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بھٹو کیوں زندہ ہے

 

بھٹو کیوں زندہ ہے ؟

یہ محبت کی کہانی نہیں مرتی لیکن

لوگ کردار نبھاتے ہوئے مر جاتے ہیں

 

مشکوٰۃ المصابیح پر شیخ عبدالحق محدث دہلوی کے کام کا جائزہ

"Mishkāt al-Maṣābīḥ" has a sound rank among the Hadith collections. Its importance can be gauged from the fact that it has been described and summarized by several scholars. The works of Sheikh Abdul Haq Muḥaddith Dehlavi over that is a great contribution and have a special place in the context of his Hadith services. He is one of the prominent muhaddithin of the Subcontinent. He was pioneer in teaching and disseminating Hadith knowledge in the subcontinent. Firstly, he described the Mishkāt al-Maṣābīḥ in the Persian language of that time, which gained immense popularity among the people and increased the taste for understanding Hadith. Secondly, He accumulated a treasure trove of mysteries and secrets in Arabic for the use of Researchers. The name of the Persian commentary is Ash‘atul Lam‘āt while the Arabic commentary is called Lam‘āt al-Tanqīh. They are more than one in usefulness, which has created a taste for reading and understanding Hadith among the people and Researchers. In the said article, an introduction and methodological study of the work done by Sheikh Abdul Haq on Mishkāt al-Maṣābīḥ will be presented.

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
Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

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