Content and English Language Integrated Learning: The use of Moodle in Aircraft Maintenance Training Programs

The aim of this work is to develop a prototype of an e-learning environment that can foster Content and Language Integrated Learning (CLIL) for students enrolled in an aircraft maintenance training program, which allows them to obtain a license valid in all EU member states. Background research is conducted to retrace the evolution of the field of educational technology, analyzing different learning theories – behaviorism, cognitivism, and (socio-)constructivism – and reflecting on how technology and its use in educational contexts has changed over time. Particular attention is given to technologies that have been used and proved effective in Computer Assisted Language Learning (CALL). Based on the background research and on students’ learning objectives, i.e. learning highly specialized contents and aeronautical technical English, a bilingual approach is chosen, three main tools are identified – a hypertextbook, an exercise creation activity, and a discussion forum – and the learning management system Moodle is chosen as delivery medium. The hypertextbook is based on the technical textbook written in English students already use. In order to foster text comprehension, the hypertextbook is enriched by hyperlinks and tooltips. Hyperlinks redirect students to webpages containing additional information both in English and in Italian, while tooltips show Italian equivalents of English technical terms. The exercise creation activity and the discussion forum foster interaction and collaboration among students, according to socio-constructivist principles. In the exercise creation activity, students collaboratively create a workbook, which allow them to deeply analyze and master the contents of the hypertextbook and at the same time create a learning tool that can help them, as well as future students, to enhance learning. In the discussion forum students can discuss their individual issues, content-related, English-related or e-learning environment-related, helping one other and offering instructors suggestions on how to improve both the hypertextbook and the workbook based on their needs.

Domain-Specific Program Checking

Lint-like program checkers are popular tools that ensure code quality by verifying compliance with best practices for a particular programming language. The proliferation of internal domain-specific languages and models, however, poses new challenges for such tools. Traditional program checkers produce many false positives and fail to accurately check constraints, best practices, common errors, possible optimizations and portability issues particular to domain-specific languages. We advocate the use of dedicated rules to check domain-specific practices. We demonstrate the implementation of domain-specific rules, the automatic fixing of violations, and their application to two case-studies: (1) Seaside defines several internal DSLs through a creative use of the syntax of the host language; and (2) Magritte adds meta-descriptions to existing code by means of special methods. Our empirical validation demonstrates that domain-specific program checking significantly improves code quality when compared with general purpose program checking.

Simulation of titration experiments

Nowadays computer simulation is used in various fields, particularly in laboratories where it is used for the exploration data which are sometimes experimentally inaccessible. In less developed countries where there is a need for up to date laboratories for the realization of practical lessons in chemistry, especially in secondary schools and some higher institutions of learning, it may permit learners to carryout experiments such as titrations without the use of laboratory materials and equipments. Computer simulations may also permit teachers to better explain the realities of practical lessons, given that computers have now become very accessible and less expensive compared to the acquisition of laboratory materials and equipments. This work is aimed at coming out with a virtual laboratory that shall permit the simulation of an acid-base titration and an oxidation-reduction titration with the use of synthetic images. To this effect, an appropriate numerical method was used to obtain appropriate organigram, which were further transcribed into source codes with the help of a programming language so as to come out with the software.

Hip2Norm: an object-oriented cross-platform program for 3D analysis of hip joint morphology using 2D pelvic radiographs

We developed an object-oriented cross-platform program to perform three-dimensional (3D) analysis of hip joint morphology using two-dimensional (2D) anteroposterior (AP) pelvic radiographs. Landmarks extracted from 2D AP pelvic radiographs and optionally an additional lateral pelvic X-ray were combined with a cone beam projection model to reconstruct 3D hip joints. Since individual pelvic orientation can vary considerably, a method for standardizing pelvic orientation was implemented to determine the absolute tilt/rotation. The evaluation of anatomically morphologic differences was achieved by reconstructing the projected acetabular rim and the measured hip parameters as if obtained in a standardized neutral orientation. The program had been successfully used to interactively objectify acetabular version in hips with femoro-acetabular impingement or developmental dysplasia. Hip(2)Norm is written in object-oriented programming language C++ using cross-platform software Qt (TrollTech, Oslo, Norway) for graphical user interface (GUI) and is transportable to any platform.

