489 research outputs found
Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus
We produce explicit low-discrepancy infinite sequences which can be used to
approximate the integral of a smooth periodic function restricted to a convex
domain with positive curvature in R^2. The proof depends on simultaneous
diophantine approximation and a general version of the Erdos-Turan inequality.Comment: 14 pages, 2 figure
A result on polynomials derived via graph theory
We present an example of a result in graph theory that is used to obtain a
result in another branch of mathematics. More precisely, we show that the
isomorphism of certain directed graphs implies that some trinomials over finite
fields have the same number of roots
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