ڈاروِن تھیوری کے مفکرینِ برصغیر پر اثرات: تحقیقی و تنقیدی جائزہ

Man is curious. Today he is stepping forward to explore the world and space, but still he is trying to know the answer to the question that how he was made? Qur’an the last holy book of Allah, which provides complete guidance in every walk of life, can give better answer to this question. Besides this many theories were presented by the scientists called evolution theories. One of these theories is “Theory of natural selection” presented by Charles Darwin in 1859 A.D. This theory got a lot of reputation. Qur’anic teachings say that the first human being Hazrat Adam (علیہ السلام) was created by Allah as a complete Man. But this theory states that all species of organisms arise and develop through the natural selection of small, inherited variations that increase the individual's ability to compete, survive, and reproduce (means there was no Adam on earth as the Father of humanity, which is contrary to Islam). Darwin theory, a non-Islamic theory about the creation of humanity has a great impact over the various thinkers of subcontinent. This research article attempts to answer the questions that what are the Qur’anic teachings about the creation of humanity on earth? And what are the different evolution theories and their effects on the various thinkers of subcontinent?

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.