An Experience-Driven Pedagogy for the Instruction of Software Testing in Computer Science

In the realm of computer programming, the experience of writing a program is used to reinforce concepts and evaluate ability. This research uses three case studies to evaluate the introduction of testing through Kolb's Experiential Learning Model (ELM). We then analyze the impact of those testing experiences to determine methods for improving future courses. The first testing experience that students encounter are unit test reports in their early courses. This course demonstrates that automating and improving feedback can provide more ELM iterations. The JUnit Generation (JUG) tool also provided a positive experience for the instructor by reducing the overall workload. Later, undergraduate and graduate students have the opportunity to work together in a multi-role Human-Computer Interaction (HCI) course. The interactions use usability analysis techniques with graduate students as usability experts and undergraduate students as design engineers. Students get experience testing the user experience of their product prototypes using methods varying from heuristic analysis to user testing. From this course, we learned the importance of the instructors role in the ELM. As more roles were added to the HCI course, a desire arose to provide more complete, quality assured software. This inspired the addition of unit testing experiences to the course. However, we learned that significant preparations must be made to apply the ELM when students are resistant. The research presented through these courses was driven by the recognition of a need for testing in a Computer Science curriculum. Our understanding of the ELM suggests the need for student experience when being introduced to testing concepts. We learned that experiential learning, when appropriately implemented, can provide benefits to the Computer Science classroom. When examined together, these course-based research projects provided insight into building strong testing practices into a curriculum.

Model-Centric, Context-Aware Software Adaptation

Software must be constantly adapted to changing requirements. The time scale, abstraction level and granularity of adaptations may vary from short-term, fine-grained adaptation to long-term, coarse-grained evolution. Fine-grained, dynamic and context-dependent adaptations can be particularly difficult to realize in long-lived, large-scale software systems. We argue that, in order to effectively and efficiently deploy such changes, adaptive applications must be built on an infrastructure that is not just model-driven, but is both model-centric and context-aware. Specifically, this means that high-level, causally-connected models of the application and the software infrastructure itself should be available at run-time, and that changes may need to be scoped to the run-time execution context. We first review the dimensions of software adaptation and evolution, and then we show how model-centric design can address the adaptation needs of a variety of applications that span these dimensions. We demonstrate through concrete examples how model-centric and context-aware designs work at the level of application interface, programming language and runtime. We then propose a research agenda for a model-centric development environment that supports dynamic software adaptation and evolution.

Playing with the Real World

In this paper we provide a framework that enables the rapid development of applications using non-standard input devices. Flash is chosen as programming language since it can be used for quickly assembling applications. We overcome the difficulties of Flash to access external devices by introducing a very generic concept: The state information generated by input devices is transferred to a PC where a program collects them, interprets them and makes them available on a web server. Application developers can now integrate a Flash component that accesses the data stored in XML format and directly use it in their application.

Parsing for agile modeling

In order to analyze software systems, it is necessary to model them. Static software models are commonly imported by parsing source code and related data. Unfortunately, building custom parsers for most programming languages is a non-trivial endeavour. This poses a major bottleneck for analyzing software systems programmed in languages for which importers do not already exist. Luckily, initial software models do not require detailed parsers, so it is possible to start analysis with a coarse-grained importer, which is then gradually refined. In this paper we propose an approach to "agile modeling" that exploits island grammars to extract initial coarse-grained models, parser combinators to enable gradual refinement of model importers, and various heuristics to recognize language structure, keywords and other language artifacts.

Temporal lobe white matter asymmetry and language laterality in epilepsy patients.

Recent studies using diffusion tensor imaging (DTI) have advanced our knowledge of the organization of white matter subserving language function. It remains unclear, however, how DTI may be used to predict accurately a key feature of language organization: its asymmetric representation in one cerebral hemisphere. In this study of epilepsy patients with unambiguous lateralization on Wada testing (19 left and 4 right lateralized subjects; no bilateral subjects), the predictive value of DTI for classifying the dominant hemisphere for language was assessed relative to the existing standard-the intra-carotid Amytal (Wada) procedure. Our specific hypothesis is that language laterality in both unilateral left- and right-hemisphere language dominant subjects may be predicted by hemispheric asymmetry in the relative density of three white matter pathways terminating in the temporal lobe implicated in different aspects of language function: the arcuate (AF), uncinate (UF), and inferior longitudinal fasciculi (ILF). Laterality indices computed from asymmetry of high anisotropy AF pathways, but not the other pathways, classified the majority (19 of 23) of patients using the Wada results as the standard. A logistic regression model incorporating information from DTI of the AF, fMRI activity in Broca's area, and handedness was able to classify 22 of 23 (95.6%) patients correctly according to their Wada score. We conclude that evaluation of highly anisotropic components of the AF alone has significant predictive power for determining language laterality, and that this markedly asymmetric distribution in the dominant hemisphere may reflect enhanced connectivity between frontal and temporal sites to support fluent language processes. Given the small sample reported in this preliminary study, future research should assess this method on a larger group of patients, including subjects with bi-hemispheric dominance.

