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A real-valued function g defined on a convex subset C subset R^n is said to be quasi-concave if for all real alpha in R, the set {x in C:g(x)>=alpha} is convex. This is ...

A real-valued function g defined on a convex subset C subset R^n is said to be quasi-convex if for all real alpha in R, the set {x in C:g(x)<alpha} is convex. This is ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

A scatter diagram, also called a scatterplot or a scatter plot, is a visualization of the relationship between two variables measured on the same set of individuals. Scatter ...

A species of structures is a rule F which 1. Produces, for each finite set U, a finite set F[U], 2. Produces, for each bijection sigma:U->V, a function F[sigma]:F[U]->F[V]. ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

A topological space fulfilling the T_2-axiom: i.e., any two points have disjoint neighborhoods. In the terminology of Alexandroff and Hopf (1972), a T_2-space is called a ...

A characterization of normal spaces with respect to the definition given by Kelley (1955, p. 112) or Willard (1970, p. 99). It states that the topological space X is normal ...

Let X be a connected topological space. Then X is unicoherent provided that for any closed connected subsets A and B of X, if X=A union B, then A intersection B is connected. ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...