Let n ≥ 3 $n\ge 3$ and R ${R}_{n}$ be a 3-polytopal graph such that for every ≤ i $3\le i\le n$ , has at least one vertex of degree $i$ . We find the minimal count then describe an algorithm to construct graphs A dual statement may formulated faces 3-polytopes. The ideas behind generalise readily solve related problems. Moreover, given 3-polytope T l ${T}_{l}$ comprising all l$ $l$ fixed, we de...

A family of k-element subsets an n-element set is called 3-wise intersecting if any three members in the have non-empty intersection. We determine maximum size such families exactly or asymptotically. One our results shows that for every ?>0 there exists n0 n>n0 and 25+?<kn<12?? then 4(n?4k?3)+(n?4k?4).

1. Generalist natural enemies are usually not considered as being capable of causing population cycles in forest insects, but they may influence the population dynamics of their prey in the low density cycle phase when specialist enemies are largely absent. 2. In the present field study, the total response of the generalist invertebrate predator community to experimentally established pupal den...

Let [n]:={1,2,…,n} and let a k-set denote set of cardinality k. A family sets is union-closed (UC) if the union any two in also family. Frankl’s conjecture states that for nonempty UC F⊆2[n] such F≠{∅}, there exists an element i∈[n] contained at least half F, where 2[n] denotes power on [n]. The 3-sets Morris smallest number distinct (whose n-set) ensure satisfied (in contains them ⌊n/2⌋+1 all ...

autosomal recessive and sporadic non-syndromic hearing loss (arsnshl) is the major form of hereditary deafness.mutations in the gjb2 gene encoding the gap-junction protein connexin 26 have been identified to be highly associated with arsnshl. in this study we have analyzed 196 deaf subjects from 179 families having one or more deaf children in 3 proviences of iran, including kordestan, khuzesta...

Invertebrate lineages tend to originate and become extinct at a higher rate in onshore than in offshore habitats over long temporal durations (more than 10 Myr), but it remains unclear whether this pattern scales down to durations of stages (less than 5 Myr) or even sequences (less than 0.5 Myr). We assess whether onshore-offshore gradients in long-term turnover between the tropical Eocene and ...