Publications 2020

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4.  Matrix Toda and Volterra lattices

Moreno, Ana Foulquié and Branquinho, Amílcar and García-Ardila, Juan C.

Applied Mathematics and Computation

Elsevier

We consider matrix Toda and Volterra lattice equations and their relation with matrix biorthogonal polynomials. From that relation, we give a method for constructing a new solution of these systems from another given one. An illustrative example is presented.

ria.ua.pt | doi | Peer Reviewed

3.  Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense

Teodoro, A. Di and Ferreira, M. and Vieira, N.

Advances in Applied Clifford Algebras

Springer

In this paper, we study the fundamental solution for natural powers of the $n$-parameter fractional Laplace and Dirac operators defined via Riemann-Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace $Delta_{a^+}^alpha$ and Dirac $D_{a^+}^alpha$ operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag-Leffler function.

ria.ua.pt | doi | Peer Reviewed

2.  CGO-Faddeev approach for complex conductivities with regular jumps in two dimensions

Pombo, Ivan

Inverse Problems

IOP Publishing

Researchers familiar with the state of the art are aware that the development of close-formed solutions for the EIT problem was not able to overpass the case of once-time differentiable conductivities beside the well known particular Astala–Päivärinta result for zero frequency. In this paper, we introduce some new techniques for the inverse conductivity problem combined with a transmission problem and achieve a reconstruction result based on an adaptation of the scattering data. The idea for these techniques, in particular the concept of admissible points is coming from Lakshtanov and Vainberg. Moreover, we are going to establish the necessary groundwork for working with admissible points which will be required in any further research in this direction.

ria.ua.pt | doi | Peer Reviewed

1.  Orthogonal gyrodecompositions of real inner product gyrogroups

Ferreira, Milton and Suksumran, Teerapong

Symmetry

MDPI

In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, Möbius, Proper Velocity, and Chen’s gyrogroups. This leads to the study of left (right) coset partition of a real inner product gyrogroup induced from a subgyrogroup that is a finite dimensional subspace. As a result, we obtain gyroprojectors onto the subgyrogroup and its orthogonal complement. We construct also quotient spaces and prove an associated isomorphism theorem. The left (right) cosets are characterized using gyrolines (cogyrolines) together with automorphisms of the subgyrogroup. With the algebraic structure of the decompositions, we study fiber bundles and sections inherited by the gyroprojectors. Finally, the general theory is exemplified for the aforementioned gyrogroups.

ria.ua.pt | doi | Peer Reviewed
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