L'activitat investigadora del grup MAPTHE s'emmarca en el context de la Matemàtica Aplicada, concretament en aplicacions de la Teoria del Potencial. Les tècniques emprades pel grup provenen essencialment dels àmbits de la Teoria Discreta del Potencial i de l'Àlgebra Lineal.
L'interès fonamental d'aquest grup és el disseny i la implementació d'algorismes de resolució del problema invers en xarxes estructurades, que es basa en determinar l'estructura interna de la xarxa a partir de dades a la seva frontera. Aquests problemes discrets tenen interès por si sols però, a més representen l'aproximació discreta de problemes en l'àmbit continu que són d'interès tecnològic, com el de la tomografia d'impedància elèctrica o el de la prospecció geofísica.
Atès que la resistència efectiva és una de les eines utilitzades per a aquesta anàlisi, estudiem també problemes relatius a la robustesa de les xarxes fent servir paràmetres relacionats amb l’esmentada resistència efectiva.

### Recent Submissions

• #### The group inverse of circulant matrices depending on four parameters ﻿

(De Gruytr, 2021-10-27)
Article
Open Access
Explicit expressions for the coefficients of the group inverse of a circulant matrix depending on four complex parameters are analytically derived. The computation of the entries of the group inverse are now reduced to the ...
• #### A combinatorial expression for the group inverse of symmetric M-matrices ﻿

(De Gruytr, 2021-04-27)
Article
Open Access
By using combinatorial techniques, we obtain an extension of the matrix-tree theorem for general symmetric M-matrices with no restrictions, this means that we do not have to assume the diagonally domi nance hypothesis. We ...
• #### The group inverse of circulant matrices with few parameters ﻿

(2021)
Conference report
Open Access
The need of solving linear systems with circulant matrices occurs in many problems related to the periodicity of that problem. This class of system appears in many applications that range from numerical solution of partial ...
• #### Overdetermined partial resolvent kernel for generalized cylinders ﻿

(2021)
Conference lecture
Open Access
Overdetermined partial boundary value problems are those where no data are prescribed onpart of the boundary, whereas both the values of the function and of its normal derivative aregiven on another part of the boundary. ...
• #### The group inverse of circulant matrices with few parameters ﻿

(2021)
Conference lecture
Open Access
The need of solving linear systems with circulant matrices occursin many problems related to the periodicity of that problem. This class ofsystem appears in many applications that range from numerical solution ofpartial ...
• #### On spectra of symmetric Jacobi matrices ﻿

(2021)
Conference lecture
Open Access
A square symmetric matrix A is said bisymmetric if AS=SA, whereS is the matrix with ones along the secondary diagonal and zeroselsewhere. We denote by J(a,b) the real symmetric Jacobi matrixwith main ...
• #### Perturbing networks ﻿

(2012)
Conference lecture
Open Access
Semi-definite positive Schrödinger operators on finite connected networks are particular examples of a general class of self-adjoint operators called elliptic operators. Any elliptic operator defines an automorphism on the ...

Article
Open Access
• #### Eigenvalues with respect to a weight for general boundary value problems on networks ﻿

(Elsevier, 2021-04-01)
Article
Restricted access - publisher's policy
In this work we analyze self-adjoint boundary value problems on networks for Schrödinger operators, in which a part of the boundary with a Neumann condition is always considered. We first characterize when the energy is ...
• #### Drazin inverse of singular adjacency matrices of directed weighted cycles ﻿

(2020-09-25)
Article
Open Access
We present a necessary and sufficient condition for the singularity of circulant matrices associated with directed weighted cycles. This condition is simple and independent of the order of matrices from a complexity point ...
• #### Group inverse matrix of the normalized Laplacian on subdivision networks ﻿

(2020)
Article
Open Access
In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian ...
• #### The group inverse of some circulant matrices ﻿

(Elsevier, 2020-11-12)
Article
Restricted access - publisher's policy
In a previous work the authors presented the necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three real parameters and, moreover, we obtained a closed formula for their ...