Orthogonal term rewriting systems (also known as regular systems) provide an elegant framework for programming in equational logic. O'Donnell showed that the parallel-outermost strategy, which replaces all outermost redexes in each step, is complete for such systems. Many of the reductions performed by this strategy could be wasteful in general. A lazy normalization algorithm that completely el...

In this paper, by considering the notion of $Sigma$-hyperalgebras for an arbitrary signature $Sigma$, we study the notions of regular and strongly regular relations on a $Sigma$-hyperalgebra, $mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $mathf...

We prove that it is strongly NP-complete to decide whether a given orthogonal polyhedron has a (nonoverlapping) edge unfolding. The result holds even when the polyhedron is topologically convex, i.e., is homeomorphic to a sphere, has faces that are homeomorphic to disks, and where every two faces share at most one edge.

Amicable orthogonal designs have renewed interest because of their use in mobile communications. We show the existence of strong amicable orthogonal designs, AOD(n : 1, n − 1; 1, n − 1), for n = p + 1, p ≡ 3 (mod 4) a prime and for n = 2, n a non-negative integer in a form more suitable for communications. Unfortunately the existence of amicable Hadamard matrices is not enough to demonstrate th...

An overview of geminal-based wavefunctions is given, allowing for singlet-triplet mixing within the two-electron units. Spin contamination of the total wavefunction (obtained as an antisymmetrized product) is restored by spin projection. Full variation after projection is examined for two models. One is the long known spin-projected, extended Hartree-Fock (EHF). The other is a yet unexplored fu...