Green functions on product networks

We aim here at determining the Green function for general Schrödinger operators on product networks. The first step consists in expressing Schrödinger operators on a product network as sum of appropriate Schrödinger operators on each factor network. Hence, we apply the philosophy of the separation of variables method in PDE, to express the Green function for the Schrödinger operator on a product network using Green functions on one of the factors and the eigenvalues and eigenfunctions of some Schrödinger operator on the other factor network. We emphasize that our method only needs the knowledge of eigenvalues and eigenfunctions of one of the factors, whereas other previous works need the spectral information of both factors. We apply our results to compute the Green function of Pm×Sh , where Pm is a Path with m vertices and Sh is a Star network with h+1 vertices.Peer ReviewedPostprint (author's final draft

Computing the Green function for a Dirichlet problem on spider networks

Postprint (published version

Discrete trace function and Poincaré inequality for the study of some linear systems

Postprint (published version

Green functions for boundary value problems on product networks

Postprint (published version

Group inverses of matrices of simple symmetric directed graphs

A new class of simple symmetric digraphs called $\mathbb{D}$ is defined and studied here. Any digraph in $\mathbb{D}$ has the property that each non-pendant is adjacent to at least one pendant vertex. A graph theoretical description for the entries of the group inverse of a real square matrix $A$ with any digraph belonging to this class is given. We classify all the real square matrix $A$ such that the digraphs associated with $A$ and $A^{\#}$ both are in $\mathbb{D}$, that is the digraph related to $A$ is either a corona or a star digraph.Comment: 16 pages, 2 figure

Algoritmos numéricos de reconstrucción de conductancias

La idea de este trabajo surge de la investigación que están llevando a cabo mis tutores del departamento de matemáticas de la EEBE. Es una investigación que estudia los problemas inversos ydeduce algoritmos para la recuperación de las características interiores de un elemento a partirde aplicarle una entrada y obtener la respuesta . Este trabajo trata de implementar algunos de éstos algoritmos en Matlab y demostrar su vera-cidad además de visualizar el potencial que pueden llegar a tener, ya que se pueden aplicar enmúltiples ámbitos. Este proyecto se puede ampliar en múltiples áreas ya que es el principiode una potente herramienta para el uso industrial, médico, astronómico,... En esta memoria serecoge los fundamentos teóricos del trabajo como los algoritmos implementados. Estos algo-ritmos proceden de los artículos citados en las referencias. Para finalizar, se ofrecen una seriede conclusiones sobre el desarrollo de este trabajo y el cumplimiento de los objetivos marcados

Green functions on product networks

We aim here at determining the Green function for general Schrödinger operators on product networks. The first step consists in expressing Schrödinger operators on a product network as sum of appropriate Schrödinger operators on each factor network. Hence, we apply the philosophy of the separation of variables method in PDE, to express the Green function for the Schrödinger operator on a product network using Green functions on one of the factors and the eigenvalues and eigenfunctions of some Schrödinger operator on the other factor network. We emphasize that our method only needs the knowledge of eigenvalues and eigenfunctions of one of the factors, whereas other previous works need the spectral information of both factors. We apply our results to compute the Green function of Pm×Sh , where Pm is a Path with m vertices and Sh is a Star network with h+1 vertices.Peer Reviewe