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 ...