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For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.

The topological entropy of a map M is defined as h_T(M)=sup_({W_i})h(M,{W_i}), where {W_i} is a partition of a bounded region W containing a probability measure which is ...

A totally disconnected space is a space in which all subsets with more than one element are disconnected. In particular, if it has more than one element, it is a disconnected ...

The transitive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same transitive closure as R. Thus aR^'b for any elements a and b of X, ...

Also called indiscrete topology, the trivial topology is the smallest topology on a set X, namely the one in which the only open sets are the empty set and the entire set X. ...

Any discrete finite wavelet transform can be represented as a matrix, and such a wavelet matrix can be computed in O(n) steps, compared to O(nlgn) for the Fourier matrix, ...

The Wilcoxon test statistic is equivalent to the T_+ statistic in the Wilcoxon signed rank test (Kanji 1999).

A discrete fast Fourier transform algorithm which can be implemented for N=2, 3, 4, 5, 7, 8, 11, 13, and 16 points.

Theory of Computation

Let {f_n} and {a_n} be sequences with f_n>=f_(n+1)>0 for n=1, 2, ..., then |sum_(n=1)^ma_nf_n|<=Af_1, where A=max{|a_1|,|a_1+a_2|,...,|a_1+a_2+...+a_m|}.