Numerical experiments with a modified regularization scheme for mathematical programs with complementarity constraints

On this paper we present a modified regularization scheme for Mathematical Programs with Complementarity Constraints. In the regularized formulations the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In our approach both the complementarity condition and the nonnegativity constraints are relaxed. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.

Modellus: Learning Physics with Mathematical Modelling

Tese de doutoramento em Ciências da Educação, área de Teoria Curricular e Ensino das Ciências

Mathematical modeling and simulation of heat flow through pultrusion die assembly system for thermoset composites

Pultrusion is an industrial process used to produce glass fibers reinforced polymers profiles. These materials are worldwide used when performing characteristics, such as great electrical and magnetic insulation, high strength to weight ratio, corrosion and weather resistance, long service life and minimal maintenance are required. In this study, we present the results of the modelling and simulation of heat flow through a pultrusion die by means of Finite Element Analysis (FEA). The numerical simulation was calibrated based on temperature profiles computed from thermographic measurements carried out during pultrusion manufacturing process. Obtained results have shown a maximum deviation of 7%, which is considered to be acceptable for this type of analysis, and is below to the 10% value, previously specified as maximum deviation. © 2011, Advanced Engineering Solutions.

Geography of the Information Society

All every day activities take place in space. And it is upon this that all information and knowledge revolve. The latter are the key elements in the organisation of territories. Their creation, use and distribution should therefore occur in a balanced way throughout the whole territory in order to allow all individuals to participate in an egalitarian society, in which the flow of knowledge can take precedence over the flow of interests. The information society depends, to a large extent, on the technological capacity to disseminate information and, consequently, the knowledge throughout territory, thereby creating conditions which allow a more balanced development, from the both the social and economic points of view thus avoiding the existence of info-exclusion territories. Internet should therefore be considered more than a mere technology, given that its importance goes well beyond the frontiers of culture and society. It is already a part of daily life and of the new forms of thinking and transmitting information, thus making it a basic necessity essential, for a full socio-economic development. Its role as a platform of creation and distribution of content is regarded as an indispensable element for education in today’s society, since it makes information a much more easily acquired benefit.”…in the same way that the new technologies of generation and distribution of energy allowed factories and large companies to establish themselves as the organisational bases of industrial society, so the internet today constitutes the technological base of the organisational form that characterises the Information Era: the network” (CASTELLS, 2004:15). The changes taking place today in regional and urban structures are increasingly more evident due to a combination of factors such as faster means of transport, more efficient telecommunications and other cheaper and more advanced technologies of information and knowledge. Although their impact on society is obvious, society itself also has a strong influence on the evolution of these technologies. And although physical distance has lost much of the responsibility it had towards explaining particular phenomena of the economy and of society, other aspects such as telecommunications, new forms of mobility, the networks of innovation, the internet, cyberspace, etc., have become more important, and are the subject of study and profound analysis. The science of geographical information, allows, in a much more rigorous way, the analysis of problems thus integrating in a much more balanced way, the concepts of place, of space and of time. Among the traditional disciplines that have already found their place in this process of research and analysis, we can give special attention to a geography of new spaces, which, while not being a geography of ‘innovation’, nor of the ‘Internet’, nor even ‘virtual’, which can be defined as one of the ‘Information Society’, encompassing not only the technological aspects but also including a socio-economic approach. According to the last European statistical data, Portugal shows a deficit in terms of information and knowledge dissemination among its European partners. Some of the causes are very well identified - low levels of scholarship, weak investments on innovation and R&D (both private and public sector) - but others seem to be hidden behind socio-economical and technological factors. So, the justification of Portugal as the case study appeared naturally, on a difficult quest to find the major causes to territorial asymmetries. The substantial amount of data needed for this work was very difficult to obtain and for the islands of Madeira and Azores was insufficient, so only Continental Portugal was considered for this study. In an effort to understand the various aspects of the Geography of the Information Society and bearing in mind the increasing generalised use of information technologies together with the range of technologies available for the dissemination of information, it is important to: (i) Reflect on the geography of the new socio-technological spaces. (ii) Evaluate the potential for the dissemination of information and knowledge through the selection of variables that allow us to determine the dynamic of a given territory or region; (iii) Define a Geography of the Information Society in Continental Portugal.

