This paper compares two methods, inferential statistics and Systems Dynamics, to study the evolution of individual happiness after a single dose of drug consumption. In an application case, the effect of alcohol and caffeine on happiness is analyzed through a single-case experimental design, with replication, involving two participants. Both inferential statistical analysis and Systems Dynamics methods have been used to analyze the results. Two scales were used to measure happiness—the Euphoria Scale (ES) and the Smiling Face Scale (SFS)—in trait and state format. A single-case experimental ABC design was used. Phase A had no treatment, and Phases B and C saw both subjects receiving 26.51 mL of alcohol and 330 mg of caffeine, respectively. The participants filled in a form with both scales in a state format every 10 min over a 3 h period, operating in each one of the three phases A, B and C. The main conclusion of the analysis performed is that both methods provide similar results about the evolution of individual happiness after single dose consumption. Therefore, the article shows that inferential statistics and the stimulus response model derived from the Systems Dynamics approach can be used in a complementary and enriching way to obtain prediction results.

This article presents the revision of the STEAM model originally proposed by Yakman, in 2008, introducing the Human variable, as an extremely important element for the model, which was defined as STEAM ∀H, where ∀H is for all Humanity. This proposal is motivated by several factors. On the one hand, the evolution of industrial design from the 19th century to present, going from designing objects focused on facilitating industrialization and focused on the user, to design focused on the human being and humanity. On the other hand, since the formulation of the STEAM model, different improvements have been proposed in the literature in order to introduce humanistic disciplines into the model, also seeking to introduce society as a fundamental element. For example, the literature has proposed the STREAM model, where R is religion, or STEAM-ED, where -ED implies an approach based on the constructivist social theory. The STEAMS model, where S is Society, has also been proposed to try to improve training in understanding society and the implications of designing for it. Initially Yakman introduces the “A” in the STEM model as the sum of different disciplines that use the word “art” in their description: Fine Arts, Physical Arts, Manual Arts and Liberal Arts. The first three disciplines are associated with the practical and also creative part, while the Liberal Arts approach various disciplines in the humanities and social areas. Yakman’s definition of STEAM was quickly accepted and assimilated by the scientific community. However, for the purposes of application, the “A” is treated fundamentally as that creative and artistic component transversal to the rest of the model, relegating humanistic and social learning to the background. In the first section of this article the redefinition of the “A” in the STEAM model is proposed, which was originally defined by Yakman, by integrating the areas of Fine Arts, Physical Arts and Manual Arts; adding ∀H, as STEAM ∀H, which integrates the Liberal Arts, defining the model as: “the learning of Science and Technology interpreted through Engineering and Art based on the language of Mathematics and taking into account the implications of Science, Technology, Engineering, Art and Math’ for all Humanity” The second section of this article proposes the implementation in detail of the STEAM ∀H model in higher education, specifically, in the first year of the Degree in Industrial Design Engineering and Product Development, where the STEAM areas represented by the subjects of Physics, Mathematics, Basic Design, Representation of Shapes, etc., must be integrated with the subject of Social Doctrine of the Church. The model has been tested in three consecutive courses. An empirical qualitative study, case study method was carried out thorugh multiple-question Likert scale questionnaries to analize the perpective and perception of the participants to the new method. The frequency of the results obtained are shown and analized at the end of the article.

This study presents a generalization of a mathematical model, called the “bridge model” in Literature, to study the co-evolution or dynamical relationship between the General Factor of Personality (GFP) and the Big Five Factors (B5F) as a consequence of a stimulus. This generalization permits its application here to study such co-evolution after a dose intake of methylphenidate. On the one hand, a stimulus-response model, an integro-differential equation called the “response model,” predicts the short-term effects of a stimulus on the GFP and on the B5F. The fact that both the GFP and the B5F dynamics can be described by the response model is here referred as the “invariance principle.” On the other hand, the invariance principle leads to the derivation of the bridge model: a second order partial differential equation that relates every B5F to the GFP and time. The outcomes of both experimental designs permit the validation of the response model and of the new bridge model.

