الأبعاد النفسية والتربوية في نظر سيدنا عمر بن الخطاب تجاه القدس

When looking at the history of every human civilization, one may find some people or places that go down in history, and their biography does not disappear until God inherits the land and those on it. One of these places is the city of Jerusalem, a city where no two differ on its importance. A city that is home for sanctuaries, history, and monuments and every inch speaks of its greatness. Especially in the history of Islam, which linked it wonderfully to the Qibla of Muslims (the Sacred Mosque) after it was the first Qibla in the history of Islam. This high standing link was perpetuated by the Holy Qur’an in Surat Al-Isra and in many other places. This research has shown its importance to Muslims, the reason Muslims love it and their dedication to defending every single grain of its sand, and how did the esteemed Companions view it? This research spoke about some of the aspects that are related to the personality of our master Omar bin Al-Khattab, may God be pleased with him, (which are the psychological and educational aspects) while looking at the importance of Jerusalem to him, may God be pleased with him, which existed since pre-Islamic time and how it extended to the time of Islam and has emerged during his caliphate, may God be pleased with him.

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.