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.

Updating the marine biostratigraphy of the Granada Basin (central Betic Cordillera). Insight for the Late Miocene palaeogeographic evolution of the Atlantic – Mediterranean seaway

The marine stratigraphic record of the Granada Basin (central Betic Cordillera, Spain) is composed of three Late Miocene genetic units deposited in different sea-level contexts (from base to top): Unit I (sea-level rise), Unit II (high sea-level), and Unit III (low sea-level). The latter mainly consists of evaporites precipitated in a shallow-basin setting. Biostratigraphic analyses based on planktonic foraminifera and calcareous nannoplankton indicate four late Tortonian bioevents (PF1-CN1, PF2, PF3, and PF4), which can be correlated with astronomically-dated events in other sections of the Mediterranean. PF1-CN1 (7.89 Ma) is characterized by the influx of the Globorotalia conomiozea group (including typical forms of Globorotalia mediterranea) and by the first common occurrence of Discoaster surculus; PF2 (7.84 Ma) is marked by the first common occurrence of Globorotalia suterae; PF3 (7.69 Ma) is typified by the influx of dextral Neogloboquadrina acostaensis; and PF4 (7.37 Ma) is defined by the influx of the Globorotalia menardii group II (dextral forms). The PF1 event occurred in the upper part of Unit I, whereas PF2 to PF4 events occurred successively within Unit II. The age of Unit III (evaporites) can only be estimated in its lower part based on the presence of dextral Globorotalia scitula, which, together with the absence of the first common occurrence of the G. conomiozea group (7.24 Ma), points to the latest Tortonian. Comparisons with data from the other Betic basins indicate that the evaporitic phase of the Granada Basin (7.37–7.24 Ma) is not synchronous with those from the Lorca Basin (7.80 Ma) and the Fortuna Basin (7.6 Ma). In the Bajo Segura Basin (easternmost Betic Cordillera), no evaporite deposition occurred during the late Tortonian. The evaporitic unit of the Granada Basin (central Betics) records the late Tortonian restriction of the Betic seaway (the marine connection between the Atlantic and Mediterranean). The diachrony in the restriction of the Betic seaway is related to differing tectonic movements in the central and eastern sectors of the Betic Cordillera.

Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl. 154(2), 2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements—normals and/or subdifferentials.

The episcopal complex of Eio-El Tolmo de Minateda (Hellín, Albacete, Spain). Architecture and spatial organization. 7th to 8th centuries AD

The episcopal complex of Eio, located in El Tolmo de Minateda, was built between the end of the 6th century and the beginning of the 7th century, possibly as a political decision taken by the ecclesiastical authority in the capital of the Visigothic kingdom (Toletum). With the comprehensive study of the whole complex presented below (construction cycles, furniture, decoration and location of spaces), we can interpret the function of each space in the basilica and the domus episcopi, the liturgical and general movement routes, the existence of some hierarchical environments, and specify the chronological development of the buildings. After the Arab-Berber conquest of Hispania in the early 8th century, the whole complex will experience a series of transformations that will convert the religious and monumental public area into a private, residential and industrial Islamic quarter.

Numerical resolution of Emden's equation using Adomian polynomials

Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.

Tourism potential analysis of the castles of Vinalopó, Spain: an opportunity for social and tourist development of cultural heritage

Within the overall framework of the renewal process of coastal tourist destinations, cultural heritage has frequently been used as a key argument for the introduction and development of strategies for the diversification and differentiation of the traditional tourist product based on sun and sand. This is the situation of the province of Alicante, identified with the Costa Blanca geotourism brand, where there are important economic issues that could contribute to the renewal of this coastal tourist destination. One of the most significant heritage values of this space consists of a series of medieval fortresses located along the axis of the Vinalopó River, which has acted since prehistoric times as a natural route from within the provincial mainland to the coast. It is precisely the argument of this historical, territorial and landscape content that has been used repeatedly in recent years to develop initiatives aimed at the creation of a tourist product, currently inexistent, based on the route of the castles of Vinalopó. This communication aims to analyse the degree of tourism potential of the fortresses located in the towns of Biar, Banyeres de Mariola, Sax, Villena, Novelda, Elda, Petrer and Elche, which constitute the core of municipalities where these medieval fortresses are located, finally pointing out some proposals for the creation of a heritage tourism product.