Abstract. In an accumulation game, the Hider secretly distributes his given total wealth h among n locations, while the Searcher picks r locations and confiscates the material placed there. The Hider wins if what is left at the remaining n − r locations is at least 1; otherwise the Searcher wins. Ruckle's Conjecture says that an optimal Hider strategy is to put an equal amount h/k at k randomly chosen locations, for some k. We extend the work of Kikuta and Ruckle by proving the Conjecture for several cases, among others: r = 2 or n − 2; n ≤ 7; n = 2r − 1; h < 2 + 1/ (n − r − 1) and n ≤ 2r. The last result uses the Erdos-Ko-Rado theorem. We establish a connection between Ruckle's Conjecture and the difficult Hoeffding problem of bounding tail probabilities of sums of random variables.

We study search games in which the hider may hide in a finite number of locations. We assume that the cost of searching these locations does not depend on the order in which the locations are searched. From these assumptions we derive that the cost function is submodular, thus placing search games with an immobile hider in the context of coalitional games.

Direct electrospinning of small molecules has great potential to fabricate a new class of fiber materials because this approach realizes the creation of various functional materials through the numerous molecular combinations. In this paper, we demonstrate a proof-of-concept to fabricate supramolecular fiber materials composed of cyclodextrin (CD)–fullerene inclusion complexes by electrospinning. Similar to the molecular state of fullerenes in solution, the resulting fibers include molecularly-dispersed fullerenes. We believe such a concept could be expanded to diverse host–guest complexes, opening up supramolecular solid materials science and engineering.