Semihyperbolic transcendental semigroups

Semihyperbolic Transcendental Semigroups

This paper deals with semihyperbolic semigroups which are generated by entire (possibly transcendental) functions. In particular, a criterion is given assuring that a given entire semigroup is semihyperbolic. Note that a semihyperbolic semigroup G admit holomorphic scaling, that is to say, the branches of local inverses of functions f 2 G are of bounded degree and that the preimages shrink to z...

Quasi-flats in Semihyperbolic Groups

We prove that the Cayley graph of a group which is semihyperbolic but not hyperbolic contains a subset quasi-isometric to R2.

Transcendental Elitism

On Transcendental Numbers

Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and proved in Section 4. Also, in relationship with these topics, we study the exponential function axioms related to the Yang-Baxter equation.

Algebraic and Transcendental Numbers

To begin with, recall that a complex number α is said to be a root of a polynomial P (X) if P (α) = 0. A complex number α is said to be algebraic if there is a nonzero polynomial P (X), with integer coefficients, of which α is a root. The set of algebraic numbers is denoted by Q̄. A complex number α which is not algebraic is said to be transcendental. The following numbers are obviously algebrai...