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Asymptote. The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2 x). A curve intersecting an asymptote infinitely many times. In analytic geometry, an asymptote (/ ˈæsɪmptoʊt /) of a curve is a line such that the distance between the curve and the line approaches zero as one ...
A sigmoid function refers specifically to a function whose graph follows the logistic function. It is defined by the formula: In many fields, especially in the context of artificial neural networks, the term "sigmoid function" is correctly recognized as a synonym for the logistic function. While other S-shaped curves, such as the Gompertz curve ...
Hyperbola. A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case. Hyperbola (red): features. In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its ...
Logistic function. A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint.
Asymptotic analysis. In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared ...
Function. In mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve. The graphical representation of the graph of a function is also known as a plot. In the case of functions of two variables ...
In fluid dynamics a shear mapping depicts fluid flow between parallel plates in relative motion. In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed distance from a given line parallel to that direction. [1] This type of mapping is also called ...
In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). In linear algebra, it is synonymous with a linear form, which is a linear mapping from a vector space. V {\displaystyle V} into its field of scalars (that is, it is an element of the dual ...
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