Internet Geography: New Spaces of Information

The objective of great investments in telecommunication networks is to approach economies and put an end to the asymmetries. The most isolated regions could be the beneficiaries of this new technological investments wave disseminating trough the territories. The new economic scenarios created by globalisation make high capacity backbones and coherent information society polity, two instruments that could change regions fate and launch them in to an economic development context. Technology could bring international projection to services or products and could be the differentiating element between a national and an international economic strategy. So, the networks and its fluxes are becoming two of the most important variables to the economies. Measuring and representing this new informational accessibility, mapping new communities, finding new patterns and localisation models, could be today’s challenge. In the physical and real space, location is defined by two or three geographical co-ordinates. In the network virtual space or in cyberspace, geography seems incapable to define location, because it doesn’t have a good model. Trying to solve the problem and based on geographical theories and concepts, new fields of study came to light. The Internet Geography, Cybergeography or Geography of Cyberspace are only three examples. In this paper and using Internet Geography and informational cartography, it was possible to observe and analyse the spacialisation of the Internet phenomenon trough the distribution of the IP addresses in the Portuguese territory. This work shows the great potential and applicability of this indicator to Internet dissemination and regional development studies. The Portuguese territory is seen in a completely new form: the IP address distribution of Country Code Top Level Domains (.pt) could show new regional hierarchies. The spatial concentration or dispersion of top level domains seems to be a good instrument to reflect the info-structural dynamic and economic development of a territory, especially at regional level.

Internet Geography: Spaces of Innovation

Information Society plays an important role in all kinds of human activity, inducing new forms of economic and social organization and creating knowledge. Over the last twenty years of the 20th century, large investments in telecommunication networks were made to approach economies and put an end to the asymmetries. The most isolated regions were the beneficiaries of this new technological investment’s wave disseminating trough the territories. The new economic scenarios created by globalisation make high capacity backbones and coherent information society polity, two instruments that could change regions fate and launch them in to an economic development context. Technology could bring international projection to services, products and could be the differentiating element between a national and an international economic strategy. So, the networks and its fluxes are becoming two of the most important variables to the economies. Measuring and representing this new informational accessibility, mapping new communities, finding new patterns and localisation models, could be today’s challenge. In the physical/real space, location is defined by two or three geographical co-ordinates. In the network/virtual space or in cyberspace, geography seems incapable to define location, because it doesn’t have a good model. Trying to solve the problem and based on geographical theories and concepts, new fields of study came to light. Internet Geography is one example. In this paper and using Internet Geography and informational cartography, it was possible to observe and analyse the spacialisation of the Internet phenomenon trough the distribution of the IP addresses in the Portuguese territory. This work shows the great potential and applicability of this indicator to regional development studies, and at the same time. The IP address distribution of Country Code Top Level Domains (.pt for Portugal) could show the same economic patterns, reflecting territorial inflexibility or, by opposition, new regional hierarchies. The spatial concentration or dispersion of top level domains seems to be a good instrument to analyse the info-structural dynamic and economic development of a territory, especially at regional level. At the same time it shows that information technologies are essential to innovation and competitive advantage.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

A mathematical model for supermarket order picking

Order picking consists in retrieving products from storage locations to satisfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best international practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.

Scheduling aircraft’s engines repair process: a mathematical model

In this talk, we discuss a scheduling problem that originated at TAP - Maintenance & Engineering - the maintenance, repair and overhaul organization of Portugal’s leading airline. In the repair process of aircrafts’ engines, the operations to be scheduled may be executed on a certain workstation by any processor of a given set, and the objective is to minimize the total weighted tardiness. A mixed integer linear programming formulation, based on the flexible job shop scheduling, is presented here, along with computational experiment on a real instance, provided by TAP-ME, from a regular working week. The model was also tested using benchmarking instances available in literature.

Knowledge Society and Geography: A Theoretical Approach

The transition process between information and knowledge is faster and so the inputs that influence social and political practises. The dissemination of information is now determinant in terms of territorial competitiveness and both public and private sector take large benefits when the data-information- knowledge value chain repeats itself trough space and time. Mankind depends nowadays on the creation and diffusion of good and reliable information. Speed is also important and the greater the speed, the faster the opportunities for global markets. Information must be an input for knowledge and obviously for decision. So, the power of information is unquestionable. This paper focuses on concepts like information, knowledge and other, more geographical and tries to explain how territories change from real to virtual. Knowledge society appears on an evolutional context in which information dissemination is wider and technological potential overwrites traditional notions of Geography. To understand the mutations over the territories, the causes and the consequences emerges the Geography of the Knowledge Society, a new discipline inside Geography with a special concern about modern society and socio-economical developing models.

Geodupa - a geography-driven partial membership algorithm

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

Mathematical modelling of shallow flows: closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics

Canadian Journal of Civil Engineering 36(10) 1605–16