This note focuses on the coupling of a type IIA D2-brane to a background B field. It is shown that the D0-brane charge arising from the integral over the D2-brane of the pullback of the B field is cancelled by bulk contributions, for a compact D2-brane wrapping a homotopically trivial cycle in space-time. In M-theory this cancellation is a straightforward consequence of momentum conservation. T...

An ultrafilter U is Hausdorff if for any two functions f, g ∈ ω ω , f (U) = g(U) iff f ↾X = g↾X for some X ∈ U. We will show that it is consistent that there are no Hausdorff ultrafilters.

A method is proposed for detecting whether two CCITT group 4 images were scanned from the same document. Features are extracted from rectangular patches of text and compared with a modified Hausdorff distance measure. Two images are said to be ‘‘equivalent’’ (i.e., they were scanned from the same document) if the Hausdorff measure finds that a specified number of features are located within a g...

For a closed subset K of a compact metric space A possessing an α-regular measure μ with μ(K) > 0, we prove that whenever s > α, any sequence of weighted minimal Riesz s-energy configurations ωN = {x i,N} N i=1 on K (for ‘nice’ weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as N grows large. Furthermore, if K is an α-rectifiable com...

We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve γ : R → R , N ≥ 2, is locally 1-monotone.

Using the Chu-construction, we define a group algebra for topological Hausdorff groups. Furthermore, for isometric, weakly continuous representations of a subgroup H of a Hausdorff group G induced representations are constructed.