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Recently, Constantinescu and Ilie proved a variant of the well-known periodicity theorem of Fine and Wilf in the case of two relatively prime abelian periods, and conjectured a result for the case of two non-relatively prime abelian periods. More precisely, they proved that any full word having two coprime abelian periods p, q and length at least 2pq − 1(More)
The notion of a primitive word, one that is not a power of another word, is useful in many areas including coding theory, combinatorics on words, formal language theory, and text algorithms. The proportion of such words turns out to be very high. We investigate operations that preserve the primi-tivity of partial words with one hole, or words that have an(More)
Recently, Constantinescu and Ilie proved a variant of the well-known periodicity theorem of Fine and Wilf in the case of two relatively prime abelian periods and conjectured a result for the case of two non-relatively prime abelian periods. In this paper, we answer some open problems they suggested. We show that their conjecture is false but we give bounds,(More)
Many nutrition models rely on summative equations to estimate feed and diet energy concentrations. These models partition feed into nutrient fractions and multiply the fractions by their estimated true digestibility, and the digestible mass provided by each fraction is then summed and converted to an energy value. Nonfiber carbohydrate (NFC) is used in many(More)
The Food and Drug Administration (FDA) is conducting research on developing reference lung cancer lesions, called phantoms, to test computed tomography (CT) scanners and their software. FDA loaned two semi-spherical phantoms to the National Institute of Standards and Technology (NIST), called Green and Pink, and asked to have the phantoms' volumes(More)
As a variation on the t-Equal Union Property (t-EUP) introduced by Lindström, we introduce the t-Equal Valence Property (t-EVP) for hypergraphs: a hypergraph satisfies the t-EVP if there are t pairwise edge-disjoint subhypergraphs such that for each vertex v, the degree of v in all t subhypergraphs is the same. In the t-EUP, the subhypergraphs just have the(More)
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