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.     

Hitherto-Unexplored Photodynamic Therapy of Ag2S and Enhanced Regulation Based on Polydopamine In Vitro and Vivo

Given their superior penetration depths, photosensitizers with longer absorption wavelengths present broader application prospects in photodynamic therapy (PDT). Herein, Ag₂S quantum dots were discovered, for the first time, to be capable of killing tumor cells through the photodynamic route by near-infrared light irradiation, which means relatively less excitation of the probe compared with traditional photosensitizers absorbing short wavelengths. On modification with polydopamine (PDA), PDA-Ag₂S was obtained, which showed outstanding capacity for inducing reactive oxygen species (increased by 1.69 times). With the addition of PDA, Ag₂S had more opportunities to react with surrounding O₂, which was demonstrated by typical triplet electron spin resonance (ESR) analysis. Furthermore, the PDT effects of Ag₂S and PDA-Ag₂S achieved at longer wavelengths were almost identical to the effects produced at 660 nm, which was proved by studies in vitro. PDA-Ag₂S showed distinctly better therapeutic effects than Ag₂S in experiments in vivo, which further validated the enhanced regulatory effect of PDA. Altogether, a new photosensitizer with longer absorption wavelength was developed by using the hitherto-unexplored photodynamic function of Ag₂S quantum dots, which extended and enhanced the regulatory effect originating from PDA.     

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.     

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.     

Tween 20-stabilized gold nanoparticles combined with adenosine triphosphate-BODIPY conjugates for the fluorescence detection of adenosine with more than 1000-fold selectivity

This study describes the development of a simple, enzyme-free, label-free, sensitive, and selective system for detecting adenosine based on the use of Tween 20-stabilized gold nanoparticles (Tween 20-AuNPs) as an efficient fluorescence quencher for boron dipyrromethene-conjugated adenosine 5′-triphosphate (BODIPY-ATP) and as a recognition element for adenosine. BODIPY-ATP can interact with Tween 20-AuNPs through the coordination between the adenine group of BODIPY-ATP and Au atoms on the NP surface, thereby causing the fluorescence quenching of BODIPY-ATP through the nanometal surface energy transfer (NSET) effect. When adenosine attaches to the NP surface, the attached adenosine exhibits additional electrostatic attraction to BODIPY-ATP. As a result, the presence of adenosine enhances the efficiency of AuNPs in fluorescence quenching of BODIPY-ATP. The AuNP-induced fluorescence quenching of BODIPY-ATP progressively increased with an increase in the concentration of adenosine; the detection limit at a signal-to-noise ratio of 3 for adenosine was determined to be 60 nM. The selectivity of the proposed system was more than 1000-fold for adenosine over any adenosine analogs and other nucleotides. The proposed system combined with a phenylboronic acid-containing column was successfully applied to the determination of adenosine in urine.