On Highly Factorable Numbers

On Highly Composite and Similar Numbers

Heralded single-photon source utilizing highly nondegenerate, spectrally factorable spontaneous parametric downconversion.

We report on the generation of an indistinguishable heralded single-photon state, using highly nondegenerate spontaneous parametric downconversion (SPDC). Spectrally factorable photon pairs can be generated by incorporating a broadband pump pulse and a group-velocity matching (GVM) condition in a periodically-poled potassium titanyl phosphate (PPKTP) crystal. The heralding photon is in the near...

Factorable Congruences and Strict Refinement

We show that universal algebras with factorable congruences such as rings with 1 and semirings with 0 and 1 enjoy some of the properties of universal algebras whose congruence lattices are distributive, such as the strict refinement property and a variant of Jónsson’s lemma. A universal algebra A is said to have factorable congruences if whenever A ∼= B × C and θ is a congruence on A, then θ = ...

Arc consistency for factorable relations

An optimal arc consistency algorithm AC-4 was given by Mohr and Henderson [8]. AC4 has cost 0(ea), and cost (na) for scene labelling. Although their algorithm is indeed optimal, under certain conditions a constraint satisfaction problem can be transformed into a less complex problem. In this paper, we present conditions and mechanisms for such transformations, and show how to factor relations i...

Subdivision of the spectra for factorable matrices on c and `

There are many different ways to subdivide the spectrum of a bounded linear operator; some of them are motivated by applications to physics (in particular, quantum mechanics). In a series of papers, B.E. Rhoades and M. Yildirim previously investigated the spectra and fine spectra for factorable matrices, considered as bounded operators over various sequence spaces. In the present paper, approxi...