Top-Down Parsing with Parsing Contexts

The domain of context-free languages has been extensively explored and there exist numerous techniques for parsing (all or a subset of) context-free languages. Unfortunately, some programming languages are not context-free. Using standard context-free parsing techniques to parse a context-sensitive programming language poses a considerable challenge. Im- plementors of programming language parsers have adopted various techniques, such as hand-written parsers, special lex- ers, or post-processing of an ambiguous parser output to deal with that challenge. In this paper we suggest a simple extension of a top-down parser with contextual information. Contrary to the tradi- tional approach that uses only the input stream as an input to a parsing function, we use a parsing context that provides ac- cess to a stream and possibly to other context-sensitive infor- mation. At a same time we keep the context-free formalism so a grammar definition stays simple without mind-blowing context-sensitive rules. We show that our approach can be used for various purposes such as indent-sensitive parsing, a high-precision island parsing or XML (with arbitrary el- ement names) parsing. We demonstrate our solution with PetitParser, a parsing-expression grammar based, top-down, parser combinator framework written in Smalltalk.

On Understanding How Developers Use the Spotter Search Tool

Analyzing how software engineers use the Integrated Development Environment (IDE) is essential to better understanding how engineers carry out their daily tasks. Spotter is a code search engine for the Pharo programming language. Since its inception, Spotter has been rapidly and broadly adopted within the Pharo community. However, little is known about how practitioners employ Spotter to search and navigate within the Pharo code base. This paper evaluates how software engineers use Spotter in practice. To achieve this, we remotely gather user actions called events. These events are then visually rendered using an adequate navigation tool chain. Sequences of events are represented using a visual alphabet. We found a number of usage patterns and identified underused Spotter features. Such findings are essential for improving Spotter.

Automatic Categorization for Improving Spanish into Spanish Sign Language Machine Translation

This paper describes a preprocessing module for improving the performance of a Spanish into Spanish Sign Language (Lengua de Signos Espanola: LSE) translation system when dealing with sparse training data. This preprocessing module replaces Spanish words with associated tags. The list with Spanish words (vocabulary) and associated tags used by this module is computed automatically considering those signs that show the highest probability of being the translation of every Spanish word. This automatic tag extraction has been compared to a manual strategy achieving almost the same improvement. In this analysis, several alternatives for dealing with non-relevant words have been studied. Non-relevant words are Spanish words not assigned to any sign. The preprocessing module has been incorporated into two well-known statistical translation architectures: a phrase-based system and a Statistical Finite State Transducer (SFST). This system has been developed for a specific application domain: the renewal of Identity Documents and Driver's License. In order to evaluate the system a parallel corpus made up of 4080 Spanish sentences and their LSE translation has been used. The evaluation results revealed a significant performance improvement when including this preprocessing module. In the phrase-based system, the proposed module has given rise to an increase in BLEU (Bilingual Evaluation Understudy) from 73.8% to 81.0% and an increase in the human evaluation score from 0.64 to 0.83. In the case of SFST, BLEU increased from 70.6% to 78.4% and the human evaluation score from 0.65 to 0.82.

