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A single-valued function is function that, for each point in the domain, has a unique value in the range. It is therefore one-to-one or many-to-one. A single-valued complex ...

A basin of attraction in which every point on the common boundary of that basin and another basin is also a boundary of a third basin. In other words, no matter how closely a ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

An n-dimensional closed disk of radius r is the collection of points of distance <=r from a fixed point in n-dimensional Euclidean space. Krantz (1999, p. 3) uses the symbol ...

A subset X of R^n is star convex if there exists an x_0 in X such that the line segment from x_0 to any point in X is contained in X. A star-shaped figure is star convex but ...

Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for ...

If f:[a,b]->[a,b] (where [a,b] denotes the closed interval from a to b on the real line) satisfies a Lipschitz condition with constant K, i.e., if |f(x)-f(y)|<=K|x-y| for all ...

Define T as the set of all points t with probabilities P(x) such that a>t=>P(a<=x<=a+da)<P_0 or a<t=>P(a<=x<=a+da)<P_0, where P_0 is a point probability (often, the ...