Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

On the nature of the galactic early-B hypergiants

Aims. Despite their importance to a number of astrophysical fields, the lifecycles of very massive stars are still poorly defined. In order to address this shortcoming, we present a detailed quantitative study of the physical properties of four early-B hypergiants (BHGs) of spectral type B1-4 Ia+; Cyg OB2 #12, ζ1 Sco, HD 190603 and BP Cru. These are combined with an analysis of their long-term spectroscopic and photometric behaviour in order to determine their evolutionary status. Methods. Quantitative analysis of UV–radio photometric and spectroscopic datasets was undertaken with a non-LTE model atmosphere code in order to derive physical parameters for comparison with apparently closely related objects, such as B supergiants (BSGs) and luminous blue variables (LBVs), and theoretical evolutionary predictions. Results. The long-term photospheric and spectroscopic datasets compiled for the early-B HGs revealed that they are remarkably stable over long periods ( ≥ 40 yrs), with the possible exception of ζ1 Sco prior to the 20th century; in contrast to the typical excursions that characterise LBVs. Quantitative analysis of ζ1 Sco, HD 190603 and BP Cru yielded physical properties intermediate between BSGs and LBVs; we therefore suggest that BHGs are the immediate descendants and progenitors (respectively) of such stars, for initial masses in the range ~30−60 M⊙. Comparison of the properties of ζ1 Sco with the stellar population of its host cluster/association NGC 6231/Sco OB1 provides further support for such an evolutionary scenario. In contrast, while the wind properties of Cyg OB2 #12 are consistent with this hypothesis, the combination of extreme luminosity and spectroscopic mass (~110 M⊙) and comparatively low temperature means it cannot be accommodated in such a scheme. Likewise, despite its co-location with several LBVs above the Humphreys-Davidson (HD) limit, the lack of long term variability and its unevolved chemistry apparently excludes such an identification. Since such massive stars are not expected to evolve to such cool temperatures, instead traversing an O4-6Ia → O4-6Ia+ → WN7-9ha pathway, the properties of Cyg OB2 #12 are therefore difficult to understand under current evolutionary paradigms. Finally, we note that as with AG Car in its cool phase, despite exceeding the HD limit, the properties of Cyg OB2 #12 imply that it lies below the Eddington limit – thus we conclude that the HD limit does not define a region of the HR diagram inherently inimical to the presence of massive stars.

Synthesis of Robust Hierarchical Silica Monoliths by Surface-Mediated Solution/Precipitation Reactions over Different Scales: Designing Capillary Microreactors for Environmental Applications

A synthetic procedure to prepare novel materials (surface-mediated fillings) based on robust hierarchical monoliths is reported. The methodology includes the deposition of a (micro- or mesoporous) silica thin film on the support followed by growth of a porous monolithic SiO2 structure. It has been demonstrated that this synthesis is viable for supports of different chemical nature with different inner diameters without shrinkage of the silica filling. The formation mechanism of the surface-mediated fillings is based on a solution/precipitation process and the anchoring of the silica filling to the deposited thin film. The interaction between the two SiO2 structures (monolith and thin film) depends on the porosity of the thin film and yields composite materials with different mechanical stability. By this procedure, capillary microreactors have been prepared and have been proved to be highly active and selective in the total and preferential oxidation of carbon monoxide (TOxCO and PrOxCO).

Synthesis of palladium nanoparticles over graphite oxide and carbon nanotubes by reduction in ethylene glycol and their catalytic performance on the chemoselective hydrogenation of para-chloronitrobenzene

Pd nanoparticles have been synthesized over carbon nanotubes (CNT) and graphite oxide (GO) by reduction with ethylene glycol and by conventional impregnation method. The catalysts were tested on the chemoselective hydrogenation of p-chloronitrobenzene and the effect of the synthesis method and surface chemistry on their catalytic performance was evaluated. The catalysts were characterized by N2 adsorption/desorption isotherms at 77 K, TEM, powder X-ray diffraction, thermogravimetry, infrared and X-ray photoelectron spectroscopy and ICP-OES. It was observed that the synthesis of Pd nanoparticles employing ethylene glycol resulted in metallic palladium particles of smaller size compared to those prepared by the impregnation method and similar for both supports. The presence of oxygen groups on the support surface favored the activity and diminished the selectivity. It seems that ethylene glycol reacted with the surface groups of GO, this favoring the selectivity. The activity was higher over the CNT-based catalysts and both catalysts prepared by reduction in ethylene glycol were quite stable upon recycling.

NOx storage and reduction over copper-based catalysts. Part 2: Ce0.8M0.2Oδ supports (M = Zr, La, Ce, Pr or Nd)

5% copper catalysts with Ce0.8M0.2Oδ supports (M = Zr, La, Ce, Pr or Nd) have been studied by rapid-scan operando DRIFTS for NOx Storage and Reduction (NSR) with high frequency (30 s) CO, H2 and 50%CO + 50%H2 micropulses. In the absence of reductant pulses, below 200–250 °C NOx was stored on the catalysts as nitrite and nitro groups, and above this temperature nitrates were the main species identified. The thermal stability of the NOx species stored on the catalysts depended on the acid/basic character of the dopant (M more acidic = NOx stored less stable ⇒ Zr4+ < none < Nd3+ < Pr3+ < La3+ ⇐ M more basic = NOx stored more stable). Catalysts regeneration was more efficient with H2 than with CO, and the CO + H2 mixture presented an intermediate behavior, but with smaller differences among the series of catalyst than observed using CO alone. N2 is the main NOx reduction product upon H2 regeneration. The highest NOx removal in NSR experiments performed at 400 °C with CO + H2 pulses was achieved with the catalyst with the most basic dopant (CuO/Ce0.8La0.2Oδ) while the poorest performing catalyst was that with the most acidic dopant (CuO/Ce0.8Zr0.2Oδ). The poor performance of CuO/Ce0.8Zr0.2Oδ in NSR experiments with CO pulses was attributed to its lower oxidation capacity compared to the other catalysts.