Abstract Let L be a full-rank lattice in ℝ d and write + for the semigroup of all vectors with nonnegative coordinates . We call basis X positive if it is contained There are infinitely many such bases, each them spans conical S ( ) consisting integer linear combinations Such sub-semigroup , we investigate distribution gaps i.e. points ∖ ). describe some basic properties counting estimates thes...

Let / be a monotone and strictly convex (or concave) function on a real interval and let g be the inverse function. Let I(x) = x. For a real valued function and N a positive integer let (t>pf(x) denote the rounding of (x) to N significant figures. Let h = gff » fa, the composition of f^ and g^¡. It is shown that h » ft » Iff = h o h » h « Ifj, and that equality can fail for fewer iterati...