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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 .
The Milnor–Thurston kneading theory is a mathematical theory which analyzes the iterates of piecewise monotone mappings of an interval into itself. The emphasis is on understanding the properties of the mapping that are invariant under topological conjugacy.
In mathematics, a quasisymmetric homeomorphism between metric spaces is a map that generalizes bi-Lipschitz maps. While bi-Lipschitz maps shrink or expand the diameter of a set by no more than a multiplicative factor, quasisymmetric maps satisfy the weaker geometric property that they preserve the relative sizes of sets: if two sets A and B have diameters t and are no more than distance t ...
The Urdu Dictionary Board (Urdu: اردو لغت بورڈ, romanized: Urdu Lughat Board) is an academic and literary institution of Pakistan, administered by National History and Literary Heritage Division of the Ministry of Information & Broadcasting. Its objective is to edit and publish a comprehensive dictionary of the Urdu language.
It is the most comprehensive, detailed and thick dictionary in the history of Urdu language. [ citation needed ] It is published by the Urdu Lughat Board, Karachi. The dictionary was edited by the honorary director general of the board Maulvi Abdul Haq who had already been working on an Urdu dictionary since the establishment of the Urdu ...
meaning "If each is true, then is true". Logic programs compute the set of facts that are implied by their rules. Many implementations of Datalog, Prolog, and related languages add procedural features such as Prolog's cut operator or extra-logical features such as a foreign function interface. The formal semantics of such extensions are beyond ...
Farhang-e-Asifiya (Urdu: فرہنگ آصفیہ, lit. 'The Dictionary of Asif') is an Urdu-to-Urdu dictionary compiled by Syed Ahmad Dehlvi. [1] It has more than 60,000 entries in four volumes. [2] It was first published in January 1901 by Rifah-e-Aam Press in Lahore, present-day Pakistan. [3] [4]
In mathematics, specifically in the field of topology, a monotonically normal space is a particular kind of normal space, defined in terms of a monotone normality operator. It satisfies some interesting properties; for example metric spaces and linearly ordered spaces are monotonically normal, and every monotonically normal space is ...