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Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) = 2/pisin^(-1)[sin(pix)] (1) = 1-2|1-[2(1/2x+1/4 (mod 1))]| (2) = ...

Calculus II

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

The transformation of a sequence a_1, a_2, ... with a_n=sum_(d|n)b_d (1) into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n=sum_(d|n)mu(n/d)a_d. (2) The ...

The power tower of order k is defined as a^^k=a^(a^(·^(·^(·^a))))_()_(k), (1) where ^ is Knuth up-arrow notation (Knuth 1976), which in turn is defined by ...