Low-cost transition-metal dichalcogenides (MS) have attracted great interest as alternative catalysts for hydrogen evolution. However, a significant challenge is the formation of sulfur-hydrogen bonds on MS (S-H), which will severely suppress hydrogen evolution reaction (HER). Here we report Cu nanodots (NDs)-decorated NiS nanotubes (NTs) supported on carbon fibers (CFs) (Cu NDs/NiS NTs-CFs) as efficient electrocatalysts for HER in alkaline media. The electronic interactions between Cu and NiS result in Cu NDs that are positively charged and can promote water adsorption and activation. Meanwhile, NiS NTs are negatively charged and can weaken S-H bonds formed on catalyst surfaces. Therefore, the Cu/NiS hybrids can optimize H adsorption and desorption on electrocatalysts and can promote both Volmer and Heyrovsky steps of HER. The strong interactions between Cu and NiS cause the Cu NDs/NiS NTs-CFs electrocatalysts to exhibit the outstanding HER catalytic performance with low onset potential, high catalytic activity, and excellent stability.

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Metal-organic frameworks (MOFs) with carboxylate ligands as co-catalysts are very e cient for oxygen evolution reaction (OER). However, the role of local adsorbed carboxylate ligands around the in situ transformed metal (oxy)hydroxides during OER is often overlooked. Here we reveal the extraordinary role and mechanism of surface adsorbed carboxylate ligands on bi/trimetallic layered double hydroxides (LDHs)/MOFs for OER catalytic activity enhancement. The results of X-ray photoelectron spectroscopy (XPS), synchrotron X-ray absorption spectroscopy and theoretical calculations show that the carboxylic groups around metal (oxy)hydroxides can e ciently induce the interfacial electron redistribution, facilitate abundant high-valence state of nickel species with partial distorted octahedral structure, and optimize the d-band center together with the bene cial Gibbs free energy of intermediate. Furthermore, the results of in-situ Raman and FI-IR spectra rstly reveal that the surface adsorbed carboxylate ligands as Lewis base can promote the sluggish OER kinetics by accelerating proton transfer and facilitating adsorption/ activation/dissociation of hydroxyl ions (OH − ). Our ndings will offer unique insights into the reason for disclosing the origin of excellent electrocatalytic activity for MOF/NiFe-LDHs catalysts.

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The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases for finite groups and finite dimensional Kac algebras. We prove the Hausdorff-Young inequality, Young's inequality, the Hirschman-Beckner uncertainty principle, the Donoho-Stark uncertainty principle. We characterize the minimizers of the uncertainty principles. We also prove that the minimizer is uniquely determined by the supports of itself and its Fourier transform. The proofs take the advantage of the analytic and the categorial perspectives of subfactor planar algebras. Our method to prove the uncertainty principles also works for more general cases, such as Popa's λ-lattices, modular tensor categories etc.