Análisis comparativo de series temporales de precio de diferentes metales : obtención de una serie -resumen

El objetivo de este proyecto de investigación es analizar el conjunto de las diez series temporales, relativas a los precios de diez metales (plata, aluminio, oro, cobre, níquel, paladio, plomo, platino, estaño y zinc), comprendidos en el periodo de enero de 2008 a septiembre de 2013, con el objetivo de reducir la dimensionalidad del conjunto de datos y facilitar la comparación de los mismos y la predicción de valores futuros. Para ello pretendemos aplicar una metodología, que nos permitirá deducir, a partir de una serie resumen y de unos coeficientes multiplicativos, la evolución del comportamiento de cualquier otro metal. Pese a la escasísima documentación existente al respecto, se valorará e intentará aplicarse una reciente metodología denominada “Metodología del haz de rectas” Como herramienta de trabajo para los programas informáticos desarrollados y para representar las gráficas asociadas al proyecto, se utilizó Matlab®, habida cuenta de su enorme potencia y por disponer de un lenguaje de programación sencillo y lo suficientemente versátil para las tareas que necesitamos. Abstract. The objective of this research project is to analyze the set of ten time series on prices of the ten metals (silver, aluminum, gold, copper, nickel, palladium, lead, platinum, tin and zinc), included in the period January 2008 to September 2013, with the aim of reducing the dimensionality of the data set and to facilitate comparison of the data and the prediction of future values To apply this methodology, allowing us to predict, from a series summarizes the evolution of the behavior of any other metal. This methodology is called "straight beam Methodology" As a tool for developing computer software and associated graphs to represent the project, Matlab® was used in view of its enormous power and have a simple programming language and versatile enough for the tasks we need

Simulación en tiempo real de vehículos industriales con modelos multicuerpo de gran complejidad

