Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

The semigroup ring of a restriction semigroup with an inverse skeleton

In this paper we investigate some classes of semigroup rings with respect to (semi)primeness and (semi)primitivity. We do so by extending the techniques developed by Munn in (Proc R Soc Edinbur Sect A 107:175-196, 1987) and (Proc R Soc Edinbur Sect A 115:109-117, 1990) for the study of semigroup rings of inverse semigroups. Restriction, weakly ample and ample semigroups are considered.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Fractional calculus analysis of the cosmic microwave background

Cosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.

The idempotent-separating degree of a block-group

Semigroup Forum, nº76 (2008), pg.579-583

Characterisation of noisy speech channels in 2G and 3G mobile networks

As the wireless cellular market reaches competitive levels never seen before, network operators need to focus on maintaining Quality of Service (QoS) a main priority if they wish to attract new subscribers while keeping existing customers satisfied. Speech Quality as perceived by the end user is one major example of a characteristic in constant need of maintenance and improvement. It is in this topic that this Master Thesis project fits in. Making use of an intrusive method of speech quality evaluation, as a means to further study and characterize the performance of speech codecs in second-generation (2G) and third-generation (3G) technologies. Trying to find further correlation between codecs with similar bit rates, along with the exploration of certain transmission parameters which may aid in the assessment of speech quality. Due to some limitations concerning the audio analyzer equipment that was to be employed, a different system for recording the test samples was sought out. Although the new designed system is not standard, after extensive testing and optimization of the system's parameters, final results were found reliable and satisfactory. Tests include a set of high and low bit rate codecs for both 2G and 3G, where values were compared and analysed, leading to the outcome that 3G speech codecs perform better, under the approximately same conditions, when compared with 2G. Reinforcing the idea that 3G is, with no doubt, the best choice if the costumer looks for the best possible listening speech quality. Regarding the transmission parameters chosen for the experiment, the Receiver Quality (RxQual) and Received Energy per Chip to the Power Density Ratio (Ec/N0), these were subject to speech quality correlation tests. Final results of RxQual were compared to those of prior studies from different researchers and, are considered to be of important relevance. Leading to the confirmation of RxQual as a reliable indicator of speech quality. As for Ec/N0, it is not possible to state it as a speech quality indicator however, it shows clear thresholds for which the MOS values decrease significantly. The studied transmission parameters show that they can be used not only for network management purposes but, at the same time, give an expected idea to the communications engineer (or technician) of the end-to-end speech quality consequences. With the conclusion of the work new ideas for future studies come to mind. Considering that the fourth-generation (4G) cellular technologies are now beginning to take an important place in the global market, as the first all-IP network structure, it seems of great relevance that 4G speech quality should be subject of evaluation. Comparing it to 3G, not only in narrowband but also adding wideband scenarios with the most recent standard objective method of speech quality assessment, POLQA. Also, new data found on Ec/N0 tests, justifies further research studies with the intention of validating the assumptions made in this work.

Largest 2-generated subsemigroups of the symmetric inverse semigroup

Proceedings of the Edinburgh Mathematical Society, nº50 (2007), p.551-561

Towards a unified European electricity market: The contribution of data-mining to support realistic simulation studies

Worldwide electricity markets have been evolving into regional and even continental scales. The aim at an efficient use of renewable based generation in places where it exceeds the local needs is one of the main reasons. A reference case of this evolution is the European Electricity Market, where countries are connected, and several regional markets were created, each one grouping several countries, and supporting transactions of huge amounts of electrical energy. The continuous transformations electricity markets have been experiencing over the years create the need to use simulation platforms to support operators, regulators, and involved players for understanding and dealing with this complex environment. This paper focuses on demonstrating the advantage that real electricity markets data has for the creation of realistic simulation scenarios, which allow the study of the impacts and implications that electricity markets transformations will bring to the participant countries. A case study using MASCEM (Multi-Agent System for Competitive Electricity Markets) is presented, with a scenario based on real data, simulating the European Electricity Market environment, and comparing its performance when using several different market mechanisms.

Realistic Multi-Agent Simulation of Competitive Electricity Markets

The dynamism and ongoing changes that the electricity markets sector is constantly suffering, enhanced by the huge increase in competitiveness, create the need of using simulation platforms to support operators, regulators, and the involved players in understanding and dealing with this complex environment. This paper presents an enhanced electricity market simulator, based on multi-agent technology, which provides an advanced simulation framework for the study of real electricity markets operation, and the interactions between the involved players. MASCEM (Multi-Agent Simulator of Competitive Electricity Markets) uses real data for the creation of realistic simulation scenarios, which allow the study of the impacts and implications that electricity markets transformations bring to different countries. Also, the development of an upper-ontology to support the communication between participating agents, provides the means for the integration of this simulator with other frameworks, such as MAN-REM (Multi-Agent Negotiation and Risk Management in Electricity Markets). A case study using the enhanced simulation platform that results from the integration of several systems and different tools is presented, with a scenario based on real data, simulating the MIBEL electricity market environment, and comparing the simulation performance with the real electricity market results.

On the iteration of Katsuno and Mendelzon update

In this dissertation we present a model for iteration of Katsuno and Mendelzon’s Update, inspired in the developments for iteration in AGM belief revision. We adapt Darwiche and Pearls’ postulates of iterated belief revision to update (as well as the independence postulate proposed in [BM06, JT07]) and show two families of such operators, based in natural [Bou96] and lexicographic revision [Nay94a, NPP03]. In all cases, we provide a possible worlds semantics of the models.

Characterization of the portuguese SSS into the Europe: a contribution

Nowadays, Short Sea Shipping (SSS) is an essential part in European multi-modal transport system, representing approximately thirty-seven per cent of intra-Community transactions in tonnes per kilometre (tkm). Since 2001, the European Shortsea Network (ESN) in partnership with the short-sea Promotion Centres (SPC) of each Member State of the European Union (EU) have managed to make significant progress in the promotion and development of this mode of transport. This paper aims to assess and analyse the SSS of containerised goods in Portugal and its articulation with other EU routes and also other transport modes. The current SSS infrastructure, how the sector is organized, as well as the future perspectives for the sector are also analysed for the case of Portugal. The analyses are based on a survey that was carried out on the logistics operators, navigation agents, freight forwarders, and the leading imports and exports manufacturers in Portugal.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.