اعجاز القرآن کا تحقیقی و تجزیاتی مطالعہ Research and analytical review of I‘jāz-al-Qurān

The Holy Qurān which was revealed to the last Prophet Muhammadﷺ, Just as you are a collection of perfections, so is the word revealed to you a collection of perfections. One of the most important perfections of the Holy Qurān is the miracle of the Holy Qurān. The unique and unique way of reciting the Qurān is called I‘jāz-al-Qurān in Islamic terminology. The Holy Qurān challenged the opponents and deniers of the Holy Qurān to explain its uniqueness.O Beloved! Say: If man and jinn come together and strive to be like the Qurān, they will not be able to make the likeness of it, even if they become helpers of one another. The Qurān is a book of miracles, and miracles are those that are beyond human power and beyond the reach of everyone, power and courage, especially a miracle that lasts for a couple of years or a limited time. Not for the sake of it, but for the challenge of the creation which will come after its coming, and which will make the way of guidance easy for those who ponder within themselves. In this article, I will try to explain the different aspects of I‘jāz-al-Qurān and embellish it with arguments.

Nonlinear Structures in Nonuniform Magnetoplasma With Non-Maxwellian Distributions

One and two dimensional nonlinear dissipative structures are studied with non-Maxwellian electrons in nonuniform magnetized plasmas. In 1D (one dimension), nonlinear drift-wave is derived by employing the drift approximation whereas, in 2D (two dimensions) under the weak nonlinearity limit, coupled drift-ion acoustic wave is derived. In the linear regime, it is observed that the nonthermal electron population modi es the frequency of coupled drift ion acoustic wave. Formation of shock structures is observed with nonthermal Cairns and kappa distributed electrons and it is found that the presence of these distributions signi cantly modi es these nonlinear structures. Velocity of nonlinear structures and diamagnetic drift velocity are found to play a signi cant role in the formation of these structures. Existence regimes for one and two dimensional drift shock waves are found and it is observed that kappa distributed electrons for 1D case can give rise to compressive as well as rarefactive shock structures whereas, Cairns distributed electrons are found to behave in a di erent way for the formation of these drift shock structures. Coupling of drift waves and ion-acoustic waves in linear and nonlinear regime are studied in a nonuniform magnetized plasma comprising of two ion species (i.e. Oxygen and Hydrogen ions) in the presence of nonthermal distribution of electrons. Dispersion characteristics of coupled drift-ion acoustic waves are found to be modi ed for kappa and Cairns distributed nonthermal electrons population as well as for di erent ratios of ion number densities. Drift solitary waves are studied by deriving the one dimensional KdV and two dimensional KP like equations for pure drift and coupled drift-ion acoustic waves respectively. These solitary structures are observed to be modi ed in the presence of di erent ratios of ion number densities as well as nonthermal distribution of electrons. Existence regimes for drift solitary waves are determined with the help of the velocity of the nonlinear structure and diamagnetic drift velocity. Further, using non-Maxwellian Cairns, kappa and q-nonextensive electron distributions along-with sheared ion ow, coupling of drift vortex modes and ion acoustic modes are investigated in a nonuniform magnetized plasma comprising of hot ions. Nonlinear vortex structures are observed in the presence of non-Maxwellian electrons population iii and it is found that there is a shift in the position of these structures because of nonthermal populated electrons. The importance of these particles in the Earth''s auroral zone is pointed out and comparison with their Maxwellian counterpart is also made. Shear ow in dust dynamics driven waves in combination with the dust-neutral drag is studied in a plasma containing ions, electrons and dust. Non-thermal population of ions is considered which has been observed by many satellite missions. It is found that the dissipative instability produced by dust sheared ow and dust-neutral drag gets modi ed because of these nonthermal ions. It is also observed that the dissipative instability enhances for the Cairns distribution whereas, the kappa distribution arrests the growth of this instability. In the nonlinear regime, formation of vortices in the system is studied. It is found that the nonthermal population of ions signi cantly alter these structures by comparison with their Maxwellian counterpart.