Transmetallation Versus β‐Hydride Elimination: The Role of 1,4‐Benzoquinone in Chelation‐Controlled Arylation Reactions with Arylboronic Acids

The formation of an atypical, saturated, diarylated, Heck/Suzuki, domino product produced under oxidative Heck reaction conditions, employing arylboronic acids and a chelating vinyl ether, has been investigated by DFT calculations. The calculations highlight the crucial role of 1,4‐benzoquinone (BQ) in the reaction. In addition to its role as an oxidant of palladium, which is necessary to complete the catalytic cycle, this electron‐deficient alkene opens up a low‐energy reaction pathway from the post‐insertion σ‐alkyl complex. The association of BQ lowers the free‐energy barrier for transmetallation of the σ‐alkyl complex to create a pathway that is energetically lower than the oxidative Heck reaction pathway. Furthermore, the calculations showed that the reaction is made viable by BQ‐mediated reductive elimination and leads to the saturated diarylated product.     

Transmetallation versus β-hydride elimination: the role of 1,4-benzoquinone in chelation-controlled arylation reactions with arylboronic acids

The formation of an atypical, saturated, diarylated, Heck/Suzuki, domino product produced under oxidative Heck reaction conditions, employing arylboronic acids and a chelating vinyl ether, has been investigated by DFT calculations. The calculations highlight the crucial role of 1,4-benzoquinone (BQ) in the reaction. In addition to its role as an oxidant of palladium, which is necessary to complete the catalytic cycle, this electron-deficient alkene opens up a low-energy reaction pathway from the post-insertion σ-alkyl complex. The association of BQ lowers the free-energy barrier for transmetallation of the σ-alkyl complex to create a pathway that is energetically lower than the oxidative Heck reaction pathway. Furthermore, the calculations showed that the reaction is made viable by BQ-mediated reductive elimination and leads to the saturated diarylated product.     

Geometry of Diffeomorphism Groups, Complete integrability and Geometric statistics

We study the geometry of the space of densities Dens(M), which is the quotient space Diff(M)/Diff _μ (M) of the diffeomorphism group of a compact manifold M by the subgroup of volume-preserving diffeomorphisms, endowed with a right-invariant homogeneous Sobolev ${\dot{H}^1}$ -metric. We construct an explicit isometry from this space to (a subset of) an infinite-dimensional sphere and show that the associated Euler–Arnold equation is a completely integrable system in any space dimension whose smooth solutions break down in finite time. We also show that the ${\dot{H}^1}$ -metric induces the Fisher–Rao metric on the space of probability distributions and its Riemannian distance is the spherical version of the Hellinger distance.     

Multiple Andreev reflections in diffusive SNS structures

We report new measurements on subgap energy structures originating from multiple Andreev reflections in mesoscopic SNS junctions. The junctions were fabricated in a planar geometry with high-transparency superconducting contacts of Al deposited on highly diffusive and surface δ -dopedn ^{+ +} -GaAs. For samples with a normal GaAs region of active length 0.3μ m, the Josephson effect with a maximal supercurrent I_c = 3μ A at T = 237 mK was observed. The subgap structure was observed as a series of local minima in the differential resistance at dc bias voltages V = ± 2Δ / (ne) with n = 1, 2, 4, i.e. only the even subgap positions. While at V = ± 2Δ / e(n = 1) only one dip is observed, then = 2 and the n = 4 subgap structures each consists of two separate dips in the differential resistance. The mutual spacing of these two dips is independent of temperature, and the mutual spacing of the n = 4 dips is half the spacing of the n = 2 dips. The voltage bias positions of the subgap differential resistance minima coincide with the maxima in the oscillation amplitude when a magnetic field is applied in an interferometer configuration, where one of the superconducting electrodes has been replaced by a flux-sensitive open loop.     

Rigidity and Bifurcation Results for CMC Hypersurfaces in Warped Product Spaces

In this paper, we deduce some rigidity results in warped product spaces under normal variations of CMC hypersurfaces. In particular, we prove the existence of one-parameter families locally rigid on the spatial fiber of Anti-de Sitter Schwarzschild spacetime and one-parameter families with bifurcation points on the spatial fiber of de Sitter Schwarzschild spacetime.