n-APR tilting and $$\tau $$ τ -mutations

Journal of Algebraic Combinatorics - APR tilts for path algebra kQ can be realized as the mutation of the quiver Q in $${\mathbb Z}Q$$ with respect to the translation. In this paper, we show that...     

Normal approximation and fourth moment theorems for monochromatic triangles

Given a graph sequence denote by T₃(G_n) the number of monochromatic triangles in a uniformly random coloring of the vertices of G_n with colors. In this paper we prove a central limit theorem (CLT) for T₃(G_n) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T₃(G_n), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].     

Chemical Composition and Antifungal Activity of Essential Oil from the Roots of Tinomiscium petiolare

Chemistry of Natural Compounds -     

Surface Engineering of Conjugated Polybenzothiadiazoles and Integration with Cobalt Oxides for Photocatalytic Water Oxidation

Conjugated polymers feature promising structure and properties for photocatalytic water splitting. Herein, a hydrolysis strategy was demonstrated to rationally modulate the surface hydrophilicity and band structures of conjugated poly-benzothiadiazoles. High hydrophilicity not only enhances the dispersions of polymeric solids in an aqueous solution but also reduces the absorption energy of water molecules. Besides, both theoretical and experimental results reveal that a more positive valence band potential is generated, which contributes to enhancing the photocatalytic water oxidation performance. Accordingly, the surface-modified conjugated polymers show largely promoted photocatalytic water oxidation activities by deposition of cobalt oxides as cocatalysts.     

Design of Functional Carbon Composite Materials for Energy Conversion and Storage

The carbon composite materials have been a research hotspot in the fields of catalysis, energy conversion and so on, because of their features of large structure and morphology variety, good chemical and electrochemical stability, and high electronic conductivity, large specific surface area and rich active sites. This paper summarizes some research progress of carbon composite materials, including assembly methodologies, their structure regulation, properties, and related applications. Moreover, the current challenges and the prospects of these materials are also discussed.     

Injectable Micromotor@Hydrogel System for Antibacterial Therapy

The drug delivery system based on nano/micromotors has become a research hot spot in recent years. However, naked micromotors may be ruptured or passivated under the complex biological environment, which will result in the leakage of drugs in advance or limited self-propulsion performance. Herein, an injectable micromotor@hydrogel drug delivery system to protect micromotors from the external environment is proposed. The micromotors were prepared through layer-by-layer assembly technology. The asymmetric decomposition of hydrogen peroxide catalyzed by the locally distributed platinum nanoparticles enabled efficient propulsion of the micromotors in low concentration of hydrogen peroxide. In order to protect micromotors, they were loaded into the Schiff base hydrogel. The micromotor@hydrogel system can be injected directly into the lesion to release micromotors in response to the environment, reducing external influence on micromotors and improving the sustained-release effect. Erythromycin (Ery) loaded into the micromotors and the micromotor@hydrogel system demonstrated excellent antibacterial effect. Micromotors released from the hydrogel underwent enhanced diffusion in the surroundings of bacteria without addition of exogenous hydrogen peroxide, which was manifested by their appearance in edge of the inhibition zone. The proposed micromotor@hydrogel drug delivery system offers a new strategy for the treatment of bacterial infections.     

Bicomponent Cocatalyst Decoration on Flux-assisted CaTaO2N Single Crystals for Photocatalytic CO2 Reduction under Visible Light

Cubic-like CaTaO₂N photocatalysts with high crystallinity and uniform particle size were successfully prepared by the flux-assisted nitridation method. The growth of CaTaO₂N single crystals under different synthesis conditions was systematically investigated to understand the effects of the crystallinity and optical property on photocatalytic performance of CO₂ reduction. Moreover, the modification of CaTaO₂N single crystals with core-shell Ni−Ag bicomponent cocatalyst by two-step decoration process gave a 2.4 times higher amount of CO evolution than the deposition of sole Ag cocatalyst, because of the synergistic effects of bicomponent cocatalyst on the interfacial electron transfer and surface catalytic process. This study provides a valuable way to construct high-crystalline photocatalysts with effective bicomponent cocatalyst for visible-light-driven CO₂ reduction with H₂O.     

Highly insulating alkane rings with destructive σ-interference

Science China Chemistry - Destructive quantum interference (DQI) provides a unique approach to controlling the leakage current in the OFF state of molecular devices. However, the DQI in...     

On lower iteration complexity bounds for the convex concave saddle point problems

Mathematical Programming - In this paper, we study the lower iteration complexity bounds for finding the saddle point of a strongly convex and strongly concave saddle point problem: $$\min _x\max...