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A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...

If A=>B and B=>A (i.e., A=>B ^ B=>A, where => denotes implies), then A and B are said to be equivalent, a relationship which is written symbolically in this work as A=B. The ...

Exterior algebra is the algebra of the wedge product, also called an alternating algebra or Grassmann algebra. The study of exterior algebra is also called Ausdehnungslehre ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

A notion introduced by R. M. Wilson in 1974. Given a finite graph G with n vertices, puz(G) is defined as the graph whose nodes are the labelings of G leaving one node ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...