Regularity and Rigidity for Nonlocal Curvatures in Conformal Geometry

In this paper, we will explore the geometric effects of conformally covariant operators and the induced nonlinear curvature equations in certain nonlocal nature. Mainly, we will prove some regularity and rigidity results for the distributional solutions to those equations.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

Synthesis and characterization of VO–vanillin complex immobilized on MCM-41 and its facile catalytic application in the sulfoxidation reaction,and synthesis of 2,3-dihydroquinazolin-4(1H)-ones and disulfides in green media

In this work, a vanillin complex is immobilized onto MCM-41 and characterized by FT-IR, X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, thermogravimetric analysis, and BET techniques. This supported Schiff base complex was found to be an efficient and recoverable catalyst for the chemoselective oxidation of sulfides into sulfoxides and thiols into their corresponding disulfides (using hydrogen peroxide as a green oxidant) and also a suitable catalyst for the preparation of 2,3-dihydroquinazolin-4(1H)-one derivatives in water at 90°C. Using this protocol, we show that a variety of disulfides, sulfoxides, and 2,3-dihydroquinazolin-4(1H)-one derivatives can be synthesized in green conditions. The catalyst can be recovered and recycled for further reactions without appreciable loss of catalytic performance.     

考虑地表反射类型的气溶胶散射偏振特性

采用逐次阶散射法求解矢量辐射传输方程来研究气溶胶在不同地表反射模型下的散射偏振特性.首先,选取单一地表反射模型和耦合地表反射模型两种地表反射模型.然后,根据地表反射模型计算得到相应的地表反射率,进而采用逐次阶散射法对矢量辐射传输方程进行求解,得到散射光的Stokes矢量.最后,由Stokes矢量计算得出散射光的偏振度.仿真结果表明,两种地表反射模型下气溶胶单次散射的散射辐射强度和线偏振度均相等;耦合地表反射模型的总散射辐射强度和线偏振度总是大于单一地表反射模型;单一地表反射模型的气溶胶单次散射相对总散射的贡献总是大于耦合地表反射模型.研究结果对气溶胶光学特性的反演具有一定意义.     

A solvent-governed surface state strategy for rational synthesis of N and S co-doped carbon dots with multicolour fluorescence

ABSTRACT

Multicolour emissive carbon dots (CDs) are widely investigated by virtue of their merits on fluorescent properties. Method on heteroatom doping assisted with various solvents has been proved efficient in achieving multiple-colour-emissive CDs, especially long-wavelength emission. Herein, a synthesis of multicolour-emissive CDs by controlled surface function is reported. By tuning the thermal-pyrolysis temperature and molar ratio of reactants, optimal emission of the resulted CDs gradually shifts from blue to yellow light with the assistance of different solvents. According to the emissive relationship dependent on excitation, fluorescence lifetimes, and FT-IR of these CDs, the different surface states participated with S and N elements on the surface of carbogenic core govern fluorescent colours of the CDs. In terms of the applications, blue CDs (B-CDs) exhibits high sensitivity for ion detections of Ag⁺ and Fe³⁺, which is further illustrated to have different quenching mechanisms each other because that these ions have the affinity interaction with different surface groups of the CDs. Moreover, blue and yellow CDs solutions are mixed with PVP water solution to fabricate white-light CDs/PVP film, which exhibits stable fluorescence with a CIE coordinate of (0.32, 0.33) and endows these CDs as potentially fluorescent nanomaterial in the solid state lighting field.     

新型非对称二苯并[b,f][1,5]二氮杂环辛四烯的合成

以两种不同取代的2-氨基二苯甲酮为原料,氯苯为溶剂,BF3-Et2O为脱水剂,通过分子间脱水一步环化缩合制备非对称二苯并[b,f][1,5]二氮杂环辛四烯衍生物。运用HPLC监控反应过程,优化合成工艺,得到最佳反应条件为:等物质的量的两种不同取代2-氨基二苯甲酮和BF3-Et2O,在氯苯中回流反应12 h。化合物4a^4c为新化合物,其结构经1H NMR,13C NMR和MS(ESI)表征。