Conditions and Qualification for Being a Judge in the Light of the Islamic Law

‘Adl and Qisṭ is indeed a manifestation of God’s mercy, rather, it may also be seen as a principal objective of Shariʿah. The origin or sources of administration of justice in Islām are the Quran, Sunnah of the holy Prophet, consensus of opinions of the jurists of Islamic jurisprudence and Analogy (Qiyās). Justice is a sacred obligation of supererogatory. It is obligatory upon the Muslim rulers to appoint judges for the dispensation of justice to attain equality, to protect the human rights from their violation, to safeguard the lives and properties, and to maintain law and order in society. As a judge is supposed to accomplish a very important and noble task being a regent of Allāh, hence, some vital merits and criteria regarding the conditions and qualifications for the appointment of the Qāḍī or judge in the light of the Qur’ān, Sunnah and Islamic jurisprudence and the code of conduct for the Pakistani judges must be observed at all costs. The author of this paper has discussed these conditions and qualifications in this article. There are some unanimous conditions for the appointment of judges, while some others are not agreed upon. While presenting the difference of opinions of the Islamic jurists, the author tried to explain, reconcile the opinions and at some places presented her own view in the light of her analysis and arguments. These conditions are around thirty, but the author according to her own discretion chose some of the most important ones to discuss in this paper.

Combinatorial and Arithmetic Study of Binomial Edge Ideal

Let J G denote the binomial edge ideal of a connected undirected graph G on n vertices. This is the ideal generated by the binomials x i y j −x j y i , 1 ≤ i < j ≤ n, in the polynomial ring S = K[x 1 , . . . , x n , y 1 , . . . , y n ] where {i, j} is an edge of G. Our aim in this thesis is to compute certain algebraic invariants like dimension, depth, system of parameters, regular sequence, Hilbert series and multiplicity of J G of some particular classes of binomial edge ideals of graphs. A large amount of information of an ideal is carried by its minimal free resolution. So we give information on the minimal free resolution on certain binomial edge ideals. We also give a complete description of the structure of the modules of deficiencies of binomial edge ideals of some classes of graphs. A generalization of the concept of a Cohen-Macaulay ring was introduced by S. Goto [7] under the name approximately Cohen-Macaulay. In this thesis we collect a few graphs G such that the associated ring S/J G is approximately Cohen-Macaulay. We also characterize all the trees that are approximately Cohen-Macaulay. As more generalized notion than approximately Cohen-Macaulay we also study se- quentially Cohen-Macaulay property for binomial edge ideals. We give a nice con- struction principle in this topic. ̃ on n vertices has the property that S/J̃ is a Cohen-Macaulay The complete graph G G domain with a 1-linear resolution. As one of the main results we clarify the structure of S/J K m,n , where K m,n denotes the complete bipartite graph.