This paper describes how the elliptic and hyperbolic regions of a surface are related to stable Gauss maps on closed orientable surfaces immersed in three-dimensional space. We will show that for certain connected, closed, orientable surfaces containing a finite number of embedded circles that delineate two distinct types of regions, if all regions of one type are homeomorphic to a cylinder, then there exists an immersion f: M →ℝ^3 for which the Gauss map is a fold Gauss map.

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 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.

En Mathematical Methods in the Applied Sciences. Hoboken (Nueva Jersey, Estados Unidos): John Wiley & Sons. Vol. 43, n. 14 (30 sep. 2020), pp. 8177-8191. ISSN 0170-4214. e-ISSN 1099-1476.

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.

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 as follows: 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 it is an immediate early gene (c-fos) and D3 dopamine receptor gene (DRD3) gens and the glutamate neurotransmitter (body). Findings An application case is presented by setting up two experimental designs: a previous pilot AB pseudo-experimental design (AB) pseudo-experimental design with one subject and a subsequent ABC experimental design (ABC) experimental design with another subject. The stimulus used is the stimulant drug methylphenidate. 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 past 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 present immersions of a given closed and oriented surface M in R 3 , where the two applications are stable: projection on the plane xy and a Gauss map. The projection on the plane can be seen as a stable map of surfaces on the plane.

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 define the concept of graph extension, embedded on a closed and orientable surface, associated to a 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 $$g\le 3$$.

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 (ie, fold maps) from closed surfaces to the projective plan.

The present paper addresses the goal of encouraging the students' interest in both mathematics and technology at the same time in University degrees. The idea is to make understandable the abstract part of mathematics through the use of robotics, as robot programming implies the use of mathematical expressions that model the physical reality. In this manner, robots can stimulate the students' interest in mathematics in a changing world where graduates with a high knowledge of mathematics and technology will be needed. Mobile robots are tools for students to interact with their learning process. Moreover, this type of interaction connects technology with theoretical subjects that students find difficult to understand, such as maths subjects. Robotics is commonly used during Primary, Secondary or High School. Nevertheless, it is less common in University degrees. The combination of math subjects with robotics allows us the connection of our research with our teaching. The direct consequence is the innovation in our teaching methodologies as well as the enhancement of the technological skills of the new generations of students, which will be very useful in their uncertain technological jobs.

In this paper, we establish sufficient conditions for the existence of optimal non-linear 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.

Purpose The purpose of this paper is to suggest a formalism given by an equation suitable for simulating discrete systems with space-time variation in addition to other change variables. With such formalism, multidimensional dynamical models of discrete complex systems, such as the social systems and ecosystems, can be built. Design/methodology/approach This formalism is named as discrete multidimensional dynamic system (DMDS). The DMDS provides a way to consider the variation of the density of a state variable with regard to the variables of the change space as a function of multidimensional rates. Multidimensional rates describe this evolution as a consequence of the relation of each multidimensional-point with a given set of other points of the change space. This relation contains the accessibility domains (sets of space points with which each space point is related). Findings This equation is compared with both the reaction-diffusion equation written in its finite difference form and the cellular-automata model, demonstrating its compatibility with them and an increase in generality, widening the scope of application. The steps to construct models of systems with multidimensional variation based on the equation that defines the DMDS are specified and tested. Research limitations/implications Through the DMDS and a well-stated methodology, an application case is provided in order to describe the multidimensional demographic dynamics of an urban system. In this case, the numerical evolution of the population density by districts and cohorts is determined by the DMDS based on some hypothesis about functions of population diffusion between the different districts of the system. Originality/value The scope of application of the space-time dynamic system (STDS), given by the authors in a previous work, has been extended to discrete and multidimensional systems. STDS model produces better results than the reaction-diffusion model in validation.

Queremos mostrar um metodo computacional para verificar quando um grafo e balanceado, no sentido de ter um equilibrio entre seus pesos nos vertices e a diferenca entre as duas cores nos vertices. Este equilibrio determina se o grafo dado pode ser um invariante para aplicacoes estaveis entre superficies.

We present a method for deconvolution of images by means of an inversion of fractional powers of the Gaussian. The main feature of our model is the introduction of a regularizing term which is also a fractional power of the Laplacian. This term allows us to recover higher frequencies. The model is particularly useful to devise an algorithm for blind deconvolution. We will show, analyze and illustrate through examples the performance of this algorithm.