On global location-domination in graphs

A dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the location-domination number $\lambda(G)$. An LD-set $S$ of a graph $G$ is global if it is an LD-set of both $G$ and its complement $\overline{G}$. The global location-domination number $\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$. In this work, we give some relations between locating-dominating sets and the location-domination number in a graph and its complement.Comment: 15 pages: 2 tables; 8 figures; 20 reference

Escoles i programes acadèmics a la Barcelona del segle XV. L'escola de mestre Ramon Llull i l'ensenyament de disciplines gramaticals i d'arts

During the XV century continued in Barcelona the union of education professionals to the formation of societys for private schools administration, different from the public ones (the cathedral and de city of Barcelona ones) and reading and writing education (primary education) and grammar and arts (trivium and quadrivium, secundary education). The academic programme of these schools and textbooks used were set up and regulated on these agreements or society contracts. On a documentary appendix are published 15 documents about the school called Escola de Mestre Ramon Llull and the academic programmes used in these schools

Sobre un seudónimo de fray Hortensio Félix Paravicino

En 1623, Juan Ruiz de Alarcón preparó por encargo el Elogio descriptivo, una relación de las fiestas de toros y cañas celebradas para honrar al príncipe de Gales. Esta serie de setenta y tres octavas inspiró las décimas satíricas de varios poetas, entre ellos Góngora, Quevedo y Lope de Vega. Una de las espinelas está firmada por fray Juan Centeno, del que no hay información en los repertorios bibliográficos. Tal nombre se corresponde con el seudónimo que empleó fray Hortensio Félix Paravicino en un certamen poético organizado en Toledo en 1616. Este artículo analiza la tendencia del trinitario a ocultarse bajo seudónimos y su renuencia a publicar sus poemas, así como las décimas contra Alarcón y su difusión, y propone que Paravicino es el autor del poema satírico atribuido a fray Juan Centeno.In 1623, Juan Ruiz de Alarcón prepared the Elogio descriptivo, a commissioned narration of the bullfight and cañas celebration in honour of the Prince of Wales. This series of seventy-three octavas inspired the satirical decimas by several poets, as Góngora, Quevedo and Lope de Vega. One of them is signed by fray Juan Centeno, of which there is no information in bibliographical catalogues. This name corresponds to the pseudonym used by fray Hortensio Félix Paravicino in a literary competition organised in Toledo in 1616. This article analyses the tendency of the trinitarian friar to hide himself behind pseudonyms and his reluctance to publish his poems, as well as the décimas against Alarcón and their transmission, and suggests that Paravicino is the author of the satirical poem attributed to fray Juan Centeno