انسانی صحت کے متعلق سائنسی ا ثبات احادیث نبویہﷺ کی روشنی میں تجزیاتی مطالعہ

The preachings of the Prophet (P.B.U.H) are equally beneficial for both  believers  and non-believers. While Muslims have reaped many benefits from prophetic teachings, those who do not believe in the Holy Prophet (saw) are also inclined to study his teachings and conclude that the scientific  principles we are  formulating now, were revealed by the Prophet  (P.B.U.H) many centuries ago. Whether it be the secrets of hygiene, medicine  and treatment, or matters of implicit principles of creation, Prophet Muhammad (P.B.U.H)'s teachings contain golden principles that encompass   the secrets of success in all matters ranging from the survival of human health to the matters of creation. The purpose of this article is to explain the sayings of the holy prophet*( P.B.U.H) which lead to scientific proofs and indicate that it is the teachings of the Prophet (P.B.U.H), from which today’s intellectuals deduce principles. But the Prophet ( PBUH) many years ago, made those golden principles clear  through his edicts and rulings in the time of technology scarcity.

Scattering from Different Geometries in the Presence of Topological Insulator and Metamaterials

Kobayashi potential is a semi-analytical method frequently used to solve scattering problems mainly related to geometries containing strip, grating, aperture, disk. Kobayashi potential method has been applied in this dissertation for solving scattering problems. According to Kobayashi potential method, longitudinal component of the unknown scattered field is assumed in terms of unknown weighting functions. Moreover, use of the relevant boundary conditions of discussed problems leads to the formation of algebraic equations and dual integral equations. Further, Integrands of the dual integral equations are expanded in terms of the characteristic functions with unknown expansion coefficients which must satisfy, simultaneously, the required edge and boundary conditions. The expressions derived from expansion of the integrands are combined with algebraic equations in order to express the unknown weighting function in terms of unknown expansion coefficients. The weighting functions, in terms of expansion coefficients, are then substituted in the dual integral equations. Moreover, the projection treatment is applied using properties of the Jacobi polynomials which yields matrix equation being solved numerically for unknown expansion coefficients. The far-zone field expressions have been derived using Saddle point method of integration. Finally, the scattered field has been calculated with aid of matrix equation. In this dissertation, scattering from a canonical object has been investigated by using Kobayashi potential method. Different geometries have been considered in this aspect. In the start of this dissertation, perfectly conducting strip has been placed inside of unbounded topological insulator medium. Additionally, an impedance strip has been taken as canonical object surrounded with topological insulator medium. Furthermore, a planar interface of topological insulator and chiral medium has been examined with presence of perfectly conducting strip. Finally, another planar interface with different non-integer dimensional dielectric media has been observed. These different geometries have been worked out analytically by using Kobayashi potential method. The geometries have been ex- 6 cited by plane wave. The numerical results have been plotted by applying Matlab software and subsequent discussion has also been made in this regard. Different parameters have been considered as special parameters for different geometries namely topological, impedance, chirality, non-integer dimensional parameters. In the end of the dissertation, conclusions along with directions for future researchers have been discussed.