https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14225 n+m+k ( n² + m² + k²) ^-1/2, the summation being over all non-zero integer triples. Such "sums" occur naturally in the study of crystal potentials. For example, (1.1) is meant to measure the potential at the origin of an infinite cubic crystal with unit Coulomb charges at each integer lattice point. As such the sum is considered to represent an electrochemical constant (Madelung's constant) for sodium chloride. An excellent account of such lattice sums can be found in Glasser and Zucker's recent survey [3].]]> Thu 03 Oct 2024 09:34:19 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:55980 Sun 14 Jul 2024 15:30:27 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13078 0 has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space X, the set of all (equivalent) norms on X having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal norms in Banach spaces with the convex point of continuity property (CPCP). Other questions related to the existence of antiproximinal bodies are also discussed.]]> Sat 24 Mar 2018 08:15:36 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:24680 0, making it significantly harder than Dominating Set, while it remains hard even on severely restricted special cases, such as cubic graphs (APX-hard), and planar subcubic graphs (NP-hard). We complement our negative results by showing that the problem admits an O(Δ) approximation on graphs of maximum degree Δ, as well as an EPTAS on planar graphs. Along the way, we also derive essentially tight n1−1d upper and lower bounds on the approximability of the related problem Maximum Minimal Hitting Set on d-uniform hypergraphs, generalising known results for Maximum Minimal Vertex Cover.]]> Sat 24 Mar 2018 07:10:51 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12948 Mon 23 Sep 2024 14:01:20 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:47569 Mon 23 Jan 2023 13:39:29 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:54739 Mon 11 Mar 2024 14:20:03 AEDT ]]>