In this thesis a series solution to linear or nonlinear problems has been considered which are arising in the field of applied mathematics. In the first chapter of this dissertation a brief history of our problems and methods is given. In the second chapter, some basic definitions and concepts are given which have been used in our work. In the third chapter, we examined the motion of an incompressible unidirectional magneto-hydrodynamics (MHD) thin film flow of a third grade fluid over an oscillating inclined belt embedded in a porous medium. Moreover, heat transfer analysis has also been discussed in the present work. We modeled the proposed physical problem in terms of PDEs. The equations obtained through PDEs were then solved by two different methods i.e., Homotopy Perturbation Method (HPM) and Optimal Homotopy Asymptotic Method (OHAM). Comparisons of these two methods for different time level were analyzed graphically. Comparison of the results shows that both the methods are in full agreement. The effects of various non-dimensional parameters have also been linerated graphically. In the fourth chapter of this thesis the unsteady thin film flow of a fourth grade fluid over a moving and oscillating vertical belt is given. The proposed problem was modeled in terms of PDEs together with physical boundary conditions. Two different cases were discussed. The first one is the lift case, while the second one is the drainage case. Two different techniques, namely the Adomian Decomposition Method (ADM) and the Optimal Homotopy Asymptotic Method (OHAM) were used for finding the analytical solutions of the above mentioned cases. These solutions were compared and found in excellent agreement. For the physical analysis of the problem, graphical results were provided and discussed for various embedded flow parameters. In the fifth chapter, the Optimal Homotopy Asymtotic Method (OHAM) [45-46] was used for approximate solution of singularly perturbed two-point boundary value problems. We concluded that the proposed method gives efficient results. We solved some numerical examples, that include initial and boundary value problems. In the sixth chapter, the solution of higher order boundary value problems by our proposed method “Modified Optimal Homotopy Perturbation Method” (MOHPM) has been given. A homotopy with an embedding parameter and Daftardar-Jafari polynomials were used. To control the convergence of solution, some auxiliary functions which depended upon variables and some constants were used. The proposed method was simple, rapid, effective and accurate. The accuracy has been proved by comparing our results with the solutions of optimal homotopy perturbation method (OHPM), optimal homotopy asymptotic method (OHAM), variational iterative method (VIM), variational iteration method using He’s polynomials (VIMHP), homotopy perturbation method (HPM) and Adomain decomposition method (ADM).
مولانا خلیل الرحمن افسوس کہ مولانا خلیل الرحمن صاحب سابق ناظم ندوۃ العلماء نے ۴؍ فروری ۱۹۳۶ء کی شب کو اپنے وطن سہارنپور میں اس دار فانی کو الوداع کہا، مولانائے مرحوم مولانا احمد علی صاحب محدث سہارنپوری (محشی بخاری و تلمیذ مولانا شاہ محمد اسحق دہلوی) کے چشم و چراغ تھے، مولانا احمد علی مرحوم پچھلی صدی کے آخری دور میں ہندوستان کے ان باکمالوں میں تھے جن کی مسندِ درس سے علم دین کی شمع روشن تھی اور تشنگانِ علم اس سرچشمہ سے سیراب ہونے کے لئے سینکڑوں میل کی منزلیں پاپیادہ طے کرکے وہاں تک پہنچتے تھے، مولانا خلیل الرحمن نے علم کے اسی گہوارہ میں آنکھ کھولی اور اپنے والد ماجد کے دامنِ فیض میں تعلیم و تربیت پاکر فارغ التحصیل ہوئے۔ مرحوم ندوۃ العلماء کے دور اول کے محسنین میں سے تھے، مولانا محمد علی مونگیریؒ ناظم ندوۃ العلماء کی معیت میں اس ملی و علمی خدمت میں شریک ہوئے اور آخر تک رہے، مرحوم خوش خلق، متواضع، رحمدل، اور عزیزوں سے دلی محبت فرمانے والے تھے، اتفاق وقت کہ دارالعلوم ندوۃ العلماء کی ہنگامہ خیز اسٹرائک کا واقعہ انہی کے دور نظامت میں پیش آیا تھا، اس نازک وقت اور ناسازگار حالات میں بھی مولانائے مرحوم دارالعلوم کے طلبہ کے ساتھ جس عدیم المثال شفقت و محبت سے پیش آئے، اسکی یاد اس عہد کے فارغ التحصیل علمائے ندوہ کے دلوں میں ہمیشہ کے لئے باقی رہ گئی، اور مدت گزرنے کے بعد انہیں جب کبھی مرحوم سے شرف ملاقات کا موقع حاصل ہوا انھوں نے ان کے دل کو شفقت و محبت سے لبریز پایا ندوۃ العلماء کی خدمات انجام دینے کے علاوہ مرحوم کی زندگی کا ایک اہم کارنامہ صحیح بخاری کے اس نادر نسخہ کی اشاعت ہے، جس پر ان کے والد ماجد کے حواشی ثبت ہیں، یہ...
Islam is the religion of peace and mercy for all creatures. But, now-adays, some extremist has spread misconception about the Islam, that as, it is the religion of sword for terror. But, the actual fact is that, Islam is the religion of peace and it condemns extremism and violence. Islam promotes the peace, calm, harmony, any tranquility in society. Islam is a peaceful religion, its best examples, we can see, in the practical life of Holy Prophet (SAW). He was the Messenger of Allah (SWT) to convey the message of honesty, piousness, peace, mercy, integrity, and love. He had never done any activity which indicate act of terrorizing, misconduct, racism and violation against humanity. Even though, he showed the mercy on animals, insects and plants. The world knows him, as a 'Rahmatul-lil-Aālamyn'(Mercy into the world). From the life of Holy Prophet (SAW), it is concluded that Islam is the religion of peace and humanity. It did not spread by the forced of sword, rather, it spread by its golden quality.
Strategic stability remains a contested concept and has been described by various scholars differently, based on their understanding and reading of particular strategic environment. Most explanations, however, stem from the ―Cold War‖ experience but contain instructive lessons for a region like ―South Asia‖ that has some similarities as well as significant differences. Introduction of nuclear weapons in 1998 that was followed by two successive military crises between the two nuclear armed neighbors in 1999 and 2001-02, further reinforced commonly held precepts that nuclear weapons help deter war between two nuclear armed states. Some, however, disagree with this conclusion, citing the increased number of crises in the post-1998 period that continues to threaten strategic stability in the region. This study therefore aims to discuss the concept of strategic stability from a Pakistani perspective in the post-1998 security environment that continues to be shaped by various external and internal factors besides evolving military capabilities and doctrines in the region. Besides, providing historical narrative and underlying causes of perpetual animosity between the two South Asian neighbors that had led to number of wars in the pre-1998 era, the study aims to highlight Pakistan‘s political, diplomatic, and economic challenges that continue to influence national decision-making process in the country. So far, Pakistan has managed to balance its shortcomings by developing potent conventional and nuclear deterrence to deal with an existential threat emanating from its Eastern neighbor; nevertheless, the growing IndioUS strategic partnership that is aimed to help build India as a regional hegemon could adversely affect strategic stability in the region. Based on these factors this study would aim to offer recommendations that could address Pakistan‘s national security challenges besides providing a path towards long-term and enduring stability in the region.