Difficulties in the passage from secondary to tertiary education.
A general form of the Vitali theorem
On the derivation and covering properties of a differentiation basis
An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases
A covering lemma with applications to differentiability of measures and singular integral operators
Escuchando a Luis A. Santaló.
The envelope of the Wallace-Simpson lines of a triangle. A simple proof of the Steiner problem on the deltoid.
A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious.
Un proyecto para la detección y el estímulo del talento precoz en matemáticas en la Comunidad de Madrid.
From graphs to tensegrity structures: geometric and symbolic approaches.
A form-finding problem for tensegrity structures is studied; given an abstract graph, we show an algorithm to provide a necessary condition for it to be the underlying graph of a tensegrity in Rd (typically d=2,3) with vertices in general position. Furthermore, for a certain class of graphs our algorithm allows to obtain necessary and sufficient conditions on the relative position of the vertices in order to underlie a tensegrity, for what we propose both a geometric and a symbolic approach.
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