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If W is a simply connected, compact manifold with a boundary that has two components, M_1 and M_2, such that inclusion of each is a homotopy equivalence, then W is ...

Borsuk conjectured that it is possible to cut an n-dimensional shape of generalized diameter 1 into n+1 pieces each with diameter smaller than the original. It is true for ...

A strongly regular graph with parameters (n,k,a,c) has graph eigenvalues k, theta, and tau, where theta = ((a-c)+sqrt(Delta))/2 (1) tau = ((a-c)-sqrt(Delta))/2 (2) where ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

The Jahangir graph J_(n,m) is a kind of generalized wheel graph with consisting of mn circular vertices and a central vertex connected to every mth vertex around the circle. ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a modular Hilbert algebra if A has an inner product <··> and a ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

Every smooth nonzero vector field on the 3-sphere has at least one closed orbit. The conjecture was proposed in 1950 and proved true for Hopf maps. The conjecture was ...

A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...