Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Chemical versus Electrochemical Synthesis of Carbon Nano‐onion/Polypyrrole Composites for Supercapacitor Electrodes

The development of high‐surface‐area carbon electrodes with a defined pore size distribution and the incorporation of pseudo‐active materials to optimize the overall capacitance and conductivity without destroying the stability are at present important research areas. Composite electrodes of carbon nano‐onions (CNOs) and polypyrrole (Ppy) were fabricated to improve the specific capacitance of a supercapacitor. The carbon nanostructures were uniformly coated with Ppy by chemical polymerization or by electrochemical potentiostatic deposition to form homogenous composites or bilayers. The materials were characterized by transmission‐ and scanning electron microscopy, differential thermogravimetric analyses, FTIR spectroscopy, piezoelectric microgravimetry, and cyclic voltammetry. The composites show higher mechanical and electrochemical stabilities, with high specific capacitances of up to about 800 F g^?1 for the CNOs/SDS/Ppy composites (chemical synthesis) and about 1300 F g^?1 for the CNOs/Ppy bilayer (electrochemical deposition).     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

Preparation and gas sensing activity of La and Y co-doped titania nanoparticles

Journal of Sol-Gel Science and Technology - A novel gas sensing material, La–Y co-doped TiO2 nanoparticles, was synthesized by sol–gel method and applied to detect organic pollutants...     

Achieving Rich and Active Alkaline Hydrogen Evolution Heterostructures via Interface Engineering on 2D 1T‐MoS2 Quantum Sheets

Large‐scale production of hydrogen from water‐alkali electrolyzers is impeded by the sluggish kinetics of hydrogen evolution reaction (HER) electrocatalysts. The hybridization of an acid‐active HER catalyst with a cocatalyst at the nanoscale helps boost HER kinetics in alkaline media. Here, it is demonstrated that 1T–MoS₂ nanosheet edges (instead of basal planes) decorated by metal hydroxides form highly active ${\text{edge}}_{{\text{1T‐MoS}}_{\text{2}}}$/ ${\text{edge}}_{\text{Ni}{(\text{OH})}_{\text{2}}}$ heterostructures, which significantly enhance HER performance in alkaline media. Featured with rich ${\text{edge}}_{{\text{1T‐MoS}}_{\text{2}}}$/ ${\text{edge}}_{\text{Ni}{(\text{OH})}_{\text{2}}}$ sites, the fabricated 1T–MoS₂ QS/Ni(OH)₂ hybrid (quantum sized 1T–MoS₂ sheets decorated with Ni(OH)₂ via interface engineering) only requires overpotentials of 57 and 112 mV to drive HER current densities of 10 and 100 mA cm^?2, respectively, and has a low Tafel slope of 30 mV dec^?1 in 1 m KOH. So far, this is the best performance for MoS₂‐based electrocatalysts and the 1T–MoS₂ QS/Ni(OH)₂ hybrid is among the best‐performing non‐Pt alkaline HER electrocatalysts known. The HER process is durable for 100 h at current densities up to 500 mA cm^?2. This work not only provides an active, cost‐effective, and robust alkaline HER electrocatalyst, but also demonstrates a design strategy for preparing high‐performance catalysts based on edge‐rich 2D quantum sheets for other catalytic reactions.