Carleson measure characterization of Bloch functions

We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized Carleson measure;f B ₀ if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized vanishing Carleson measure, whereD f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province.     

Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

Characterization of individual atmospheric particles by element mapping in electron probe microanalysis

In this paper procedures for the characterization of individual aerosol particles by element mapping in the electron microprobe are presented. The number, size and qualitative chemical composition of particles is derived from a combination of secondary or backscattered electron images and element distribution maps. Accuracy of the size distribution and reliability of the qualitative analysis procedure were checked with silicate samples. In order to obtain a semi-quantitative estimate of the chemical composition of individual particles the count rates taken from element distribution maps are corrected for matrix and geometric effects using particle ZAF procedures.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

PHOTOEMISSION WITHIN AND BEYOND THE ONE-STEP MODEL

Photoemission in the vacuum ultraviolet photon regime has proved to be an effective tool for the investigation of valence band surface electronic structure. The interpretation cannot be exclusively confined to the valence bands but has to consider cross sections with realistic final states consistently designed within the one-step model. Therefore especially in the surface sensitive photoemission, several effects hide the final goal of deducing the energetic and wavefunction structure together with microscopic potential parameters through a convincing agreement of calculated with measured spectra. The final states band structure is much less well understood than the valence band structure under consideration. The optical potential, which controls the surface sensitivity through the underlying damping mechanisms, widely relies on empirical assumptions. Furthermore, the photon field is not only strongly influenced but in the vicinity of the plasma frequency also deteriorated by the electronic response. In view of high resolution spectroscopy the accuracy of the data interpretation is affected, and in fact, band-mapping methods are no longer valid. Examples of recent calculations to account for these effects are reviewed.     

Insoluble eggshell matrix proteins--their peptide mapping and partial characterization by capillary electrophoresis and high-performance liquid chromatography

Avian eggshell matrix proteins were studied by two analytical approaches. Peptide mapping was done by trypsin and pepsin followed by collagenase cleavage; analyses were carried out by capillary electrophoresis and reversed-phase high-performance liquid chromatography (HPLC). Comparison of peptide maps obtained by both methods revealed a complex mixture of peptides in the insoluble layers of the eggshell; it was concluded that there are at least three different insoluble protein/peptide layers in the avian eggshell (cuticle, palisade, and mammillary layer). Partial characterization of peptides in each layer was made by HPLC-mass spectrometry analysis. There is an evidence that the eggshell insoluble proteins contain species susceptible to collagenase cleavage, however, the sequences split by this enzyme probably are not those typical for the main triple-helical core of collagenous proteins. It is proposed that the action of collagenase upon eggshell proteins is caused by the side effect of collagenase described previously with synthetic peptides. Some of the proteins present are probably glycosylated. Fatty acid content in the insoluble eggshell layers (after decalcification) was in the range of 2-4% (which reflected both lipid and lipoproteins bound fatty acids). Porphyrin pigments are dominant in the cuticle layer.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Autoignition temperature: comprehensive data analysis and predictive models

ABSTRACT

Here we report a new predictive model for autoignition temperature (AIT), an important physical parameter widely used to assess potential safety hazards of combustible materials. Available structure-AIT data extracted from different sources were critically analysed. Support vector regression (SVR) models on different data subsets were built in order to identify a reliable compound set on which a realistic model could be built. This led to a selection of the dataset containing 875 compounds annotated with AIT values. The thereupon-based SVR model performs reasonably well in cross-validation with the determination coefficient r ² = 0.77 and mean absolute error MAE = 37.8°C. External validation on 20 industrial compounds missing in the training set confirmed its good predictive power (MAE = 28.7°C).     

Using a process-centered approach to minimize the effort of compliance

 The complexity of different quality standards can, in principle, be covered by different approaches and strategies. In-depth process mapping of quality control (QC) work streams was used by the analytical laboratories of Lonza AG to show up the principle differences in being compliant to different quality systems. The results identified two main drivers for all necessary actions: process-related activities and infrastructure-related activities. In addition, a clear indication of the economic impact of these driving forces was gained, which led the laboratories to decide on a process-oriented approach. This approach has the advantage of being able to reflect the different demands of different quality assurance (QA) regulations within the same QC organizational structure. Following the process helps avoid unnecessary efforts in analytical work and represents a very economical approach, at the same time, providing high flexibility to react to different QA or customer demands. Received: 5 July 2002 Accepted: 12 November 2002 Acknowledgements The process-oriented approach resulted from many, very challenging discussions for which I would like to thank the staff of my organization (Analytics & QC), especially, the QA staff and the LIMS team. Presented at Analytica Conference, 23–26 April 2002, Munich, Germany Correspondence to B. Ciommer     

A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

地外样品研究中电子探针元素面扫描分析技术的应用

由于月壤等地外样品十分珍贵,在实验室研究中优先使用原位、微区、无损的元素分析方法。电子探针元素面扫描是地外样品研究中常用的分析方法之一。该方法可获取样品整体或者感兴趣区域的多种元素分布数据,应用于矿物相识别与含量估算,锆石等定年矿物的快速定位,矿物环带、出溶、反应边结构等特殊岩相和矿物接触关系等分析和研究。本研究中以嫦娥五号月壤、月球陨石、火星陨石研究为例,介绍了目前元素面扫描的应用方法。此外,本文还对比、分析了电子探针面扫描技术与其它面扫描技术的优缺点和适用范围。未来十年,我国将实施一系列月球、火星、小行星等天体采样返回任务。电子探针元素面扫描分析未来将在这些地外样品研究中广泛使用。同时,建议行星科学家围绕所关心的科学问题,合理搭配多种分析方法以实现各种技术优势互补和样品科学价值最大化,服务我国月球与深空探测任务科学产出和行星科学发展。