We study whether the entropy (or growth rate) of minimal forbidden patterns of symbolic dynamical shifts of dimension 2 or more, is a conjugacy invariant. We prove that the entropy of minimal forbidden patterns is a conjugacy invariant for uniformly semi-strongly irreducible shifts. We prove a weaker invariant in the general case.

Introduction A special monoid is a monoid presented by generators and defining relations of the form w = e, where w is a non-empty word on generators and e is the empty word. Groups are special monoids. But there exist special monoids that are not groups. Special monoids have been extensively studied by Adjanfl] and Makanin[7] (see also [2]). The present paper is a sequel to [11]. In [11], we s...

In this paper we suggest a new conjugate gradient algorithm that for all both the descent and the conjugacy conditions are guaranteed. The search direction is selected as a linear combination of 0 k ≥ 1 k g + − and where , k s 1 1 ( ) k k g f x + + = ∇ , and the coefficients in this linear combination are selected in such a way that both the descent and the conjugacy condition are satisfied at ...

We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...

— Let r > 1 be a real. In this paper, we study piecewise class P Cr circle homeomorphisms with irrational rotation numbers. We give characterizations for such homeomorphisms that are piecewise Cr conjugate to Cr diffeomorphisms. As a consequence, we obtain a criterion of piecewise Cr conjugacy to diophantine rotations. This characterization extends those obtained by Liousse for the PL circle ho...