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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 ]
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ] [ 2 ] [ 3 ] This concept first arose in calculus , and was later generalized to the more abstract setting of order theory .
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 ...
Monotone preferences, a property of a consumer's preference ordering. Monotonicity (mechanism design), a property of a social choice function. Monotonicity criterion, a property of a voting system. Resource monotonicity, a property of resource allocation rules and bargaining systems.
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]
As this article's first figure shows, in the presence of monotonicity violations the resulting interpolated curve will have flat (constant) intervals. In dose-response applications it is usually known that f ( x ) {\displaystyle f(x)} is not only monotone but also smooth .
Under a flat tax system, taxpayers owe the same rate whether they earn $10 or $10 million. This appeals to the sense of fairness for those who believe higher earners shouldn’t be penalized for ...
In the mathematical field of numerical analysis, monotone cubic interpolation is a variant of cubic interpolation that preserves monotonicity of the data set being interpolated. Monotonicity is preserved by linear interpolation but not guaranteed by cubic interpolation .