Ascensión Hernández Encinas

Spatial and temporal patterns of annual precipitation variability over the Iberian Peninsula

In this study we have examined the spatial and temporal variability of the annual precipitation observations over the Iberian Peninsula (IP) for 47 years and 51 stations. Empirical orthogonal functions (EOFs) were obtained in order to characterise the variability. Four regional precipitation regimes have been identified and the corresponding principal components (PCs) were subjected to spectral analysis in order to obtain the structure of the temporal variations. The relationship between the precipitation and circulation patterns is also investigated. The four leading PCs of annual precipitation are associated with the following patterns: East Atlantic (EA); North Atlantic Oscillation (NAO); Southern Oscillation Index (SOI); Scandinavia (SCAND). The spectra of the precipitation PCs show statistically significant oscillations coherent with those found in the time series of the teleconnection indices. A reconstruction of the time series as a function of the PCs is provided in order to obtain a characterisation of precipitation climatology over the IP.

Numerical algorithms for diffusion–reaction problems with non-classical conditions

Abstract Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the linear diffusion–reaction problem are derived. The convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion–reaction equations with these non classical conditions.

Graphic cryptography with pseudorandom bit generators and cellular automata

In this paper we propose a new graphic symmetrical cryptosystem in order to encrypt a colored image defined by pixels and by any number of colors. This cryptosystem is based on a reversible bidimensional cellular automaton and uses a pseudorandom bit generator. As the key of the cryptosystem is the seed of the pseudorandom bit generator, the latter has to be cryptographically secure. Moreover, the recovered image from the ciphered image has not loss of resolution and the ratio between the ciphered image and the original one, i.e., the factor expansion of the cryptosystem, is 1.

CAS and real life problems to learn basic concepts in Linear Algebra course

In this paper we examine the effect of the use of a Computer Algebra System (CAS) to solve interdisciplinary problems. We have been working for some years in the application of mathematics to different engineering problems, the main reason was to improve the motivation of our students and to make possible for them to connect and apply what they learn in Linear Algebra class to other engineering subjects. We describe a case study with students of Electromechanical and Mechanical Engineering from the Coimbra Institute of Engineering and from Geological and Industrial Engineering students from the University of Salamanca in a Linear Algebra course. The study involves the application of digital image processing to develop the basic skills of Linear Algebra. Furthermore, we include the results of a pre‐test and post‐test control group study using that application in the classroom. The results indicate that the experiences were very enriching for the students in different subjects. We tested at different centers from two different countries with similar results.

Variable step length algorithms with high-order extrapolated non-standard finite difference schemes for a SEIR model

Abstract In the present manuscript, higher-order methods are derived to solve a SEIR model for malware propagation. They are obtained using extrapolation techniques combined with nonstandard finite difference (NSFD) schemes used in Jansen and Twizell (2002). Thus, the new algorithms are more efficient computationally, and are dynamically consistent with the continuous model. Later, different procedures are considered to control the error in the discrete schemes. Numerical experiments are provided to illustrate the theory, and for the comparison of the different strategies in the adaptation of the variable step length.

How Engineers Deal with Mathematics Solving Differential Equation

Abstract Numerical methods are tools for approximating solutions to problems that may have complicated developments or cannot be solved analytically. In engineering courses, students must address problems related other disciplines such as structural or rock mechanics, biology, chemistry or physics. Prior to solving these problems it is important to define and adopt a rational framework. The students of fourth course out of five, of the bachelors degree in Computer Sciences or Industrial Engineering at the University of Salamanca (Spain), they learn mathematics solving real problems with the help of the already acquired interdisciplinary knowledge. We have proposed the students a term project that summarizes some of the knowledge and competences acquired during the lessons. We will describe in this study the software and specific applications that will be use during the whole course.

Disclosure of Sensitive Information in the Virtual Learning Environment Moodle

In recent years, the use of Virtual Learning Environments (VLEs) has greatly increased. Due to the requirements stated by the Bologna process, many European universities are changing their education systems to new ones based on information and communication technologies. The use of web environments makes their security an important issue, which must be taken into full consideration. Services or assets of the e-learning systems must be protected from any threats to guarantee the confidentiality of users’ data. In this contribution, we provide an initial overview of the most important attacks and countermeasures in Moodle, one of the most widely used VLEs, and then we focus on a type of attack that allows illegitimate users to obtain the username and password of other users when making a course backup in specific versions of Moodle. In order to illustrate this information we provide the details of a real attack in a Moodle 1.9.2 installation.

Minecraft as a Tool in the Teaching-Learning Process of the Fundamental Elements of Circulation in Architecture

In this paper, we make a pedagogical proposal to study the basic elements of circulation in architecture undergraduate degrees, using the Minecraft game as a tool. The theoretical basis for the proposal are Vygotsky’s sociointeractional theory and Ausubel’s theory of meaningful learning. We find ourselves reflecting on Information and Communication Technologies (ICT), gamification and video games in education. We outline some basic elements about circulation in buildings, its types, functionality, and accessibility, and the creativity needed to solve circulation problems in architecture. We introduce the Minecraft game, its characteristics, elements and use it as educational tool. We conclude that video games, specifically Minecraft, are of high interest in education as they develop skills for problem solving, collaborative work, research motivation and proactivity.

A study on the efficiency and stability of high-order numerical methods for Form-II and Form-III of the nonlinear Klein–Gordon equations

In this paper, we discuss the problem of solving nonlinear Klein–Gordon equations (KGEs), which are especially useful to model nonlinear phenomena. In order to obtain more exact solutions, we have derived different fourth- and sixth-order, stable explicit and implicit finite difference schemes for some of the best known nonlinear KGEs. These new higher-order methods allow a reduction in the number of nodes, which is necessary to solve multi-dimensional KGEs. Moreover, we describe how higher-order stable algorithms can be constructed in a similar way following the proposed procedures. For the considered equations, the stability and consistency of the proposed schemes are studied under certain smoothness conditions of the solutions. In addition to that, we present experimental results obtained from numerical methods that illustrate the efficiency of the new algorithms, their stability, and their convergence rate.

Efficient high-order finite difference methods for nonlinear Klein-Gordon equations. I: Variants of the phi-four model and the form-I of the nonlinear Klein-Gordon equation

In this paper, the problem of solving some nonlinear Klein-Gordon equations (KGEs) is considered. Here, we derive different fourth- and sixth-order explicit and implicit algorithms to solve the phi-four equation and the form-I of the nonlinear Klein-Gordon equation. Stability and consistency of the proposed schemes are studied under certain conditions. Numerical results are presented and then compared with others obtained from some methods already existing in the scientific literature to explain the efficiency of the new algorithms. It is also shown that similar schemes can be proposed to solve many classes of nonlinear KGEs.