A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

TICAI 2008

TICAI 2008 é o terceiro volume de uma série que recolhe as contribuições mais significativas dos melhores congressos de língua espanhola e Portuguesa no âmbito da Sociedade de Educação do IEEE. Este volume corresponde aos eventos realizados no ano de 2008, é promovido pelos Capítulos Português e Espanhol desta Sociedade. Como os volumes anteriores, o âmbito centra-se na investigação e aplicações da tecnologia na educação e engloba o desenho e investigação de novas ferramentas, materiais e técnicas que facilitem o ensino/ aprendizagem e aplicações, métodos pedagógicos e experiências concretas de uso destas novas técnicas e ferramentas. Tudo com um enfoque particular no ensino/ aprendizagem das disciplinas próprias do IEEE, fundamentalmente nas áreas da Engenharia Electrotécnica, Tecnologia Electrónica, Engenharia de Telecomunicações e Engenharia Informática. Assim, os capítulos deste livro passaram pelo crivo apertado de duas revisões: primeiro do próprio congresso e depois uma segunda selecção de entre os artigos aceites para o congresso. Para esse processo, contamos com membros destacados de cada um dos Comités de Organização ou de programa dos respectivos congressos.

Standard commercial education robotic platform: intermediate solution to teaching robotics

Teaching robotics to students at the beginning of their studies has become a huge challenge. Simulation environments can be an effective solution to that challenge where students can interact with simulated robots and have the first contact with robotic constraints. From our previous experience with simulation environments it was possible to observe that students with lower background knowledge in robotics where able to deal with a limited number of constraints, implement a simulated robotic platform and study several sensors. The question is: after this first phase what should be the best approach? Should the student start developing their own hardware? Hardware development is a very important part of an engineer's education but it can also be a difficult phase that could lead to discouragement and loss of motivation in some students. Considering the previous constraints and first year engineering students’ high abandonment rate it is important to develop teaching strategies to deal with this problem in a feasible way. The solution that we propose is the integration of a low-cost standard robotic platform WowWee Rovio as an intermediate solution between the simulation phase and the stage where the students can develop their own robots. This approach will allow the students to keep working in robotic areas such as: cooperative behaviour, perception, navigation and data fusion. The propose approach proved to be a motivation step not only for the students but also for the teachers. Students and teachers were able to reach an agreement between the level of demand imposed by the teachers and satisfaction/motivation of the students.

Teaching accounting and management through business simulation

Everyday accounting and management teachers face the challenge of creating learning environments that motivate students. This chapter describes the Business Simulation (BS) experience that has taken place at the Polytechnic Institute of Porto, Institute of Accounting and Administration (IPP/ISCAP). The chapter presents students’ perceptions about the course and the teaching/learning approach. The results show that pedagogical methods used (competency-oriented), generic competencies (cooperation and group work), and interpersonal skills (organisational and communication skills) are relevant for future accounting professionals. In addition, positive remarks and possible constraints based on observation, staff meetings, and past research are reported. The chapter concludes with some recommendations from the project implementation

Adhesive selection for single lap bonded joints: Experimentation and advanced techniques for strength prediction

The integrity of multi-component structures is usually determined by their unions. Adhesive-bonding is often used over traditional methods because of the reduction of stress concentrations, reduced weight penalty, and easy manufacturing. Commercial adhesives range from strong and brittle (e.g., Araldite® AV138) to less strong and ductile (e.g., Araldite® 2015). A new family of polyurethane adhesives combines high strength and ductility (e.g., Sikaforce® 7888). In this work, the performance of the three above-mentioned adhesives was tested in single lap joints with varying values of overlap length (LO). The experimental work carried out is accompanied by a detailed numerical analysis by finite elements, either based on cohesive zone models (CZM) or the extended finite element method (XFEM). This procedure enabled detailing the performance of these predictive techniques applied to bonded joints. Moreover, it was possible to evaluate which family of adhesives is more suited for each joint geometry. CZM revealed to be highly accurate, except for largely ductile adhesives, although this could be circumvented with a different cohesive law. XFEM is not the most suited technique for mixed-mode damage growth, but a rough prediction was achieved.

