Lattice norms on the unitization of a truncated normed Riesz space

Positivity - Truncated Riesz spaces was first introduced by Fremlin in the context of real-valued functions. An appropriate axiomatization of the concept was given by Ball. Keeping only the first...     

What is the role of acid–acid interactions in asymmetric phosphoric acid organocatalysis? A detailed mechanistic study using interlocked and non-interlocked catalysts

Organocatalysis has revolutionized asymmetric synthesis. However, the supramolecular interactions of organocatalysts in solution are often neglected, although the formation of catalyst aggregates can have a strong impact on the catalytic reaction. For phosphoric acid based organocatalysts, we have now established that catalyst–catalyst interactions can be suppressed by using macrocyclic catalysts, which react predominantly in a monomeric fashion, while they can be favored by integration into a bifunctional catenane, which reacts mainly as phosphoric acid dimers. For acyclic phosphoric acids, we found a strongly concentration dependent behavior, involving both monomeric and dimeric catalytic pathways. Based on a detailed experimental analysis, DFT-calculations and direct NMR-based observation of the catalyst aggregates, we could demonstrate that intermolecular acid–acid interactions have a drastic influence on the reaction rate and stereoselectivity of asymmetric transfer-hydrogenation catalyzed by chiral phosphoric acids.

Supramolecular acid–acid interactions lead to competing monomeric and dimeric pathways in phosphoric acid catalysis – so that stereoselectivities depend on catalyst concentration.     

Impact of the Oxygen Defects and the Hydrogen Concentration on the Surface of Tetragonal and Monoclinic ZrO2 on the Reduction Rates of Stearic Acid on Ni/ZrO2

The role of the specific physicochemical properties of ZrO₂ phases on Ni/ZrO₂ has been explored with respect to the reduction of stearic acid. Conversion on pure m‐ZrO₂ is 1.3 times more active than on t‐ZrO₂, whereas Ni/m‐ZrO₂ is three times more active than Ni/t‐ZrO₂. Although the hydrodeoxygenation of stearic acid can be catalyzed solely by Ni, the synergistic interaction between Ni and the ZrO₂ support causes the variations in the reaction rates. Adsorption of the carboxylic acid group on an oxygen vacancy of ZrO₂ and the abstraction of the α‐hydrogen atom with the elimination of the oxygen atom to produce a ketene is the key to enhance the overall rate. The hydrogenated intermediate 1‐octadecanol is in turn decarbonylated to heptadecane with identical rates on all catalysts. Decarbonylation of 1‐octadecanol is concluded to be limited by the competitive adsorption of reactants and intermediate. The substantially higher adsorption of propionic acid demonstrated by IR spectroscopy and the higher reactivity to O₂ exchange reactions with the more active catalyst indicate that the higher concentration of active oxygen defects on m‐ZrO₂ compared to t‐ZrO₂ causes the higher activity of Ni/m‐ZrO₂.     

Catalytic Generation and Chemoselective Transfer of Nucleophilic Hydrides from Dihydrogen

Copper(I)–N-heterocyclic-carbene (NHC) complexes enabled the catalytic generation of nucleophilic hydrides from dihydrogen (H₂) and their subsequent transfer to allylic chlorides. The highly chemoselective catalyst displayed no concomitant hydrogenation reactivity; in fact, the terminal double bond formed in the hydride transfer remained intact. Switching to deuterium gas (D₂) allowed for regioselective monodeuteration with excellent isotope incorporation.     

Doping radius effects on an erbium-doped fiber amplifier

In an erbium-doped fiber amplifier(EDFA), erbium ions act as a three-level system. Therefore, much higher pump energy is required to achieve the population inversion in an erbium-doped fiber(EDF). This higher pump energy requirement complicates the efficient design of an EDFA. However, efficient use of the pump power can improve the EDFA performance. The improved performance of an EDFA can be obtained by reducing the doping radius of the EDF. A smaller doping radius increases pump–dopant interactions and subsequently increases the pump–photon conversion efficiency. Decreasing the doping radius allows a larger proportion of dopant ions,which are concentrated near the core, to interact with the highest pump intensity. However, decreasing the doping radius beyond a certain limit will bring the dopant ions much closer and introduce detrimental ion–ion interaction effects. In this Letter, we show that an optimal doping radius in an EDF can provide the best gain performance. Moreover, we have simulated the well-known numerical aperture effects on EDFA gain performance to support our claim.