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Cross-electrophile coupling has emerged as an attractive and efficient method for the synthesis of C(sp2)–C(sp3) bonds. These reactions are most often catalyzed by nickel complexes of nitrogenous ligands, especially 2,2’-bipyridines. Precise prediction, selection, and design of optimal ligands remains challenging, despite significant increases in reaction scope and mechanistic understanding. Molecular parame-terization and statistical modeling provide a path to the development of improved bipyridine ligands that will enhance the selectivity of existing reactions and broaden the scope of electrophiles that can be coupled. Herein, we describe the generation of a computational lig-and library, correlation of observed reaction outcomes with features of the ligands, and in silico design of improved bipyridine ligands for Ni-catalyzed cross-electrophile coupling. The new nitrogen-substituted ligands display a fivefold increase in selectivity for product formation versus homodimerization when compared to the current state of the art. This increase in selectivity and yield was general for several cross-electrophile couplings, including the challenging coupling of an aryl chloride with an N-alkylpyridinium salt. 

We characterize the Hilbert–Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten classS_presult for dyadic paraproducts, where$1< p < \infty $$1<p<\infty$. We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.

 

Abstract We study almost surely separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0–1 Komolgorov law for a sequence to be interpolating almost surely for all the Besov–Sobolev spaces $$B_{2}^{\sigma }\left( \mathbb {B}_{d}\right) $$ B 2 σ B d , in the range $$0 < \sigma \le 1 / 2$$ 0 < σ ≤ 1 / 2 . For those spaces, such interpolating sequences coincide with interpolating sequences for their multiplier algebras, thanks to the Pick property. This is not the case for the Hardy space $$\mathrm {H}^2(\mathbb {D}^d)$$ H 2 ( D d ) and its multiplier algebra $$\mathrm {H}^\infty (\mathbb {D}^d)$$ H ∞ ( D d ) : in the polydisc, we obtain a sufficient and a necessary condition for a sequence to be $$\mathrm {H}^\infty (\mathbb {D}^d)$$ H ∞ ( D d ) -interpolating almost surely. Those two conditions do not coincide, due to the fact that the deterministic starting point is less descriptive of interpolating sequences than its counterpart for the unit ball. On the other hand, we give the $$0-1$$ 0 - 1 law for random interpolating sequences for $$\mathrm {H}^2(\mathbb {D}^d)$$ H 2 ( D d ) .