https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 An elementary proof of the irrationality of Tschakaloff series https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11923 q(z)= ∞/∑/n=0 znq-n(n-1)/2 in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to Tq(z).]]> Sat 24 Mar 2018 11:09:02 AEDT ]]> Approximations to q-logarithms and q-dilogarithms, with applications to q-zeta values https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11926 q(1) = L₁(1; q), ζq+00B2(1) and 1, ζq(1), ζq(2) = L₂(1; q) for q = 1/p, p ε ℤ {0,±1}.]]> Sat 24 Mar 2018 11:09:02 AEDT ]]> Notions of relative interior in Banach spaces https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13077 n to the case of a Banach space. We study the relations between these extensions and develop their basic calculus rules. Several explicit examples and counterexamples in general Banach spaces are given and the tools for development of further examples are explained. Various implications for infinite-dimensional optimization are highlighted.]]> Sat 24 Mar 2018 08:15:36 AEDT ]]>