On irrationality measure functions for several real numbers

An Irrationality Measure for Regular Paperfolding Numbers

Let F(z) = ∑ n>1 fnz n be the generating series of the regular paperfolding sequence. For a real number α the irrationality exponent μ(α), of α, is defined as the supremum of the set of real numbers μ such that the inequality |α − p/q| < q−μ has infinitely many solutions (p, q) ∈ Z × N. In this paper, using a method introduced by Bugeaud, we prove that μ(F(1/b)) 6 275331112987 137522851840 = 2....

Irrationality measures for some automatic real numbers

This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive upper bounds for the irrationality exponent of famous automatic real numbers associated with the Thue–Morse, Rudin–Shapiro, paperfolding and Baum–Sweet sequences. These upper bounds arise from the construction o...

Belief functions on real numbers

We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbersR = [−∞,∞], under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality functions become integrals of these densities and pignistic probabilities become pignistic densities. The m...

Complexity theory on real numbers and functions

Effective Irrationality Measures for Certain Algebraic Numbers

A result of Chudnovsky concerning rational approximation to certain algebraic numbers is reworked to provide a quantitative result in which all constants are explicitly given. More particularly, Padé approximants to the function (1 jc)1/3 are employed to show, for certain integers a and b, that |(a/fc) p/q\> cq~* when q > 0. Here, c and k are given as functions of a and b only. In 1964 Baker [1...