Non-commutative entropy computations for continuous fields and cross-products

Non-commutative Entropy Computations for continuous fields and cross-products

We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable group. The second is about continuous fields of C∗-algebras and C(X)automorphisms and shows that one need more than the knowledge of ent...

Non-commutative Polynomial Computations

In [6] Mora described an algorithm which, if it terminates, returns a noncommutative Gröbner basis. Here we follow that paper to prove the correctness of the algorithm as implemented by Dié Gijsbers and the author in GAP, cf. [1]. The algorithm is the core algorithm of the GAP package GBNP for computing with non-commutative polynomials. Earlier versions of this section were written with the hel...

A cross entropy algorithm for continuous covering location problem

Covering problem tries to locate the least number of facilities and each demand has at least one facility located within a specific distance.This paper considers a cross entropy algorithm for solving the mixed integer nonlinear programming (MINLP) for covering location model.The model is solved to determine the best covering value.Also, this paper proposes aCross Entropy (CE) algorithm consider...

Dimension Computations in Non-Commutative Associative Algebras

Entropy operator for continuous dynamical systems of finite topological entropy

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.