Properties of solutions for nonlinear Volterra integral equations

Some properties of non-locally bounded solutions for Abel integral equations are given. The case in which there exists two non-trivial solutions for such equations is also studied. Besides, some known results about existence, uniqueness and attractiveness of solutions for some Volterra equations are improved

A note on the uniqueness and attractive behavior of solutions for nonlinear Volterra equations

In this paper we prove that positive solutions of some nonlinear Volterra integral equations must be locally bounded and global attractors of positive functions. These results complete previous results about the existence and uniqueness of solutions and their attractive behavior

A New wavelet tool to quantify non-periodicity of non-stationary economic time series

We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of the Haar wavelet, reinforcing the interpretation of the windowed scale index as a useful tool to quantify non-periodicity. In addition, the applicability of this wavelet-based measure is illustrated through several examples, including an economic application which compares the non-periodicity of two major commodities in the world economy, such as crude oil and gold. Finally, we discuss the relationship between non-periodicity and unpredictability, comparing the windowed scale index with the sample entropy

Dear-shiny: an interactive web app for data envelopment analysis

In this paper, we describe an interactive web application (deaR-shiny) to measure efficiency and productivity using data envelopment analysis (DEA). deaR-shiny aims to fill the gap that currently exists in the availability of online DEA software offering practitioners and researchers free access to a very wide variety of DEA models (both conventional and fuzzy models). We illustrate how to use the web app by replicating the main results obtained by Carlucci, Cirà and Coccorese in 2018, who investigate the efficiency and economic sustainability of Italian regional airport by using two conventional DEA models, and the results given by Kao and Liu in their papers published in 2000 and 2003, who calculate the efficiency scores of university libraries in Taiwan by using a fuzzy DEA model because they treat missing data as fuzzy numbers

Continuous models combining slacks-based measures of efficiency and super-efficiency

In the framework of data envelopment analysis (DEA), Tone (Eur J Oper Res 130(3):498–509, 2001) introduced the slacks-based measure (SBM) of efficiency, which is a nonradial model that incorporates all the slacks of the evaluated decision-making units (DMUs) into their efficiency scores, unlike classical radial efficiency models. Next, Tone (Eur J Oper Res 143(1):32–41, 2002) developed the SBM super-efficiency model in order to differentiate and rank efficient DMUs, whose SBM efficiency scores are always 1. However, as pointed out by Chen (Eur J Oper Res 226(2):258–267, 2013), some interpretation problems arise when the so-called super-efficiency projections are weakly efficient, leading to an overestimation of the SBM super-efficiency score. Moreover, this overestimation is closely related to discontinuity issues when implementing SBM super-efficiency in conjunction with SBM efficiency. Chen (Eur J Oper Res 226(2):258–267, 2013) and Chen et al. (Ann Oper Res 278(1):101–121, 2019) treated these problems, but they did not arrive to a fully satisfactory solution. In this paper, we review these papers and propose a new complementary score, called composite SBM, that actually fixes the discontinuity problems by counteracting the overestimation of the SBM super-efficiency score. Moreover, we extend the composite SBM model to different orientations and variable returns to scale, and propose additive versions. Finally, we give examples and state some open problems

Measurements of total ozone amount over Badajoz (Southwestern Spain) by means of a GUV multiband radiometer

The Ultraviolet Index (UVI) obtained by a multichannel radiometer GUV‐2511 (Biospherical Instruments Inc.) is analyzed in this paper. This instrument has been recently installed in the radiometric station of Extremadura University in Badajoz (Spain). The UV Index has been calculated by a linear combination of three and four GUV channel irradiance values. In order to test these results, simultaneous values of UVI were calculated with the data provided by a well calibrated broadband UVS‐E‐T instrument colocated side by side the GUV multichannel. This radiometer has a spectral response that is adapted to the erythemal (sunburn) action spectrum of the human skin. One‐minute simultaneous values of both instruments have been used to calculate ultraviolet Index (UVI). Although the measurement period is limited, it covers all sky conditions, from cloud‐free to overcast days. UVI calculated with the whole data set by both methods are well correlated, but not as well as using only clear day data. It was observed that GUV underestimates UVI values (mean bias error, MBE=18.9%), being the four channel method the most successful

