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There is an increasing concern about the control of customs operations. While globalization incentives the opening of the market, increasing amounts of imports and exports have been used to conceal several illicit activities, such as, tax evasion, smuggling, money laundry, and drug traffic. This fact makes it paramount for governments to find automatic or… (More)

- Pietro Kreitlon Carolino, Amit Sahai, Igor Pak, Matthias J. Aschenbrenner, Terence Chi-Shien
- 2015

of the Dissertation A subset A of a locally compact group G is said to be a K-approximate group if it contains the identity, is closed under inverses, and if the product set A·A = {ab | a, b ∈ A} can be covered by K left translates of A. In this work we prove a structure theorem on open precompact K-approximate groups that describes them as a combination of… (More)

We investigate a conjecture of Paul Erd˝ os, the last unsolved problem among those proposed in his landmark paper [2]. The conjecture states that there exists an absolute constant C > 0 such that, if v1,. .. , vn are unit vectors in a Hilbert space, then at least C 2 n n of all ∈ {−1, 1} n are such that | P n i=1 ivi |≤ 1. We disprove the conjecture. For… (More)

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