We show constructively that every quasi-convex uniformly continuous function f : C → R+ has positive infimum, where C is a convex compact subset of Rn. This implies a constructive separation theorem for convex sets.

In this note we will construct an example of a quasi-geodesic in the Te-ichm uller space of a surface with the following instability property: Theorem For any hyperbolic surface S whose Teichm uller space T (S) has dimension at least 4, there is a bi-innnite quasi-geodesic L in T (S) such that 1. L projects to a compact part of the moduli space M(S), but 2. L does not lie in a bounded neighborh...

We prove that any noetherian quasi-excellent scheme of characteristic zero admits a strong desingularization which is functorial with respect to all regular morphisms. We show that as an easy formal consequence of this result one obtains strong functorial desingularization for many other spaces of characteristic zero including quasi-excellent stacks and formal schemes, and complex and non-archi...

For any abelian category C satsifying (AB5) over a separated, quasicompact scheme S , we construct a stack of 2-groups GL(C) over the flat site of S. We will give a concrete description of GL(C) when C is the category of quasi-coherent sheaves on a separated, quasi-compact scheme X over S. We will show that the tangent space gl(C) of GL(C) at the origin has a structure as a Lie 2-algebra.

We give a new proof of the well-known fact that the pinned Wiener measure on a Lie group is quasi-invariant under right multiplication by 1nite energy paths. The main technique we use is the time reversal. This approach is di3erent from what B. Driver used to prove quasi-invariance for the pinned Brownian motion on a compact Riemannian manifold. c © 2002 Elsevier Science B.V. All rights reserved.

A compact receiver front-end comprised of subharmonic direct conversion mixers integrated with a planar quasi-Yagi antenna is presented. The front-end generates I and Q baseband outputs, using the quasi-Yagi antenna as a circuit element to split the incoming signal into an I and Q component. Furthermore, the subharmonic design cancels even mixing products, thereby improving even-order distortio...