El objetivo de esta Tesis ha sido la consecución de simulaciones en tiempo real de vehículos industriales modelizados como sistemas multicuerpo complejos formados por sólidos rígidos. Para el desarrollo de un programa de simulación deben considerarse cuatro aspectos fundamentales: la modelización del sistema multicuerpo (tipos de coordenadas, pares ideales o impuestos mediante fuerzas), la formulación a utilizar para plantear las ecuaciones diferenciales del movimiento (coordenadas dependientes o independientes, métodos globales o topológicos, forma de imponer las ecuaciones de restricción), el método de integración numérica para resolver estas ecuaciones en el tiempo (integradores explícitos o implícitos) y finalmente los detalles de la implementación realizada (lenguaje de programación, librerías matemáticas, técnicas de paralelización). Estas cuatro etapas están interrelacionadas entre sí y todas han formado parte de este trabajo. Desde la generación de modelos de una furgoneta y de camión con semirremolque, el uso de tres formulaciones dinámicas diferentes, la integración de las ecuaciones diferenciales del movimiento mediante métodos explícitos e implícitos, hasta el uso de funciones BLAS, de técnicas de matrices sparse y la introducción de paralelización para utilizar los distintos núcleos del procesador. El trabajo presentado en esta Tesis ha sido organizado en 8 capítulos, dedicándose el primero de ellos a la Introducción. En el Capítulo 2 se presentan dos formulaciones semirrecursivas diferentes, de las cuales la primera está basada en una doble transformación de velocidades, obteniéndose las ecuaciones diferenciales del movimiento en función de las aceleraciones relativas independientes. La integración numérica de estas ecuaciones se ha realizado con el método de Runge-Kutta explícito de cuarto orden. La segunda formulación está basada en coordenadas relativas dependientes, imponiendo las restricciones por medio de penalizadores en posición y corrigiendo las velocidades y aceleraciones mediante métodos de proyección. En este segundo caso la integración de las ecuaciones del movimiento se ha llevado a cabo mediante el integrador implícito HHT (Hilber, Hughes and Taylor), perteneciente a la familia de integradores estructurales de Newmark. En el Capítulo 3 se introduce la tercera formulación utilizada en esta Tesis. En este caso las uniones entre los sólidos del sistema se ha realizado mediante uniones flexibles, lo que obliga a imponer los pares por medio de fuerzas. Este tipo de uniones impide trabajar con coordenadas relativas, por lo que la posición del sistema y el planteamiento de las ecuaciones del movimiento se ha realizado utilizando coordenadas Cartesianas y parámetros de Euler. En esta formulación global se introducen las restricciones mediante fuerzas (con un planteamiento similar al de los penalizadores) y la estabilización del proceso de integración numérica se realiza también mediante proyecciones de velocidades y aceleraciones. En el Capítulo 4 se presenta una revisión de las principales herramientas y estrategias utilizadas para aumentar la eficiencia de las implementaciones de los distintos algoritmos. En primer lugar se incluye una serie de consideraciones básicas para aumentar la eficiencia numérica de las implementaciones. A continuación se mencionan las principales características de los analizadores de códigos utilizados y también las librerías matemáticas utilizadas para resolver los problemas de álgebra lineal tanto con matrices densas como sparse. Por último se desarrolla con un cierto detalle el tema de la paralelización en los actuales procesadores de varios núcleos, describiendo para ello el patrón empleado y las características más importantes de las dos herramientas propuestas, OpenMP y las TBB de Intel. Hay que señalar que las características de los sistemas multicuerpo problemas de pequeño tamaño, frecuente uso de la recursividad, y repetición intensiva en el tiempo de los cálculos con fuerte dependencia de los resultados anteriores dificultan extraordinariamente el uso de técnicas de paralelización frente a otras áreas de la mecánica computacional, tales como por ejemplo el cálculo por elementos finitos. Basándose en los conceptos mencionados en el Capítulo 4, el Capítulo 5 está dividido en tres secciones, una para cada formulación propuesta en esta Tesis. En cada una de estas secciones se describen los detalles de cómo se han realizado las distintas implementaciones propuestas para cada algoritmo y qué herramientas se han utilizado para ello. En la primera sección se muestra el uso de librerías numéricas para matrices densas y sparse en la formulación topológica semirrecursiva basada en la doble transformación de velocidades. En la segunda se describe la utilización de paralelización mediante OpenMP y TBB en la formulación semirrecursiva con penalizadores y proyecciones. Por último, se describe el uso de técnicas de matrices sparse y paralelización en la formulación global con uniones flexibles y parámetros de Euler. El Capítulo 6 describe los resultados alcanzados mediante las formulaciones e implementaciones descritas previamente. Este capítulo comienza con una descripción de la modelización y topología de los dos vehículos estudiados. El primer modelo es un vehículo de dos ejes del tipo chasis-cabina o furgoneta, perteneciente a la gama de vehículos de carga medianos. El segundo es un vehículo de cinco ejes que responde al modelo de un camión o cabina con semirremolque, perteneciente a la categoría de vehículos industriales pesados. En este capítulo además se realiza un estudio comparativo entre las simulaciones de estos vehículos con cada una de las formulaciones utilizadas y se presentan de modo cuantitativo los efectos de las mejoras alcanzadas con las distintas estrategias propuestas en esta Tesis. Con objeto de extraer conclusiones más fácilmente y para evaluar de un modo más objetivo las mejoras introducidas en la Tesis, todos los resultados de este capítulo se han obtenido con el mismo computador, que era el top de la gama Intel Xeon en 2007, pero que hoy día está ya algo obsoleto. Por último los Capítulos 7 y 8 están dedicados a las conclusiones finales y las futuras líneas de investigación que pueden derivar del trabajo realizado en esta Tesis. Los objetivos de realizar simulaciones en tiempo real de vehículos industriales de gran complejidad han sido alcanzados con varias de las formulaciones e implementaciones desarrolladas. ABSTRACT The objective of this Dissertation has been the achievement of real time simulations of industrial vehicles modeled as complex multibody systems made up by rigid bodies. For the development of a simulation program, four main aspects must be considered: the modeling of the multibody system (types of coordinates, ideal joints or imposed by means of forces), the formulation to be used to set the differential equations of motion (dependent or independent coordinates, global or topological methods, ways to impose constraints equations), the method of numerical integration to solve these equations in time (explicit or implicit integrators) and the details of the implementation carried out (programming language, mathematical libraries, parallelization techniques). These four stages are interrelated and all of them are part of this work. They involve the generation of models for a van and a semitrailer truck, the use of three different dynamic formulations, the integration of differential equations of motion through explicit and implicit methods, the use of BLAS functions and sparse matrix techniques, and the introduction of parallelization to use the different processor cores. The work presented in this Dissertation has been structured in eight chapters, the first of them being the Introduction. In Chapter 2, two different semi-recursive formulations are shown, of which the first one is based on a double velocity transformation, thus getting the differential equations of motion as a function of the independent relative accelerations. The numerical integration of these equations has been made with the Runge-Kutta explicit method of fourth order. The second formulation is based on dependent relative coordinates, imposing the constraints by means of position penalty coefficients and correcting the velocities and accelerations by projection methods. In this second case, the integration of the motion equations has been carried out by means of the HHT implicit integrator (Hilber, Hughes and Taylor), which belongs to the Newmark structural integrators family. In Chapter 3, the third formulation used in this Dissertation is presented. In this case, the joints between the bodies of the system have been considered as flexible joints, with forces used to impose the joint conditions. This kind of union hinders to work with relative coordinates, so the position of the system bodies and the setting of the equations of motion have been carried out using Cartesian coordinates and Euler parameters. In this global formulation, constraints are introduced through forces (with a similar approach to the penalty coefficients) are presented. The stabilization of the numerical integration is carried out also by velocity and accelerations projections. In Chapter 4, a revision of the main computer tools and strategies used to increase the efficiency of the implementations of the algorithms is presented. First of all, some basic considerations to increase the numerical efficiency of the implementations are included. Then the main characteristics of the code’ analyzers used and also the mathematical libraries used to solve linear algebra problems (both with dense and sparse matrices) are mentioned. Finally, the topic of parallelization in current multicore processors is developed thoroughly. For that, the pattern used and the most important characteristics of the tools proposed, OpenMP and Intel TBB, are described. It needs to be highlighted that the characteristics of multibody systems small size problems, frequent recursion use and intensive repetition along the time of the calculation with high dependencies of the previous results complicate extraordinarily the use of parallelization techniques against other computational mechanics areas, as the finite elements computation. Based on the concepts mentioned in Chapter 4, Chapter 5 is divided into three sections, one for each formulation proposed in this Dissertation. In each one of these sections, the details of how these different proposed implementations have been made for each algorithm and which tools have been used are described. In the first section, it is shown the use of numerical libraries for dense and sparse matrices in the semirecursive topological formulation based in the double velocity transformation. In the second one, the use of parallelization by means OpenMP and TBB is depicted in the semi-recursive formulation with penalization and projections. Lastly, the use of sparse matrices and parallelization techniques is described in the global formulation with flexible joints and Euler parameters. Chapter 6 depicts the achieved results through the formulations and implementations previously described. This chapter starts with a description of the modeling and topology of the two vehicles studied. The first model is a two-axle chassis-cabin or van like vehicle, which belongs to the range of medium charge vehicles. The second one is a five-axle vehicle belonging to the truck or cabin semi-trailer model, belonging to the heavy industrial vehicles category. In this chapter, a comparative study is done between the simulations of these vehicles with each one of the formulations used and the improvements achieved are presented in a quantitative way with the different strategies proposed in this Dissertation. With the aim of deducing the conclusions more easily and to evaluate in a more objective way the improvements introduced in the Dissertation, all the results of this chapter have been obtained with the same computer, which was the top one among the Intel Xeon range in 2007, but which is rather obsolete today. Finally, Chapters 7 and 8 are dedicated to the final conclusions and the future research projects that can be derived from the work presented in this Dissertation. The objectives of doing real time simulations in high complex industrial vehicles have been achieved with the formulations and implementations developed.

