فتنہ انکار حدیث کا ایک جائزہ

Human rights are an important issue of every century. The importance of this issue has increased immensely in this age of information and technology where every person is well aware of his rights, among which is social justice. Islam has designed rules and regulations for social justice. It has provided a well-balanced system for it, has made people aware of their social rights, and encouraged them to get those rights. The life and teachings of Prophet Muhammad S.A.W are true reflections of a social justice system that is needed in this age. The Prophet’s last sermon delivered at the occasion of Hajjatul Wida is considered to be the first detailed charter of human rights. He mentioned in that sermon the value of life, property and the esteem of a human being. Islam urges Muslims to deal with women, the oppressed, orphans, those in debt, laborers, neighbors and non-Muslims with sympathy and equality. This article attempts to present the true teachings of Islam regarding social justice, in light of the Quran and the Prophet’s life.

On Generation of Non-Equivalent Combinatorial Objects

The rapid growth in fields of computational biology, data mining and combinatorial chemistry results in an increased demand of combinatorial algorithms which produce exhaustive lists of combinatorial objects especially those objects which are symmetric under some equivalence relation. In this thesis we develop efficient algorithms for generation of bracelets with fixed density, bracelets with fixed content, and non- isomorphic unicyclic graphs. All of the above mentioned algorithms list only one representative object from each equivalence class. A bracelet is said to be of fixed density, if number of occurrences of the symbol 0 is fixed. The algorithm for generation of bracelets with fixed density generates a complete set of bracelets with fixed density of arbitrary base in lexicographic order. A simple mapping technique is used to prove that our algorithm works in constant amortized time. Bracelets with fixed content are those in which number of occurrences of each symbol is fixed. We devise an efficient algorithm to list bracelets with fixed content in reverse lexicographic order. Again, by using an injective mapping we prove that the algorithm works in constant amortized time with the condition that number of occurrences of the largest symbol is maximum. Our analysis also gives a simpler alternate proof for the original bracelet algorithm presented in “Generating bracelets in constant amortized time” by J. Sawada. Moreover, an enumeration formula for bracelets with fixed content is obtained. Listing of non-isomorphic graphs is known to be computationally very hard. However, when we restrict the graphs to have exactly one cycle, the problem can be efficiently solved in constant amortized time. In this thesis, we give a CAT algorithm to list all unlabeled non-isomorphic unicyclic graphs.