Using Serre’s proposed complement to Shih’s Theorem, we obtain PSL2(Fp) as a Galois group over Q for at least 614 new primes p. Under the assumption that rational elliptic curves with odd analytic rank have positive rank, we obtain Galois realizations for 3 8 of the primes that were not covered by previous results.

A (smooth) K3 surface X defined over a field k of characteristic 0 is called singular if the Néron-Severi lattice NS(X) of X ⊗ k is of rank 20. Let X be a singular K3 surface defined over a number field F . For each embedding σ : F →֒ C, we denote by T (Xσ) the transcendental lattice of the complex K3 surface Xσ obtained from X by σ. For each prime ideal p of F at which X has a supersingular red...

The relations among a set, its complement, and its boundary are examined constructively. A crucial tool is a theorem that allows the construction of a point where a segment comes close to the boundary of a set in a Banach space. Brouwerian examples show that many of the results are the best possible.

Introduction. For'several years one of the outstanding problems of lattice theory has been the following: Is every lattice with unique complements a Boolean algebra? Any number of weak additional restrictions are sufficient for an affirmative answer. For example, if a lattice is modular (G. Bergman [l](1)) or ortho-complemented (G. Birkhoff [l]) or atomic (G. Birkhoff and M. Ward [l]), then uni...

Let d be a square-free positive integer, let Od denote the ring of integers in Q( √ −d), and let Qd denote the Bianchi orbifold H/PSL(2,Od). A non-compact finite volume hyperbolic 3-manifold X is called arithmetic if X and Qd are commensurable, that is to say they share a common finite sheeted cover (see [26] Chapter 8 for more on this). If N is a closed orientable 3-manifold and L ⊂ N a link, ...

Much of the existing bx literature, especially that from the PL community on lenses, has described extensional, state-based formalisms. More recently, attention has turned to incorporating intensional information about edits (typically based on monoid actions), or more generally, deltas (typically based on categories), describing how models are updated. Pervasive in both the conceptual modellin...

Finding mutations in nuclear genes responsible for disorders in the mitochondrial oxidative phosphorylation system has been a tedious matter. A "Venn diagram" approach--not unlike a classic complementation experiment--reported in this issue will now make the search easier.