AproductADF1 : : : FN of invertible block-diagonalmatrices will be bandedwith a banded inverse. We establish this factorization with the numberN controlled by the bandwidthsw and not by the matrix size n:When A is an orthogonal matrix, or a permutation, or banded plus finite rank, the factors Fi have w D 1 and generate that corresponding group. In the case of infinite matrices, conjectures rema...

We study iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.

In cryptosystem theory, it is well-known that a logical mapping that returns the same value that was used as its argument can be inverted with a zero failure probability in linear time. In this paper, however, I show that such a mapping, while trivially assigning a logical state to itself, comes up against an impassable entropy wall such that its computational path is undone inside the threshol...

In this paper we introduce the notion of invertible dynamic system, we indicate a very general method to determine the inverse of such a system and we give evidence of the numerous applications of the subclass of dynamic systems defined by this notion. Key-Words: Invertible dynamic system, the inverse of a dynamic system, Lagrange interpolation polynomial.

Our main goal is to study the freeness of Schützenberger groups defined by primitive substitutions. findings include a simple test for these groups, which applied exhibit invertible substitution with corresponding non-free group. This constitutes counterexample result Almeida dating back 2005. We also give some early results concerning relative question remains largely unexplored.

We give a general approach to N -periodic sequences over a finite field Fq constructed via a subgroup D of the group of invertible elements modulo N . Well known examples are Legendre sequences or the two-prime generator. For some generalizations of sequences considered in the literature and for some new examples of sequence constructions we determine the linear complexity.

The article describes Euler’s group Γ (z), formed by the invertible elements of the ring of the residues of the integer complex numbers modulo numbers divisible by z. The answers are proved for the primary cases z = (1+ i)m and z = (p+ iq)m, p2 +q2 = 4k+3 being prime.

Throughout this lecture, we let k denote an algebraically closed field, a prime number which is invertible in k. Let X be an algebraic curve over k and G a smooth affine group scheme over X whose generic fiber is semisimple and simply connected. Our goal over the next few lectures is to prove the following result:

First and second fundamental theorems are given for polynomial invariants of an infinite class of pseudo-reflection groups (including the Weyl groups of type Bn), under the assumption that the order of the group is invertible in the base field. MSC: 13A50, 14L30, 20G05

In these notes, we present a number of interesting and diverse applications of the Spectral Theorem for Normal Operators. These include a Spectral Mapping Theorem for Normals Operators, a Spectral Characterization of Algebraic Operators, von Neumann’s Mean Ergodic Theorem, Pathconnectivity of the Group of Invertible Operators, and some Polynomial Approximation Results for Operators.