The cardinal of various monoids of transformations that preserve a uniform partition

Bulletin of the Malaysian Mathematical Sciences Society

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

FROM NON-PLACE TO PLACE: A STUDY OF EUROPEAN PUBLIC SPACE AS A SPACE OF IDENTITY

Master Erasmus Mundus Crossways in European Humanities

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

State Space Analysis of Forest Fires

This paper studies forest fires from the perspective of dynamical systems. Burnt area, precipitation and atmospheric temperatures are interpreted as state variables of a complex system and the correlations between them are investigated by means of different mathematical tools. First, we use mutual information to reveal potential relationships in the data. Second, we adopt the state space portrait to characterize the system’s behavior. Third, we compare the annual state space curves and we apply clustering and visualization tools to unveil long-range patterns. We use forest fire data for Portugal, covering the years 1980–2003. The territory is divided into two regions (North and South), characterized by different climates and vegetation. The adopted methodology represents a new viewpoint in the context of forest fires, shedding light on a complex phenomenon that needs to be better understood in order to mitigate its devastating consequences, at both economical and environmental levels.

Fractional State Space Analysis of Economy Systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Quasi-periodic Gaits in Multi-legged Robots

5th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines

An Exact Schedulability Test for Global FP Using State Space Pruning

Presented at 23rd International Conference on Real-Time Networks and Systems (RTNS 2015). 4 to 6, Nov, 2015, Main Track. Lille, France.

Otimização do Funcionamento da ETAR das Termas de S. Vicente, Penafiel

A água é um recurso natural único, escasso e essencial a todos os seres vivos, o que a torna um bem de extrema importância. Nos dias de hoje, o desperdício deste bem, aliado ao aumento da sua procura, tornou-se um problema devido à decrescente disponibilidade de água doce no nosso planeta. Todas as águas que rejeitamos depois da sua utilização para diversos fins, designadas de águas residuais, necessitam de tratamento antes de serem devolvidas ao meio ambiente. O seu tratamento é realizado numa Estação de Tratamento de Águas Residuais (ETAR) e o processo de tratamento depende das suas características. A ETAR das Termas de S. Vicente, em Penafiel, trabalha no seu limite de capacidade, apresenta uma sobrecarga hidráulica gerada por uma afluência de águas pluviais e o processamento das lamas geradas não permite uma secagem tão completa como seria desejável. Assim, este trabalho teve como objetivo o estudo do funcionamento desta ETAR com a finalidade de propor soluções que o possam otimizar. As soluções propostas para otimizar o funcionamento da ETAR em estudo são: i) a substituição de grades de limpeza manual por grades de limpeza automática de forma a reduzir a necessidade da intervenção do operador ao nível da remoção e condicionamento dos gradados; ii) a construção de um desarenador arejado que além de remover areias de diâmetro superior a 0,2 mm promove também a remoção de gorduras, protegendo desta forma os equipamentos a jusante da abrasão/desgaste prematuros e reduzindo a formação de depósitos nas tubagens; iii) a construção de um tanque de equalização de forma a garantir uma distribuição mais uniforme dos caudais e da carga poluente; iv) a substituição do enchimento do leito percolador por um meio de suporte plástico que permite atingir melhores eficiências de remoção neste tratamento biológico; v) a alteração do agente de desinfeção para radiação ultravioleta, evitando a adição de produtos químicos na água residual e possível formação de subprodutos prejudiciais ao ambiente, como ocorreria no caso da cloragem; e vi) a substituição da desidratação de lamas em leitos de secagem por filtros de banda, que é um processo mais rápido, que ocupa menos espaço e permite atingir elevadas eficiências de remoção de humidade. Para cada uma das sugestões são apresentadas as correspondentes especificações técnicas e dimensionamento. As sugestões de melhoria apresentadas neste trabalho constituem uma alternativa mais económica do que a ampliação da ETAR, que genericamente corresponde à duplicação da linha de tratamento atual. Devido à menor complexidade em termos de construção, estas sugestões podem vir a ser implementadas num futuro próximo, prolongando assim um pouco mais a vida útil da ETAR atual.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Performance of state space and ARIMA models for consumer retail sales forecasting

Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail businesses. For profitable retail businesses, accurate demand forecasting is crucial in organizing and planning production, purchasing, transportation and labor force. Retail sales series belong to a special type of time series that typically contain trend and seasonal patterns, presenting challenges in developing effective forecasting models. This work compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. On both methodologies the model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample. Both one-step and multiple-step forecasts were produced. The results show that when an automatic algorithm the overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts. We also conclude that state space and ARIMA produce coverage probabilities that are close to the nominal rates for both one-step and multi-step forecasts.

Public Participation geographic information systems in developing countries: lessons from Uganda on the impacts of interactive screens PPGIS and community perceptions of space

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Structural transformation and specialization patterns in the product space: assessing China and India

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Economics from the NOVA – School of Business and Economics

Renova black toilet paper: The creation of a glocal market space

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

THE U.S. and European M&A cycles: A Markov switching and state space approach

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics