Surface enhanced Raman scattering of water on an Ag electrode

Surface enhanced Raman scattering of adsorbates on an Ag electrode in various electrolytes (e.g., 0.1–1.0 M KF, KCl, KBr, KI, K₃PO₄, and NaN₃) has been investigated in an effort to elucidate the mechanism of the enhancement of water compared to that for other adsorbates. (It is well known, for example, that pyridine exhibits large enhancement in 0.1 M KCl while SERS from water is not detectable unless the salt concentration is raised to almost 1 M.) Use of an optical multichannel analyzer allowed rapid recording of Raman spectra, and SERS intensities of adsorbates could therefore be monitored simultaneously during a continuous oxidation-reduction cycle. Potential dependencies of SERS intensities when the electrode potential is cycled in a non-faradiac potential range immediately following oxidation and reduction indicate that adatoms are partially responsible for the Raman enhancement. Furthermore, the anions in the electrolyte play an important role in stabilizing these “active sites.” For this reason, the degree of enhancement is influenced by the solubility of the Ag compound formed during oxidation and the specific adsorption of the anions to the Ag surface. Preferential alignment of H₂O molecules with their oxygen ends facing the surface at positive potentials, the tendency of anions in the electrolyte to disrupt hydrogen bonding with the water network, and the weak hydrogen bonding of H₂O with the anions give rise to a SERS lineshape from adsorbed H₂O molecules which is narrower than, and thus distinguishable from, the Raman line of bulk water. Thus, the degree to which the particular anions in the electrolyte disrupt hydrogen bonding among water molecules and reform hydrogen bonding between the anions and H₂O molecules influences the SERS lineshape and the apparent enhancement of the H₂ Raman emission.     

Optimal volume-corrected laplace-metropolis method

The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccioet al. The correction volume of probability α in DiCiccioet al. is fixed and suggested to take the value α=0.05. In this article α is selected based on an asymptotic analysis to minimize the mean square relative error (MSRE). This optimal choice of α is shown to be invariant under linear transformations. The invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical use. A simulation study and a real data example are presented.     

Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

Another approach to the heat flow for Plateau problem

For the minimal surfaces in Rⁿ with Plateau boundary condition and establish the global existence and uniqueness of the flow as well as the continuous dependence of the initial datum.     

小间隙高放大多丝室及其放电机制

对以强猝灭气体工作的小间隙多丝室及其放电机制进行了研究,实验表明,因为工作在饱和模式区,这种室同时具有很高的气体放大和相当快的时间特性.文中探讨了放电机制,雪崩中空间电荷效应以及电离光子的产生和作用是重要的因素,而其中后一因素又受到强猝灭气体的抑制.     

更新时间概率模型及其无偏估计定理的论证

本文提出应用小参数法 ,探讨 Markov链中相邻两次更新时刻内稀疏事件的概率估计问题 .建立了三种最重要的具有更新时间的概率模型 .通过小参数的引入和对概率式的幂展开 ,进而推证出幂渐近展开系数的模型估算法 .论证了无偏估计的重要定理 ,给出了概率估计式和无偏估计精度 .亦将许多算法扩展到Markov链的任意状态空间     

Herstein定理的推广

1955年Herstein将著名的Jacobson定理推广为:定理A.如果对R中任意x,y,存在可依赖于x,y的整系数多项式p(t),使[x-x2p(x),y]=0,则R是交换的.本文利用多项式的系数和定义了n元多项式,f(x1,x2…,xn)的Fk性质,并以此证明了一个环的交换性定理,当n=1时,即得到定理A.     

一类齐次对称多项式上的切比雪夫不等式

本文借助于控制不等式及数学归纳法，将著名的切比雪夫不等式推广到m次一般齐次对称多项式上(如文中定理及引理7)，并将此结果用于对称平均等．旨在展示证明解析不等式的一些有效的方法和技巧，同时为数学研究特别是高维几何研究提供一些新的有趣而有用的解析不等式．