4 papers
Variations on the Post Correspondence Problem for free groups
Laura Ciobanu, Alan D. Logan
The Post Correspondence Problem is a classical decision problem about equalisers of free monoid homomorphisms. We prove connections between several variations of this classical pro…
Fixed points and stable images of endomorphisms for the free group of rank two
Laura Ciobanu, Alan D. Logan
We give an algorithm which computes the fixed subgroup and the stable image for any endomorphism of the free group of rank two , answering for a question posed by Stalli…
The Post Correspondence Problem and equalisers for certain free group and monoid morphisms
Laura Ciobanu, Alan D. Logan
A marked free monoid morphism is a morphism for which the image of each generator starts with a different letter, and immersions are the analogous maps in free groups. We show that…
400%/W second harmonic conversion efficiency in -diameter gallium phosphide-on-oxide resonators
Alan D. Logan, Michael Gould, Emma R. Schmidgall +7
Second harmonic conversion from 1550~nm to 775~nm with an efficiency of 400% W is demonstrated in a gallium phosphide (GaP) on oxide integrated photonic platform. The platfo…