In the theory of hyperplane arrangements, most important and difficult problem is combinatorial dependency several properties. this article, we prove that Terao's celebrated addition theorem for free arrangements combinatorial. Combining other developments in these days, can show all addition-deletion framework As a corollary, define new class called additively arrangement hyperplanes, which be...

background: chewing-gum may serve as an effective oral hygiene device when brushing may not be possible. the aim of the present study was to evaluate the effect of chewing sugar-free gum twice a day after meals in addition to tooth brushing on dental plaque and interdental debris.     methods: twenty four (12 males and 12 females aged 20-21 years) healthy third-year dental students participated...

We look at 1-region membrane computing systems which only use rules of the form , where is a catalyst, is a noncatalyst, and is a (possibly null) string of noncatalysts. There are no rules of the form . Thus, we can think of these systems as “purely” catalytic. We consider two types: (1) when the initial configuration contains only one catalyst, and (2) when the initial configuration contains m...

We look at 1-region membrane computing systems which only use rules of the form , where is a catalyst, is a noncatalyst, and is a (possibly null) string of noncatalysts. There are no rules of the form . Thus, we can think of these systems as “purely” catalytic. We consider two types: (1) when the initial configuration contains only one catalyst, and (2) when the initial configuration contains m...