67 documents found, page 1 of 7
Symbolic and numerical computation of coquaternionic functions in mathematica
Miranda, Fernando; Falcão, M. I.; Severino, RicardoThis paper presents an updated version of the Mathematica package Coquaternions, originally introduced by the authors in 2019. The new release extends the package's functionality by incorporating the definition and manipulation of elementary functions within the algebra of coquaternions. In addition to their implementation in Mathematica, several properties of these functions are formally introduced and proved.
The Mandelbrot set for a coquaternionic family of quadratics
Falcão, M. I.; Miranda, Fernando; Severino, RicardoThe Mandelbrot set stands as one of the most fascinating and visually striking mathematical objects ever discovered, representing a fundamental milestone in dynamical systems theory and fractal geometry. Extending this set into the coquaternionic domain introduces significant mathematical challenges and unveils structures of remarkable complexity. In this work, we investigate the generalization of the Mandelbro...
Girl, what do you want to become when you grow up? Audio-visual creation at school
Miranda, Fernando; Acerbi, GracielaGirl, what do you want to become when you grow up? Filmmaking at school. When does the possibility of the dream of filmmaking appear in women's horizons? If contemporary school is regarded as that time and place suitable for inviting new generations to get involved in the world, it is fair to wonder: what place is given to cinema at school for the new generation of women to imagine themselves being part of the ...
A pegada do “Ouro Líquido” Mediterrânico nos ecossistemas aquáticos: estudo dos...
Costa, Silvana Teixeira; Miranda, Fernando; Teixeira, Fernando; Zidouh, Aya; Fernandes, Conceição; Dias, Luís; Hernandez, Zulimar; Teixeira, AmílcarAtualmente, 80.000 t de bagaço de azeitona são processadas numa única unidade extratora localizada na região de Trás-os-Montes e Alto Douro, produzindo águas-ruças (OMWW) que são altamente fitotóxicas. A falta de medidas de gestão para este resíduo em específico, levanta a importância de compreender como este pode impactar a integridade ecológica dos ecossistemas aquáticos. Assim, oito locais espalhados pelo Ri...
The zeros of quadratic coquaternionic polynomials revisited
Falcão, M. I.; Miranda, Fernando; Severino, RicardoIn this paper, we address the problem of solving the quadratic equation x<sup>2</sup>+bx+c=0, where b and c are elements of the algebra of coquaternions. The nature of this algebra leads, as expected, to results very different from the ones obtained in the classical complex case, making the root-finding problem much more demanding. In this paper we derive straightforward conditions to characterize the number an...
On Appell-Vietoris polynomials
Cação, Isabel; Falcão, M. I.; Malonek, Helmuth R.; Miranda, Fernando; Tomaz, GraçaIn this paper we introduce a polynomial sequence (Vn(x))<inf>n≥0</inf> involving the Vietoris’ number sequence and satisfying the Appell property. We derive several equivalent representations of V<inf>n</inf>(x) and we deduce important relations closely related to the aforementioned Appell property. Finally, we address the problem of the zeros distribution of V<inf>n</inf>(x) and conclude that, when n is even, ...
The silent extinction of freshwater mussels in Portugal
Lopes-Lima, Manuel; Reis, Joaquim; Alvarez, Maria G.; Anastácio, Pedro M.; Banha, Filipe; Beja, Pedro; Castro, Paulo; Gama, Mafalda; Gil, Maria G.Freshwater mussels are one of the most threatened animal groups in the world. In the European Union, threatened and protected mussel species are not adequately monitored, while species considered to be common and widespread receive even less attention. This is particularly worrying in the Mediterranean region, where species endemism is high and freshwater habitats are severely affected by water scarcity. In the...
The stability of complex dynamics for two families of coquaternionic quadratic ...
Falcão, M. I.; Miranda, Fernando; Severino, Ricardo; Soares, M. J.In this work, we begin by demonstrating that attractors, both periodic and aperiodic, of the one-parameter family of complex quadratic maps x2+ c, where c is a complex number, maintain their stability when we transition from the complex plane C to the coquaternions Hcoq as the map’s phase space. Next, we investigate the same question for a different family of quadratic maps, x2+ bx, and find that this is not th...
Remarks on the Vietoris sequence and corresponding convolution formulas
Cação, Isabel; Falcão, M. I.; Malonek, Helmuth R.; Miranda, Fernando; Tomaz, GraçaIn this paper we consider the so-called Vietoris sequence, a sequence of rational numbers of the form ck=12k(k⌊k2⌋), k= 0, 1, ⋯. This sequence plays an important role in many applications and has received a lot of attention over the years. In this work we present the main properties of the Vietoris sequence, having in mind its role in the context of hypercomplex function theory. Properties and patterns of the c...
A Two-step Quaternionic Root-finding Method
Falcão, M. I.; Miranda, Fernando; Severino, Ricardo; Soares, M. J.In this paper we present a new method for determining simultaneously all the simple roots of a quaternionic polynomial. The proposed algorithm is a two-step iterative Weierstrass-like method and has cubic order of convergence. We also illustrate a variation of the method which combines the new scheme with a recently proposed deflation procedure for the case of polynomials with spherical roots.