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The surface with three cross-caps (Francis and Collins 1993, Francis and Weeks 1999).

Handles and cross-handles are equivalent in the presence of a cross-cap.

For any two ergodic measure-preserving transformations on nonatomic probability spaces, there is an isomorphism between the two probability spaces carrying orbits onto orbits.

Let Jones and Smith be the only two contestants in an election that will end in a deadlock when all votes for Jones (J) and Smith (S) are counted. What is the expectation ...

The Eberlein polynomials of degree 2k and variable x are the orthogonal polynomials arising in the Johnson scheme that may be defined by E_k^((n,v))(x) = ...

The second-order ordinary differential equation y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0, where eta=e^(deltax).

A Padé approximant perturbed with a Chebyshev polynomial of the first kind to reduce the leading coefficient in the error.

136·2^(256) approx 1.575×10^(79). According to Eddington, the exact number of protons in the universe, where 136 was the reciprocal of the fine structure constant as best as ...

An edge automorphism of a graph G is a permutation of the edges of G that sends edges with common endpoint into edges with a common endpoint. The set of all edge ...

The set of all edge automorphisms of G, denoted Aut^*(G). Let L(G) be the line graph of a graph G. Then the edge automorphism group Aut^*(G) is isomorphic to Aut(L(G)), ...