Adhesive thickness effects of a ductile adhesive by optical measurement techniques

Adhesive bonding is an excellent alternative to traditional joining techniques such as welding, mechanical fastening or riveting. However, there are many factors that have to be accounted for during joint design to accurately predict the joint strength. One of these is the adhesive layer thickness (tA). Most of the results are for epoxy structural adhesives, tailored to perform best with small values of tA, and these show that the lap joint strength decreases with increase of tA (the optimum joint strength is usually obtained with tA values between 0.1 and 0.2 mm). Recently, polyurethane adhesives were made available in the market, designed to perform with larger tA values, and whose fracture behaviour is still not studied. In this work, the effect of tA on the tensile fracture toughness (View the MathML source) of a bonded joint is studied, considering a novel high strength and ductile polyurethane adhesive for the automotive industry. This work consists on the fracture characterization of the bond by a conventional and the J-integral techniques, which accurately account for root rotation effects. An optical measurement method is used for the evaluation of crack tip opening (δn) and adherends rotation at the crack tip (θo) during the test, supported by a Matlab® sub-routine for the automated extraction of these parameters. As output of this work, fracture data is provided in traction for the selected adhesive, enabling the subsequent strength prediction of bonded joints.

Tensile fracture characterization of adhesive joints by standard and optical techniques

The use of adhesive joints has increased in recent decades due to its competitive features compared with traditional methods. This work aims to estimate the tensile critical strain energy release rate (GIC) of adhesive joints by the Double-Cantilever Beam (DCB) test. The J-integral is used since it enables obtaining the tensile Cohesive Zone Model (CZM) law. An optical measuring method was developed for assessing the crack tip opening (δn) and adherends rotation (θo). The proposed CZM laws were best approximated by a triangular shape for the brittle adhesive and a trapezoidal shape for the two ductile adhesives.

Effects of self-administered exercises based on Tuina techniques on musculoskeletal disorders of professional orchestra musicians: a randomized controlled trial

Background Musicians are frequently affected by playing-related musculoskeletal disorders (PRMD). Common solutions used by Western medicine to treat musculoskeletal pain include rehabilitation programs and drugs, but their results are sometimes disappointing. Objective To study the effects of self-administered exercises based on Tuina techniques on the pain intensity caused by PRMD of professional orchestra musicians, using numeric visual scale (NVS). Design, setting, participants and interventions We performed a prospective, controlled, single-blinded, randomized study with musicians suffering from PRMD. Participating musicians were randomly distributed into the experimental (n = 39) and the control (n = 30) groups. After an individual diagnostic assessment, specific Tuina self-administered exercises were developed and taught to the participants. Musicians were instructed to repeat the exercises every day for 3 weeks. Main outcome measures Pain intensity was measured by NVS before the intervention and after 1, 3, 5, 10, 15 and 20 d of treatment. The procedure was the same for the control group, however the Tuina exercises were executed in points away from the commonly-used acupuncture points. Results In the treatment group, but not the control group, pain intensity was significantly reduced on days 1, 3, 5, 10, 15 and 20. Conclusion The results obtained are consistent with the hypothesis that self-administered exercises based on Tuina techniques could help professional musicians controlling the pain caused by PRMD. Although our results are very promising, further studies are needed employing a larger sample size and double blinding designs.

Immediate effects of Tuina techniques on working-related musculoskeletal disorder of professional orchestra musicians

BACKGROUND: Musicians are a prone group to suffer from working-related musculoskeletal disorder (WRMD). Conventional solutions to control musculoskeletal pain include pharmacological treatment and rehabilitation programs but their efficiency is sometimes disappointing. OBJECTIVE: The aim of this research is to study the immediate effects of Tuina techniques on WRMD of professional orchestra musicians from the north of Portugal. DESIGN, SETTING, PARTICIPANTS AND INTERVENTIONS: We performed a prospective, controlled, single-blinded, randomized study. Professional orchestra musicians with a diagnosis of WRMD were randomly distributed into the experimental group (n=39) and the control group (n=30). During an individual interview, Chinese diagnosis took place and treatment points were chosen. Real acupoints were treated by Tuina techniques into the experimental group and non-specific skin points were treated into the control group. Pain was measured by verbal numerical scale before and immediately after intervention. RESULTS: After one treatment session, pain was reduced in 91.8% of the cases for the experimental group and 7.9% for the control group. CONCLUSION: Although results showed that Tuina techniques are effectively reducing WRMD in professional orchestra musicians of the north of Portugal, further investigations with stronger measurements, double-blinding designs and bigger simple sizes are needed.

