Displaying similar documents to “A Characterization of Multidimensional S -Automatic Sequences”

Substitutions with Cofinal Fixed Points

Bo TAN, Zhi-Xiong WEN, Jun WU, Zhi-Ying WEN (2006)

Annales de l’institut Fourier

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Let ϕ be a substitution over a 2-letter alphabet, say { a , b } . If ϕ ( a ) and ϕ ( b ) begin with a and b respectively, ϕ has two fixed points beginning with a and b respectively. We characterize substitutions with two cofinal fixed points (i.e., which differ only by prefixes). The proof is a combinatorial one, based on the study of repetitions of words in the fixed points.

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let D be a nonempty compact subset of a Banach space X and denote by S ( X ) the family of all nonempty bounded closed convex subsets of X . We endow S ( X ) with the Hausdorff metric and show that there exists a set ℱ ⊂ S ( X ) such that its complement S ( X ) ∖ ℱ is σ -porous and such that for each A ∈ ℱ and each x ˜ ∈ D , the set of solutions of the best approximation problem ∥ x ˜ - z ∥ → min , z ∈ A , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

On the eigenvalues of a Robin problem with a large parameter

Alexey Filinovskiy (2014)

Mathematica Bohemica

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We consider the Robin eigenvalue problem Δ u + λ u = 0 in Ω , ∂ u / ∂ ν + α u = 0 on ∂ Ω where Ω ⊂ ℝ n , n ≥ 2 is a bounded domain and α is a real parameter. We investigate the behavior of the eigenvalues λ k ( α ) of this problem as functions of the parameter α . We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative λ 1 ' ( α ) . Assuming that the boundary ∂ Ω is of class C 2 we obtain estimates to the difference λ k D - λ k ( α ) between the k -th eigenvalue of the Laplace operator with...