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An independent edge set, also called a matching, of a graph G is a subset of the edges such that no two edges in the subset share a vertex in G. A maximum independent edge ...

For a sequence {chi_i}, the Levine-O'Sullivan greedy algorithm is given by chi_1 = 1 (1) chi_i = max_(1<=j<=i-1)(j+1)(i-chi_j) (2) for i>1. The sequence generated by this ...

A fractal based on iterating the map F(x)=ax+(2(1-a)x^2)/(1+x^2) (1) according to x_(n+1) = by_n+F(x_n) (2) x_(y+1) = -x_n+F(x_(n+1)). (3) The plots above show 10^4 ...

For a point y in Y, with f(y)=x, the ramification index of f at y is a positive integer e_y such that there is some open neighborhood U of y so that x has only one preimage ...

The power of a fixed point A with respect to a circle of radius r and center O is defined by the product p=AP×AQ, (1) where P and Q are the intersections of a line through A ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

An isosceles tetrahedron is a nonregular tetrahedron in which each pair of opposite polyhedron edges are equal, i.e., a^'=a, b^'=b, and c^'=c, so that all triangular faces ...

A 4-state two-dimensional Turing machine invented in the 1980s. The ant starts out on a grid containing black and white cells, and then follows the following set of rules. 1. ...

The Laplacian matrix, sometimes also called the admittance matrix (Cvetković et al. 1998, Babić et al. 2002) or Kirchhoff matrix, of a graph G, where G=(V,E) is an ...

A method for finding recurrence relations for hypergeometric polynomials directly from the series expansions of the polynomials. The method is effective and easily ...