Let M be a compact surface without boundary, and n≥2. We analyse the quotient group Bn(M)/Γ2(Pn(M)) of braid Bn(M) by commutator subgroup Γ2(Pn(M)) pure Pn(M). If is different from 2-sphere S2, we prove that Bn(M)/Γ2(Pn(M))≅Pn(M)/Γ2(Pn(M))⋊φSn, crystallographic if only orientable. orientable, number results regarding structure Bn(M)/Γ2(Pn(M)). characterise finite-order elements this group, dete...

electrochemical behavior of the new mono and dinuclear co (iii)  complexes of  the types trans-[pyco((do)(doh)pn )(l)]pf6   and [{py co((do)(doh)pn)}2 (μ-dicyd)] (pf6)2   have been studied in acetonitrile solution.  all the  mono nuclear complexes  show two quasi- reversible reduction couples associate  to co(iii/ii)and  co(ii/i). each of these redox couples split to two  one electron  waves in...

Electrochemical behavior of the new mono and dinuclear Co (III)  complexes of  the types trans-[pyCo((DO)(DOH)pn )(L)]PF6   and [{py Co((DO)(DOH)pn)}2 (μ-dicyd)] (PF6)2   have been studied in acetonitrile solution.  All the  mono nuclear complexes  show two quasi- reversible reduction couples associate  to Co(III/II)an...

So, we have (1.2) p1p2 · · · pn < (pn 2 )n (n ≥ 9), where also holds true by computation for 5 ≤ n ≤ 8. In other hand, one can get a trivial lower bound for that product using Euclid’s proof of infinity of primes; Letting En = p1p2 · · · pn−1 for every n ≥ 2, it is clear that pn < En. So, if pn < En < pn+1 then En should has a prime factor among p1, p2, · · · , pn which isn’t possible. Thus En ...

Proof-Number (PN) search is a best-first adversarial search algorithm especially suited for finding the game-theoretical value in game trees. The strategy of the algorithm may be described as developing the tree into the direction where the opposition characterised by value and branching factor is to expect to be the weakest. In this chapter we start by providing a short description of the orig...