Efficiency of strengthening techniques assessed for existing masonry buildings

The Azores archipelago is a zone with a vast cultural heritage, presenting a building stock mainly constructed in traditional stone masonry. It is known that this type of construction exhibits poor behaviour under seismic excitations; however it is extensively used in seismic prone areas, such as this case. The 9th of July of 1998 earthquake was the last seismic event in the islands, leaving many traditional stone constructions severely damaged or totally destroyed. This scenario led to an effort by the local government of improving the seismic resistance of these constructions, with the application of several reinforcement techniques. This work aims to study some of the most used reinforcement schemes after the 1998 earthquake, and to assess their effectiveness in the mitigation of the construction’s seismic vulnerability. A brief evaluation of the cost versus benefit of these retrofitting techniques is also made, seeking to identify those that are most suitable for each building typology. Thus, it was sought to analyze the case of real structures with different geometrical and physical characteristics, by establishing a comparison between the seismic performance of reinforced and non-reinforced structures. The first section contains the analysis of a total of six reinforcement scenarios for each building chosen. Using the recorded 1998 earthquake accelerograms, a linear time-history analysis was performed for each reinforcement scenario. A comparison was then established between the maximum displacements, inter-storey drift and maximum stress obtained, in order to evaluate the global seismic response of each reinforced structure. In the second part of the work, the examination of the performance obtained in the previous section, in relation to the cost of implementing each reinforcement technique, allowed to draw conclusions concerning the viability of implementing each reinforcement method, based on the book value of the buildings in study.

Teaching mathematics using Massive Open Online Courses

Distance learning - where students take courses (attend classes, get activities and other sort of learning materials) while being physically separated from their instructors, for larger part of the course duration - is far from being a “new event”. Since the middle of the nineteenth century, this has been done through Radio, Mail and TV, taking advantage of the full educational potential that these media resources had to offer at the time. However, in recent times we have, at our complete disposal, the “magic wonder” of communication and globalization - the Internet. Taking advantage of a whole new set of educational opportunities, with a more or less unselfish “look” to economic interests, focusing its concern on a larger and collective “welfare”, contributing to the development of a more “equitable” world, with regard to educational opportunities, the Massive Open Online Courses (MOOCs) were born and have become an important feature of the higher education in recent years. Many people have been talking about MOOCs as a potential educational revolution, which has arrived from North America, still growing and spreading, referring to its benefits and/or disadvantages. The Polytechnic Institute of Porto, also known as IPP, is a Higher Education Portuguese institution providing undergraduate and graduate studies, which has a solid history of online education and innovation through the use of technology, and it has been particularly interested and focused on MOOC developments, based on an open educational policy in order to try to implement some differentiated learning strategies to its actual students and as a way to attract future ones. Therefore, in July 2014, IPP launched the first Math MOOC on its own platform. This paper describes the requirements, the resulting design and implementation of a mathematics MOOC, which was essentially addressed to three target populations: - pre-college students or individuals wishing to update their Math skills or that need to prepare for the National Exam of Mathematics; - Higher Education students who have not attended in High School, this subject, and who feel the need to acquire basic knowledge about some of the topics covered; - High School Teachers who may use these resources with their students allowing them to develop teaching methodologies like "Flipped Classroom” (available at http://www.opened.ipp.pt/). The MOOC was developed in partnership with several professors from several schools from IPP, gathering different math competences and backgrounds to create and put to work different activities such video lectures and quizzes. We will also try to briefly discuss the advertising strategy being developed to promote this MOOC, since it is not offered through a main MOOC portal, such as Coursera or Udacity.