混合齐次向量值多线性交换子的奇异积分

The boundedness of vector-valued multilinear commutators of singular integral operators whose kernels are variable with mixed homogeneity on Lebesgue spaces is obtained.     

SUPER-GEOMETRIC CONVERGENCE OF A SPECTRAL ELEMENT METHOD FOR EIGENVALUE PROBLEMS WITH JUMP COEFFICIENTS

We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model.     

A priori bounds and existence of positive solutions of an elliptic system of Kirchhoff type in three or four space dimensions

Let \(\Omega \subseteq \mathbb {R}^n(n\ge 3)\) be a bounded and smooth domain. Assuming that \(\alpha ,a,b>0\), \(p,q>0\), we consider the following elliptic problem of Kirchhoff type

$$\begin{aligned} \left\{ \begin{array}{llll} -(a+b\Vert \nabla u_1\Vert ^{2\alpha }_2)\Delta u_1= u_2^{p}+h_1(x, u_1, u_2, \nabla u_1, \nabla u_2) &{} \quad \text{ in }&{}\quad \Omega , \\ -\Delta u_2= u_1^{q}+h_2(x, u_1, u_2, \nabla u_1, \nabla u_2) &{}\quad \text{ in } &{}\quad \Omega , \\ u_1,u_2>0 &{} \quad \text{ in } &{}\quad \Omega , \\ u_1=u_2=0 &{} \quad \text{ on }&{}\quad \partial \Omega . \end{array} \right. \end{aligned}$$

(0.1)

Under some assumptions of \(h_i(x, u_1, u_2, \nabla u_1, \nabla u_2)(i=1, 2)\), we get a priori bounds of the positive solutions to the problem (0.1) when \(n=3,4\) and p, q satisfy \(p,q>1\), \(pq>2\alpha +1\) and \(\frac{1}{p+1}+\frac{1}{q+1}>\frac{n-2}{n}\). By these estimates and the method of continuity, we get the existence for the positive solutions to the problem (0.1). Moreover, the effect of the term \(b\Vert \nabla u_1\Vert ^{2\alpha }_2\) on the solution set of the problem (0.1) also can be given in section 2.

     

电化学石英晶体微天平研究碱性介质中单层级铂原子修饰的金电极上甲醇的电催化氧化

通过在Au电极表面欠电位沉积(UPD)Cu、再与Pt源(H2PtCl6或K2PtCl4)进行置换反应,制得单层级Pt原子修饰的金电极(对H2PtCl6或K2PtCl4,所制电极分别记为Pt(CuUPD-Pt4+)n/Au或Pt(CuUPD-Pt2+)n/Au,n表示欠电位沉积-置换过程的重复次数).用电化学石英晶体微天平(EQCM)技术定量研究了所制电极,评估了其在碱性环境中催化甲醇氧化的质量比活性(SECA).结果表明,以H2PtCl6为Pt源所制电极(Pt(CuUPD-Pt4+)3/Au)的活性更高,最大SECA高达35.7mAμg-1.根据EQCM结果计算了置换效率,籍此讨论了Pt原子在Au电极表面的层层组装结构,发现所制电极表面的裸Au位点分布百分数与实验结果(由AuOx还原峰电量测算)吻合.我们认为,EQCM技术是一种定量研究电极支撑的超薄催化剂的有效手段,这种高效的单层级贵金属催化剂有望在生物、能源、环境相关的电催化研究中进一步应用.     

Electrochemical quartz crystal microbalance study on Au-supported Pt adlayers for electrocatalytic oxidation of methanol in alkaline solution

Underpotential deposition (UPD) of Cu on an Au electrode followed by redox replacement reaction (RRR) of Cu_UPD with a Pt source (H₂PtCl₆ or K₂PtCl₄) yielded Au-supported Pt adlayers (for short, Pt(CuUPD-Pt⁴⁺)n/Au for H₂PtCl₆, or Pt(CuUPD-Pt²⁺)n/Au for K₂PtCl₄, where n denotes the number of UPD-redox replacement cycles). The electrochemical quartz crystal microbalance (EQCM) technique was used for the first time to quantitatively study the fabricated electrodes and estimate their mass-normalized specific electrocatalytic activity (SECA) for methanol oxidation in alkaline solution. In comparison with Pt(CuUPD-Pt²⁺)n/Au, Pt(CuUPD-Pt⁴⁺)n/Au exhibited a higher electrocatalytic activity, and the maximum SECA was obtained to be as high as 35.7 mA μg^?1 at Pt(CuUPD-Pt⁴⁺)3/Au. The layer-by-layer architecture of Pt atoms on Au is briefly discussed based on the EQCM-revealed redox replacement efficiency, and the calculated distribution percentages of bare Au sites agree with the experimental results deduced from the charge under the AuO _x -reduction peaks. The EQCM is highly recommended as an efficient technique to quantitatively examine various electrode-supported catalyst adlayers, and the highly efficient catalyst adlayers of noble metals are promising in electrocatalysis relevant to biological, energy and environmental sciences and technologies.     

一维链状三正丁基锡2,4-二氯苯氧乙酸酯的合成、结构和电化学性质研究

<正>有机锡化合物因具有抗癌活性和杀菌、杀螨作用,以及结构特点多变、反应性丰富,近年来引起了人们的高度关注,已合成出许多结构新颖和性能特殊的有机锡化合物[1-4]。研究发现,有机锡化合物中,中心锡原子的配位形式取决于与锡原子直接相连的     

三正丁基锡3-氨基-2-吡嗪甲酸酯聚合物的合成、结构和电化学性质研究

The tri(n-butyl)tin 3-amino-2-pyrazine formic ester polymer [n-Bu₃Sn(O₂CC₄H₂N₂NH₂-o)]_n has been synthesized and characterized by IR, ¹H NMR spectra and elemental analysis. Its crystal structure has been determined by X-ray diffraction. The crystal belongs to monoclinic space group P2₁/c with a=1.057 7(2) nm, b=1.083 6(2) nm, c=1.905 2(4) nm, β=100.604(3)°, Z=4, V=2.146 3(8) nm³, D_c=1.325 Mg·m^-3, μ(Mo Kα)=1.202 mm^-1, F(000)=880, R₁=0.039 3, wR₂=0.113 3. In the complex, tin atoms are five-coordinated distorted trigonal bipyramid configuration. Through the intermolecular N-H…N hydrogen bonds to form network structure with a “double bridge”. The result of analysis shows that the Sn(Ⅳ)/Sn(Ⅱ) electron transfer in electrode reaction is irreversible. CCDC: 779860.     

求解刚性Volterra延迟积分微分方程的隐显单支方法的稳定性与误差分析

本文主要研究用隐显单支方法求解一类刚性Volterra延迟积分微分方程初值问题时的稳定性与误差分析.我们获得并证明了结论:若隐显单支方法满足2阶相容条件,且其中的隐式单支方法是A-稳定的,则隐显单支方法是2阶收敛且关于初值扰动是稳定的.最后,由数值算例验证了相关结论.     

随机利率下有股利分配的可转换债券的鞅定价

从定量的角度分析了随机利率下有股利分配的可转换债券的价值构成, 并在股票价格服从对数正态分布的条件下, 利用Martingale Pricing方法推导出其定价公式.     

弹性需求下路段相互影响的交通网络均衡模型

本文利用网络用户均衡原理,对弹性需求下路段相互影响的交通配流问题进行研究,给了弹性需求下路段相互影响的网络均衡条件,建立了与均衡条件等价的变分不等式模型,论证了模型解的存在性和唯一性.