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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.
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.
is the electromagnetic contraction (propagator) in the Feynman gauge. This term is represented by the Feynman diagram at the right. This diagram gives contributions to the following processes: e − e − scattering (initial state at the right, final state at the left of the diagram);
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.
The proper length of an object is the length of the object in the frame in which the object is at rest. Also, this contraction only affects the dimensions of the object which are parallel to the relative velocity between the object and observer. Thus, lengths perpendicular to the direction of motion are unaffected by length contraction.
Contractions in the right ventricle provide pulmonary circulation by pulsing oxygen-depleted blood through the pulmonary valve then through the pulmonary arteries to the lungs. Simultaneously, contractions of the left ventricular systole provide systemic circulation of oxygenated blood to all body systems by pumping blood through the aortic ...
In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. [1] The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface.
An increase in preload results in an increased force of contraction by Starling's law of the heart; this does not require a change in contractility. An increase in afterload will increase contractility (through the Anrep effect). [4] An increase in heart rate will increase contractility (through the Bowditch effect). [4]