Multiplicative Automorphisms of Incidence Algebras

We present necessary and sufficient conditions for a multiplicative automorphism of an incidence algebra of a finite partially ordered set X to be an inner automorphism. These conditions are related to the structure of X as a directed graph.     

Full Graphs and Koszul Algebras I

The main result of this article is the establishment of a new connection between combinatorics and noncommutative algebra. This is done by linking a certain class of directed graphs, called full graphs, to quotients of path algebras that are Koszul algebras.     

Iridium-catalyzed carbonyl group-directed oxidative coupling of arenes with alkenes

The iridium complex [Cp¹IrCl₂]₂ is a good catalyst for the directed oxidative coupling of arenes with alkenes; a wide range of carbonyl functionalities (NHCOR, CONH₂ and COR) can be employed as the directing group.     

Enantioselective Hydrosilylation of β,β-Disubstituted Enamides to Construct α-Aminosilanes with Vicinal Stereocenters

Despite the advances in the area of catalytic alkene hydrosilylation, the enantioselective hydrosilylation of alkenes bearing a heteroatom substituent is scarce. Here we report a rhodium-catalyzed hydrosilylation of β,β-disubstituted enamides to directly afford valuable α-aminosilanes in a highly regio-, diastereo-, and enantioselective manner. Stereodivergent synthesis could be achieved by regulating substrate geometry and ligand configuration to generate all the possible stereoisomers in high enantio-purity.     

Spatially Directed Pyrolysis via Thermally Morphing Surface Adducts

Combustion is often difficult to spatially direct or tune associated kinetics—hence a run-away reaction. Coupling pyrolytic chemical transformation to mass transport and reaction rates (Damköhler number), however, we spatially directed ignition with concomitant switch from combustion to pyrolysis (low oxidant). A ‘surface-then-core’ order in ignition, with concomitant change in burning rate,is therefore established. Herein, alkysilanes grafted onto cellulose fibers are pyrolyzed into non-flammable SiO₂ terminating surface ignition propagation, hence stalling flame propagating. Sustaining high temperatures, however, triggers ignition in the bulk of the fibers but under restricted gas flow (oxidant and/or waste) hence significantly low rate of ignition propagation and pyrolysis compared to open flame (Liñán's equation). This leads to inside-out thermal degradation and, with felicitous choice of conditions, formation of graphitic tubes. Given the temperature dependence, imbibing fibers with an exothermically oxidizing synthon (MnCl₂) or a heat sink (KCl) abets or inhibits pyrolysis leading to tuneable wall thickness. We apply this approach to create magnetic, paramagnetic, or oxide containing carbon fibers. Given the surface sensitivity, we illustrate fabrication of nm- and μm-diameter tubes from appropriately sized fibers.