Use of local rank‐based spatial information for resolution of spectroscopic images

Spectroscopic images are singular chemical measurements that enclose chemical and spatial information about samples. Resolution of spectroscopic images is focused on the recovery of the pure spectra and distribution maps of the image constituents from the sole raw spectroscopic measurement. In image resolution, constraints are generally limited to non‐negativity and the spatial information is generally not used. Local rank analysis methods have been adapted to describe the local spatial complexity of an image, providing specific pixel information. This local rank information combined with reference spectral information allows the identification of absent compounds in pixels with low compound overlap. The introduction of this information in the resolution process under the form of constraints helps to increase the performance of the resolution method and to decrease the ambiguity linked to the final solutions. Copyright © 2008 John Wiley & Sons, Ltd.     

Rank annihilation correction for the amendment of instrumental inconsistencies

The globalisation of the analysis of a series of individual measurements often results in more robust and reliable outcomes. However, instrumental drifts that can occur between individual measurements destroy the ideal data structure and thus the advantages. A method based on rank annihilation factor analysis (RAFA) is introduced for the correction of several types of instrumental inconsistencies. It can be applied to many series of bilinear datasets. Experimental examples discussed in this paper comprise the successful correction of non-uniform retention time drifts in chromatography due to temperature or pressure changes, wavelength shifts in IR spectroscopy in an industrial control situation, and background absorption shifts in UV-VIS spectroscopy applied to equilibrium investigations.     

Sigma models withA k singularities in Euclidean spacetime of dimension 0 ≤D < 4 and in the limitN → ∞

For the case of the single-O(N)-vector linear sigma models the critical behaviour following from anyA _k singularity in the action is worked out in the double scaling limitN→∞,f _r →f _r ^c , 2≤r≤k. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for allA _k and spacetime dimensions 0≤D<4. There appear exceptional spacetime dimensions where the degreek of the singularityA _k is more strongly constrained than by the renormalizability requirement.     

A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data

Soft modelling or multivariate curve resolution (MCR) are well-known methodologies for the analysis of multivariate data in many different application fields. Results obtained by soft modelling methods are very likely impaired by rotational and scaling ambiguities, i.e. a full range of feasible solutions can describe the data equally well while fulfilling the constraints of the system. These issues are severely limiting the applicability of these methods and therefore, they can be considered as the most challenging ones. The purpose of the current review is to describe and critically compare the available methods that attempt at determining the range of ambiguity for the case of 3-component systems. Theoretical and practical aspects are discussed, based on a collection of simulated examples containing noise-free and noisy data sets as well as an experimental example.     

Imprints of fast-rotating massive stars in the Galactic Bulge

The first stars that formed after the Big Bang were probably massive, and they provided the Universe with the first elements heavier than helium ('metals'), which were incorporated into low-mass stars that have survived to the present. Eight stars in the oldest globular cluster in the Galaxy, NGC?6522, were found to have surface abundances consistent with the gas from which they formed being enriched by massive stars (that is, with higher α-element/Fe and Eu/Fe ratios than those of the Sun). However, the same stars have anomalously high abundances of Ba and La with respect to Fe, which usually arises through nucleosynthesis in low-mass stars (via the slow-neutron-capture process, or s-process). Recent theory suggests that metal-poor fast-rotating massive stars are able to boost the s-process yields by up to four orders of magnitude, which might provide a solution to this contradiction. Here we report a reanalysis of the earlier spectra, which reveals that Y and Sr are also overabundant with respect to Fe, showing a large scatter similar to that observed in extremely metal-poor stars, whereas C abundances are not enhanced. This pattern is best explained as originating in metal-poor fast-rotating massive stars, which might point to a common property of the first stellar generations and even of the 'first stars'.     

Quantification of a known component in an unknown mixture

A method is described for quantifying individual absorbing species in mixtures of unknown composition. The algorithm can be applied to the resolution of chromatographic peaks, to the evaluation of spectrophotmetric titrations, and to related methods producing ordered, two-dimensional arrays of data. In contrast to rank-annihilation factor analysis, it is sufficient to know the absorption spectrum of the species in question. All information about the response in the second dimension, e.g., the concentration profile(s), results from the numerical analysis.     

The influence of turbulence on the transfer of heat to cylinders near the stagnation point

Zusammenfassung Es wird das problem des Einflusses der Turbulenz auf den Wärmeübergang an einem quer angeströmten Zylinder untersucht. Die Untersuchung beschränkt sich auf den Teil des Umfangs, über den sich die laminare Grenzschicht erstreckt. Einige ältere Messungen an der Vorderseite eines Zylinders werden miteinander verglichen, und es zeigt sich, dass ein wichtiger Parameter, nämlich die Intensität der Vorturbulenz bei den Untersuchungen nicht berücksichtigt worden ist. Die bekannten Messungen von Schmidt und Wenner werden kritisch untersucht und der genannte Effekt wird an ihnen aufgezeigt.Weiter werden eigene Messungen der lokalen Nusseltschen Zahl beschrieben. Die Messungen waren durchgeführt worden an der Vorderseite eines einzelnen Zylinders im Querstrom, und zwar in drei sich nicht überdeckenden Gebieten der Intensität der Vorturbulenz. Die Versuchsanordnung wird beschrieben und mögliche Einflüsse der Veränderung der Druckverteilung am Zylinder werden diskutiert. Obwohl dieser letztere Effekt nicht völlig eliminiert worden war, zeigen die Versuche doch klar, dass steigende Turbulenz ein starkes Anwachsen der lokalen Nusselt-Zahl bedingt. Dieses Anwachsen ist bei kleiner Turbulenz besonders stark. Ein Vergleich mit der theoretischen Lösung Froesslings, die für Turbulenz 0 gilt, zeigt, dass die Turbulenz den Wärmeübergang in der Staulinie bis zu 80% erhöhen kann, bei einer Turbulenzvariation von 0–3%.Diese Ergebnisse, die qualitativ interpretiert werden, stützen die Hypothese einer früheren Veröffentlichung, die annimmt, dass der Effekt durch Änderungen der laminaren Grenzschicht, die hervorgerufen werden durch Schwankungen von zunehmender Amplitude, wie sie bei zunehmenden Vorturbulenzen auftreten, bedingt ist.