Estudio de la aplicabilidad de las aproximaciones uniformes al análisis de series históricas : aplicación al caso de los precios del cobre

El objetivo de este proyecto de investigación es comparar dos técnicas matemáticas de aproximación polinómica, las aproximaciones según el criterio de mínimos cuadrados y las aproximaciones uniformes (“minimax”). Se describen tanto el mercado actual del cobre, con sus fluctuaciones a lo largo del tiempo, como los distintos modelos matemáticos y programas informáticos disponibles. Como herramienta informática se ha seleccionado Matlab®, cuya biblioteca matemática es muy amplia y de uso muy extendido y cuyo lenguaje de programación es suficientemente potente para desarrollar los programas que se necesiten. Se han obtenido diferentes polinomios de aproximación sobre una muestra (serie histórica) que recoge la variación del precio del cobre en los últimos años. Se ha analizado la serie histórica completa y dos tramos significativos de ella. Los resultados obtenidos incluyen valores de interés para otros proyectos. Abstract The aim of this research project is to compare two mathematical models for estimating polynomial approximation, the approximations according to the criterion of least squares approximations uniform (“Minimax”). Describes both the copper current market, fluctuating over time as different computer programs and mathematical models available. As a modeling tool is selected main Matlab® which math library is the largest and most widely used programming language and which is powerful enough to allow you to develop programs that are needed. We have obtained different approximating polynomials, applying mathematical methods chosen, a sample (historical series) which indicates the fluctuation in copper prices in last years. We analyzed the complete historical series and two significant sections of it. The results include values that we consider relevant to other projects