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On the Convex Hull of the Points on Modular Hyperbolas
congruence modular hyperbola integral polygon convex hull
2011/1/19
Given integers a and m ≥ 2, let Ha(m) be the following set of integral points Ha(m) = {(x, y) : xy ≡ a (mod m), 1 ≤ x, y ≤ m − 1} We improve several previously known upper bounds on va(m), the n...
A Note on the Closedness of the Convex Hull and Its Applications
Convex Hull Applications spannability
2009/1/22
This paper answers the following question motivated by the problem of spannability of functions. When is the convex hull of an unbounded (closed) set closed? We provide necessary and sufficient condit...