Let p/q be a rational number. Numeration in base is defined by function that evaluates each finite word over A_p={0,1,...,p-1} to some We let N_p/q denote the image of this evaluation function. In particular, contains all nonnegative integers and literature on usually focuses set words are evaluated integers; it rather chaotic language which not context-free. On contrary, we study here subsets ...

In this paper we give a GAP program for computing the Szeged and the PI indices of any graph. Also we compute the Szeged and PI indices of VC(5)C(7) [ p,q] and HC(5)C(7) [ p,q] nanotubes by this program.

let $g $ be a finite group and let $gamma(g)$ be the prime graph‎ ‎of g‎. ‎assume $2 < q = p^{alpha} < 100$‎. ‎we determine finite groups‎ ‎g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $u_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $g$ is a finite group with the same prime graph as the‎ ‎finite simple group $u_3(q)$‎, ‎then $g$ has a un...