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The 9.1.2 equation A^9=B^9+C^9 (1) is a special case of Fermat's last theorem with n=9, and so has no solution. No 9.1.3, 9.1.4, 9.1.5, 9.1.6, 9.1.7, 9.1.8, or 9.1.9 ...

A tree (also called a bicentral tree) having two nodes that are graph centers. The numbers of bicentered trees on n=1, 2, ... nodes are 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108 ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

A tree (also called a central tree) having a single node that is a graph center. The numbers of centered trees on n=1, 2, ... nodes are 1, 0, 1, 1, 2, 3, 7, 12, 27, 55, 127, ...

Define the correlation integral as C(epsilon)=lim_(N->infty)1/(N^2)sum_(i,j=1; i!=j)^inftyH(epsilon-|x_i-x_j|), (1) where H is the Heaviside step function. When the below ...

A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

Let (q_1,...,q_n,p_1,...,p_n) be any functions of two variables (u,v). Then the expression ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...