic Sharia there are two types of texts, as for the first one, there is no need for any interpretations. For instance: Tauhid (unity of Allah), while few interpretations have modiefied with the changing circumstances. The expertises of Islamic jurists highlight the interpretations of the text according to prevailing social and political environment which can create harmony between Islamic Sharia and importunity of nature. Imam Sharani and Shah Wali Ullah are those personalities who evaluated the intellectual efforts of Islamic jurists and describe their diligencial and margenial secondary level differences. They created a road of conformity between their minor level marginal differences which are legitimate. Imam Sharani and Shah Wali Ullah‘s methodologies of uniformity represent the facts that differences in the approaches of jurists, which are considered as segregation in the reality that is benevolence for Muslim Ummah. Their methodologies of uniformity are not only practical but also very useful in the context of global village. In this age ethical, social, and family problems can be solved through the method of uniformity. For the solution of issues like intellectual extremism, prejudice and terrorism, Imam Sharani and Shah Wali Ullah‘s methodologies of uniformity are beaconhouse.

Nonlinear Electromagnetic Waves in Dense Plasmas

The formation and propagation of electromagnetic waves, specifically the magnetoacoustic waves are studied in this thesis for dense electron-ion magnetoplasmas. The linear and nonlinear waves such as shocks and solitons for small but finite amplitude perturbations are described for various plasma models by taking into account the quantum magnetohydrodynamic model. Further, the possible magnetoacoustic solitary wave interactions, i.e., overtaking and head-on interactions are discussed. The results are numerically analyzed by choosing the plasma parameters consistent with compact astrophysical systems. The properties of nonlinear fast magnetoacoustic waves in dense dissipative magnetoplasmas with degenerate electrons are studied theoretically. For this purpose, the quantum magnetohydrodynamic equations and the reductive perturbation technique are employed to derive the Khokhlov-Zabolotskaya- Kuznetsov (KZK) equation. The assumptions to obtain KZK equation in plasma system and the limiting cases have been identified clearly. Shock solutions of KZK equation are obtained by employing a method based upon Hirota and Clarkson-Kruskal approach. The magnetoacoustic shock waves have been examined numerically to ascertain how the plasma parameters such as ion kinematic viscosity, number density and magnetic field alter the characteristics and dynamics of shock waves. The propagation characteristics of magnetoacoustic shock waves are further investigated in a dense magnetoplasma with spin-1/2 electrons and geometrical effects by deriving the planar Korteweg-de Vries Burgers (KdVB) and cylindrical KdVB equations. Numerically, cylindrical KdVB equation is analyzed and it is observed that the number density, magnetic field and ion kinematic viscosity are the parameters that bring about significant modifications in the structure and propagation of magnetoacoustic shock waves. The spin effects are found to mitigate the phase speed of magnetoacoustic waves and the amplitude of shock structures in a dense magnetoplasma. The amplitude of the shock wave is observed to be greater for the case of cylindrical geometry and is found to propagate faster than that of planar shock waves. Furthermore, the numerical results are compared with the approximate analytical solution to show an excellent agreement of the results in the limit of earlier times. Overtaking interaction of fast magnetoacoustic solitons in dense magnetoplasmas is investigated. In this regard, one dimensional propagation of magnetoacoustic solitary waves in electron-ion plasmas with degenerate electrons is considered by deriving the Korteweg-de Vries (KdV) equation. Numerically, the characteristics of solitary waves are studied by varying the plasma parameters i.e., number density and magnetic field. Hirota bilinear formalism is applied to get the multi-soliton solutions and overtaking interaction of fast magnetoacoustic solitons is explored by utilizing them. It is observed that the values of the propagation vectors determine the interaction of solitary waves. The taller soliton being faster, overtakes the shorter soliton such that the amplitude of the respective solitary waves remain unchanged after the interaction, however they do experience a phase shift. Further, the head-on interaction of two magnetoacoustic solitons is studied in a dense magnetoplasma with spin-1/2 electrons and geometrical effects. The extended Poincaré- Lighthill-Kuo (PLK) technique and quantum magnetohydrodynamic equations are utilized to derive a pair of nonplanar Korteweg-de Vries equations. The PLK method is an analytical approach, which explicitly provides the relations of post collision trajectories and the phase shifts encountered by the magnetoacoustic solitons after interaction. The head-on interaction of two concentric ring solitons is numerically analysed. It is observed that the spin-1/2 effects, statistical pressure, displacement current and geometry of the system significantly modify the phase shifts encountered by the solitons. It is noticed that the increasing the number density decreases the phase shift of the colliding solitons. Furthermore, the cylindrical geometry is observed to decrease the phase shift by comparison with the planar geometry. The investigations carried out in this thesis shall hopefully equip us to comprehend the formation, propagation and interaction of magnetoacoustic solitons in dense magnetoplasmas which exist in compact astrophysical objects like white dwarfs and neutron stars.