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قاری محمد یعقوب

مولانا محمد یوسف بنوری/قاری محمد یعقوب
سیمینار میں مولانا محمد یوسف صاحب بنوری کی وفات حسرت آیات کی اطلاع ملی اورواپسی میں جناب قاری محمد یعقوب صاحب(کراچی)کے حادثۂ انتقال کاعلم ہوا توسخت صدمہ اورملال ہوا۔ رحمھما اﷲ رحمۃ واسعۃً۔ اکتوبر اور نومبر میں بعض ضروری علمی کاموں میں، میں اس درجہ مصروف رہا کہ برہان کی طرف بالکل توجہ نہیں کرسکا۔یہ نظرات لکھنے کے لیے بھی بڑی مشکل سے وقت نکال سکاہوں۔ آئندہ انشاء اﷲ’’وفیات‘‘کے زیر عنوان مرحوم بزرگوں کا تذکرہ ہوگا۔ [نومبر۱۹۷۷ء]

کارڈز میں کفالہ کی شرعی و فقہی حیثیت اور عصرِ حاضر کے مالیاتی اداروں میں اس کا عملی تطبیق

Cards are the plastic money of current era, and Kafala by means of their warranty is little much we know about. In this article we will discuss the necessity, use and framework of Kafala for the Debit & Credit cards issued by banks and financial institutes, in the light of Qur’an and Sunnah, Ijma-e-Umma and religious researchers.

Boundary Element Methods for Compressible Fluid Flow Problems

The boundary element method is a numerical technique which consists of sub– dividing the boundary of the body into a series of discrete elements, over which the function can vary. This technique offers important advantages over domain type solutions such as finite elements and finite differences. One of the most important features of this method is the much smaller system of equations and the considerable reduction in data required to run a program. Furthermore, the method is well–suited to problems with an infinite domain. Boundary element methods can be formulated using two different approaches called the ‘direct’ and the ‘indirect’ methods. In this thesis, the direct and indirect boundary element methods have been used for the calculation of the compressible fluid flow around arbitrary bodies. The results obtained using boundary element methods have been compared with analytical solutions. These methods have been implemented with the help of computer programming using FORTRAN 77. In chapter (1), statement of the problem, literature survey and brief description of the method of solution are discussed. In chapter (2) the fundamental equations for compressible fluid are given and in chapter (3) mathematical formulation of the equation for inviscid compressible fluid flow is given. In chapter (4) the constitutive equations for the boundary element methods for the interior and exterior domains are derived, and in chapter (5) the various types of boundary elements, the matrix formulation for the8 equation of the direct method. The numerical evaluation of the integrals over an element and the solution of the resultant system of equations are discussed. In chapter (6) the direct and indirect boundary element methods are applied to the three – dimensional potential flow problems and the comparisons of the analytical and computed results are presented. In chapter (7) both the direct and indirect boundary element methods have been used to calculate two dimensional inviscid compressible flow past a symmetric and Joukowski aerofoils. It has been seen that the computed results in all the above mentioned cases are in good agreement with the analytical results. Finally, conclusions and suggestions for future work are given at the end.
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