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An efficient version of the Walsh transform that requires O(nlnn) operations instead of the n^2 required for a direct Walsh transform (Wolfram 2002, p. 1072).

If {f_n} is a sequence of nonnegative measurable functions, then intlim inf_(n->infty)f_ndmu<=lim inf_(n->infty)intf_ndmu. (1) An example of a sequence of functions for which ...

The Faulkner-Younger graphs (Faulkner and Younger 1974) are the cubic polyhedral nonhamiltonian graphs on 42 and 44 vertices illustrated above that are counterexamples to ...

Given a sequence of independent random variates X_1, X_2, ..., if sigma_k^2=var(X_k) and rho_n^2=max_(k<=n)((sigma_k^2)/(s_n^2)), then lim_(n->infty)rho_n^2=0. This means ...

A self-avoiding polygon containing three corners of its minimal bounding rectangle. The anisotropic area and perimeter generating function G(x,y) and partial generating ...

A fibered category F over a topological space X consists of 1. a category F(U) for each open subset U subset= X, 2. a functor i^*:F(U)->F(V) for each inclusion i:V↪U, and 3. ...

Let F and G be fibered categories over a topological space X. A morphism phi:F->G of fibered categories consists of: 1. a functor phi(U):F->G(U) for each open subset U ...

The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

A formula for numerical integration, (1) where C_(2n) = sum_(i=0)^(n)f_(2i)cos(tx_(2i))-1/2[f_(2n)cos(tx_(2n))+f_0cos(tx_0)] (2) C_(2n-1) = ...