In this talk I will discuss necessary and sufficient conditions on a nonsingular matrix A, such that for any initial vector r0, an orthogonal basis of the Krylov subspaces Kn(A, r0) is generated by a short recurrence. Orthogonality here is meant with respect to some unspecified positive definite inner product. This question is closely related to the question of existence of optimal Krylov subsp...

We establish the following result related to Erdős’s problem on distinct distances. Let V be an n-element planar point set such that any p members of V determine at least ( p 2 ) − p+ 6 distinct distances. Then V determines at least n 8 7 −o(1) distinct distances, as n tends to infinity.

Human intelligence has evolved along with the use of more and more sophisticated tools, allowing Homo Faber (from Homo Habilis to Homo Sapiens Sapiens) to cope with environment changes, as well as to adapt the environment to his needs. Analogously, in this seminal paper we introduce the notion of Agens Faber, conveying the idea that agent intelligence should not be considered as separated by th...

Article history: Received 7 June 2012 Available online 24 February 2013

When revisiting the Faber-Krahn inequality for the principal pLaplacian eigenvalue of a bounded open set in Rn with smooth boundary, we simply rename it as the p-Faber-Krahn inequality and interestingly find that this inequality may be improved but also characterized through Maz’ya’s capacity method, the Euclidean volume, the Sobolev type inequality and MoserTrudinger’s inequality. 1. The p-Fab...

The Faber-Krahn theorem states that among all bounded domains with the same volume in Rn (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been shown that a similar result holds for (semi)regular trees. In this article we show that such a theorem also hold for other classes of (not necessarily non-regular) trees. However, for these new resu...

Consider a Doint set C in the complex plane whose complement K is connected and regular (i .e. K possesses a Green ' s function with pole at infini ty). Let denote the transfini te diameter of C . Recall that d m = l /U ' C®)! where <{>(z) irans >C onto tl ê exterior of the uni t circle. Equivalent ly , d^ = Lin | |T^(z) | Ij.] where | |g(z) | | c = max] <*(z) | ,zeC and T..(z) is t^e Tchebyche...

A new tool to assist in the use of the Faber Birren Collection of Books on Color was introduced in August 2005. A Web site with a personality to match the collection and an image database to facilitate virtual browsing increase accessibility for researchers at Yale and around the world. The Library Gazette published two bibliographies of the collection written by Robert L. Herbert in 1974 and 1...

Recensión de: de Prada García, Aurelio. El proceso Sócrates: del ‘nosotros’ al ‘yo’. Contra el prejuicio individualista no percibido. Madrid: Ápeiron, Faber &amp; Sapiens, 2022.