Articles
4.
Matrix Toda and Volterra lattices
Moreno, Ana Foulquié and Branquinho, Amílcar and GarcíaArdila, 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.
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Peer Reviewed
3.
Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the RiemannLiouville 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 RiemannLiouville 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 MittagLeffler function.
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2.
CGOFaddeev 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
closeformed solutions for the EIT problem was not able to overpass the case
of oncetime 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.
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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 wellknown 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.
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doi

Peer Reviewed