Let G be a compact connected and simply connected Lie group, and Σ be a compact topological Riemann surface with a point p marked on it. One can associate to this data the moduli space of flat G connections on the punctured Riemann surface Σ denoted by MG = M[Σp]. This space decomposes into a union MG = ∪σM G(σ) of moduli spaces of flat connections with the holonomy around the point p fixed in ...

The problem of the commutative equivalence context-free and regular languages is studied. Conditions ensuring that a language exponential growth commutatively equivalent with are investigated.

A sufficient condition for the convergence of a generalized formal power series solution to an algebraic q-difference equation is provided. The main result leans on geometric property related semi-group (complex) exponents such series. This corresponds situation in which small divisors phenomenon does not arise. Some examples illustrating cases where obtained can or cannot be applied are also d...