New rules for improving CAS capabilities when computing improper integrals. Applications in Math Education

In many Engineering applications the computation of improper integrals is a need. In [1] we pointed out the lack of some CAS when computing some types of improper integrals. Even more, the work developed showed that some improper integrals can not be computed with CAS using their build-in procedures. In this talk we will develop new rules to improve CAS capabilities in order to compute new improper integrals We will show some examples of improper integrals that CAS asMATHEMATICA, MAPLE, DERIVE or MAXIMA can not compute. Using advance techniques as Laplace and Fourier transforms or Residue Theorem in Complex Analysis, we will be able to develop new rules schemes for these improper integrals. We will also describe the conclusions obtained after using these new rules with our Engineering students when teaching Advanced Calculus. [1] José L.Galán-García, Gabriel Aguilera-Venegas, María Á. Galán-García, Pedro Rodríguez-Cielos, Iván Atencia-Mc.Killop. Improving CAS capabilities: New rules for computing improper integrals. Applied Mathematics and Computation. Volume 316, 1 January 2018, Pages 525-540.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Pop-Rock Festivals Today: counterculture hippie transformed into a mainstream commodity

In recent years, outdoor pop-rock festivals are becoming a global phenomenon due to their power for attracting tourists and encouraging the economic development of the area that hosts them, but also because they have adapted to the cultural practices of the younger generations, which are dominated by speed, condensation and the search for experiences. Nowadays, it can be argued that festivals, especially outdoor festivals, are products elaborated, designed, planned and commodified by the current cultural and creative industries, in particular by the music business, but also by other actors involved in the process of their development. As a result, festivals have proliferated all over the world, whose organisers have used the collective imaginary of the Counterculture festivals of the 70s and 80s in order to produce commercially marketable, saleable, experienced products that are more typical from the entertainment economy than from culture. Using an in-depth documentary review and interviews with experts, this paper aims to offer a conceptual delimitation that describes the current nature of the phenomenon, which is heir to the hippie counterculture, but is more like an experience and leisure destination. The results suggest that contemporary outdoor pop-rock festivals have transcended beyond the musical product to convert themselves into ecosystems where the players involved —organisers, sponsors, artists, festival-goers, authorities, mass media, etc.— develop their own narratives, rooted in the collective imaginary of popular culture regarding rock festivals, in order to create a product that can be consumed in an experiential way. In the same way, the study shows that, despite the differences and specificities of each event, we are faced with a truly uniform and global phenomenon that responds to common and recognisable characteristics in each one of them.This participation has been funded by the PAIDI Group of the University of Malaga (Spain), SEJ-435 “Contenidos audiovisuales avanzados”, coordinated by Miguel de Aguilera Moyano. Campus de Excelencia Internacional Andalucía Tech

Making more flexible ATISMART+ model for traffic simulations using a CAS

Traffic simulations usually require the search of a path to join two different points. Dijkstra’s algorithm [1] is one of the most commonly used for this task due to its easiness and quickness. In [2, 3] we developed an accelerated time simulation of car traffic in a smart city using Dijkstra’s algorithm to compute the paths. Dijkstra’s algorithm provides a shortest path between two different points but this is not a realistic situation for simulations. For example, in a car traffic situa- tion, the driver may not know the shortest path to follow. This ignorance can be produced, among others, because one of the following two facts: the driver may not know the exact length of the lanes, or, even knowing the exact length, the driver may not know how to find the shortest path. Even more, in many cases, a mixture of both facts occurs. A more realistic simulation should therefore consider these kind of facts. The algorithm used to compute the path from one point to another in a traffic simulation might consider the possibility of not using the shortest path. In this talk, we use a new probabilistic extension of Dijkstra’s algorithm which covers the above two situations. For this matter, two different modifications in Di- jkstra’s algorithm have been introduced: using non-exact length in lanes, and the choice of a non-shortest path between two different points. Both modifications are used in a non-deterministic way by means of using probability distributions (classi- cal distributions such as Normal or Poisson distributions or even "ad hoc" ones). A precise, fast, natural and elegant way of working with such probability distributions is the use of a CAS in order to deal with exact and explicit computations. As an example of use of this extension of Dijkstra’s algorithm, we will show the ATISMART+ model. This model provides more realistic accelerated time sim- ulations of car traffics in a smart city and was first introduced in [4] and extended in [5]. This model was developed combining J AVA for the GUI and M AXIMA for the mathematical core of the algorithm. The studies developed in the above mentioned works, dealt with Poisson, Ex- ponential, Uniform and Normal distributions. In this talk we will introduce, as a novelty, the possibility of using other continuous probability distributions such as: Lognormal, Weibul, Gamma, Beta, Chi-Square, Student’s t, Z, Pareto, Lo- gistic, Cauchy or Irwin-Hall, and other discrete distributions such as: Bernouille, Rademacher, Binomial, Geometric, Negative Binomial or Hypergeometric. Even 1 more, this new version allows to deal with any “ad-hoc” continuous, discrete or mixed user’s distributions. This fact improves the flexibility of ATISMART+ model.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Random samples generation with Stata from continuous and discrete distributions

