Gold-Catalyzed Divergent Ring-Opening Rearrangement of Cyclopropenes Enabled by Dichotomous Gold−Carbenes

The gold-catalyzed ring-opening rearrangement of cyclopropenes affords an efficient route to either polysubstituted naphthols or aryl-substituted furans. Owing to the unique dichotomy of gold−carbenes, this protocol provides a switchable reaction selectivity between naphthols and furans enabled by the use of TFP−Au(MeCN)SbF₆ (tri(2-furyl) phosphine) or PNP(AuNTf₂)₂ (bis(diphenylphosphino)(isopropyl) amine) as catalysts respectively. It is proposed that the gold−carbene intermediate might be involved in the cyclopropene→naphthol rearrangement while the gold-carbocation is more likely to be involved in the cyclopropene→furan rearrangement.     

Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.     

Donor-Flexible Bis(pyridylidene amide) Ligands for Highly Efficient Ruthenium-Catalyzed Olefin Oxidation

An exceptionally efficient ruthenium-based catalyst for olefin oxidation has been designed by exploiting N,N′-bis(pyridylidene)oxalamide (bisPYA) as a donor-flexible ligand. The dynamic donor ability of the bisPYA ligand, imparted by variable zwitterionic and neutral resonance structure contributions, paired with the redox activity of ruthenium provided catalytic activity for Lemieux–Johnson-type oxidative cleavage of olefins to efficiently prepare ketones and aldehydes. The ruthenium bisPYA complex significantly outperforms state-of-the-art systems and displays extraordinary catalytic activity in this oxidation, reaching turnover frequencies of 650 000 h⁻¹ and turnover numbers of several millions.     

Catalytic Behavior of Mono-N-Protected Amino-Acid Ligands in Ligand-Accelerated C−H Activation by Palladium(II)

Mono-N-protected amino acids (MPAAs) are increasingly common ligands in Pd-catalyzed C−H functionalization reactions. Previous studies have shown how these ligands accelerate catalytic turnover by facilitating the C−H activation step. Here, it is shown that MPAA ligands exhibit a second property commonly associated with ligand-accelerated catalysis: the ability to support catalytic turnover at substoichiometric ligand-to-metal ratios. This catalytic role of the MPAA ligand is characterized in stoichiometric C−H activation and catalytic C−H functionalization reactions. Palladacycle formation with substrates bearing carboxylate and pyridine directing groups exhibit a 50–100-fold increase in rate when only 0.05 equivalents of MPAA are present relative to Pd^II. These and other mechanistic data indicate that facile exchange between MPAAs and anionic ligands coordinated to Pd^II enables a single MPAA to support C−H activation at multiple Pd^II centers.     

Existence and Uniqueness of Solution for a Class of Nonlinear Degenerate Elliptic Equations

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations■,in the setting of the weighted Sobolev spaces.     

On the Generalized Porous Medium Equation in Fourier-Besov Spaces

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.