Linear‐Time Algorithms for Scattering Number and Hamilton‐Connectivity of Interval Graphs

We prove that for all an interval graph is ‐Hamilton‐connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best‐known time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k‐Hamilton‐connected can be computed in time.     

Hyperfinite Lévy Processes

A hyperfinite Lévy process is an infinitesimal random walk (in the sense of nonstandard analysis) which with probability one is finite for all finite times. We develop the basic theory for hyperfinite Lévy processes and find a characterization in terms of transition probabilities. The standard part of a hyperfinite Lévy process is a (standard) Lévy process, and we show that given a generating triplet (γ, C, μ) for standard Lévy processes, we can construct hyperfinite Lévy processes whose standard parts correspond to this triplet. Hence all Lévy laws can be obtained from hyperfinite Lévy processes. The paper ends with a brief look at Malliavin calculus for hyperfinite Lévy processes including a version of the Clark-Haussmann-Ocone formula.     

Silica hydrogel formation and aging monitored by pyrene-based fluorescence probes

Fluorescent probes pyrene (Py), di(1-pyrenylmethyl)ether (DiPyM) and newly synthesized 2,3-bis-[4-(1-pyrenemethoxy)methylphenyl]butane (DiPyS) were used to monitor the formation and aging of silica hydrogel prepared from poly(glyceryl silicate) (PGS) sol. The fluorescence emission spectra of these probes are sensitive to their environment and this feature is utilized for monitoring the evolution of silica hydrogels prepared in this work. The polarity of hydrogel matrix during sol–gel transition assessed by all three pyrene probes decreases in the first stage of hydrogel formation, for about 2 h, followed by a gradual increase in polarity and reaching the constant level after 24 h for at least 2 weeks. The process of crosslinking was assessed by DiPyM and DiPyS. These fluorescent probes possess two pyrene structures, which ability to form a dynamic intramolecular excimer can be used to monitor the degree of hydrogel crosslinking with time. These data support the polarity measurements that the hydrogel network is predominatly formed within the first 2 h, stabilized within the 24 h, and that there is a minor increase in the network density for about 10 days until reaching the constant level. In addition, utilizing the second-order diffraction of scattered excitation light may also be used to obtain an adequate information about the silica hydrogel evolution. In summary, this paper demonstrates that pyrene-type fluorescent probes represent simple and precise tool for characterization of formation and aging of the silica hydrogels.     

Strong anion‐exchange liquid chromatography coupled with isotope ratio mass spectrometry using a Liquiface interface

The introduction of liquid chromatography coupled with isotope ratio mass spectrometry (LC/IRMS) as an analytical tool for the measurement of isotope ratios in non‐volatile analytes has somewhat simplified the analytical cycle from sample collection to analysis mainly due to the avoidance of the extensive sample processing and derivatisation that were necessary for gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS). Here we test the performance of coupling strong anion exchange to IRMS using only the second commercially available interface; the Liquiface. The system was modified from installation specification to improve peak resolution in the interface and maintain peak separation from the column to the mass spectrometer. The system performance was assessed by the determination of sensitivity, accuracy and precision attained from carbohydrate separations. The system performed satisfactorily after modifications, resulting in maintenance of peak resolution from column to mass spectrometer. The sensitivity achieved suggested that ～150 ng carbon could be analysed with acceptable precision (<0.3‰). Accuracy was maintained in the interface as determined by correlation with offline techniques, resulting in regression coefficient of r² = 0.98 and a slope of 0.99. The average precision achieved for the separation of seven monosaccharides was 0.36‰. The integration of a carbonate removal device limited the effect of background carbon perturbations in the mass spectrometer associated with eluent gradients, and the coupling of strong anion‐exchange chromatography with IRMS was successfully achieved using the Liquiface. Copyright © 2010 John Wiley & Sons, Ltd.     

Laser desorption ionization time‐of‐flight mass spectrometric study of binary As‐Se glasses

Binary chalcogenide As‐Se glasses and their thin films are important for optics, computers, materials science and technological applications. To increase understanding of the properties of thin films fabricated by plasma deposition techniques, more information concerning the physics of plasma plume is needed. In this study the formation of clusters in plasma plume from different As‐Se glasses by laser desorption ionization (LDI) or laser ablation (LA) was studied by time‐of‐flight mass spectrometry (TOF MS) in positive and negative ion modes. Formation of a number of As_pSe_q singly charged clusters As₃Se (q = 1–5), AsSe (q = 1–3), As₂Se (q = 2–4), and As₃Se (q = 2–5) was found from As‐Se glasses with the molar ratio As:Se in the range from 1:2 to 7:3. The stoichiometry of the As_pSe_q clusters was determined via isotopic envelope analysis and computer modeling. The structure of the clusters is proposed and the relationship to the structure of the parent glasses, as also suggested by Raman scattering spectra, is discussed. Copyright © 2010 John Wiley & Sons, Ltd.