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13. Ar-Ra’d/The Thunder

13. Ar-Ra’d/The Thunder

I/We begin by the Blessed Name of Allah

The Immensely Merciful to all, The Infinitely Compassionate to everyone.

13:01
Alif. Lam. Mim. Ra’.
These are the Messages of the Divine Book – The Qur’an.
What is revealed on to you – O The Prophet - from your Rabb - The Lord is the truth.
Yet most people do not believe it to be so.

13:02
It is Allah WHO raised up the celestial realm without any visible support as you can see.
Then, HE established HIMSELF upon the Throne of Almightiness.
And made the sun and the moon subservient to HIS laws, each running its predetermined course until the Last Hour.
Thus, HE directs all matters, distinctly explaining every sign of HIS Almightiness so that you may be convinced of the meeting with your Rabb - The Lord.

13:03
And it is HE WHO spread out the earth, and placed firm mountains upon it, and running
rivers,
and made two of a pair of every fruit/plant-vegetation,
and HE covers up the daytime with the nighttime.
Indeed, these are the wonders of HIS Unique Creative Power for a people who reflect.

13:04
And on the earth, there are tracts of land adjoining one another, and yet different from one another, and
vineyards, and
sown fields, and
date-palms,
growing in clusters from a shared root or not of a shared root,
yet they are all irrigated by the same one water stream.
And yet WE favor some of its fruit in flavor and taste over others.
Surely in that are wonders of HIS Unique Creative Power for a people of understanding.

13:05
And if you...

مولانا غلام اللہ خان کی تفسیر جواہر القرآن: منہج اور خصوصیات

Maulana Ghulamullah khan is considered one of the best commentators of the Quran from  Punjab. Ghulamullah Khan was born in 1905 in Chaj Darya, Attock district of Punjab. He got his Quranic education from Maulana Rashid Ahmad Gangohi, who was a disciple of Maulana Hussain, a well-known and a leading commentator of the Quran. He studied hadith  from Hussain Ahmad Madni, Maulana Shabir Ahmad Usmani and Anwar Shah Kashmeri. This tafseer consists of fifteen hundred pages. It has a long preface and covred up in three volumes over all. Maulana Hussain Ali named him a true successor of the Quranic studies and acknowledged that he had done this duty well. Among his works, TAFSEER JAWAHIR -UL- QURAN, has its own uniqueness and usefulness. Millions of copies have been published of this Tafsier. This tafseer is a compilation of rabat bain surulayat (connection between sura and ayat) of  Maulana Hussain Ali by Ghulamullah khan and has been revised by Maulana Said Ahmad Hussain Sajad Bukhari.  He is termed as Shaikh ul Quran and was called so by Maulana Hussain Ali.I have hinted at different sources for my article so that readers may expand their knowledge about the Quran and Tafseer. This article is about JAWAHIR -UL- QURAN and it will throw light on its features.

Applications of Fractional Derivatives in Adaptive Signal Processing Systems

Adaptive algorithms are mostly optimized using integer order derivatives for error minimization. The Least Mean Squares (LMS) and Recursive Least Squares (RLS) adaptive filters are among the most commonly employed schemes. The LMS algo rithm is simple to implement, has robust tracking performance in nonstationary environments and is less sensitive to floating point precision effects. However, it has the issue of slow convergence especially when the number of weights is large. The RLS achieves faster convergence but is computationally expensive, and prob lematic in nonstationary environments. This study introduces fractional calculus techniques in stochastic gradient algo rithms. In addition to first order derivative, Fractional Order (FO) derivatives are proposed in the optimization of gradient algorithms. Four configurations have been considered based on whether the fractional derivative is applied to the in stantaneous present or posterior error. For evaluation of the FO algorithms, three applications have been considered, that is, (a) adaptive equalization of multi path channels (b) Active Noise Control Systems (ANCS) and (c) tracking of time varying Rayleigh fading sequences. In equalization, both supervised and unsu pervised algorithms are considered. For the supervised case, FO variants of LMS and Normalized LMS (NLMS) are applied in both feed-forward and decision feed back configurations. In the unsupervised case, FO variants of Gordad and con stant modulus algorithms are developed. In ANCS, FO variants of the NLMS, Filtered-x (input) LMS, Modified FxLMS and Filtered-error LMS algorithms are developed. The noises are modelled as binary, Gaussian and impulsive sources characterized by fractional lower order moments. In tracking, the behavior of FO variants is evaluated for nonstationary environments. A Rayleigh channel has also been considered having Doppler frequency shifts of 0.8KHz to 3KHz. The frac tional algorithms are compared with the standard NLMS, RLS and Extended-RLS schemes. The main performance metrics include (1) mean squared error (2) mean squared deviation (3) relative modelling error (4) model accuracy using both frequency and time domain analysis and (5) symbol error rate. The former three performance metrics help compare the convergence speed and steady state performance; the latter two are application specific. Simulation results are shown for different step sizes and fractional orders. It is seen that the fractional variants show superior performance in all the three applications and hold great promise for future use.
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