منابع مشابه
Note on Integral Distances
A planar point set S is called an integral set if all the distances between the elements of S are integers. We prove that any integral set contains many collinear points or the minimum distance should be relatively large if |S| is large.
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In this note, we generalize two retarded Ouyang integral inequalities. One of these inequalities says: under suitable assumptions of functions w,α, h, f, g and p on [0,∞), if w(t) ≤ h(t) + 2 ∫ α(t) 0 { f(s)w(s) [ w(s) + ∫ s 0 g(r)w(r)dr ] + p(s)w(s) } ds, then w(t) ≤ [ h(t) + ∫ α(t) 0 p(s)ds ] exp {∫ α(t) 0 [ f(s) + (∫ s 0 g(r)dr ) ds ]} , t ≥ 0. AMS Subject Classifications: 26D15.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1934
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1934-05865-8