A theoretical study of the XP and NEXAFS spectra of alanine: gas phase molecule, crystal, and adsorbate at the ZnO(10 ̅10) surface

The adsorption of alanine on the mixed-terminated ZnO(10 ?10) surface is studied by means of quantum-chemical ab initio calculations. Using a finite cluster model and the adsorption geometry as obtained both by periodic CPMD and embedded cluster calculations, the C1s, N1s and O1s X-ray photoelectron spectra (XPS) and near-edge X-ray absorption fine structure (NEXAFS) spectra are calculated for single alanine molecules on ZnO(10 ?10). These spectra are compared with the spectra calculated for alanine in the gas phase and in its crystalline form and with experimental XPS and NEXAFS data for the isolated alanine molecule and for alanine adsorbed on ZnO(10 ?10) at multilayer and monolayer coverage. The excellent agreement between the experimental and calculated XP and NEXAFS spectra confirms the calculated adsorption geometry: A single alanine molecule is bound to ZnO(10 ?10) in a dissociated bidentate form with the two O atoms of the acid group bound to two Zn atoms of the surface and the proton transferred to one O atom of the surface. Other possible structures, such as adsorption of alanine in one of its neutral or zwitterionic forms in which the proton of the -COOH group remains at this group or is transferred to the amino group, can be excluded since they would give rise to quite different XP spectra. In the multilayer coverage regime, on the other hand, alanine is in its crystalline form as is also shown by the analysis of the XP spectra.     

Density symmetries for a class of 2-D diffusions with applications to finance

We study densities of two-dimensional diffusion processes with one non-negative component. For such diffusions, the density may explode at the boundary, thus making a precise specification of the boundary condition in the corresponding forward Kolmogorov equation problematic. We overcome this by extending a classical symmetry result for densities of one-dimensional diffusions to our case, thereby reducing the study of forward equations with exploding boundary data to the study of a related backward equation with non-exploding boundary data. We also discuss applications of this symmetry for option pricing in stochastic volatility models and in stochastic short rate models.     

On the Effect of Misspecifying the Density Ratio Model

The density ratio model specifies that the log-likelihood ratio of two unknown densities is of known linear form which depends on some finite dimensional parameters. The model can be broadened to allow for m-samples in a quite natural way. Estimation of both parametric and nonparametric part of the model is carried out by the method of empirical likelihood. However the assumed linear form has an impact on the estimation and testing for the parametric part. The goal of this study is to quantify the effect of choosing an incorrect linear form and its impact to inference. The issue of misspecification is addressed by embedding the unknown linear form to some parametric transformation family which yields ultimately to its identification. Simulated examples and data analysis integrate the presentation.     

New synthesis of hexamethyltungsten(VI); hexamethylrhenium(VI) and dioxotrimethylrh enium(VII)

A new synthesis of hexamethyltungsten involves the reaction of WCl₆ and AlMe₃, while interaction of AlMe₃ and ReOMe₄ gives ReMe₆; a dioxorhenium(VII) methyl, ReO₂ Me₃, is reported.     

Integer points on the curve

We completely solve diophantine equations of the form where is a positive integer, using a reduction to some quartic elliptic equations, which can be solved with well known methods.

     

Ancient shrinking spherical interfaces in the Allen–Cahn flow

We consider the parabolic Allen–Cahn equation in ${\mathbb{R}}^n$, $n\ge 2$,

$u_t=\mathrm{\Delta }u+(1?u^2)u\text{ in }{\mathbb{R}}^n\times (?\infty ,0].$

We construct an ancient radially symmetric solution $u(x,t)$ with any given number k of transition layers between ?1 and +1. At main order they consist of k time-traveling copies of w with spherical interfaces distant $O(\log ?|t|)$ one to each other as $t\to ?\infty$. These interfaces are resemble at main order copies of the shrinking sphere ancient solution to mean the flow by mean curvature of surfaces: $|x|=\sqrt{?2(n?1)t}$. More precisely, if $w(s)$ denotes the heteroclinic 1-dimensional solution of $w^{″}+(1?w^2)w=0$$w(\pm \infty )=\pm 1$ given by $w(s)=\tanh ?\left(\frac{s}{\sqrt{2}}\right)$ we have

$u(x,t)\approx \sum _{j=1}^k{(?1)}^{j?1}w(|x|?{\rho }_j(t))?\frac{1}{2}(1+{(?1)}^k)\text{ as }t\to ?\infty$

where

${\rho }_j(t)=\sqrt{?2(n?1)t}+\frac{1}{\sqrt{2}}(j?\frac{k+1}{2})\log ?\left(\frac{|t|}{\log ?|t|}\right)+O(1),j=1,\dots ,k.$