1,234 research outputs found

    On sets of integers which contain no three terms in geometric progression

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    The problem of looking for subsets of the natural numbers which contain no 3-term arithmetic progressions has a rich history. Roth's theorem famously shows that any such subset cannot have positive upper density. In contrast, Rankin in 1960 suggested looking at subsets without three-term geometric progressions, and constructed such a subset with density about 0.719. More recently, several authors have found upper bounds for the upper density of such sets. We significantly improve upon these bounds, and demonstrate a method of constructing sets with a greater upper density than Rankin's set. This construction is optimal in the sense that our method gives a way of effectively computing the greatest possible upper density of a geometric-progression-free set. We also show that geometric progressions in Z/nZ behave more like Roth's theorem in that one cannot take any fixed positive proportion of the integers modulo a sufficiently large value of n while avoiding geometric progressions.Comment: 16 page

    Liberty’s Honors Manager, Mrs. Laura Kline: Service to Lord and Family

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    Meet the Manager of LU Honors\u27 Program, Mrs. Laura Kline


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    A point-space model of interregional trade is used to define market integration and to explore its implications for modeling spatial price relationships. This analysis indicates that spatial prices are related nonlinearly, contrary to much of the work on spatial price analysis which uses linear models. As an empirical example, corn market integration along the Mississippi River is examined during the Midwest flood of 1993. Higher transport costs during this period significantly reduced the extent of integration and thereby decreased excess demand shock transference across regions.Agribusiness,

    Loan Deficiency Payments and Minor Crops

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    Agricultural Finance,

    Physiology of chimpanzees in orbit. Part 1: Scientific Report

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    Major achievements and accomplishments are reported for the Physiology of Chimpanzees in Orbit Program. Scientific studies relate to behavior and physiology, and engineering studies cover telemetry, behavioral training, systems tests, life support subsystems, and program plan