The first catalytic hydrocarboxylation of enamides and imines with CO to generate valuable α,α-disubstituted α-amino acids is reported. Notably, excellent chemo- and regio-selectivity are achieved, significantly different from previous reports on β-carboxylation of enamides, homocoupling or reduction of imines. Moreover, this transition-metal-free procedure exhibits low loading of an inexpensive catalyst, easily available substrates, mild reaction conditions, high efficiency, facile scalability and easy product derivatization, providing great potential for application in organic synthesis, pharmaceutical chemistry, and biochemistry.

Cross-electrophile couplings between two electrophiles are powerful and economic methods to generate C−C bonds in the presence of stoichiometric external reductants. Herein, we report a novel strategy to realize the first external-reductant-free cross-electrophile coupling via visible-light photoredox catalysis. A variety of tetraalkyl ammonium salts, bearing primary, secondary, and tertiary C−N bonds, undergo selective couplings with aldehydes/ketone and CO 2 . Notably, the in situ generated byproduct, trimethylamine, is efficiently utilized as the electron donor. Moreover, this protocol exhibits mild reaction conditions, low catalyst loading, broad substrate scope, good functional group tolerance, and facile scalability. Mechanistic studies indicate that benzyl radicals and anions might be generated as the key intermediates via photocatalysis, providing a new direction for cross-electrophile couplings.

Abstract. In this paper, we consider the following problem involving fractional Laplacian operator:where Ω is a smooth bounded domain in. We show that for any sequence of solutions u n of (1) corresponding to ε n ∈ [0, 2 * α − 2), satisfying u n H ≤ C in the Sobolev space H defined in (1.2), u n converges strongly in H provided that N > 6α and λ > 0. An application of this compactness result is that problem (1) possesses infinitely many solutions under the same assumptions.

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The first direct use of carbon dioxide in the lactamization of alkenyl and heteroaryl C-H bonds to synthesize important 2-quinolinones and polyheterocycles in moderate to excellent yields is reported. Carbon dioxide, a nontoxic, inexpensive, and readily available greenhouse gas, acts as an ideal carbonyl source. Importantly, this transition-metal-free and redox-neutral process is eco-friendly and desirable for the pharmaceutical industry. Moreover, these reactions feature a broad substrate scope, good functional group tolerance, facile scalability, and easy product derivatization.