The Finite Embeddability Property for some noncommutative knotted varieties of RL and DRL.

Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus

Photogenerated o-Azaxylylenes: Mechanistic Studies and Synthetic Applications

This research sets out to build upon excited state o-azaxylylene cycloaddition. The mechanism behind the excitation and cycloaddition process of photogenerated o-azaxylylenes was determined experimentally. Time-correlated single-photon counting, steady-state spectroscopy, triplet quenching experiments, and quantum yield studies provided evidence suggesting that excited state intramolecular proton transfer is followed by intersystem crossing and stepwise addition to the tethered unsaturated pendant. In keeping with the principles of diversity oriented synthesis, a modular approach was taken to gain access to a diverse array of N,O,S-Polyheterocycles which were modified postphotochemically via Suzuki coupling to yield fused biaryls. Cycloaddition products, outfitted with halogens in the aromatic ring of the o-azaxylylene, proved to be reactive with a variety of boronic acids resulting in a rapid growth in structural complexity. A novel procedure was developed that utilized multiple o-azaxylylene cores in a photochemical cascade transformation yielding complex scaffolds of unprecedented topology. The photoprecursors were produced in a one-pot two-step sequence from commercially available starting materials, and upon irradiation yield structures containing up to five fused hetrocyclic rings, and showed complete diastereoselectivity.