In the last round of FIFA World Cup group stage, games for which outcome does not affect selection qualified teams are played with little enthusiasm. Furthermore, a team that has already may take into account other factors, such as opponents it will face in next stage competition so that, depending on results groups and scheduling winning game be its best interest. Even more critically, there s...

the increasing and unlimited cases of burdensome dowries beyond the husband's solvency, leading finally to the enforcement of dowry and divorce, had led some commentators to fix a certain maximum for dowry. the authors, in this article, intend to find a proper theory to resolve this matrimonial problem through reviewing the earlier and later islamic jurisprudents’ opinions. although according t...

The fixing number of a graph G is the minimum cardinality of a set S ⊂ V (G) such that every nonidentity automorphism of G moves at least one member of S, i.e., the automorphism group of the graph obtained from G by fixing every node in S is trivial. We provide a formula for the fixing number of a disconnected graph in terms of the fixing numbers of its components and make some observations abo...

The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the order of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branchand-cut tree. We present a general tool, called orbi...

Microorganisms decompose herbicides and they may serve as bioindicators of soil changes following herbicide application. Certain microbial species may be used as bioherbicides. This study has shown that Azotobacter is most sensitive to herbicide application; it is, therefore, a reliable indicator of the biological value of soil. The numbers of this group of nitrogen-fixing bacteria decrease con...