Sstarting from a set of strands (or other types of building blocks) a variant of forbidding-enforcing systems for graphs is proposed which models the DNA self-assembly process. The possible outcomes of the self-assembly process comply with necessary constraints arising from the physical and chemical properties of DNA. A set of forbidding and enforcing rules that describe these constraints are p...

Following a conjecture of P. Erdos, we show that if 9 is a family of k-subsets of an n-set no two of which intersect in exactly I elements then for k 2 21+ 2 and n sufficiently large IF:/ < (;:‘,I:) with equality holding if and only if 9 consists of all the k-sets containing a fixed (I+ I)-set. In general we show 19) <dknmax(‘.k-‘-l), where dk is a constant depending only on k. These results ar...

"A Valediction: Forbidding Mourning" shows many features associated with seventeenth-century metaphysical poetry in general, and with Donne's work in particular. Donne's contemporary, the English writer Izaak Walton, tells us the poem dates from 1611, when Donne, about to travel to France and Germany, wrote for his wife this valediction, or farewell speech. Like most poetry of Donne's time, it ...

Background and Objectives: Enjoining good and forbidding (EGFE) evil are two fundamental topics in Islam. Many verses and narratives underscore the social, religious and political duties implied by enjoining good and forbidding evil. After all, these two divine treasures have been neglected because of indulgence and forgetfulness. The prime reason for this negligence seems to be the obliviousne...

Background and Objectives: Enjoining good and forbidding (EGFE) evil are two fundamental topics in Islam. Many verses and narratives underscore the social, religious and political duties implied by enjoining good and forbidding evil. After all, these two divine treasures have been neglected because of indulgence and forgetfulness. The prime reason for this negligence seems to be the obliviousne...

Even though there is a consensus among Muslim scholars that rebellion without valid grounds not acceptable, they have disagreed on the permissibility of against an unjust ruler. Abū Ḥanīfa has pivotal place in these debates, as he eponym law school first dedicated special chapter to (baghy) its legal texts. Interestingly, however, views attributed him topic are inconsistent: Some sources claim ...

The proof of Theorem 1 consists of the following two lemmas. Recall that K r is the complete r-partite graph with p vertices in each class. In other words, K r = Tr(pr), the Turán graph with pr many vertices. It is easy to see that χ(K r ) = r. Lemma 2. For all c, η > 0, n > 8/η, if G is a graph on n vertices with e(G) ≥ (c + η) ( n 2 ) , then G has a subgraph G′ with n′ ≥ 1 2 √ ηn vertices suc...

background and objectives: enjoining good and forbidding (egfe) evil are two fundamental topics in islam. many verses and narratives underscore the social, religious and political duties implied by enjoining good and forbidding evil. after all, these two divine treasures have been neglected because of indulgence and forgetfulness. the prime reason for this negligence seems to be the obliviousne...