A transcendental dynamical degree

Residual Transcendental Extensions of A

Let K be a field and v a valuation on K. We discuss some properties of extensions w of v to the field K(X1, . . . , Xn) of rational functions in n variables over K, for which the residue field of w has transcendence degree n over the residue field of v. 2000 Mathematics Subject Classification: 12J20, 12F20. 1.Introduction LetK be a field and v a valuation onK. Residual transcendental extensions...

Transcendental Elitism

Admissible Vectors of a Covariant Representation of a Dynamical System

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

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...