امنا عائشة ملكة العفاف رضي االله عنها

This research aims to explore various features of Syyidah some highlights paper This. Personage noble s'(ر الله عا) ishah‘A’ distinguished aspects of her biographical account, her extraordinary intelligence, eminent rank amongst other wives of the Prophet Muḥammad (r), excellence over women of the world and being mentioned in the Qur’ān for her praiseworthy character. The scholarly areas, in which, she outshone others in Islamic intellectual heritage, include the Quranic exegesis, Ḥadīth narratives, jurisprudence, scholastic reasoning: analysis of jurisprudential methodology and principles of deduction of rulings and opinions. She adopted multifarious modes in this regards including explicit, direct, generalized, inductive and analogous approaches in the Islamic intellectual scholarship. By acknowledged was (ر الله عا) ishah‘A of grandeur The the companions of the Prophet, her scholarly point of view in conciliation of the problems of the Qur'ān and Ḥadīth made her stand out amongst all. She was a keen researcher, peaceful preacher and the greatest scholar of Islām of all times. Her knowledge and command over religious and social matters made her one of the most reliable experts of the Qur'ān, Ḥadīth and Fiqh. Such was her stature as the archangel Jibrā’īl presented his salutation to her.

Limiting Reiteration for Real Interpolation and Optimal Sobolev Embeddings

Firstly, sharp reiteration theorems for the K−interpolation method in limiting cases are proved using two-sided estimates of the K−functional. As an application, sharp mapping properties of the Riesz potential are derived in a limiting case. Secondly, we prove optimal embeddings of the homogeneous Sobolev spaces built-up over function spaces in R n with K−monotone and rearrangement invariant norm into another rearrangement invariant function spaces. The investigation is based on pointwise and integral estimates of the rearrangement or the oscillation of the rearrangement of f in terms of the rearrangement of the derivatives of f .