CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION

In this article,we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation.Based on defining a Finsler-type norm on the tangent space for solutions,we first establish the Lipschitz metric for smooth solutions,then by proving the generic regularity result,we extend this metric to general weak solutions.     

Performance guarantees of local search for minsum scheduling problems

Mathematical Programming - We study the worst-case performance guarantee of locally optimal solutions for the problem of minimizing the total weighted and unweighted completion time on parallel...     

Hierarchical Microtubular Covalent Organic Frameworks Achieved by COF-to-COF Transformation

Pore environment and aggregated structure play a vital role in determining the properties of porous materials, especially regarding the mass transfer. Reticular chemistry imparts covalent organic frameworks (COFs) with well-aligned micro/mesopores, yet constructing hierarchical architectures remains a great challenge. Herein, we reported a COF-to-COF transformation methodology to prepare microtubular COFs. In this process, the C₃-symmetric guanidine units decomposed into C₂-symmetric hydrazine units, leading to the crystal transformation of COFs. Moreover, the aggregated structure and conversion degree varied with the reaction time, where the hollow tubular aggregates composed of mixed COF crystals could be obtained. Such hierarchical architecture leads to enhanced mass transfer properties, as proved by the adsorption measurement and chemical catalytic reactions. This self-template strategy was successfully applied to another four COFs with different building units.     

Semiconductor SERS on Colourful Substrates with Fabry-Pérot Cavities

Non-metallic materials have emerged as a new family of active substrates for surface-enhanced Raman scattering (SERS), with unique advantages over their metal counterparts. However, owing to their inefficient interaction with the incident wavelength, the Raman enhancement achieved with non-metallic materials is considerably lower with respect to the metallic ones. Herein, we propose colourful semiconductor-based SERS substrates for the first time by utilizing a Fabry-Pérot cavity, which realize a large freedom in manipulating light. Owing to the delicate adjustment of the absorption in terms of both frequency and intensity, resonant absorption can be achieved with a variety of non-metal SERS substrates, with the sensitivity further enhanced by ≈100 times. As a typical example, by introducing a Fabry-Pérot-type substrate fabricated with SiO₂/Si, a rather low detection limit of 10⁻¹⁶ M for the SARS-CoV-2S protein is achieved on SnS₂. This study provides a realistic strategy for increasing SERS sensitivity when semiconductors are employed as SERS substrates.     

Palladium and Ruthenium Dual-Single-Atom Sites on Porous Ionic Polymers for Acetylene Dialkoxycarbonylation: Synergetic Effects Stabilize the Active Site and Increase CO Adsorption

Heterogeneous single-metal-site catalysts usually suffer from poor stability, thereby limiting industrial applications. Dual Pd₁−Ru₁ single-atom-sites supported on porous ionic polymers (Pd₁−Ru₁/PIPs) were constructed using a wetness impregnation method. The two isolated metal species in the form of a binuclear complex were immobilized on the cationic framework of PIPs through ionic bonds. Compared to the single Pd- or Ru-site catalyst, the dual single-atom system exhibits higher activity with 98 % acetylene conversion and near 100 % selectivity to dialkoxycarbonylation products, as well as better cycling stability for ten cycles without obvious decay. Based on DFT calculations, it was found that the single-Ru site exhibited a strong CO adsorption energy of −1.6 eV, leading to an increase in the local CO concentration of the catalyst. Notably, the Pd₁−Ru₁/PIPs catalyst had a much lower energy barrier of 2.49 eV compared to 3.87 eV of Pd₁/PIPs for the rate-determining step. The synergetic effect between neighboring single sites Pd₁ and Ru₁ not only enhanced the overall activity, but also stabilized Pd^II active sites. The discovery of synergetic effects between single sites can deepen our understanding of single-site catalysts at the molecular level.     

The Molecular Basis of Catalysis by SDR Family Members Ketoacyl-ACP Reductase FabG and Enoyl-ACP Reductase FabI in Type-II Fatty Acid Biosynthesis

The short-chain dehydrogenase/reductase (SDR) superfamily members acyl-ACP reductases FabG and FabI are indispensable core enzymatic modules and catalytic orientation controllers in type-II fatty acid biosynthesis. Herein, we report their distinct substrate allosteric recognition and enantioselective reduction mechanisms. FabG achieves allosteric regulation of ACP and NADPH through ACP binding across two adjacent FabG monomers, while FabI follows an irreversible compulsory order of substrate binding in that NADH binding must precede that of ACP on a discrete FabI monomer. Moreover, FabG and FabI utilize a backdoor residue Phe187 or a “rheostat” α8 helix for acyl chain length selection, and their corresponding triad residues Ser142 or Tyr145 recognize the keto- or enoyl-acyl substrates, respectively, facilitating initiation of nucleophilic attack by NAD(P)H. The other two triad residues (Tyr and Lys) mediate subsequent proton transfer and (R)-3-hydroxyacyl- or saturated acyl-ACP production.     

Synthesis and characterisation of poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) Zr(IV) monothiophosphate composite cation exchanger: analytical application in the selective separation of lead metal ions

In this study, poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) zirconium(IV) monothiophosphate composite cation exchanger was prepared by sol–gel precipitation method. The presence of sulphur in the cation exchanger enhances affinity towards the heavy metal ions which can improve the selectivity of the material. The selectivity studies showed that the material is selective towards Pb(II) ions. To characterise the material, several physicochemical properties were also studied which includes X-ray, scanning electron microscopy and transmission electron microscopy studies. The ion-exchange behaviour of this cation exchanger was studied by using some of the selected properties like ion-exhange capacity for various metal ions, elution, effect of eluent concentration, thermal effect on ion-exchange capacity (IEC). The results of IEC and physicochemical properties revealed that the material is nanocomposite, crystalline, chemically, mechanically and thermally stable. The analytical ability of this cation exchanger was demonstrated in binary separation of Pb(II) ions from a mixture of other metal ions. The recovery is qualitative and the separations are reproducible.