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The tetrix is the three-dimensional analog of the Sierpiński sieve illustrated above, also called the Sierpiński sponge or Sierpiński tetrahedron. The nth iteration of the ...

An isolated point of a graph is a node of degree 0 (Hartsfield and Ringel 1990, p. 8; Harary 1994, p. 15; D'Angelo and West 2000, p. 212; West 2000, p. 22). The number of ...

The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two nonconcentric circles. By the chordal theorem, it is ...

A fractal which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 1 0; 1 1 1; 0 1 0],1->[1 1 1; 1 1 1; 1 1 1]}. (1) The size ...

A piecewise linear, one-dimensional map on the interval [0,1] exhibiting chaotic dynamics and given by x_(n+1)=mu(1-2|x_n-1/2|). (1) The first few iterations of (1) give x_1 ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

Let O be an order of an imaginary quadratic field. The class equation of O is the equation H_O=0, where H_O is the extension field minimal polynomial of j(O) over Q, with ...

Any real function u(x,y) with continuous second partial derivatives which satisfies Laplace's equation, del ^2u(x,y)=0, (1) is called a harmonic function. Harmonic functions ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

Given two functions f and g analytic in A with gamma a simple loop homotopic to a point in A, if |g(z)|<|f(z)| for all z on gamma, then f and f+g have the same number of ...