Inverse Scattering Problem for a Two Dimensional Random Potential

We study an inverse problem for the two-dimensional random Schrödinger equation (Δ + q + k ²)u = 0. The potential q(x) is assumed to be a Gaussian random function whose covariance operator is a classical pseudodifferential operator. We show that the backscattered field, obtained from a single realization of the random potential q, determines uniquely the principal symbol of the covariance operator of q. The analysis is carried out by combining harmonic and microlocal analysis with stochastic methods.     

Determination of HCN sampled from gasification product gases by headspace gas chromatography with atomic emission detector

Nitrogen-containing fuels produce hydrogen cyanide when the fuel is gasified. The gas is poisonous and produces nitrogen oxides when it is burned. HCN is usually sampled into alkaline solutions and analysed using an ion selective electrode. The method is tedious and the electrode response is temperature-dependent. Samples are not stable and must be analysed immediately, and they contain ions which are poisonous to the electrode. Therefore a new gas chromatographic method was developed. In this new method HCN is released from the alkaline solutions with sulphuric acid in a headspace sampler and analysed by a gas chromatograph connected to an atomic emission detector. Measurements on carbon emission line 193.1 nm gave the limit of detection 0.05 mg CN^–/l in the solution. The calibration curve was linear to 1000 mg CN^–/l and the correlation was 0.997. The relative standard deviation of the calibration was 1.7% at the concentration of 5 mg CN^–/l and 1.0% at 25 mg CN^–/l. The developed headspace method allows automated analysis and it needs less sample preparations than the ion selective electrode method. This paper also reports the effect of sample preparation and storage time on the stability of the samples.     

Electronic and vibrational signatures of the Au102(p-MBA)44 cluster

Optical absorption of a gold nanocluster of 102 Au atoms protected by 44 para-mercaptobenzoic acid (p-MBA) ligands is measured in the range of 0.05-6.2 eV (mid-IR to UV) by a combination of several techniques for purified samples in solid and solution phases. The results are compared to calculations for a model cluster Au(102)(SMe)(44) based on the time-dependent density functional theory in the linear-response regime and using the known structure of Au(102)(p-MBA)(44). The measured and calculated molar absorption coefficients in the NIR-vis region are comparable, within a factor of 2, in the absolute scale. Several characteristic features are observed in the absorption in the range of 1.5-3.5 eV. The onset of the electronic transitions in the mid-IR region is experimentally observed at 0.45 ± 0.05 eV which compares well with the lowest calculated transition at 0.55 eV. Vibrations in the ligand layer give rise to fingerprint IR features below the onset of low-energy metal-to-metal electronic transitions. Partial exchange of the p-MBA ligand to glutathione does not affect the onset of the electronic transitions, which indicates that the metal core of the cluster is not affected by the ligand exchange. The full spectroscopic characterization of the Au(102)(p-MBA)(44) reported here for the first time gives benchmarks for further studies of manipulation and functionalization of this nanocluster to various applications.     

Core versus graded core, and global sections of line bundles

We find formulas for the graded core of certain -primary ideals in a graded ring. In particular, if is the section ring of an ample line bundle on a Cohen-Macaulay complex projective variety, we show that under a suitable hypothesis, the core and graded core of the ideal of generated by all elements of degrees at least (for some, equivalently every, large ) are equal if and only if the line bundle admits a non-zero global section. We also prove a formula for the graded core of the powers of the unique homogeneous maximal ideal in a standard graded Cohen-Macaulay ring of arbitrary characteristic. Several open problems are posed whose solutions would lead to progress on a non-vanishing conjecture of Kawamata.

     

Local independence of fractional Brownian motion

Let _σ(t,t′)${\sigma }_{(t,t^{\prime })}$ be the sigma-algebra generated by the differences _Xs−_Xs′$X_s-X_{s^{\prime }}$ with s,s^′∈(t,t^′)$s,s^{\prime }\in (t,t^{\prime })$, where _{(Xt)−∞<t<∞}${\left(X_t\right)}_{-\infty <t<\infty }$ is the fractional Brownian motion with Hurst index H∈(0,1)$H\in (0,1)$. We prove that for any two distinct timepoints _t1$t_1$ and _t2$t_2$ the sigma-algebras _{σ(t1−ε,t1+ε)}${\sigma }_{(t_1-\epsilon ,t_1+\epsilon )}$ and _{σ(t2−ε,t2+ε)}${\sigma }_{(t_2-\epsilon ,t_2+\epsilon )}$ are asymptotically independent as ε↘0$\epsilon \searrow 0$. We show the independence in the strong sense that Shannon’s mutual information between the two σ$\sigma$-algebras tends to zero as ε↘0$\epsilon \searrow 0$. Some generalizations and quantitative estimates are also provided.     

Cellulose--model films and the fundamental approach

This critical review describes the recent arrival of ultrathin films of cellulose. The methodology of preparation as well as the applications of the films for fundamental research is fully covered. The review places cellulose in a wider scientific context where cellulose research is no longer a field of interest for specialised scientists only. Cellulose and cellulosic materials should interest communities such as biochemists, physical chemists, surface chemists, organic chemists, polymer chemists and also physicists working close the disciplines mentioned. (149 references.).     

Modification of olefin polymerization catalysts. I. Mechanism of the interaction between AIEt3 and silyl ethers

The interaction between AlEt₃ and silyl ethers, Ph_nSi(OMe)_4-n (n = 0–3), was followed by ¹³C- and ²⁹Si-NMR techniques in conditions close to those typical for an olefin polymerization reaction with supported Ziegler–Natta catalysts (A1Et₃:silyl ether ratios from 1 to 10, temperature range 25–75°C). A1Et₃ and silyl ethers form instantaneously at ambient temperature a donor-acceptor complex, which is stable at a 1:1 molar ratio. In the presence of excess A1Et₃ the complex decomposes via a mechanism consisting, in the case of PhSi(OMe)₃, of five consecutive steps: alternating complexation and ether reductions with the formation of alkylated silyl ethers, Ph(Et)_nSi(OMe)_3-n (n = 1,2), and dialkyl-aluminum alkoxides, (Et₂A1OMe₃)_n (n = 2,3). The rate of decomposition was enhanced by the increasing number of methoxy groups present in the silyl ether, heating, or a high A1Et₃:silyl ether ratio. The decomposition was not inhibited by the presence of 1-hexene.