الاصابہ فی تمییز الصحابہ میں نماز و روزے سے متعلقہ روایاتِ اَحکام کا تحقیقی جائزہ Research Review of the Traditions of Rulings on Prayer and Fasting in Al-Aṣābah Fī Tamīz al-Ṣaḥābah

The book “Al-Aṣābah Fī Tamīz al-Ṣaḥābah” is a famous book of Ibn Ḥajar ‘Asqalānī on the life and contribution of the Companions. This book is quoted as a reference to decide the status of companions. It would not be wrong to call it the encyclopedia of the companions of the Holy Prophetﷺ. Apart from its status as a reference book regarding the companions this book encompasses the Seerah of Holy Prophet in a detailed and well composed manner. The distinction of the book is not hidden from the experts of science and research. In the book and other similar books, the life of the companions was discussed and the biography of the Prophet ﷺwas also described, but another aspect that remained unexplored in these books is the virtues and commandments mentioned in it. There are also narrations about virtues. In this paper the researcher has evaluated the Hadiths related to prayer and fasting that are narrated in Al-Aṣābah Fī Tamīz al-Ṣaḥābah. The evaluation comprises of authenticity of narrators and text, narrators’ mutual association or disassociation and the final decree about the authenticity of a hadith in the light of all available evidences.

Application of Evolutionary Pplications Computing Techniques to Non-Linear Ing Systems

This dissertation presents an application of heuristic computational intelligence for the solution of non-linear systems in engineering. The design scheme is comprised of mathematical model based on feed-forward artificial neural network (ANN). The linear combination of these networks defines the unsupervised error for the system. The most suitable weights to minimize the error are obtained by training the networks employing stochastic solvers. These techniques are based on nature inspired heuristics including Pattern Search (PS), Simulated Annealing (SA), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithms. Rapid local convergent algorithms such as Interior Point (IP) and Active Set (AS) methods are hybridized with these global search techniques. To validate the scheme, a number of linear and non-linear initial and boundary value problems have been solved. The design methodology is also applied to a number of problems having special applications in engineering including, singular systems based on non-linear Lane Emden Fowler equation, non-linear van der Pol oscillator with stiff and non-stiff conditions and systems with high nonlinearity governed by Painlevé transcendent I. In addition to that, the scheme also provides an alternate solution for biomedical application like model of heart for low, high and normal blood pressure. It is found that the proposed results are in good agreement with available exact solution and numerical solvers like Adomian decomposition method, Homotopy Perturbation method, Homotopy analysis method and Optimal Homotopy asymptotic method, ODE15i and Runge Kutta method. The comparative studies of stochastic solvers are carried out under a stringent criterion of accuracy, effectiveness, reliability and robustness of the results based on Monte Carlo simulation and its analysis. The solvers based on SA, PS, GA, PSO, GA and PSO hybrid with IP or AS algorithms are used for optimization of neural network. It is found that the GA-IP, GA-AS, PSO-IP and PSO-AS algorithms are the best stochastic optimizers. The other perk up of the scheme have in its simplicity of the concept, ease in use, efficiency and unlike other numerical techniques, it provides the solution on continuous inputs with finite interval instead of predefine discrete grid of inputs.