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A function that is absolutely monotonic on [,) can be extended to a function that is not only analytic on the real line but is even the restriction of an entire function to the real line. The big Bernshtein theorem : A function f ( x ) {\displaystyle f(x)} that is absolutely monotonic on ( − ∞ , 0 ] {\displaystyle (-\infty ,0]} can be ...
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 .
Similarly, a polygonal chain C is called monotone with respect to a straight line L, if every line orthogonal to L intersects C at most once. For many practical purposes this definition may be extended to allow cases when some edges of P are orthogonal to L , and a simple polygon may be called monotone if a line segment that connects two points ...
A polygonal chain is called monotone if there is a straight line L such that every line perpendicular to L intersects the chain at most once. Every nontrivial monotone polygonal chain is open. In comparison, a monotone polygon is a polygon (a closed chain) that can be partitioned into exactly two monotone chains. [2]
In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible.
The following result is a generalisation of the monotone convergence of non negative sums theorem above to the measure theoretic setting. It is a cornerstone of measure and integration theory with many applications and has Fatou's lemma and the dominated convergence theorem as direct consequence.
The "passivity" agreement FDIC wants BlackRock to sign is designed to assure bank regulators that the giant money manager will remain a "passive" owner of an FDIC-supervised bank and won’t exert ...
In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. Conversely, the integral of any continuous, non-negative, bell-shaped function (with one local maximum and no local minimum, unless degenerate) will be sigmoidal.