The antipode of a quasitriangular quasi-Turaev group coalgebra is bijective

In order to construct a class of new Turaev-braided group category with nontrivial associativity, the concept of a quasitriangular quasi-Turaev group coalgebras was recently introduced. Inside the definition, the conditions of invertibility of the R-matrix R and bijectivity of the antipode S are required. In this article, we prove that the antipode of a quasitriangular quasi-Turaev group coalgebra without the assumptions about invertibility of the antipode and R-matrix is inner, and a fortiori, bijective. As an application, we prove that for a quasitriangular quasi-Turaev group coalgebra, two conditions mentioned above are unnecessary.     

Continuity of the solution to the even logarithmic Minkowski problem in the plane

This paper investigates continuity of the solution to the even logarithmic Minkowski problem in the plane. It is shown that the weak convergence of a sequence of cone-volume measures in R~2 implies the convergence of the sequence of the corresponding origin-symmetric convex bodies in the Hausdorff metric.     

Facile Synthesis of Ultra-Small Few-Layer Nanostructured MoSe2 Embedded on N,P Co-Doped Bio-Carbon for High-Performance Half/Full Sodium-Ion and Potassium-Ion Batteries

Sodium/potassium-ion batteries (SIBs/PIBs) arouse intensive interest on account of the natural abundance of sodium/potassium resources, the competitive cost and appropriate redox potential. Nevertheless, the huge challenge for SIBs/PIBs lies in the scarcity of an anode material with high capacity and stable structure, which are capable of accommodating large-size ions during cycling. Furthermore, using sustainable natural biomass to fabricate electrodes for energy storage applications is a hot topic. Herein, an ultra-small few-layer nanostructured MoSe₂ embedded on N, P co-doped bio-carbon is reported, which is synthesized by using chlorella as the adsorbent and precursor. As a consequence, the MoSe₂/NP-C-2 composite represents exceedingly impressive electrochemical performance for both sodium-ion batteries (SIBs) and potassium-ion batteries (PIBs). It displays a promising reversible capacity (523 mAh g⁻¹ at 100 mA g⁻¹ after 100 cycles) and impressive long-term cycling performance (192 mAh g⁻¹ at 5 A g⁻¹ even after 1000 cycles) in SIBs, which are some of the best properties of MoSe₂-based anode materials for SIBs to date. To further probe the great potential applications, full SIBs pairing the MoSe₂/NP-C-2 composite anode with a Na₃V₂(PO₄)₃ cathode also exhibits a satisfactory capacity of 215 mAh g⁻¹ at 500 mA g⁻¹ after 100 cycles. Moreover, it also delivers a decent reversible capacity of 131 mAh g⁻¹ at 1 A g⁻¹ even after 250 cycles for PIBs.     

AuPt Bipyramid Nanoframes as Multifunctional Platforms for In Situ Monitoring of the Reduction of Nitrobenzene and Enhanced Electrocatalytic Methanol Oxidation

Multifunctional metal nanostructures with a hollow feature, especially for nanoframes, are highly attractive owing to their high surface-to-volume ratios. However, pre-grown metal nanocrystals are always involved during the preparation procedure, and a synthetic strategy without the use of a pre-grown template is still a challenge. In this article, a template-free strategy is reported for the preparation of novel AuPt alloy nanoframes through simply mixing HAuCl₄ and H₂PtCl₆ under mild conditions. The alloy nanostructures show a bipyramid-frame hollow architecture with the existence of only the ten ridges and absence of their side faces. This is the first report of bipyramid-like nanoframes and a template-free method under mild conditions. This configuration merges the plasmonic features of Au and highly active catalytic sites of Pt in a single nanostructure, making it an ideal multifunctional platform for catalyzing and monitoring the catalytic reaction in real time. The superior catalytic activity is demonstrated by using the reduction of nitrobenzene to the corresponding aminobenzene as a model reaction. More importantly, the AuPt nanoframes can track the reduction process on the basis of the SERS signals of the reactants, intermediates, and products, which helps to reveal the reaction mechanism. In addition, the AuPt nanoframes show much higher electrocatalytic properties toward the methanol oxidation reaction than commercial Pt/C electrocatalysts.     

