Of the use of the “English sector” in trigonometry: what amount of mathematical training was necessary in the 18th century?

In 1723 Edmund Stone published The construction and principal uses of mathematical instruments, which was essentially a translation from the French of Bion’s Traité de la construction et des principaux usages des instrumens de mathématique (1709). As the title of the book indicated, Stone annexed a number of instruments that had been omitted by Bion, in particular, those invented or improved by the English. Hence, after the translation of Book II, on the construction and uses of the “French sector”, Stone added a chapter on the “English sector”. In the 17th century there had been a number of debates concerning the amount of mathematical training required for the study of mathematical instruments. In the context of the study of mathematical instruments in the 18th century, it is worth exploring the link theory-practice in the books on instruments. The aim of this contribution is to explore the mathematical knowledge involved in the use and applications of the “English sector” in trigonometry in a number of 18th-century books on mathematical instruments.Peer ReviewedPostprint (published version

El Mètode de Newton-Raphson... i Simpson: una aplicació d'eines de programació per a analitzar textos matemàtics històrics

The Newton-Raphson method is a well-known numerical method for finding approximations to the real roots of a real-valued function. It is named after Isaac Newton (1643-1727) and Joseph Raphson (1668-1715), who, towards the end of the 17th century, elaborated their methods for finding the approximate roots of polynomial equations. However, from the original sources, it is clear that both methods differ not only from each other, but also from the algorithm used at present.Postprint (published version

Comparative study of Sustainability Metrics for Face Milling AISI 1045 in different Machining Centers

Comunicación presentada a MESIC 2019 8th Manufacturing Engineering Society International Conference (Madrid, 19-21 de Junio de 2019)The objective of this study is to compare a set of sustainability metrics between different manufacturing resources applied to high performances machining centers. The research compares distributed scenarios in order to find the optimal conditions that allow the minimum consumed power and the minimum roughness when performing face milling operations of AISI 1045 steel. The set of experiments for the surface machining was carried out considering different path strategies in three main directions for two dimensional movements of the tool. The selected experiments considered the main axis movement, the perpendicular axis movement and a 45 degrees movement. Besides, it was considered the feed rate speed and the cutting depth. The design of experiments was developed with the Taguchi method considering an orthogonal matrix of L27 design type, and three levels of experimental design, and the analysis of variance and noise signal were performed. The methodology to determine the lowest power consumed and the best surface quality allowed to establish the working condition in the most sustainable machining. The results show how the cutting parameters influence in each manufacturing resource

Completing an uncertainty criterion of classification

We present a variation of a method of classification based in uncertainty on credal set. Similarly to its origin it use the imprecise Dirichlet model to create the credal set and the same uncertainty measures. It take into account sets of two variables to reduce the uncertainty and to seek the direct relations between the variables in the data base and the variable to be classified. The success are equivalent to the success of the first method except in those where there are a direct relations between some variables that decide the value of the variable to be classified where we have a notable improvement

Las obras completas de Leo Strauss

Sin resume

Nota informativa de la Comisión de Bioética de SEFAC

Entre las conclusiones de los trabajos de la Comisión de Bioética de SEFAC, que propiciaron el manual Recetas sencillas para consultas complejas. Cómo resolver los 15 conflictos tipo en la relación asistencial farmacéutico-paciente, editado en 2009 gracias a la colaboración de la Fundación AstraZeneca, se puso de manifiesto la conveniencia de la llevanza en las farmacias comunitarias de un Libro de incidencias que permitiera registrar y dejar constancia escrita de las motivaciones que subyacen a las decisiones clínicas más complejas o comprometidas que se ve obligado a adoptar en ocasiones el farmacéutico comunitario

Model-based observer proposal for surface roughness monitoring

Comunicación presentada a MESIC 2019 8th Manufacturing Engineering Society International Conference (Madrid, 19-21 de Junio de 2019)In the literature, many different machining monitoring systems for surface roughness and tool condition have been proposed and validated experimentally. However, these approaches commonly require costly equipment and experimentation. In this paper, we propose an alternative monitoring system for surface roughness based on a model-based observer considering simple relationships between tool wear, power consumption and surface roughness. The system estimates the surface roughness according to simple models and updates the estimation fusing the information from quality inspection and power consumption. This monitoring strategy is aligned with the industry 4.0 practices and promotes the fusion of data at different shop-floor levels

On local fibrations of (∞,2)(\infty,2)-categories

In this work we provide a model-independent notion of local fibrations of $(\infty,2)$-categories which generalises the well-known theory of locally coCartesian fibrations of $(\infty,1)$-categories. Based on previous work, we construct a model category which serves as a specific combinatorial model for this type of fibrations. Our main result is a generalisation of the locally coCartesian straightening and unstraightening construction of Lurie, which yields for any scaled simplicial set $S$ an equivalence of $(\infty,2)$-categories between the $(\infty,2)$-category of $(0,1)$-fibrations over $S$ (also known as inner coCartesian fibrations) and the $(\infty,2)$-category of functors $S \to \mathbb{C}\!\operatorname{at}_{(\infty,2)}$ with values in $(\infty,2)$-categories. Given an $(\infty,2)$-category $\mathbb{B}$, our Grothendieck construction can be specialised to produce an equivalence between the $(\infty,2)$-category of local fibrations over $\mathbb{B}$ and the $(\infty,2)$-category of oplax unital functors with values in $\mathbb{C}\!\operatorname{at}_{(\infty,2)}$. Finally, as an application of our results we provide a version of the Yoneda lemma for $(\infty,2)$-categories.Comment: Comments welcome

Jurisprudencia del Tribunal Constitucional en materia de derechos fundamentales (septiembre de 1992-febrero de 1993)

SUMARIO: 1. El principio de igualdad. 2. La libertad de información y e) derecho al honor. 3. La libertad de cátedra. 4. La libertad sindical.Publicad