Acercamiento a la modelación matemática en el tratamiento didáctico de los contenidos de la Física (Revisión)

An observation of the interdisciplinary becomes a structural foundation for a pertinent didactic treatment of the knowledge about the existence of the objects, processes, phenomena and relations among themselves. Based in the above, a revision of some tendencies is accomplished, like approximation to the conception of the didactic treatment of the particular knowledge. Specifically, the mathematical modeling applies to Physics, highlighting the importance of the integrative learning.Una adecuada observación del alcance de la interdisciplinariedad, se convierte en un fundamento estructural para un pertinente tratamiento didáctico del conocimiento en virtud de la existencia de los objetos, procesos, fenómenos, y las relaciones entre ellos como entes naturales. Basado en lo anterior, se realiza una revisión de algunos posicionamientos teóricos y metodológicos, como aproximación a la concepción del tratamiento didáctico de un conocimiento en particular. En ese sentido, se analizan algunos elementos del conocimiento asociados a la aplicación de la modelación matemática en Física, resaltando la importancia del aprendizaje integrador

Un acercamiento al tratamiento didáctico de la Física en interrelación con la Matemática (Revisión)

An observation of the interdisciplinary become a structural foundation for a pertinent didactic treatment of the knowledge about the existence of the objects, processes, phenomena and relations among themselves. Based in the above, a revision of some tendencies is accomplished, like approximation to the conception of the didactic treatment of the particular knowledge. Specifically, the mathematical modeling applies to Physics, highlighting the importance of the integrative learning.Una adecuada observación del alcance de la interdisciplinariedad, se convierte en un fundamento estructural para un pertinente tratamiento didáctico del conocimiento en virtud de la existencia de los objetos, procesos, fenómenos, y las relaciones entre ellos como entes naturales. Basado en lo anterior, se realiza una revisión de algunos posicionamientos teóricos y metodológicos como aproximación a la concepción del tratamiento didáctico de un conocimiento en particular. En ese sentido, se analizan algunos elementos del conocimiento asociados a la aplicación de la modelación matemática en Física, resaltando la importancia del aprendizaje integrador

Feedback-based continuous improvement measures on the use of short mathematical videos in university education

The main objective of this work is to make a proposal for continuous improvement on the use of short educational videos in order to improve the teaching-­learning process at Mathematics I, a university subject present in the curriculum of several social-­economical degrees such as Bussiness Administration, Economics, or International Business at the Universitat de València (Spain). In order to enhance the quality of this process, it is necessary to make inquiries of the impressions that the students have about it. In this particular case, we wanted to know the perception that students had after the use of short educational videos of applied mathematics contents during the course. These videos were carefully created by their professors in order to promote autonomous and active learning. Thus, we developed an opinion survey to gather their opinions. This survey measured the students' perception on the degree of usefulness of the teaching materials of the subject and, in particular, the degree of satisfaction on the short educational videos. The results show that, in general, there is a high degree of satisfaction in the use of these videos for self-­learning of mathematical concepts. Suggestions from the students allowed us to adopt improvement measures devoted to upgrade the quality of the teaching-­learning process

Applied mathematics concepts Self-learning through the use of short educational videos

It is sometimes difficult for the student to actively participate in the learning process due to the difficulty that teachers find when trying to cover all the contents of a course with sufficient time and attention. This lack of time prevents professors from properly stimulating the student's active participation in class, which is always necessary for achieving a deep and significant learning. The present paper describes a flipped-classroom-based methodology that fosters autonomous learning of applied mathematics contents through the use of short educational videos. The use of on-line media learning resources has dramatically increased in the last decade in higher education, not only under the well-known flipped classroom approach but also as replacement of conventional face-to-face lectures. The application of this methodology will give professors more time to make students work actively and cooperatively at class in the application of mathematical techniques for solving complex exercises and problems