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.

Population synthesis of isolated neutron stars with magneto-rotational evolution

We revisit the population synthesis of isolated radio-pulsars incorporating recent advances on the evolution of the magnetic field and the angle between the magnetic and rotational axes from new simulations of the magneto-thermal evolution and magnetosphere models, respectively. An interesting novelty in our approach is that we do not assume the existence of a death line. We discuss regions in parameter space that are more consistent with the observational data. In particular, we find that any broad distribution of birth spin periods with P0 ≲ 0.5 s can fit the data, and that if the alignment angle is allowed to vary consistently with the torque model, realistic magnetospheric models are favoured compared to models with classical magneto-dipolar radiation losses. Assuming that the initial magnetic field is given by a lognormal distribution, our optimal model has mean strength 〈log B0[G]〉 ≈ 13.0–13.2 with width σ(log B0) = 0.6–0.7. However, there are strong correlations between parameters. This degeneracy in the parameter space can be broken by an independent estimate of the pulsar birth rate or by future studies correlating this information with the population in other observational bands (X-rays and γ-rays).

The Gaia-ESO Survey: The analysis of high-resolution UVES spectra of FGK-type stars

Context. The ongoing Gaia-ESO Public Spectroscopic Survey is using FLAMES at the VLT to obtain high-quality medium-resolution Giraffe spectra for about 105 stars and high-resolution UVES spectra for about 5000 stars. With UVES, the Survey has already observed 1447 FGK-type stars. Aims. These UVES spectra are analyzed in parallel by several state-of-the-art methodologies. Our aim is to present how these analyses were implemented, to discuss their results, and to describe how a final recommended parameter scale is defined. We also discuss the precision (method-to-method dispersion) and accuracy (biases with respect to the reference values) of the final parameters. These results are part of the Gaia-ESO second internal release and will be part of its first public release of advanced data products. Methods. The final parameter scale is tied to the scale defined by the Gaia benchmark stars, a set of stars with fundamental atmospheric parameters. In addition, a set of open and globular clusters is used to evaluate the physical soundness of the results. Each of the implemented methodologies is judged against the benchmark stars to define weights in three different regions of the parameter space. The final recommended results are the weighted medians of those from the individual methods. Results. The recommended results successfully reproduce the atmospheric parameters of the benchmark stars and the expected Teff-log  g relation of the calibrating clusters. Atmospheric parameters and abundances have been determined for 1301 FGK-type stars observed with UVES. The median of the method-to-method dispersion of the atmospheric parameters is 55 K for Teff, 0.13 dex for log  g and 0.07 dex for [Fe/H]. Systematic biases are estimated to be between 50−100 K for Teff, 0.10−0.25 dex for log  g and 0.05−0.10 dex for [Fe/H]. Abundances for 24 elements were derived: C, N, O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Mo, Ba, Nd, and Eu. The typical method-to-method dispersion of the abundances varies between 0.10 and 0.20 dex. Conclusions. The Gaia-ESO sample of high-resolution spectra of FGK-type stars will be among the largest of its kind analyzed in a homogeneous way. The extensive list of elemental abundances derived in these stars will enable significant advances in the areas of stellar evolution and Milky Way formation and evolution.

The Influence of Space Layout, Technology and Teaching Approach on Student Learning: An Architectural Technology Perspective

Some would argue that there is a need for the traditional lecture format to be rethought in favour of a more active approach. However, this must form part of a bipartite strategy, considered in conjunction with the layout of any new space to facilitate alternative learning and teaching methods. With this in mind, this paper begins to examine the impact of the learning environment on the student learning experience, specifically focusing on students studying on the Architectural Technology and Management programme at Ulster University. The aim of this study is two-fold: to increase understanding of the impact of learning space layout, by taking a student centered approach; and to gain an appreciation of how technology can impact upon the learning space. The study forms part of a wider project being undertaken at Ulster University known as the Learning Landscape Transition Project, exploring the relationship between learning, teaching and space layout. Data collection was both qualitative and quantitative, with use of a case study supported by a questionnaire based on attitudinal scaling. A focus group was also used to further analyse the key trends resulting from the questionnaire. The initial results suggest that the learning environment, and the technology within it, can not only play an important part in the overall learning experience of the student, but also assist with preparation for the working environment to be experienced in professional life.