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].     

One-pot,one-step,and selective terpolymerization of ethylene oxide,propylene oxide,and COS to copoly(thioether)s with tunable thermal properties

Facile construction of sulfur-rich polymers using readily available raw chemicals is an area aggressively pursued but challenging. Herein we use common feedstocks of ethylene oxide (EO), propylene oxide (PO), and carbonyl sulfide (COS) to synthesize copoly(thioether)s which are traditionally produced from unpleasant and difficult to store episulfides. In this protocol, the EO/COS coupling selectively generates a pure poly(ethylene sulfide) (PES) with melting temperature (T_m) values up to 172°C and high yields up to 98%. The EO/PO/COS terpolymerization leads to the incorporation of soft poly(propylene sulfide) (PPS) and hard PES segments together, affording a random PES-co-PPS copoly(thioether) with the complete consumption of EO and PO. Additionally, by simply varying the EO/PO feeding ratio, the obtained copoly(thioether)s possess tunable thermal properties, T_m values in the range of 76–144°C, and excellent solubility. These copolymerizations are conducted in one-pot/one-step at industrially favored reaction temperatures of 100–120°C using catalysts of common organic bases, suggesting a facile and practical manner. Especially, the copoly(thioether) exhibits high refractive indices up to 1.68 owing to its high sulfur content, suggesting a broad application prospect in optical materials.     

Highly Stable Univalent Copper of a Cu@Al/SBA-15 Nanocomposite Catalyzes the Synthesis of Fluorescent Aminobenzotriazoles Derivatives

With the development of green chemistry, it is still a challenge to maintain the unstable valence state of the metal in heterogeneous catalysts and realize new catalytic synthesis methods. In this paper, it is reported that an univalent copper nanocomposite (Cu@Al/SBA-15) can efficiently catalyze the formation of novel amino-containing benzotriazoles with great fluorescence properties in a new synthetic strategy. Subsequently, its application is further verified by an acylation reaction to produce a series of novel benzotriazoles derivatives with high yield. It is worth noting that the Cu@Al/SBA-15 nanocomposites not only enable the reaction completed with high yield in a short time, but can also be recycled many times without a significant reduction in activity, and the leaching of copper and aluminum species in reaction system is negligible. Finally, the detailed and feasible reaction mechanism is also provided.     

Monitoring the Thiol/Thiophenol Molecule-Modulated Plasmon-Mediated Silver Oxidation with Dark-Field Optical Microscopy

Surface plasmon can trigger or accelerate many photochemical reactions, especially useful in energy and environmental industries. Recently, molecular adsorption has proven effective in modulating plasmon-mediated photochemistry, however the realized chemical reactions are limited and the underlying mechanism is still unclear. Herein, by using in situ dark-field optical microscopy, the plasmon-mediated oxidative etching of silver nanoparticles (Ag NPs), a typical hot-hole-driven reaction, is monitored continuously and quantitatively. The presence of thiol or thiophenol molecules is found essential in the silver oxidation. In addition, the rate of silver oxidation is modulated by the choice of different thiol or thiophenol molecules. Compared with the molecules having electron donating groups, the ones having electron accepting groups accelerate the silver oxidation dramatically. The thiol/thiophenol modulation is attributed to the modulation of the charge separation between the Ag NPs and the adsorbed thiol or thiophenol molecules. This work demonstrates the great potential of molecular adsorption in modulating the plasmon-mediated photochemistry, which will pave a new way for developing highly efficient plasmonic photocatalysts.     

A New Carotane Sesquiterpenoid Derivative with Antifungal Activity from Gymnopus sp. 0612-9

Chemistry of Natural Compounds - A new carotane sesquiterpenoid, methyl gymnabloate (1), was isolated from the fermentation broth of the wild macrofungus Gymnopus sp. 0612-9. Its structure was...     

Guaranteed cost positive consensus for multi-agent systems with multiple time-varying delays and MDADT switching

Nonlinear Dynamics - This paper investigates the guaranteed cost positive consensus for linear multi-agent systems (MASs) with multiple time-varying delays and switching topologies. First,...     

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...     

Scalable Quantum Controlled Gates on Single-Photon Polarization Qubits Assisted by Nitrogen-Vacancy Centers Inside Single-Sided Optical Cavities

International Journal of Theoretical Physics - Quantum logic gates are the foundation of circuit-based quantum computation and quantum simulation. Multi-qubit quantum controlled gates are of vital...     

Enhancement of bioelectrochemical dioxygen reduction with oxygen-enriching materials

Bioelectrochemical dioxygen reduction reaction (ORR) catalyzed by multi-copper oxidases (MCOs) is a process of paramount importance occurring at the cathode of enzymatic biofuel cells (EBFCs), which is an energy harvester that holds promise of self-sustained implantable and wearable medical devices. The MCO biocathode is, however, frequently the limiting factor of a working EBFC. Besides the operational stability issue, enzymatic biocathodes are largely constrained by the relatively low solubility of dioxygen in aqueous solution. As an emerging topic, we here review the introduction of dioxygen-enriching materials to the cathodic bioelectrode for overcoming the dioxygen supply limitation, leading to improved ORR performance.