覆盖广义Rough集中的隶属关系

对覆盖广义Rough集中的隶属关系、隶属函数进行了定义，并利用隶属函数定义了集合的Rough包含与Rough相等，得到一些与Pawlak的Rough集不同的性质。     

数学物理方程中的通解问题

通过例证说明,通解法对于偏微分方程而言,其适用范围要比通常认为的大.并表明,只要适当变通,行波法就可用于有界情况.     

NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS

In this article,the authors investigate the existence problem for Hardy Hénon type strongly indefinite elliptic systems.Existence results are obtained for such systems with superlinear suberitical nonlinearities.     

MCM-41-supported bidentate phosphine palladium(0) complex: a highly active and recyclable catalyst for the Sonogashira reaction of aryl iodides

The first MCM-41-supported bidentate phosphine palladium(0) complex has been prepared. This complex is a highly efficient catalyst for Sonogashira reaction and can be reused at least 10 times without any decrease in activity.     

Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection

In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|^α|?u|^p?2?u) + λ 1/|x|^β |?u|^p?2?u · x = |x|^γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|^α|?u|^p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? R^N(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection.     

Electrooxidation Mechanism of Methanol at Pt-Ru Catalyst Modified GC Electrode in Electrolytes with Different pH Using Electrochemical and SERS Techniques

The electrochemical and in-situ surface-enhanced Raman spectroscopy （SERS） techniques were used to investigate the electrooxidation behavior of methanol in acidic, neutral and alkaline media at a Pt-Ru nanoparticle modified glassy carbon （Pt-Ru/GC） electrode. The results showed that methanol could be dissociated spontaneously at the Pt-Ru/GC electrode to produce a strongly adsorbed intermediate, CO. It was found that CO could be oxidized more easily in the alkaline medium than in the acidic and neutral media. The peak potential of methanol oxidation was shifted from 0.663 and 0.708 V in the acidic and neutral media to -0.030 V in the alkaline medium, which is due to that the adsorption strength of CO on the Pt surface in the alkaline medium is weaker than that in the acidic and neutral media. The final product of the methanol oxidation is CO2. However, in the alkaline medium, CO2 produced would form CO3^2- and HCO3^- resulting in the decrease in the alkaline concentration and then in the decrease in the performance of DMFC. Therefore, the performance of the alkaline DMFC is not Stable.     

A plasmonic mercury sensor based on silver–gold alloy nanoparticles electrodeposited on indium tin oxide glass

We construct silver–gold alloy nanoparticles (Ag–AuNPs) as the basis of a reagentless, sensitive and simple mercury sensor. Ag–AuNPs were electrodeposited directly on transparent indium tin oxide film coated glass. Hg(II) ions in aqueous solution could be reduced by Ag atoms existing in Ag–AuNPs; the deposition/amalgamation of Hg on the nanoparticles resulted in a blue shift of the localized surface plasmon resonance peak. Therefore, Hg^2 + can be detected quantitatively by using a spectrophotometer. The sensor response is linear in the range from 0.05 to 500 ppb of Hg(II) concentration. No sample separation or preconcentration is required for detection of ultralow levels of mercury in water samples. The results shown herein have potential applications in the development of a new optical sensor for the detection of low concentrations of mercury.     

Transient and Recyclable Halogenation Coupling (TRHC) for Isoflavonoid Synthesis with Site-Selective Arylation

A transient and recyclable C−H iodination has been designed for the synthesis of isoflavonoids through the domino reactions of o-hydroxyphenyl enaminones and aryl boronic acids in the presence of catalytic KI and Pd catalyst. Instead of the conventional cross-coupling strategy employing pre-halogenated substrates, this method transforms raw C−H bond by means of a transient C−H halogenation to smoothly relay the subsequent C-arylation. Consequently, such a method avoids the pre-functionalization for C−halogen bond installation as well as the generation of stoichiometric halogen-containing waste following the cross-coupled product, disclosing an intriguing new coupling protocol to forge the C−C bond in the virgin area between classical C−X (X=halogen) bond cross coupling and the C−H activation.     

Bayesian Estimation and Statistical Analysis of Risk Measurements

The Bayesian model are established for the VaR and related risk measurements. The relationship between VaR and other risk measurements including expect shortfall, tail condition expectation and conditional value at risk are discussed. Furthermore, the Bayesian estimates and Bayesian predictors of these risk measurement are derived. Thirdly, the consistency and asymptotic normality in the exponential risk model are proved. Finally, the numerical simulation method is used to verify the convergence rate under different sample sizes.