Difference sets in higher dimensions

Symmetries of Julia sets in higher dimensions

Small Blocking Sets in Higher Dimensions

We show that small blocking sets in PG(n, q) with respect to hyperplanes intersect every hyperplane in 1 modulo p points, where q= p. The result is then extended to blocking sets with respect to k-dimensional subspaces and, at least when p>2, to intersections with arbitrary subspaces not just hyperplanes. This can also be used to characterize certain non-degenerate blocking sets in higher dimen...

On Determining the Congruity of Point Sets in Higher Dimensions

This paper considers the following problem: given two point sets A and B (jAj = jBj = n) in d-dimensional Euclidean space, determine whether or not A is congruent to B. First, this paper presents a randomized algorithm which works in O(n (d 1)=2 (log n) 2 ) time. This improves the previous result (an O(n d 2 logn) time deterministic algorithm). The birthday paradox, which is a well-known proper...

Shadowing in Higher Dimensions

This paper presents methods using algebraic topology for showing that pseudo-trajectories are close to trajectories of a dynamical system. Our emphasis is the case where the trajectories are unstable in two or more dimensions. We develop the algebraic topology for guaranteeing the existence of such trajectories.

Bosonization in Higher Dimensions

Using the recently discovered connection between bosonization and duality transformations, we give an explicit path-integral representation for the bosonization of a massive fermion coupled to a U(1) gauge potential (such as electromagnetism) in d ≥ 2 space (D = d + 1 ≥ 3 spacetime) dimensions. We perform this integral explicitly in the limit of large fermion mass. We find that the bosonic theo...