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.

Approximate analytic solution of Hodgkin-Huxley equations

In the last century, there has been extensive research on our brain and many mathematical models and theories have been developed which describe the dynamical behavior of neurons. One of them is the widely known, Hodgkin-Huxley model. The Hodgkin-Huxley model for space clamp situation (uniform voltage over a patch of nerve membrane) is a mathematical model consisting of 4 nonlinear ordinary differential equations that describe membrane action potentials in neurons. Before this work, these equations could only be solved by numerical techniques and analytical solutions were not found. In this work, efforts are put to find the analytic solution of the Hodgkin-Huxley model by using Homotopy Perturbation Method. Homotopy Perturbation Method was developed by Ji-Huan He (1998) by merging two techniques, the standard homotopy and the perturbation technique for solving linear, nonlinear, initial and boundary value problems. Further, the solution is compared with the experimental results found by Hodgkin and Huxley. In this work, the first-order approximate analytic solution of the space-clamped Hodgkin Huxley model has been computed and algorithm for a higher-order solution is given. For plotting the solution, MATHEMATICA is used. It is found that the first-order solution can describe many key properties of the Hodgkin-Huxley model. Further, besides some differences, the general agreement of the first-order solution of space-clamped Hodgkin-Huxley Equations by Homotopy Perturbation Method with experimental results is good. Homotopy Perturbation The method is proved to be a convenient and efficient method to find an approximate or exact analytic solution of nonlinear differential equations