أساليب الحافظ الزيلعي في نقد متون السنة من خلال نصب الراية

The methods of Al-Hafiz Al-Zaili in criticizing of text of the Sunnah as described in his book Nasbu Al-Raya in analyzing the hadiths of Hidayah. The science of criticism is well known science since the era of the Companions, and critics of the hadith of the honorable companions have played a very important role in the field of narration and carefully criticizing it. And by passage of the era of the Companions and beginning the era of the followers (tabieen), the criticism became more obvious depending on the growing need, especially after spreading of lie, and creation of fake hadith, which led the critics to further research and verification, for scrutiny between the narrations and then differentiation between the right and the weak. The imams and scholars of hadith from the era of the Companions till present continuously inheriting the approach of criticizing the narratives in succession of their predecessors, whether criticizing the narrators or the texts. I have seen that it is worthwhile to stand on the efforts and methods of one of the imams in his criticism of the hadiths and I have chosen the effort of Imam Hafiz al-Zaili through his book " Nasbu Al-Raya in analyzing the hadiths of Hidayah" to learn how he was using the standards traded among the scholars of Hadith for textual criticism of Sunnah. As the those denied the hadiths from orientalists and their followers and those who follow their example simply claim that the scholars of hadith did not criticize the Sunnah in true criticism and even if they have criticized the hadiths, their criticism was only concerning the narratives not the text, now it is clear through this article that the scholars of hadith did not leave the side of the text, but they criticized text as they criticized the attribution of the hadiths. They set solid rules, which remain scholarly proven and accurate forever. We will revolve in this article around the following topics: learning about Al Hafez Zaili and the science of criticism, methods of textual criticism according to Hafiz Zaili, by focusing on: Criticism of the hadiths for violating the explicit meaning of the Qur'an, or for contradicting the Sunnah, or for contradicting the explicit consensus, or for risking and exaggerating the promise or the warning of simple action, or lack thereof in books of hadith These are the most important rules sited by al-Hafiz al-Zaili, which he practiced and criticized the hadiths and distinguished them between the correct and the weak.

Inequalities for Bregman and Burbea-Rao Divergences and Related Results

Mathematical inequalities play an important role in almost all branches of mathe- matics as well as in other areas of science. The basic work ”Inequalities” by Hardy, Littlewood and Polya appeared 1934 and the books ”Inequalities” by Beckenbach and Bellman published in 1961 and ”Analytic inequalities” by Mitronovic published in 1970 made considerable contribution to this field and supplied motivation, ideas, techniques and applications. This theory in recent years has attached the attention of large number of researchers, stimulated new research directions and influenced various aspect of mathematical analysis and applications. Since 1934 an enormous amount of effort has been devoted to the discovery of new types of inequalities and the ap- plication of inequalities in many part of analysis. The usefulness of Mathematical inequalities is felt from the very beginning and is now widely acknowledged as one of the major deriving forces behind the development of modern real analysis. This Ph.D thesis deals with the inequalities for Bregman and Burbea-Rao divergences and some of its related inequalities, namely Jensen’s inequality, majorization inequality, Slater’s inequality and inequalities obtained by Mati ́ and Peˇari ́. c c c The first chapter contains a survey of basic concepts, indications and results from theory of convex functions and theory of inequalities used in subsequent chapters to which we refer as the known facts. In the second chapter we give an improvement of Jensen’s inequality for convex monotone function and various applications for related inequalities and divergences. ˇ In the third chapter we give Sapogov’s extension of Cebyˇev’s inequality and use this extension to prove majorization inequality. We also give mean value theorems for majorization inequality. As application, we present a class of Cauchy’s means and prove logarithmic convexity for differences of power means. In the fourth chapter we generalize some results of Mati ́ and Peˇari ́. We use a c c c log-convexity criterion and establish improvements and reverses of Slater’s and related inequalities. In the fifth chapter we give Bregman and Burbea-Rao divergences for double in- tegrals and matrices. We derive mean-value theorems for the divergences induced by C 2 -functions. As application, we present certain Cauchy type means. We prove pos- itive semi-definiteness of the matrices generated by these divergences which implies exponential convexity and log-convexity of the divergences. Also show the mono- tonicity of the corresponding means of Cauchy type. At the end we consider integral power means. In the sixth chapter we give several results for functions of two variables and majorized matrices by using continuous convex functions and Green function. We prove mean value theorems and give generalized Cauchy means. We give applications of those generalized means and show that they are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from the majorization inequalities for double integrals and majorized matrices which implies exponential convexity and log-convexity of these differences.