2 citations · 3 across the 4 of their papers we have counts for
6 papers
Contact detection between an ellipsoid and a combination of quadrics
Miguel Brozos-Vázquez, M. J. Pereira-Sáez, A. B. Rodríguez-Raposo +2
We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condit…
Homotopic distance and generalized motion planning
E. Macías-Virgós, D. Mosquera-Lois, M. J. Pereira-Sáez
We prove that the homotopic distance between two maps defined on a manifold is bounded above by the sum of their subspace distances on the critical submanifol of any Morse-Bott fun…
Relative singular value decomposition and applications to LS-category
E. Macías-Virgós, M. J. Pereira-Sáez, Daniel Tanré
Let be the symplectic group of quaternionic -matrices. For any , an element of can be decomposed in $A= \begin{bmatrix} α&T\cr β&P \…
Classification of the relative positions between an ellipsoid and an elliptic paraboloid
Miguel Brozos-Vázquez, María José Pereira-Sáez, María José Souto-Salorio +1
We classify all the relative positions between an ellipsoid and an elliptic paraboloid when the ellipsoid is small in comparison with the paraboloid ({\it small} meaning that the e…
A topological approach to left eigenvalues of quaternionic matrices
E. Macías-Virgós, M. J. Pereira-Sáez
It is known that a quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher…
Trace map, Cayley transform and LS category of Lie groups
A. Gómez-Tato, E. Macías-Virgós, M. J. Pereira-Sáez
The aim of this paper is to use the so-called Cayley transform to compute the LS category of Lie groups and homogeneous spaces by giving explicit categorical open coverings. When a…