عرب عہد جاہلیت میں ’’طلاق‘‘ کا تصور: تحقیقی جائزہ

Conjugal life is an important aspect of human society, on which a prosperous life depends. Almost every Culture, civilization and religion Legislate for family life. There is a part of these laws to end the marital relationship which is denoted by "DIVORCE". Divorce is mentioned in detail in Islamic Sharia, in order to understand them truly one has to genuinely consider and understand the concept of divorce in Pre-Islamic period of ignorance. There were several specific terms for divorce that were used in the Arab culture for example Talᾱq, Īela and Khula etc. But generally decent people use the word "طلاق"(Talᾱq) to end the marital relationship. There were some common causes and reasons for divorce in Arabs before Islam for example lack of mental harmony, infertility, bigotry, family feud and apostasy etc. The divorced women become more and more vulnerable socially and economically in ancient Arab and consequently their children less attention, love and affection of their mothers turning them into rebellious, nonconformist and ruthless individuals crossing all limits of oppression and we often see examples of such incidents in Arabs before dawn of Islam. These cruel customs and practices were uprooted through teachings of Islam which is based on justice, equality and basic human rights.

A Classifier for Isolated Complete Intersection Singularities of Modality ≤ 1

The aim of the present thesis is to study, develop and implement certain algorithms in order to find the type of singularities for isolated complete intersection singularities w.r.t contact equivalence of modality ≤ 1 defined over an algebraically closed field K. The new investigation is that we do not compute the normal form of a given singularity because this would be space and time consuming. We present a charac- terization of the different types of singularities in terms of certain invariants and use the characterization to identify the singularities. We describe our implementation in computer algebra system Singular. Therefore, we discuss three problems in this thesis. • Problem 1 deals with the classification of hypersurface singularities with respect to contact equivalence when the characteristic of the field p > 2 by using blowing up as a new tool. • Problem 2 studies the classification of simple complete intersection singularities in terms of certain invariants when the characteristic of the field p = 0. • Problem 3 includes to find the complete list of unimodular complete intersection space curve singularities and the characterization of these singularities in terms of certain invariants when the characteristic of the field p = 0