Stochastic properties of the Laplacian on Riemannian submersions

Based on ideas of Pigolla and Setti (2010), we prove that isometrically immersed submanifolds with bounded mean curvature into Cartan–Hadamard manifolds are Feller. We consider Riemannian submersions π : M → N with compact minimal fibers and prove that the total space M is Feller, parabolic or stochastically complete if, and only if, the base manifold N is, respectively, Feller, parabolic or stochastically complete.     

Proton transfer reaction ion trap mass spectrometer

Proton transfer reaction mass spectrometry is a relatively new field that has attracted a great deal of interest in the last few years. This technique uses H(3)O(+) as a chemical ionization (CI) reagent to measure volatile organic compounds (VOCs) in the parts per billion by volume (ppbv) to parts per trillion by volume (pptv) range. Mass spectra acquired with a proton transfer reaction mass spectrometer (PTR-MS) are simple because proton transfer chemical ionization is "soft" and results in little or no fragmentation. Unfortunately, peak identification can still be difficult due to isobaric interferences. A possible solution to this problem is to couple the PTR drift tube to an ion trap mass spectrometer (ITMS). The use of an ITMS is appealing because of its ability to perform MS/MS and possibly distinguish between isomers and other isobars. Additionally, the ITMS duty cycle is much higher than that of a linear quadrupole so faster data acquisition rates are possible that will allow for detection of multiple compounds. Here we present the first results from a proton transfer reaction ion trap mass spectrometer (PTR-ITMS). The aim of this study was to investigate ion injection and storage efficiency of a simple prototype instrument in order to estimate possible detection limits of a second-generation instrument. Using this prototype a detection limit of 100 ppbv was demonstrated. Modifications are suggested that will enable further reduction in detection limits to the low-ppbv to high-pptv range. Furthermore, the applicability of MS/MS in differentiating between isobaric species was determined. MS/MS spectra of the isobaric compounds methyl vinyl ketone (MVK) and methacrolein (MACR) are presented and show fragments of different mass making differentiation possible, even when a mixture of both species is present in the same sample. However, MS/MS spectra of acetone and propanal produce fragments with the same molecular masses but with different intensity ratios. This allows quantitative distinction only if one species is predominant. Fragmentation mechanisms are proposed to explain the results.     

An iron-57 Mössbauer spectroscopy and EXAFS study of the hydrogen pretreatment of titania-supported iron-ruthenium catalysts

The changes in composition and structure which are induced in a titania-supported iron-ruthernium catalyst following treatment in hydrogen have been investigated in situ by⁵⁷Fe Mössbauer spectroscopy and by EXAFS. The results show that ruthenium dioxide is readily reduced at temperatures below ca. 500°C to ca. 20 Å clusters of metallic ruthenium whilst α-Fe₂O₃ is partially reduced at 130°C to Fe²⁺ and Fe⁰. The Fe³⁺ which is formed by the reoxidation of Fe²⁺ under the reducing conditions at 500°C segregates to the interface of the bimetallic phase and the titania support. It is suggested that continued treatment at 700°C produces a high dispersion of iron which is coordinated to oxygen atoms of the support. The ca. 20 Å clusters of metallic ruthenium may be envisaged as being anchored to the support via iron-ruthenium bonds     

An iron-57 Mössbauer spectroscopic study of titania-supported iron- and iron-iridium catalysts

⁵⁷Fe Mössbauer spectroscopy shows that titania-supported iron is reduced by treatment in hydrogen at significantly lower temperatures than corresponding silica- and alumina-supported catalysts. The metallic iron formed under hydrogen at 600°C is partially converted to carbide by treatment in carbon monoxide and hydrogen. In contrast to its alumina- and silica-supported counterparts, the remainder of the titania-supported iron is unchanged by this gaseous mixture. The⁵⁷Fe Mössbauer spectra and EXAFS show that iron and iridium in the titania-supported iron-iridium catalysts are reduced in hydrogen at even lower temperatures and, after treatment at 600°C, are predominantly present as the iron-iridium alloy. The treatment of these reduced catalysts in carbon monoxide and hydrogen is shown by Mössbauer spectroscopy and EXAFS to induce the segregation of iron from the iron-iridium alloy and its conversion to iron oxide.     

