Bust-a-Move/Puzzle Bobble is NP-Complete

We prove that the classic 1994 Taito video game, known as Puzzle Bobble or Bust-a-Move, is NP-complete. Our proof applies to the perfect-information version where the bubble sequence is known in advance, and it uses just three bubble colors.Comment: 9 pages, 9 figures. Corrected mistakes in gadget

A remark on the multipliers on spaces of weak products of functions

If $\mathcal{H}$ denotes a Hilbert space of analytic functions on a region $\Omega \subseteq \mathbb{C}^d$, then the weak product is defined by $$\mathcal{H}\odot\mathcal{H}=\left\{h=\sum_{n=1}^\infty f_n g_n : \sum_{n=1}^\infty \|f_n\|_{\mathcal{H}}\|g_n\|_{\mathcal{H}} <\infty\right\}.$$ We prove that if $\mathcal{H}$ is a first order holomorphic Besov Hilbert space on the unit ball of $\mathbb{C}^d$, then the multiplier algebras of $\mathcal{H}$ and of $\mathcal{H}\odot\mathcal{H}$ coincide.Comment: v1: 6 pages. To appear Concr. Ope

ECONOMIC IMPACTS OF DRYLAND SALINITY FOR GRAINS INDUSTRIES

This paper explores some possible economic impacts of worsening salinity severity and extent in the grains industry across Australia. It also looks at the potential to increase agricultural profits through remediation. The analysis is based on a spatial model of agricultural profits and salinity related crop/pasture yield losses. It is estimated that grains industry farming profits across Australia would rise by an upper limit $138 million per year were salinity costlessly removed from the landscape. It is also estimated that the present value of grains industry profit losses from worsening salinity extent and severity over the next 20 years is$237 million. These amounts can be considered against the costs of repair.Crop Production/Industries, Environmental Economics and Policy,