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The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

A Stoneham number is a number alpha_(b,c) of the form alpha_(b,c)=sum_(k=1)^infty1/(b^(c^k)c^k), where b,c>1 are relatively prime positive integers. Stoneham (1973) proved ...

The sequence of variates X_i with corresponding means mu_i obeys the strong law of large numbers if, to every pair epsilon,delta>0, there corresponds an N such that there is ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

The (m,q)-Ustimenko graph is the distance-1 or distance-2 graph of the dual polar graph on [C_m(q)] (Brouwer et al. 1989, p. 279). The Ustimenko graph with parameters m and q ...

The contraction of a pair of vertices v_i and v_j of a graph, also called vertex identification, is the operation that produces a graph in which the two nodes v_1 and v_2 are ...

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_n=f(x_n). Then Woolhouse's formulas ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...

Let union represent "or", intersection represent "and", and ^' represent "not." Then, for two logical units E and F, (E union F)^'=E^' intersection F^' (E intersection ...