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Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article explores the mathematical inquiry into the structure of (simplicial) polyhedra, tracing its historical roots and delving into contemporary algebraic formulations such as the h-vector, aiming to characterize the faces of d-dimensional polytopes. It states that by leveraging tools like the h-vector and examining properties of simplicial complexes, the article seeks to answer fundamental questions about the combinatorial and topological aspects of polyhedra.

An interview with Xavier Fernández-Real Girona, a mathematician is presented. He discussed his research focus on free boundary problems, the challenges they present, and his aspirations for the future. He highlighted his trajectory, spanning from a dual Mathematics and Physics degree to doctoral investigations under Alessio Figalli's mentorship.

The article discusses concept of a prime number is no longer the same as before. It mentions about considering only the positive integers; and the consideration or not of 1 as a prime number. It mentions the connection of the theory of premises with mathematics constructive; and highlighting its important algebraic facet.

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article offers information on the mathematics and computing including calculation of the number of real roots, geometry and informal description of the concepts, problems and methods. Topics include geometric theorems, incorporation of computational algebra techniques and algebraic geometry theorems.

Las pistas cubiertas que se usan en la temporada invernal de atletismo tienen una peculiaridad, y es que su parte curva está peraltada. Por ello, este artículo fija su atención en la forma que tienen dichas pistas, compuestas por rectas, arcos de circunferencia y pequeños tramos de transición que sirven para suavizar la curvatura. Es ahí donde se utiliza la clotoide, una curva que permite hacer transiciones graduales entre una recta y una circunferencia. [ABSTRACT FROM AUTHOR]

The article provides information on the elections to board of governments in mathematical associations, RSME including Antonio Ledesma Lopez, Irene Paniello Alastruey and Javier Martinez Torres. Topics include long term research in mathematics and special study of cyclic behavior and invariant subspaces of operators.