Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

Journal of Fourier Analysis and Applications - We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( $$SG$$ ), which is a fractal set that can be viewed as a limit...     

Synthesis of Highly Substituted γ‐Butyrolactones by a Gold‐Catalyzed Cascade Reaction of Benzyl Esters

Easily accessible benzylic esters of 3‐butynoic acids in a gold‐catalyzed cyclization/rearrangement cascade reaction provided 3‐propargyl γ‐butyrolactones with the alkene and the carbonyl group not being conjugated. Crossover experiments showed that the formation of the new C?C bond is an intermolecular process. Initially propargylic–benzylic esters were used, but alkyl‐substituted benzylic esters worked equally well. In the case of the propargylic–benzylic products, a simple treatment of the products with aluminum oxide initiated a twofold tautomerization to the allenyl‐substituted γ‐butyrolactones with conjugation of the carbonyl group, the olefin, and the allene. The synthetic sequence can be conducted stepwise or as a one‐pot cascade reaction with similar yields. Even in the presence of the gold catalyst the new allene remains intact.     

Can a Procedure for the Growth of Single-layer Graphene on Copper be used in Different Chemical Vapor Deposition Reactors?

In the last decade, catalytic chemical vapor deposition (CVD) has been intensively explored for the growth of single-layer graphene (SLG). Despite the scattering of guidelines and procedures, variables such as the surface texture/chemistry of catalyst metal foils, carbon feedstock, and growth process parameters have been well-scrutinized. Still, questions remain on how best to standardize the growth procedure. The possible correlation of procedures between different CVD setups is an example. Here, two thermal CVD reactors were explored to grow graphene on Cu foil. The design of these setups was entirely distinct, one being a “showerhead” cold-wall type, whereas the other represented the popular “tubular” hot-wall type. Upon standardizing the Cu foil surface, it was possible to develop a procedure for cm²-scale SLG growth that differed only by the carrier gas flow rate used in the two reactors.