Volume 20 (2016) No. 1
Volume 20 (2016) No. 1 
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
Abstract:
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 $\gamma(S)$. 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 $\gamma(S)$. This bound was recently improved for orientable surfaces. By extending Nakamoto and Ota’s method we improve on these bounds by showing that $n \leq 106.5\gamma(S)−33$ for any closed surface $S$.