Let w be a morphic word over a finite alphabet Σ, and let ∆ be a subalphabet. We study the behavior of maximal blocks of ∆ letters in w, and prove the following: let (ik, jk) denote the starting and ending positions, respectively, of the k’th maximal ∆-block in w. Then lim supk→∞(jk/ik) is algebraic if w is morphic, and rational if w is automatic. As a results, we show that the same holds if (i...

We prove, using a theorem of W. Schmidt, that if the sequence of partial quotients of the continued fraction expansion of a positive irrational real number takes only two values, and begins with arbitrary long blocks which are ''almost squares,'' then this number is either quadratic or transcendental. This result applies in particular to real numbers whose partial quotients form a Sturmian (or ...

For a locally quasi-convex (lqc) abelian group G, we describe all compatible lqc topologies on G and apply this result to the Mackey problem for groups. We characterize groups which are or admit topology provide characterization of two whose product is Mackey. convex spaces

Considering a frame L, we introduce the notions of stratified L-semi-topological neighborhood group, stratified L-quasi-topological neighborhood group, and stratified L-quasi-bi-topological neighborhood group. In so doing, we look at the notion of stratified L-right (left) semi-topological neighborhood group, provide some basic facts, and present a construction of a stratified L-right semi-topo...

Automatic sequences have many properties that other (in particular, non-uniformly morphic sequences) do not necessarily share. In this paper we survey a number of different methods can be used to prove given sequence is automatic. When the take their values in finite field Fq, also permits proving associated formal power series are transcendental over Fq(X).

We study the existence of quasi-representations of discrete groups G into unitary groups U(n) that induce prescribed partial maps K0(C ∗(G)) → Z on the K-theory of the group C*-algebra of G. We give conditions for a discrete group G under which the K-theory group of the classifying space BG consists entirely of almost flat classes.

A group signature scheme allows any group member to sign on behalf of the group in an anonymous and unlinkable fashion. In the event of a dispute, a designated trusted entity can reveal the identity of the signer. Group signatures are claimed to have many useful applications such as voting and electronic cash. A number of group signature schemes have been proposed to-date. However, in order for...

Let M be a closed connected manifold and let D be an elliptic operator on M . Let G be a discrete countable group and let M̃ → M be a principal G-bundle. Connes and Moscovici showed that this data defines an analytic index ind`1(G)(D) ∈ K0(`(G)). If B is a unital tracial C*-algebra, we give a formula for the trace of the image of ind`1(G)(D) in K0(B) under the map induced by a quasi-representati...

Two finite words u, v are 2-binomially equivalent if, for all words x of length at most 2, the number of occurrences of x as a (scattered) subword of u is equal to the number of occurrences of x in v. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word uv where u and v are 2-binomially equivalent. In this paper, considering pure morphic words, we prove th...