حقیقت کا اقرار
استفہام کا ایک بلیغ موقع استعمال وہ بھی ہے جب مخاطب سے کسی ایسی بات کا اقرار کرانا ہو جس کی نوعیت ہو تو ایک بدیہی حقیقت کی لیکن مخاطب اس کو تسلیم کرنے کے باوجود عملاً اس سے منحرف ہو۔ جیسے آیت ذیل :
" هَلْ أَتَى عَلَى الْإِنْسَانِ حِينٌ مِنَ الدَّهْرِ لَمْ يَكُنْ شَيْئًا مَذْكُورًا" “[ ]
"انسان پر کبھی ایسا وقت آیاہے کہ نہیں جب وہ کوئی قابل چیز نہیں تھا" کی تفسیر میں مولانا امین اصلاحی کانقطہ نظر ہے یہ محض ایک سادہ خبریہ جملہ نہیں ہے بلکہ اس کے اندر بہت سے معانی مضمر ہیں۔ مثلاً:
۱۔ ایک عظیم حق کی یاددہانی ہے جو اس پر عائد ہوتا ہے اور جس سے اس کے لیے انکار کی گنجائش نہیں ہے لیکن اس کا رویہ اس کے منافی ہے۔
۲۔اس میں ملامت ‘ غصہ ‘ رنج اور اظہار حسرت کے بھی گوناگوں پہلو ہیں۔
۳۔اس میں نہایت مبنی برحقیقت گلہ و شکوہ بھی ہے اور نہایت موثر اپیل بھی۔
۴۔ استفہامیہ اسلوب نے اس حسن فکر کو بیدار کرنا چاہا ہے کہ انسان کی نظروں سے خدا اوجھل ہے تو اس کا اپنا وجود تو اوجھل نہیں ہے ‘ وہ خود اپنے اندر خدا کی قدرت و حکمت اور اس کے عدل و رحمت کی نشانیاں دیکھ سکتا ہے۔[ ]
" قُلْ لِمَنْ مَا فِي السَّمَاوَاتِ وَالْأَرْضِ قُلْ لِلَّهِ" “[ ]
"ان سے پوچھوکہ آسمانوں اور زمین میں جو کچھ ہے وہ کس کی ملکیت ہے(پھر اگر وہ جواب نہ دیں توخود ہی )کہہ دو کہ اللہ ہی کی ملکیت ہے"۔
مولانا امین احسن اصلاحی کی تحقیق کےمطابق قرآن مجید میں جہاں جہاں سوال کر کے مخاطب کے جواب کا انتظار کیے بغیر خود اس کا جواب دیا ہے۔ غور کرنے سے معلوم ہوتا ہے کہ...
An FM Broadcast Trainer was developed to expose the students to the basic equipment needed in radio broadcasting. The cost of Portable FM Broadcast Trainer is much lower than the cost of the traditional commercial equipment because of the materials used. The FM Broadcast Trainer is laboratory equipment that can be used by schools offering academic programs in Industrial Courses specifically Electronics Communication courses. At present there is no portable FM broadcast station available in the local market. Some schools are reluctant to by new FM station equipment since these are quite costly. To resolve this problem, the researchers deemed it necessary to design and develop a portable FM Broadcast Trainer that is simple and affordable to fulfil the basic curricular requirements for offering courses in Electronics Communication Technicians. This is a requirement for our graduates to qualify to take the Radio Telephone Operator examination given by the National Telecommunication Commission the telecommunication body in the Philippines counterpart of Federal Communication Commission in the US. Aside from this, the station will be a venue for Mass Communications students and a vehicle for channelling important announcement from the School.
In this dissertation, meshfree (meshless) methods using meshless shape functions are proposed for the numerical solutions of partial differential equations (PDEs). These PDEs have either integer or fractional order time derivatives. Weighted θ-scheme (0≤θ ≤1) is used for time discretization of integer case, whereas, for fractional case, the same discretization scheme is combined with a simple quadrature formula. For space (spatial) discretization we used meshless shape functions owing Kronecker delta function property. These shape functions are obtained viapointinterpolationapproachandradialbasisfunctions(RBFs). Finallywiththehelpofcollocationmethodthe given PDE reduces to system of algebraic equations, which are then solved via LU decomposition in iterations. For the proposed numerical scheme, stability analysis is carried out theoretically and computational examples are provided to support the analysis. The proposed scheme has been tested via application to several concrete and benchmark problems of engineering interest. ApproximationqualityandaccuracyofcomputedsolutionsaremeasuredusingL∞, L2 andLrms discrete errornorms. Efficiencyandorderofapproximationoftheproposedschemeinspaceandtimeareanalyzedthrough variation of number of nodal points N and time step-size δt. The documented results, in the form of tables and figures, reveal very good agreement to true solutions as well high accuracy to earlier proposed technique available in the literature. In RBFs, the presence of shape (support) parameter c∗ plays a crucial role. Accuracy of the RBFs based scheme can be improved via proper selection of this parameter. For this purpose, an automatic optimal shape parameter selection algorithm is proposed. To check effectiveness and automatic (adaptive) nature of this algorithm in RBFs approximation method, time fractional Black-Scholes models have been solved. It has been noted that the proposed algorithm worked well and gives excellent accurate solutions for various fractional order time derivatives. The RBFs approximation (Kansa) method results in dense ill-conditioned matrix. For the treatment of this issue weproposeahybridRBFs(HRBFs)approximationmethod. Byextendingthisidea, anadaptive(automatic)algorithm is proposed for optimal parameters selection in HRBFs. For validation, again time fractional Black-Scholes models are reconsidered. Simulations revealed acceptable accurate solutions in hybrid RBFs method too. Along with that significant reduction in condition number of the resultant matrix is observed up to several manifold. Hence, HRBFs method can be seen as an alternative remedy for curing ill-conditioning in usual RBFs method. Computer simulations have been carried out via MATLAB R2013a on a personal laptop with configuration, Processor: Intel(R) Core(TM) i5-5200U CPU @ 2.20GHz 2.20GHz, RAM: 4.00 GB, System type: 64-bit Operating System, x64-based processor.