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The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]
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Such inflection was easily obtained by causing the voice at the middle and end of every psalm-verse to wander away from the monotone to some adjacent scale-degree. [ 1 ] The Annotated Book of Common Prayer similarly notes that (according to Saint Augustine ) Saint Athanasius discouraged variance in note in liturgical recitation, but that ...
The free distributive lattices of monotonic Boolean functions on 0, 1, 2, and 3 arguments, with 2, 3, 6, and 20 elements respectively (move mouse over right diagram to see description) In mathematics , the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind , who defined them in 1897. [ 1 ]
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Breaking a polygon into monotone polygons. A simple polygon may be easily cut into monotone polygons in O(n log n) time. However, since a triangle is a monotone polygon, polygon triangulation is in fact cutting a polygon into monotone ones, and it may be performed for simple polygons in O(n) time with a complex algorithm. [6]
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