Simulations are nowadays a very important way of analyzing new improvements in different areas before the physical implementation, which may require hard resources which could only be affronted in case of a high probability of success. The use of random samples from different distributions are a must in simulations. In this talk we introduce new Stata functions for generating random samples from continuous and discrete distributions that are not considered in the defined Stata random-number generation functions. In addition, we will also introduce new Stata functions for generating random samples as an alternative of the build-in Stata functions. The goodness of the generated samples will be checked using the mean squared error (MSE) of the differences between the frequencies of the sample and the theoretical expected ones. We will also provide bar charts which will allow the user to compare graphically the sample with the exact distribution function of the random distribution which is being sampled.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Teaching Partial Differential Equations with CAS

Partial Differential Equations (PDE) are one of the topics where Engineering students find more difficulties when facing Math subjects. A basic course in Partial Differential Equations (PDE) in Engineering, usually deals at least, with the following PDE problems: 1. Pfaff Differential Equations 2. Quasi-linear Partial Differential Equations 3. Using Lagrange-Charpit Method for finding a complete integral for a given general first order partial differential equation 4. Heat equation 5. Wave equation 6. Laplace’s equation In this talk we will describe how we introduce CAS in the teaching of PDE. The tasks developed combine the power of a CAS with the flexibility of programming with it. Specifically, we use the CAS DERIVE. The use of programming allows us to use DERIVE as a Pedagogical CAS (PECAS) in the sense that we do not only provide the final result of an exercise but also display all the intermediate steps which lead to find the solution of a problem. This way, the library developed in DERIVE serves as a tutorial showing, step by step, the way to face PDE exercises. In the process of solving PDE exercises, first-order Ordinary Differential Equations (ODE) are needed. The programs developed can be grouped within the following blocks: - First-order ODE: separable equations and equations reducible to them, homogeneous equations and equations reducible to them, exact differential equations and equations reducible to them (integrating factor technique), linear equations, the Bernoulli equation, the Riccati equation, First-order differential equations and nth degree in y’, Generic programs to solve first order differential equations. - First-order PDE: Pfaff Differential Equations, Quasi-linear PDE, Lagrange-Charpit Method for First-order PDE. - Second-order PDE: Heat Equation, Wave Equation, Laplace’s Equation. We will remark the conclusions obtained after using these techniques with our Engineering students.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Improving CAS Capabilities: New Rules for Computing Improper Integrals

There are diferent applications in Engineering that require to compute improper integrals of the first kind (integrals defined on an unbounded domain) such as: the work required to move an object from the surface of the earth to in nity (Kynetic Energy), the electric potential created by a charged sphere, the probability density function or the cumulative distribution function in Probability Theory, the values of the Gamma Functions(wich useful to compute the Beta Function used to compute trigonometrical integrals), Laplace and Fourier Transforms (very useful, for example in Differential Equations).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Eukaryotic microbial diversity of phototrophic microbial mats in two Icelandic geothermal hot springs

The composition of the eukaryotic community and the three-dimensional structure of diverse phototrophic microbial mats from two hot springs in Iceland (Seltun and Hveradalir geothermal areas) were explored by comparing eukaryotic assemblages from microbial mats. Samples were collected in July 2007 from 15 sampling stations along thermal and pH gradients following both hot springs. Physicochemical data revealed high variability in terms of pH (ranging from 2.8 to 7), with high concentrations of heavy metals, including up to 20 g Fe/l, 80 mg Zn/l, 117 mg Cu/l, and 39 mg Ni/l at the most acidic sampling points. Phylogenetic analysis of 18S rDNA genes revealed a diversity of sequences related to several taxa, including members of the Bacillariophyta, Chlorophyta, Rhodophyta, and Euglenophyta phyla as well as ciliates, amoebae, and stramenopiles. The closest relatives to some of the sequences detected came from acidophilic organisms, even when the samples were collected at circumneutral water locations. Electron microscopy showed that most of the microecosystems analyzed were organized as phototrophic microbial mats in which filamentous cyanobacteria usually appeared as a major component. Deposits of amorphous minerals rich in silica, iron, and aluminium around the filaments were frequently detected. [Int Microbiol 2010; 13(1):21-32

Using extensions of the residue theorem for improper integrals computations with CAS

The computation of improper integrals of the rst kind (integrals on unbounded domain) are used in di erent applications in Engineering (for example in Kynetic Energy, electric potential, probability density functions, Gamma and Beta functions, Laplace and Fourier Transforms, Di erential Equations, . . . ). Nowadays, Computer Algebra Systems (CAS) are being used for developing such computations. But in many cases, some CAS lack of the appropriate rules for computing some of these improper integrals. In a previous talk in ESCO 2016 and a later extension, we introduced new rules for computing improper integrals of the rst kind using some results from Advanced Calculus Theories (Residue Theorem, Laplace and Fourier Transforms) aimed to improve CAS capabilities on this topic. In this talk, we develop new rules for computing other types of improper integrals using different applications from extended versions of the Residue Theorem. We will show some examples of such improper integrals that current CAS can not compute. Using extensions of the Residue Theorem in Complex Analysis, we will be able to develop new rules schemes for these improper integrals. These new rules will improve the capabilities of CAS, making them able to compute more improper integrals.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech