2. Universidad Cardenal Herrera-CEU

In this paper we will study the topology of the singular set of stable Gauss maps from closed orientable surfaces immersed in the 3-space from a global point of view and we will obtain a relationship between the Euler Characteristic of the regular components and the signs of the cusps.

Our society is immersed in the Fourth Industrial Revolution due to the fast evolution of the new technologies that are modifying the labor market. In the near future, technologies related to Industry 4.0 will produce totally new goods and services. Therefore, the educational systems should adapt their programs to the future needs of an uncertain labor market. In particular, mathematics will play a key role in future jobs and there is a strong need to connect its teaching methodologies to the new technological scene. This work uses the STEAM approach (science, technology, engineering, arts and mathematics) along with active methodologies and educational robotics with the aim of developing a new strategy for the application of mathematics and physics in an engineering degree. In particular, a transportation challenge is posed to tackle the teaching–learning process of the Bézier curves and their applications in physics. A pilot project is developed using a LEGO EV3 robot and an active methodology, where students become the center of the learning process. The experimental results of the pilot study indicate an increase in the motivation due to the use of robots and the realistic context of the challenge.

The objective of our research is the implementation of STEAM (Science Technology Engineering Art Mathematics) learning in the bachelor of Engineering in industrial design and product development at CEU Cardenal Herrera University through the EXPLORIA project. This article implements and develops the proposal for the first year of this bachelor, which includes 24 students aged 18–20. This article focuses on how to integrate STEAM learning within the EXPLORIA project for the improvement in the learning of the physics subject, and in particular, regarding the part of the syllabus related to mechanical engineering through different projects, challenges and milestones that allow the student to see the use in the design and development of products. The EXPLORIA project connects the competencies of the different STEAM subjects included in the bachelor, designing a learning process as a logical, sequential and incremental itinerary. Through concepts on which the fundamentals of design are based: shape, volume, color, space and structure. In particular, this article shows the adaptation made in the physical part to be able to teach the integrated mechanics part in this learning process. The complete learning was carried out through several challenges and two milestones the students had to overcome through the application of the physical knowledge learned in class. To validate the effectiveness of the proposed methodology, at the end of the paper, an ad hoc questionnaire is carried out showing the students’ assessment regarding the new teaching methodology.

In this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces M and N with a given branch set of curves immersed on N. We will study, from a global point of view, the behavior of its families in different isotopies classes on the space of smooth maps. The main goal is to obtain different relationships between invariants. We will provide a new proof of Quine’s Theorem.

The main objective of this article has been to evaluate the effect that the implementation of the EXPLORIA project has had on the Engineering Degree in Industrial Design and Product Development. The EXPLORIA project aims to develop an integrated competence map of the learning process, where the subjects are no longer considered as isolated contents, by elaborating an integrated learning process where the competences and learning outcomes of the subjects are considered as a whole, global and comprehensive learning. The EXPLORIA project connects the competencies of the different STEAM subjects that make up the degree, designing a learning process as a logical, sequential and incremental itinerary. Through concepts on which the foundations of design are based—shape, volume, colour, space and structure—the competencies of the different subjects are defined in incremental learning levels: understanding, applying, experimenting and developing, all taken from Bloom’s taxonomy. Mathematics is linked to the rest of learning through active learning methodologies that make learning useful. This new methodology changes the student’s affective domain towards mathematics in which positive emotions are transformed into positive attitudes that will improve the learning result and therefore, the students’ academic results. To validate it, at the end of the paper, the academic results compared with previous years are shown, as well as an ad hoc survey of the students’ assessment of the new teaching methodology.

In this paper, we de ne the concept of graph extension, embedded on a closed and orientable surfaces, associated to pairing of edges of regular polygons in order to show that the K-regular pairing of edges graphs can be obtained by the canonical extension of graphs (graphs with a single vertex). We will present examples of K-regular graphs associated to surfaces with genus g < 3.

The aim of this paper is to introduce a computational tool that checks theoretical conditions in order to determine whether a weighted graph, as a topological invariant of stable maps, can be associated to stable maps without cusps (i.e. fold maps) from closed surfaces to the projective plane.

Purpose – The purpose of this paper is to investigate the body-mind problem from a mathematical invariance principle in relation to personality dynamics in the psychological and the biological levels of description. Design/methodology/approach – The relationship between the two mentioned levels of description is provided by two mathematical models: the response model and the bridge model. The response model (an integro-differential equation) is capable to reproduce the personality dynamics as a consequence of a determined stimulus. The invariance principle asserts that the response model can reproduce personality dynamics at the two levels of description. The bridge model (a second order partial differential equation) can be deduced as a consequence of this principle: it provides the co-evolution of the General Factor of Personality (GFP) (mind), the c-fos and DRD3 gens, and the glutamate neurotransmitter (body). Findings – An application case is presented by setting up two experimental designs: a previous pilot AB pseudoexperimental design with one subject and a subsequent ABC experimental design with another subject. The stimulus used is the stimulant drug Methylphenidate (MPD). The response and bridge models are validated with the outcomes of these experiments. Originality/value – The mathematical approach here presented is based on a holistic personality model developed in the last few years: the Unique Trait Personality Theory, which claims for a single personality trait to understand the overall human personality: the GFP.

In this paper, we establish sufficient conditions for the existence of optimal nonlinear approximations to a linear subspace generated by a given weakly-closed (non-convex) cone of a Hilbert space. Most non-linear problems have difficulties to implement good projection-based algorithms due to the fact that the subsets, where we would like to project the functions, do not have the necessary geometric properties to use the classical existence results (such as convexity, for instance). The theoretical results given here overcome some of these difficulties. To see this we apply them to a fractional model for image deconvolution. In particular, we reformulate and prove the convergence of a computational algorithm proposed in a previous paper by some of the authors. Finally, some examples are given.