The changes in our society in recent years and the consequent idiosyncrasy of young people demand new teaching methodologies. The methodology known as flip teaching, in which pupils study the subject before the class experience, using the material given by the teacher, makes it possible to turn the classroom into a place to solve different problems, to introduce new advanced concepts and to participate throughout collaborative learning in the classroom. Parallel to the social transformation, Information and Communication Technologies, also known as ICT, have undergone an important development accompanied by a clear reduction in costs and ease of use of different devices to create and edit quality videos, as well as the possibility of disseminating them on the network. In this way, the didactic material provided to the student can be in video format, which let us to be closer to students and also allow them to revise the class everywhere and all the times they need. In this work, we present and discuss the results of an experience carried out over several years with students of first and fourth grade of the subjects Discrete Mathematics and graphs, models and applications, respectively, at the Universitat Politècnica de València, in relation to the acceptance, advantages and drawbacks of flip teaching.

This study aims to implement and evaluate a methodological proposal using the hologram as a teaching medium for the learning of concepts related to areas and volumes of geometrical bodies. The study has been carried out with a sample of 78 students in the third year of secondary education from a privately-owned but state-funded school in Madrid. Thirty-five students who have been taught traditionally formed the control group, and 43 formed the experimental group in which the methodology was implemented. To evaluate its goodness, we have used the Student's t-test to assess the existence of significant differences between both groups. The results reported by the test show that there is a difference of 3.9 points between the scores of both groups which is significant at the level of 0.05. In addition, the user experience in the experimental group has also been evaluated to assess the students’ opinions of the hologram in the learning process. The overall results have assisted us in corroborating the efficacy of the hologram as a teaching medium.

It is still a challenge to improve the efficiency and effectiveness of image denoising and enhancement methods. There exists denoising and enhancement methods that are able to improve visual quality of images. This is usually obtained by removing noise while sharpening details and improving edges contrast. Smoothing refers to the case of denoising when noise follows a Gaussian distribution.Both operations, smoothing noise and sharpening, have an opposite nature. Therefore, there are few approaches that simultaneously respond to both goals. We will review these methods and we will also provide a detailed study of the state-of-the-art methods that attack both problems in colour images, separately.

The management of a car-rental service becomes more complex as long as one-way bookings between different depots are accepted. These bookings can increase the operational costs due to the necessity of moving vehicles from one depot to another by the company staff in order to attend previously accepted bookings. We present an iterative model based on flows on networks for the acceptance of bookings by a car-rental service that permits one-way reservations. Our model lets us also recover the movement of the fleet of vehicles between the depots over the time. In addition, it also permits including restrictions on the amount of cars managed at every single depot. These results can be of interest for an electric car-rental service that operates at different depots within a city or region.

In this paper, an unified point of view that include the most of one-point Newton-type iterative methods for solving nonlinear equations is introduced. A simple idea to design iterative methods with quadratic or cubic convergence is also described. This idea is extended to construct one-point iterative methods of order four. In addition, several numerical examples are given to illustrate and compare different known methods and some ones introduced by using this unifying idea.

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An n × n real matrix is said to be totally positive if every minor is non-negative. In this paper, we are interested in totally positive completion problems, that is, does a partial totally positive matrix have a totally positive matrix completion? This problem has, in general, a negative answer. Therefore, we analyze the question: for which labeled graphs G does every partial totally positive matrix, whose associated graph is G, have a totally positive completion? When G is a path or a cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion.

The solution of fleet assignment problems is one of the core points in the management of a car-rental company. These problems arise from the restrictions imposed by the acceptance of reservations of the customers and from the necessity of an arrangement of the cars at the different depots for attending these bookings. However, with the coming of driverless cars the rearrangement of vehicles among the depots can be simplified since no staff must be responsible of these tasks. In this note we show a heuristic algorithm that permits to minimize the number of cars that have to be subcontracted from an external provider in order to attend a list of reservations from customers. Its efficacy is shown in comparison to the solution given by the Integer Linear Programming method. These results can be of interest for other autonomous systems that need to be controlled.