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The term monotonic transformation (or monotone transformation) may also cause confusion because it refers to a transformation by a strictly increasing function. This is the case in economics with respect to the ordinal properties of a utility function being preserved across a monotonic transform (see also monotone preferences ). [ 5 ]
The rate-monotonic priority assignment is optimal under the given assumptions, meaning that if any static-priority scheduling algorithm can meet all the deadlines, then the rate-monotonic algorithm can too. The deadline-monotonic scheduling algorithm is also optimal with equal periods and deadlines, in fact in this case the algorithms are ...
The term natural mapping comes from proper and natural arrangements for the relations between controls and their movements to the outcome from such action into the world. The real function of natural mappings is to reduce the need for any information from a user’s memory to perform a task.
Then F and G form a monotone Galois connection between the power set of X and the power set of Y, both ordered by inclusion ⊆. There is a further adjoint pair in this situation: for a subset M of X, define H(M) = {y ∈ Y | f −1 {y} ⊆ M}. Then G and H form a monotone Galois connection between the power set of Y and the power set of X.
Monotone chain, a.k.a. Andrew's algorithm — O(n log n) Published in 1979 by A. M. Andrew. The algorithm can be seen as a variant of Graham scan which sorts the points lexicographically by their coordinates. When the input is already sorted, the algorithm takes O(n) time. Incremental convex hull algorithm — O(n log n)
Example showing non-monotone cubic interpolation (in red) and monotone cubic interpolation (in blue) of a monotone data set. Monotone interpolation can be accomplished using cubic Hermite spline with the tangents m i {\displaystyle m_{i}} modified to ensure the monotonicity of the resulting Hermite spline.
The SMAWK algorithm is an algorithm for finding the minimum value in each row of an implicitly-defined totally monotone matrix. It is named after the initials of its five inventors, Peter Shor , Shlomo Moran , Alok Aggarwal, Robert Wilber, and Maria Klawe .
For example, in theoretical computer science, least fixed points of monotonic functions are used to define program semantics, see Least fixed point § Denotational semantics for an example. Often a more specialized version of the theorem is used, where L is assumed to be the lattice of all subsets of a certain set ordered by subset inclusion .