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An asymptote is a straight line that a curve approaches but never meets or crosses. Informally, one may speak of the curve meeting the asymptote "at infinity" although this is not a precise definition. In the equation =, y becomes arbitrarily small in magnitude as x increases.
In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. . Their solutions lend themselves to asymptotic analysis (perturbation theory), which is widely used in modern applied mathematics, mechanics and phy
Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. [5] The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.
In metric geometry, asymptotic dimension of a metric space is a large-scale analog of Lebesgue covering dimension.The notion of asymptotic dimension was introduced by Mikhail Gromov in his 1993 monograph Asymptotic invariants of infinite groups [1] in the context of geometric group theory, as a quasi-isometry invariant of finitely generated groups.
In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some "bad" topology, [1] but can also be considered an algorithm in its own right.
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A particular case of the generalised logistic function is: = (+ ()) /which is the solution of the Richards's differential equation (RDE): ′ = (()) with initial condition
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