arXiv subjects

Solomon Marcus

Publications and source records attributed to Solomon Marcus.

3 recordsLinked to original sources

arXiv2015

On transcendental numbers: new results and a little history

Attempting to create a general framework for studying new results on transcendental numbers, this paper begins with a survey on transcendental numbers and transcendence, it then presents several properties of the transcendental numbers $e$ and $\pi$, and then it gives the proofs of new inequalities and identities for transcendental numbers. Also, in relationship with these topics, we study some implications for the theory of the Yang-Baxter equations, and we propose some open problems.

math.HO↗

arXiv2006

Quasiperiodic infinite words : multi-scale case and dynamical properties

An infinite word x is said to be quasiperiodic if there exists a finite word q such that x is covered by occurrences of q (such a q is called a quasiperiod of x). Using the notion of derivation, we show that this definition is not sufficient to imply any symmetry in an infinite word. Therefore we introduce multi-scale quasiperiodic words, i.e. quasiperiodic words that admit an infinite number of quasiperiods. Such words are uniformly recurrent, this allows us to study the subshift they generate. We prove that multi-scale quasiperiodic subshifts are uniquely ergodic and have zero topological entropy as well as zero Kolmogorov complexity. Sturmian subshifts are shown to be multi-scale quasiperiodic.

math.DS↗

arXiv2004

Passages of Proof

In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special attention. Finally, in a highly speculative part, we will anticipate the evolution of proofs under the assumption that the quantum computer will materialize. We will argue that there is little `intrinsic' difference between traditional and `unconventional' types of proofs.

math.HO↗