We examine the implications for the distribution of extrasolar planets based on the null results from two of the largest direct imaging surveys published to date. Combining the measured contrast curves from 23 of the stars observed with the VLT NACO adaptive optics system by Masciadri et al. (2005), and 47 of the stars observed with the VLT NACO SDI and MMT SDI devices by Biller et al. (2007) (...

In this paper we show that an inverse limit is 1-dimensional whenever the bonding functions are upper semi-continuous from [0, 1] into C([0, 1]) and dim(G(fi ◦ fi+1 ◦ · · · ◦ fj)) = 1 for all integers i and j, 1 ≤ i ≤ j. We apply this result to show that such an inverse limit is treelike and also to show that unions of certain finite collections of interval-valued upper semi-continuous function...

We examine several types of visibility graphs: bar and semi-bar k-visibility graphs, rectangle k-visibility graphs, arc and circle k-visibility graphs, and compact visibility graphs. We improve the upper bound on the thickness of bar k-visibility graphs from 2k(9k − 1) to 6k, and prove that the upper bound must be at least k + 1. We also show that the upper bound on the thickness of semi-bar k-...