Let E n = {[τ ]a = (τ (a1) 1 , . . . , τ (an) n )|τ ∈ Sn, 1 ≤ ai ≤ r} be the set of all signed permutations on the symbols 1, 2, . . . , n with signs 1, 2, . . . , r. We prove, for every 2-letter signed pattern [τ ]a, that the number of [τ ]a-avoiding signed permutations in E n is given by the formula n ∑ j=0 j!(r−1) ( n j 2 . Also we prove that there are only one Wilf class for r = 1, four Wil...

Bars in galaxies are mainly supported by particles trapped around closed periodic orbits. These orbits respond to the bar’s forcing frequency only and lack free oscillations. We show that a similar situation takes place in double bars: particles get trapped around orbits which only respond to the forcing from the two bars and lack free oscillations. We find that writing the successive positions...

The enumeration of independent sets in graphs with various restrictions has been a topic of much interest of late. Let i(G) be the number of independent sets in a graph G and let it(G) be the number of independent sets in G of size t. Kahn used entropy to show that if G is an r-regular bipartite graph with n vertices, then i(G) ≤ i(Kr,r). Zhao used bipartite double covers to extend this bound t...

The effectiveness of the first Iranian made gonadotropin releasing hormone analogue, [D-Ala6des-Gly10] GnRH ethylamide, alone or in combination with domperidone, a dopamine antagonist on spawningrate, latency period, working fecundity and embryo viability in common carp, Cyprinus carpio, was investigated.Fifty two fish were divided into 5 groups and treated intrapretoneally as...