On the distribution of characteristic parameters of words II

Arturo Carpi; Aldo de Luca

Displaying similar documents to “On the distribution of characteristic parameters of words II”

On the distribution of characteristic parameters of words

Arturo Carpi, Aldo de Luca (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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For any finite word $w$ on a finite alphabet, we consider the basic parameters $R_{w}$ and $K_{w}$ of $w$ defined as follows: $R_{w}$ is the minimal natural number for which $w$ has no right special factor of length $R_{w}$ and $K_{w}$ is the minimal natural number for which $w$ has no repeated suffix of length $K_{w}$ . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.

Minimum complexity of automatic non sturmian sequences

T. Tapsoba (1995)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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A two well Liouville theorem

Andrew Lorent (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we analyse the structure of approximate solutions to the compatible two well problem with the constraint that the surface energy of the solution is less than some fixed constant. We prove a quantitative estimate that can be seen as a two well analogue of the Liouville theorem of Friesecke James Müller. Let $H = (\begin{matrix} σ & 0 \\ 0 & σ^{- 1} \end{matrix})$ for $σ > 0$ . Let $0 < ζ_{1} < 1 < ζ_{2} < \infty$ . Let $K : = S O (2) \cup S O (2) H$ . Let $u \in W^{2, 1} (Q_{1} (0))$ be a $C^{1}$ invertible bilipschitz function with $Lip (u) < ζ_{2}$ , $Lip (u^{- 1}) < ζ_{1}^{- 1}$ . There exists positive constants $𝔠_{1} < 1$ and $𝔠_{2} > 1$ depending only on $σ$ , $ζ_{1}$ , $ζ_{2}$ such that if $ϵ \in (0, 𝔠_{1})$ and $u$ ...