Encontrados 144 documentos, a visualizar página 1 de 15
Local fractional variational iteration and decomposition methods for wave equat...
Baleanu, Dumitru; Machado, J. A. Tenreiro; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-JunWe perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.
Detection of quasi-periodic processes in complex systems: how do we quantitativ...
Nigmatullin, Raoul R.; Khamzin, Airat A.; Machado, J. A. TenreiroIt has been shown that in reality at least two general scenarios of data structuring are possible: (a) a self-similar (SS) scenario when the measured data form an SS structure and (b) a quasi-periodic (QP) scenario when the repeated (strongly correlated) data form random sequences that are almost periodic with respect to each other. In the second case it becomes possible to describe their behavior and express a...
Analysis of temperature time-series: embedding dynamics into the MDS method
Lopes, António M.; Machado, J. A. TenreiroGlobal warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic and health aspects of the human life. Surface temperature time-series characterise Earth as a slow dynamics spatiotemporal system, evidencing long memory behaviour, typical of fractional order systems. Such phenomena are difficult to model and analyse, demanding for alterna...
On development of fractional calculus during the last fifty years
Machado, J. A. Tenreiro; Galhano, Alexandra; Trujillo, Juan J.Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.
Probability and statistics: selected problems
Machado, J. A. Tenreiro; Pinto, Carla M. A.Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for prop...
Linear algebra: selected problems
Pinto, Carla M. A.; Machado, J. A. TenreiroLinear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to refere...
Analysis and visualization of seismic data using mutual information
Machado, J. A. Tenreiro; Lopes, António M.Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided int...
Entropy diversity in multi-objective particle swarm optimization
Pires, E. J. Solteiro; Machado, J. A. Tenreiro; Oliveira, P. B. MouraMulti-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the ...
On local fractional continuous wavelet transform
Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, Hari; Machado, J. A. TenreiroWe introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.
Fractional dynamics and MDS visualization of earthquake phenomena
Lopes, António M.; Machado, J. A. Tenreiro; Pinto, Carla M. A.; Galhano, AlexandraThis paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects t...
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