پہلا ستارہ
آفتاب نواب
کسی بھی فنکار کے فنی سفر کا پہلا قدم اظہار کے میڈیم کی تلاش ہے۔ اس مرحلے کا طے ہونا جز ثابت ذہنی سے تفکر کے ممکن نہیں۔ ڈاکٹر فہد ملک اس مرحلے پر مبارک باد کے مستحق ہیںکہ وہ اپنے اظہار کا ذریعہ تلاش کرنے میں کامیاب ہو چکے ہیں۔ کسی بھی زبان میں شعر اس وقت تخلیق ہوتا ہے جب وہ اتنی طاقت ور ہو چکی ہو کہ اس کے پاس رمز و ایما کے تمام وسائل آچکے ہوں اور آدمی تب شعر کہہ سکتا ہے جب اس کے اندر رمز و ایما سما سکتے ہوں، پک سکتے ہوں اور لفظوں میں ڈھل سکتے ہوں۔ فہد ملک رمز و ایما کی طرف سفر پر نکلے۔ اس کتاب میں آپ کی ملاقات جس فہد ملک سے ہو گی وہ انسان کو سہل نہیں جانتا۔ محبت کو سچے جذبے سے تعبیر کرتا ہے۔ اخلاص و رواداری ،حریت، سماجی جدلیات اور انسان کی باطنی کیفیات پر غور کرتا ہے۔ فنکار اپنی کائنات خود بناتا ہے اور فہد نے اپنے کائنات شعر میں بنانے کا فیصلہ کیا ہے جس کا پہلا ستارہ یہ کتاب ہے۔
اس کتاب میں کرافٹ کی طرف متوجہ ہونے ، فکر کو خاص سطح تک لے جانے کی کاوش کے نقوش ملتے ہیں۔ اس امر کو مدِ نظر رکھتے ہوئے یہ کہا جاسکتا ہے کہ فہد ملک آئندہ وقت کا دل پذیر صاحبِ سخن ہے۔
Human Milk banks have been established in many parts of the world. The main purpose of these banks is to save the babies’ lives and to ensure that the newborn babies’ rights to breast milk are fulfilled. Especially for the infants whose Mothers could not feed them due to illness, lack of milk or lack of time. The problem is that milk bank practices in the Western countries contradict with the Islamic law whereby it may result in the possibility of overlapping of the progeny (nasab) and selling the organ of human, etc. The Muslim countries have been not participating in these milk sharing activities because of these religious issues. However, due to a critical need of breast milk in hospitals, this article addresses these issues and the different opinions of Islamic scholars and suggests ways to formulate a proper model of milk bank that is compatible with the Islamic law and to avoid further problems of nasab. This study has two main objectives: firstly, to introduce Milk Bank, causes of its’ existence, method of collection and storage the milk, the benefits of breastfeeding and the unpleasant effects of Milk Banks. Secondly, to review some authoritative legal scholars’ opinions on the issue of milk bank and to recommend a proposal on how to develop a milk bank in accordance with the Islamic law. The study is expected to be able to recognize the issues of Milk Bank, to make the people become aware of its side effects and religious problem.
Black-Scholes equation is a revolutionary concept in the modern financial theory. Financial instruments such as stocks, commodities and derivatives can be evaluated using this model. Option valuation, a part of derivative products, is extremely important to trade in the stocks. The numerical solutions of Black-Scholes equations are used to simulate these options and are addressed in this dissertation. In particular, the discontinuities in the domain are addressed. The discontinuities in options create oscillations near exercise price in the solution. A grid adaptive finite difference technique is developed to evaluate financial options using Black-Scholes equation. The grid is refined near the exercise price to resolve discontinuities in the option evaluation and a coarse grid is generated otherwise. To cope with these uneven space steps, an innovative numerical finite difference schemes are developed named as adaptive explicit, adaptive fully implicit and adaptive Crank Nicolson techniques. These techniques are used to cure oscillations produced by discontinuities in the digital and butterfly options. These techniques are also used to simulate multi-asset digital and butterfly options. The numerical experiments show that the adaptive finite difference method is much more efficient than the method with uniform spacing. The technique reduces the points drastically which in turn decreases the computational cost and makes the algorithms highly efficient