Wound Healing Attributes of Polyelectrolyte Multilayers Prepared with Multi‐l‐arginyl‐poly‐l‐aspartate Pairing with Hyaluronic Acid and γ‐Polyglutamic Acid

Biodegradable multi‐l ‐arginyl‐poly‐l ‐aspartate (MAPA), more commonly cyanophycin, prepared with recombinant Escherichia coli contains a polyaspartate backbone with lysine and arginine as side chains. Two assemblies of polyelectrolyte multilayers (PEMs) are fabricated at three different concentration ratios of insoluble MAPA (iMAPA) with hyaluronic acid (iMAPA/HA) and with γ‐polyglutamic acid (iMAPA/γ‐PGA), respectively, utilizing a layer‐by‐layer approach. Both films with iMAPA and its counterpart, HA or γ‐PGA, as the terminal layer are prepared to assess the effect on film roughness, cell growth, and cell migration. iMAPA incorporation is higher for a higher concentration of the anionic polymer due to better charge interaction. The iMAPA/HA films when compared to iMAPA/γ‐PGA multilayers show least roughness. The growth rates of L929 fibroblast cells on the PEMs are similar to those on glass substrate, with no supplementary effect of the terminal layer. However, the migration rates of L929 cells increase for all PEMs. γ‐PGA incorporated films impart 50% enhancement to the cell migration after 12 h of culture as compared to the untreated glass, and the smooth films containing HA display a maximum 82% improvement. The results present the use of iMAPA to construct a new layer‐by‐layer system of polyelectrolyte biopolymers with a potential application in wound dressing.     

Synthesis and Applications of SAPO-34 Molecular Sieves

Silicoaluminophosphate zeolite (SAPO-34) has been attracting increasing attention due to its excellent form selection and controllability in the chemical industry, as well as being one of the best industrial catalysts for methanol-to-olefin (MTO) reaction conversion. However, as a microporous molecular sieve, SAPO-34 easily generates carbon deposition and rapidly becomes inactivated. Therefore, it is necessary to reduce the crystal size of the zeolite or to introduce secondary macropores into the zeolite crystal to form a hierarchical structure in order to improve the catalytic effect. In this review, the synthesis methods of conventional SAPO-34 molecular sieves, hierarchical SAPO-34 molecular sieves and nanosized SAPO-34 molecular sieves are introduced, and the properties of the synthesized SAPO-34 molecular sieves are described, including the phase, morphology, pore structure, acid source, and catalytic performance, in particular with respect to the synthesis of hierarchical SAPO-34 molecular sieves. We hope that the review can provide guidance to the preparation of the SAPO-34 catalysts, and stimulate the future development of high-performance hierarchical SAPO-34 catalysts to meet the growing demands of the material and chemical industries.     

Copper-Catalyzed Regioselective [3+3] Annulations of Alkynyl Ketimines with α-Cyano Ketones: the Synthesis of Polysubstituted 4H-Pyran Derivatives with a CF3-Containing Quaternary Center

Regioselective [3+3] annulation of alkynyl ketimines with α-cyano ketones for the synthesis of polysubstituted 4H-pyran derivatives with a quaternary CF₃-containing center has been realized by using Cu(OAc)₂ as the catalyst. The novel strategy tolerates a wide range of α-CF₃ alkynyl ketimines and α-cyano ketones with both aryl and alkyl substitutents. A preliminary asymmetric synthesis of chiral product 3 has been attempted by using copper and chiral thiourea as the cocatalyst with excellent yields (86-99 %) and good enantioselectivities (71–78 % ee). Furthermore, product 3 aa could be obtained on a gram-scale reaction with 75 % yield and 99 % ee after recrystallization. Several products were also transformed readily. Control experiments indicate that the reaction involves a process with a base-catalyzed or chiral thiourea-catalyzed Mannich-type reaction followed by a highly regioselective copper-catalyzed ring-closing reaction on the alkynyl moiety in a 6-endo-dig fashion.