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ریاض الدین احمد

ریاض الدین احمد
علمی اور تعلیمی حلقوں میں جناب ریاض احمد صاحب کی وفات سے جو خلا ہوا ہے اس قحط الرجاں میں اس کا پرُ ہونا مشکل ہے۔ ان کا اصل وطن غازی پور تھا۔ لیکن وہ الٰہ آباد میں متوطن ہوگئے تھے۔ انہوں نے مجیدیہ اسلامیہ انٹر کالج کے نیک نام اور کامیاب پرنسپل کی حیثیت سے بڑی شہرت و عزت حاصل کی وہ طلبہ کی ذہنی و دماغی اور علمی تربیت بڑی دلسوزی سے کرتے تھے، ان کے زمانے میں کالج کا معیار تعلیم بہت بلند تھا، ان سے فیض حاصل کرنے والے طلبہ کی تعداد بے شمار ہے۔
ریاض الدین احمد صاحب کا خاص مشغلہ درس و تدریس تھا لیکن انہیں علم سے شغف اور تحریر و تصنیف کا اچھا ذوق تھا، طلبہ کی درسیات کے لیے متعدد کتابیں لکھیں جو مقبول ہوئیں، سائنس ان کا خاص موضوع تھا، اس پر جو کتابیں لکھیں وہ مدارس کے طلبہ کے لئے خاص طور پر مفید ہیں، قرآن مجید کے درس و تعلیم کا اچھا منصوبہ بنایا تھا۔ ان میں بڑی دینی و ملی غیرت تھی، مسلمان بچوں کو اپنے عقیدہ و مذہب پر استوار اور ملی شناخت باقی رکھنے کے لیے انہوں نے ایمانی پرائمر وغیرہ کے نام سے کئی مفید کتابیں لکھیں۔
قدرت نے انہیں درد مند دل اور بے چین طبیعت عطا کی تھی، وہ قوم و ملت کی فلاح کے ہر کام میں پیش پیش اور مسلمانوں کی ترقی و سر بلندی کے لیے برابر فکرمند رہتے مجلس مشاورت اور دینی تعلیمی کونسل سے شروع ہی سے وابستہ رہے، دینی تعلیمی کونسل کے جلسوں اور کانفرنسوں میں دلچسپی سے شریک ہوتے تھے، ایک دفعہ اس کی ایک بڑی کانفرنس اعظم گڑھ میں ان کی صدارت میں ہوئی، ان کا خطبہ صدارت اور قاضی محمد عدیل عباسی کی اہم تقریر کو...

اسلامی ریاست میں سیاسی انتظامیہ کا تصور احتساب اسلامی تعلیمات کی روشنی میں

This research presents an overview of the principle of accountability of the executive in an Islamic state. The existence and survival of any state is not sustainable without process of accountability as per the law of the land and the provision of the constitution. The elite class was exempted from any sort of accountability and treated above the law in pre-Islamic period whereas man in the street was dealt with strict compliance of rules and regulations. This paper has provided strong evidence from the perspective of historical research that the executive in the Islamic state has not been exempted from the process of transparent of accountability. Moreover, this article also builds up strong argument in light of Quran and Sunnah as well as line of action adopted by orthodox caliphs. It also highlights various incidents of accountability and legal precedence that occurred during Khilafat e Rashda and post era as well.

Opial, Hardy and Related Inequalities Involving Kernels

The theory of inequalities has developed rapidly in last few decades. It now occupies a central position in analysis and will no doubt, continue to play an essential role in mathematics as a whole. It certainly reflected in the vast literature that exists on the subject. Inequalities are useful tools to obtain optimal results in different areas of mathematics. In particular, inequalities are found to be versatile while deciding about extrema of various functions. The theory of inequalities is in a process of unbroken onward development and have also become a very useful and commanding instrument for studying a wide range of problems in different fields of mathematics. Furthermore, the importance of fractional calculus in mathematical inequalities is enormous. Opial, Hardy and related inequalities are very famous and play significant part in mathematical inequalities. Many mathematicians gave generalizations, improvements and applications of the said inequalities and they used fractional integral and derivative operators to derive new integral inequalities. The present study has considered integral operators with non-negative kernel on measure spaces with positive σ-finite measure. This research studies the enhancement of Opial, Hardy and related inequalities for global fractional integral and derivative operators with respect to the convex, monotone convex and superquadratic functions. Different weights have been used to obtain fresh consequences of the said inequalities. The thesis is planned in the subsequent mode: The first chapter includes the essential concepts and notions from the theory of convex functions, superquadratic functions, fractional calculus and the theory of inequalities. Some constructive lemmas related to fractional integrals and derivatives are incorporated which have been frequently use in next chapters to establish results. The second chapter comprises of two sections. First section deals with some Opialtype inequalities for two functions with general kernels related to a particular class of functions U(f, k), which admits the representation: |g(t)| = | xZ a k(x, t) f(t) dt| ≤ xZ a k(x, t) |f(t)| dt, where f is a continuous function and k is an arbitrary non-negative kernel such that f(t) > 0 implies g(x) > 0 for every x ∈ [a, b]. We also assume that all integrals under consideration exist and that they are finite. At the end of this part, we provide the discrete description of the said inequalities. In the second section, we include the multiple Opial-type inequalities for general kernels by considering the monotonicity and boundedness of the weight functions. In continuation of our general results, we provide their applications for Widder’s derivative and linear differential operators. Chapter three consists of three sections. In first section, we present Hardy-type inequalities and their refinements for fractional integral and derivative operators using convex and increasing functions under certain conditions. The second section restrains the applications of refined Hardy-type inequalities for Hilfer fractional derivative and the generalized fractional integral operator involving generalized Mittag-Leffler function in its kernel via convex and monotone convex functions. In the third section, we offer the applications of refined Hardy-type inequalities for linear differential operator, Widder’s derivative and generalized fractional integral operator involving Hypergeometric function in its kernel.
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