Stack Domination Density

There are infinite sequences of graphs {G _n } where |G _n | = n such that the minimal dominating sets for G _i × H fall into predictable patterns, in light of which γ (G _n × H) may be nearly linear in n; the coefficient of linearity may be regarded as the average density of the dominating set in the H-fibers of the product. The specific cases where the sequence {G _n } consists of cycles or path is explored in detail, and the domination density of the Grötzsch graph is calculated. For several other sequences {G _n }, the limit of this density can be seen to exist; in other cases the ratio ${\frac{\gamma (G_n \times H)}{\gamma (G_n)}}$ proves to be of greater interest, and also exists for several families of graphs.     

The development of a comprehensive toolbox based on multi-level,high-throughput screening of MOFs for CO/N2 separations

The separation of CO/N₂ mixtures is a challenging problem in the petrochemical sector due to the very similar physical properties of these two molecules, such as size, molecular weight and boiling point. To solve this and other challenging gas separations, one requires a holistic approach. The complexity of a screening exercise for adsorption-based separations arises from the multitude of existing porous materials, including metal–organic frameworks. Besides, the multivariate nature of the performance criteria that needs to be considered when designing an optimal adsorbent and a separation process – i.e. an optimal material requires fulfillment of several criteria simultaneously – makes the screening challenging. To address this, we have developed a multi-scale approach combining high-throughput molecular simulation screening, data mining and advanced visualization, as well as process system modelling, backed up by experimental validation. We have applied our recent advances in the engineering of porous materials'' morphology to develop advanced monolithic structures. These conformed, shaped monoliths can be used readily in industrial applications, bringing a valuable strategy for the development of advanced materials. This toolbox is flexible enough to be applied to multiple adsorption-based gas separation applications.

The separation of challenging mixtures through adsorption is a multidimensional problem that requires a holistic approach. Our toolbox combines experiments, molecular and process simulations with data visualization to find optimal, porous materials.     

Iron-57 and iridium-193 Mössbauer spectroscopic studies of supported iron-iridium catalysts

⁵⁷Fe and¹⁹³Ir Mössbauer spectroscopy shows that silica- and alumina-supported iron-iridium catalysts formed by calcination in air contain mixtures of small particle iron (III) oxide and iridium(IV) oxide. The iridium dioxide in both supported catalysts is reduced in hydrogen to metallic iridium. The α-Fe₂O₃ in the silica supported materials is predominantly reduced in hydrogen to an iron-iridium alloy whilst in the alumina-supported catalyst the iron is stabilised by treatment in hydrogen as iron(II). Treatment of a hydrogen-reduced silica-supported iron catalyst in hydrogen and carbon monoxide is accompanied by the formation of iron carbides. Carbide formation is not observed when the iron-iridium catalysts are treated in similar atmospheres. The results from the bimetallic catalysts are discussed in terms of the hydrogenation of associatively adsorbed carbon monoxide and the selectivity of supported iron-iridium catalysts to methanol formation.     

Stereoselective synthesis of (2S,3R)- and (2R,3S)-iodoreboxetine; potential SPECT imaging agents for the noradrenaline transporter

With the aim of developing a new SPECT imaging agent for the noradrenaline transporter, a twelve-step stereoselective synthesis of iodinated analogues of (2S,3R)- and (2R,3S)-reboxetine has been achieved from 4-bromobenzaldehyde. The key steps involve a Sharpless asymmetric epoxidation to establish the stereogenic centres and a copper catalysed aromatic halogen exchange reaction to introduce the key iodine atom. In vitro testing of these compounds using a [(3)H]nisoxetine displacement assay with homogenised rat brain shows both compounds to have significant affinity, with K(i) values of 320.8 nM and 58.2 nM for (2S,3R)- and (2R,3S)-iodoreboxetine respectively.     

A Mössbauer spectroscopic investigation of the influence of iridium on the changes induced in iron-iridium catalysts when treated in hydrogen and in carbon monoxide and hydrogen

The mixtures of large- and small-particle α-Fe₂O₃ which are formed during the preparation of silica-supported iron-iridium catalysts with low concentrations of iridium in air are partially reduced by treatment in hydrogen at 270°C to Fe₃O₄ and iron (II). Increases in the iridium content of the bimetallic particles induces the formation of metallic iron when the catalysts are heated in hydrogen whilst catalysts with large concentrations of iridium are partially converted to iron-iridium alloys. Treatment of the catalysts containing metallic iron in carbon monoxide and hydrogen results in the formation of iron carbides. Small particle α-Fe₂O₃ formed on alumina-supported catalysts are partially converted to iron (II) in atmospheres of hydrogen. The remaining iron (III) suffers further reduction to iron (II). when treated in carbon monoxide and hydrogen.