Topological complexity and related invariants
Yuli B. Rudyak
Abstract:
Early this century, Michael Farber introduced and developed the notion of topological complexity, applying it to robotics (in greater detail, to robot motion planning). This is a numerical invariant of Lusternik–Schnirelmann type. We survey recent progress in the area.
Autenticación mediante conocimiento nulo en base a ecuaciones cuadráticas
José Luis Juan Herrera, García Guillermo Morales Luna, Feliú Sagols Troncoso
Resumen:
Presentamos una alternativa a los métodos actuales de autenticación con conocimiento nulo, basada ésta en el método aceite-vinagre no-equilibrado (Unbalanced Oil and Vinegar ). Con esto, se tiene un método alterno a los actuales, basados en diversos problemas computacionalmente difíciles.
A bound on the size of irreducible triangulations
Gloria Aguilar Cruz, Francisco Javier Zaragoza Martínez
Abstract:
Let S be a closed surface with Euler genus γ(S). An irreducible triangulation of S is a simple graph G without contractible edges embedded on S so that each face is a triangle and any two faces share at most one edge. Nakamoto and Ota were the first to give a linear upper bound for the number n of vertices of G in terms of γ(S). This bound was recently improved for orientable surfaces. By extending Nakamoto and Ota’s method we improve on these bounds by showing that n ≤ 106.5γ(S)−33 for any closed surface S.