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A contraction is a shortened version of the spoken and written forms of a word, syllable, or word group, created by omission of internal letters and sounds.. In linguistic analysis, contractions should not be confused with crasis, abbreviations and initialisms (including acronyms), with which they share some semantic and phonetic functions, though all three are connoted by the term ...
A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x , f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.
Some acronyms are formed by contraction; these are covered at Wikipedia:Manual of Style/Abbreviations. Some trademarks (e.g. Nabisco) and titles of published works (e.g. “Ain't That a Shame”) consist of or contain contractions; these are covered at Wikipedia:Manual of Style/Trademarks and Wikipedia:Manual of Style/Titles, respectively.
Poetic contractions are contractions of words found in poetry but not commonly used in everyday modern English. Also known as elision or syncope , these contractions are usually used to lower the number of syllables in a particular word in order to adhere to the meter of a composition. [ 1 ]
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its ... Examples are the ladder paradox and Bell's spaceship ...
For example, the Ricci tensor is a non-metric contraction of the Riemann curvature tensor, and the scalar curvature is the unique metric contraction of the Ricci tensor. One can also view contraction of a tensor field in the context of modules over an appropriate ring of functions on the manifold [ 5 ] or the context of sheaves of modules over ...
This notion is a special case of the concept of a contraction mapping, but every bounded operator becomes a contraction after suitable scaling. The analysis of contractions provides insight into the structure of operators, or a family of operators. The theory of contractions on Hilbert space is largely due to Béla Szőkefalvi-Nagy and Ciprian ...
In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces and provides a constructive method to find those fixed points.