We define a twisted $L^2$-torsion on the character variety of 3-manifold $M$ and study some its properties. In case where is hyperbolic finite volume, we prove that real analytic function neighborhood any lift holonomy representation.

The paper presents a study of local search heuristics in general and variable neighborhood search in particular for the resolution of an assignment problem studied in the practical work of universities. Here, students have to be assigned to scientific topics which are proposed and supported by members of staff. The problem involves the optimization under given preferences of students which may ...

In this paper it is shown that two-dimensional cellular automata with Von Neumann neighborhoods are not suitable for cryptographic purposes. This result is obtained after analyzing the most important cryptographic properties of boolean functions defining their local transition rules 2000 Mathematics Subject Classifications: 68Q80, 94A60, 94C10

We analyze the dynamics of a two-dimensional cellular automaton, 2D Minority, for the Moore neighborhood (eight neighbors per cell) under fully asynchronous dynamics (where only one random cell updates at each time step). Even if 2D Minority seems a simple rule, from the experience of Ising models and Hopfield nets, it is known that models with negative feedback are hard to study. This automato...

Let f(x, y) be any smooth real-valued function with f(0, 0) = 0. For a sufficiently small neighborhood U of the origin, we study the number

We establish the following fixed point theorem. Let P be a non-empty polytope in the n-dimensional Euclidean space and let f be a function from P to P satisfying that for every x in P for which f(x) 6= x there exists a neighborhood of x in P such that for any y and z in this neighborhood the inner product of f(y)− y and f(z)− z is non-negative. Then there exists x∗ ∈ P satisfying f(x∗) = x∗, i....