Enrique Arribas

Measurement of the magnetic field of small magnets with a smartphone: a very economical laboratory practice for introductory physics courses

AB thanks the Vicerectorship of Information Technologies of the University of Alicante (Spain) and the help of GITE-09006-UA. IE is grateful to the Ministry of Economy and Competitiveness for help provided through the project DPI2012-32994.

Approximate expressions for the period of a simple pendulum using a Taylor series expansion

This work was supported by the ‘Vicerrectorado de Tecnologia e Innovacion Educativa’ of the University of Alicante, Spain (GITE-09006-UA), and by the Generalitat Valenciana, Spain (project PROMETEO/2011/021).

Approximate solutions for the nonlinear pendulum equation using a rational harmonic representation

The exact expression for the maximum tension of a pendulum string is used to obtain a closed-form approximate expression for the solution of a simple pendulum in terms of elementary functions. This approximate solution has a rational harmonic expression and depends on an unknown function, which must be determined. This unknown function is expanded using the Pade approximant and two new parameters are introduced which are determined by means of a term-by-term comparison of the power series expansion for the approximate maximum tension with the corresponding series for the exact one. Using this approach, accurate approximate analytical expressions for the periodic solution are obtained. We also compared the Fourier series expansions of the approximate solutions and the exact ones. This allowed us to compare the coefficients for the different harmonics in these solutions. We also compared the approximate and exact solutions as a function of time for several oscillation amplitudes. Finally, in this procedure we used some of the approximate expressions for the simple pendulum frequency which can be found in the bibliography; however, the procedure can be applied using other approximate frequencies.

Comprehensive personal RF-EMF exposure map and its potential use in epidemiological studies

In recent years, numerous epidemiological studies, which deal with the potential effects of mobile phone antennas on health, have almost exclusively focused on their distance to mobile phone base stations. Although it is known that this is not the best approach to the problem, this situation occurs due to the numerous difficulties when determining the personal exposure to the radiofrequency electromagnetic fields (RF-EMF). However, due to the rise of personal exposimeters, the evolution of spatial statistics, the development of geographical information systems and the use of powerful software, new alternatives are available to deal with these epidemiological studies and thus overcome the aforementioned difficulties. Using these tools, this paper presents a lattice map of personal RF-EMF exposure from exterior mobile phone base stations, covering the entire 110 administrative regions in the city of Albacete (Spain). For this purpose, we used a personal exposimeter, Satimo EME Spy 140 model, performing measurements every 4s The exposimeter was located inside the plastic basket of a bicycle, whose versatility permitted the access to all the zones of the city. Once the exposure map was prepared, its relation with the known antenna locations was studied. The 64 mobile telephone antennas of the city were also georeferenced; the randomness of both variables (exposure and antennas) were studied by means of the Morans I test. Results showed that the distribution of the antennas follows a grouped pattern (p<0.001), while the distribution of the average exposure values have a random distribution (p=0.618). In addition, we showed two Spearman correlation studies: the first between the average exposure values and the number of mobile telephone antennas per administrative region, and the second, also considering the antennas of the neighbouring regions. No substantial correlation was detected in either of the two cases. This study also reveals the weaknesses of the epidemiological studies, which only take into account the distance to the antennas, which would provide a new approach to the problem. By precisely knowing the resident population of each administrative region of the city, this proves to be highly useful to rely on a prepared aggregate data map based on the mean exposure values to RF-EMF in these sections. The displayed map would permit the execution of more accurate epidemiological studies, since it would be possible to compare the exposure measurements with the incidence data of a disease.

Linear compartmental systems. I. kinetic analysis and derivation of their optimized symbolic equations

The study of many biological systems requires the application of a compartmental analysis, together with the use of isotopic tracers, parameter identification and methods to evaluate the mean parameters. For all this, the kinetic equations of the compartmental system as a function of its parameters are needed. In this paper, we present some considerations on the diagrams of connectivity of linear compartmental systems and obtain new properties from the matrix corresponding to the ordinary first-order linear differential equation systems which describe their kinetic behaviour. Using these properties, symbolic equations are obtained in a simplified form. These equations provide the instantaneous amount of substance in any compartment of the system when zero input is injected into one or more of the system compartments, solely as a function of those parameters of compartmental systems which really have an influence on the sought expression. This is unlike what happens in the other symbolic equations obtained in a previous contribution that included all the fractional transfer coefficients involved in the compartmental system, regardless of whether or not they had an influence on the instantaneous amount of substance.

Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions

Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator.

Radiofrequency electromagnetic fields and some cancers of unknown etiology: An ecological study

Simultaneously with the increase of Radiofrequency Electromagnetic Fields (RF-EMF) in recent decades, there has been increasing concern about their potential relation with the etiology of several tumors. At this time, the techniques of spatial data analysis jointly with the study of the personal exposure to these fields offer a new approach to the problem. This paper presents the results of a preliminary epidemiological study, combining Epidemiology, Statistics and Geographical Information Systems (GIS), in which we analyzed the correlation between exposure to RF-EMF in the city of Albacete (166,000 inhabitants, southeast Spain) and the incidence of several cancers with unspecific causes (lymphomas, and brain tumors). We used statistical tools to analyze the spatial point patterns and aggregate data with the aim to study the spatial randomness and to determine the zones with the highest incidence from 95 tumors studied (65 lymphomas, 12 gliomas and 18 meningiomas). We also perform a correlation (Spearman) study between the personal exposure to RF-EMF in 14 frequency bands, recorded by an EME Spy 140 (Satimo) exposimeter in the citys administrative regions, and the incidence of the tumors registered from January 2012 to May 2015. The studied cancer cases have a random spatial distribution inside the city. On the other hand, and by means of an ecological study, we verified that the exposure to RF-EMF registered in the city of Albacete shows little correlation with the incidence of the studied tumors (gliomas (ρ=0.15), meningiomas (ρ=0.19) and lymphomas (ρ=-0.03)). The proposed methodology inaugurates an unexplored analysis path in this field.

Student peer evaluation using a remote response system.

their responses. They read, commented on and supported students’ posts on the forum tool. A total of 94 of 100 students responded positively to the satisfaction questionnaire and 82% agreed that the process had positively affected their learning development. The Moodle platform was highlighted as an important tool for strengthening the integration process and student assessment. The involvement of pharmacology faculty members enhanced and strengthened disciplinary integration, enabling the proposed objective to be attained.

Computerized evaluation of mean residence times in multicompartmental linear system and pharmacokinetics

Deriving mean residence times (MRTs) is an important task both in pharmacokinetics and in multicompartmental linear systems. Taking as starting point the analysis of MRTs in open or closed (Garcia‐Meseguer et al., Bull Math Biol 2003, 65, 279) multicompartmental linear systems, we implement a versatile software, using the Visual Basic 6.0 language for MS‐Windows, that is easy to use and with a user‐friendly format for the input of data and the output of results. For any multicompartmental linear system of up to 512 compartments, whether closed or open, with traps or without traps and with zero input in one or more of the compartments, this software allows the user to obtain the symbolic expressions, in the most simplified form, and/or the numerical values of the MRTs in any of its compartments, in the entire system or in a part of the system. As far as we known from the literature, such a software has not been implemented before. The advantage of the present software is that it reduces on the work time needed and minimizes the human errors that are frequent in compartmental systems even those that are relatively staightforward. The software bioCelTer, along with instructions, can be downloaded from http://oretano.iele‐ab.uclm.es/∼fgarcia/bioCelTer/.

Linear compartmental systems. IV. A software, under MS-Windows, for obtaining the instantaneous species concentrations in enzyme systems

Software application is implemented in this work to take full advantage of the characteristics of current operating systems and to provide the optimized symbolic kinetic equations for both enzyme and ligand species involved in enzyme reactions. This software, called SKEE-w2013, is implemented using C# language and runs under all operating systems from Windows XP up to Windows 8. It is applicable to any enzyme reaction mechanism that fits the general reaction scheme proposed previously by our group. It can be downloaded, free of charge, from http://oretano.iele-ab.uclm.es/~BioChem-mg/software.php. Besides the optimized equations, the software can provide non-optimized equations, so that the user can compare the advantage of using optimized equations rather than the non-optimized ones, whenever they do not coincide. Moreover, the software circumvents the limitations of other existing previous software tools implemented with what are nowadays obsolete programming languages and that, moreover, are limited to non-optimized kinetic equations.