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

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

De las prácticas tradicionales a la supervisión médica en el ejercicio de la maternidad. Asturias 1900-1931

Las primeras décadas del siglo XX constituyen una etapa de transición en la consideración de la maternidad y respecto al modo de afrontar la crianza. Todavía con un gran peso de las prácticas tradicionales de cuidado infantil, van tomando fuerza nuevas pautas establecidas por el colectivo médico, que tratará de que sean interiorizadas por las madres, sirviéndose para ello de iniciativas de diverso tipo. Las mujeres asumirán estos discursos pero serán capaces de readaptarlos conforme a sus situaciones y necesidades particulares

Familia y trabajo en la comarca de Río Tinto.1873-1936

La comarca minera de Río Tinto va a conocer un cambio radical en su evolución a partir de 1873. La llegada de la compañía inglesa para poner en explotación las minas de cobre va a generar un mercado de trabajo en el que las relaciones de parentesco jugarán un papel fundamental. Los habitantes de la zona, centrados exclusivamente en actividades mineras, y la propia compañía, con una estrategia bien definida, propiciaron la formación de un mercado claramente segmentado._______________________________The mining county of Rio Tinto would conic to know a radical change on it's evolution from 1873. The arrival of the English Company to start expiating the copper mines generates a work market in which would come to play a fundamental role. The inhabitants of that area, centered exclusively on mining activities and the company itself with a well defined strategy, gave place to the formation of a clearly fragmented market

Aportaciones previas sobre la presencia y petrografía de rocas ultramáficas asociadas a granitoides calcoalcalinos precoces en la zona de Vivero (Lugo)

[Resumen] Asociadas con tonalitas, granodioritas y adamellitas, pertenecientes a la serie calcoalcalina precoz de granitos hercínicos, aparecen en la zona de Vivero unas rocas que muestran características diferentes a las de otros tipos relacionados con granitos hercínicos de esta serie en el NW. de la Península. Se trata de rocas ultramáficas y máficas con carácter básico en afloramientos cartografiables, presentando diversos tipos petrográficos, desde peridotitas a hornblenditas, incluyendo también gabros/ dioritas, monzonitas y melanotonalitas[Abstract] In the Vivero area (Lugo), there are some ultramafic and mafic rocks associated with tonalites, granodiorites and adamellites belonging to the older Hercynian calc-alcaline granite serie. These rocks show different characteristics to those of other types related to these granites in the NW. of Spain, appearing in quite large outcróps including severaI petrographic types from peridotites to hornblendites; gabbros/diorites, monzonites and melatonalite

Mineral carbonation of ceramic brick at low pressure and room temperature. A simulation study for a superficial CO2 store using a common clay as sealing material

This research explores the possibilities of CO2 sequestration on ceramic bricks in a short time and at surface conditions. The experiment was carried out in a specially designed reaction chamber, filled with brick wastes and sealed with common clays. The brick used were composed of quartz, wollastonite, diopside, orthoclase and anhydrite, and the common clay was a marl composed of calcite, quartz, illite, smectite and kaolinite. Experimental condition in the reaction chamber were: reaction time 5 months, pressure of CO2 0.5 bar, 4:1 solid/water ratio. The experiment was followed by XRD, XRF, BET, physical sorption by N2 and CO2, Hg porosity, TG-DTA, SEM and ICP-EOS. After the CO2 treatment, wollastonite and anhydrite were practically destroyed and some diopside and orthoclase. Calcite precipitated as new phase (up to 48 wt%), and small amount of illite was the result of orthoclase alteration. Concerning the sealing clay, the CO2 produced an increment of calcite content (from 32 to 41 wt%) and a partial destruction of smectite, particularly close to the upper part of the brick layer. These results are hopeful in relation with the possible mineral carbonation of building ceramic waste in a short time at surface conditions, and open the opportunity to use those wastes for CO2 trapping in an appropriate system, as a quarry reclamation