Displaying similar documents to “S-expansions in dimension two”

Structure of three interval exchange transformations I: an arithmetic study

Sébastien Ferenczi, Charles Holton, Luca Q. Zamboni (2001)

Annales de l’institut Fourier

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In this paper we describe a 2 -dimensional generalization of the Euclidean algorithm which stems from the dynamics of 3 -interval exchange transformations. We investigate various diophantine properties of the algorithm including the quality of simultaneous approximations. We show it verifies the following Lagrange type theorem: the algorithm is eventually periodic if and only if the parameters lie in the same quadratic extension of ℚ .

Strict maximum separability of two finite sets: an algorithmic approach

Dorota Cendrowska (2005)

International Journal of Applied Mathematics and Computer Science

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The paper presents a recursive algorithm for the investigation of a strict,linear separation in the Euclidean space. In the case when sets are linearly separable, it allows us to determine the coefficients of the hyperplanes. An example of using this algorithm as well as its drawbacks are shown. Then the algorithm of determining an optimal separation (in the sense of maximizing the distance between the two sets) is presented.

Symmetry and folding of continued fractions

Alfred J. Van der Poorten (2002)

Journal de théorie des nombres de Bordeaux

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Michel Mendès France's “Folding Lemma” for continued fraction expansions provides an unusual explanation for the well known symmetry in the expansion of a quadratic irrational integer.

Admissible disturbance sets for discrete perturbed systems

Jamal Bouyaghroumni, Abdelhaq El Jai, Mostafa Rachik (2001)

International Journal of Applied Mathematics and Computer Science

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We consider a discrete disturbed system given by the difference bilinear equation where are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function. Let be a tolerance index on the output. The disturbance is said to be -admissible if, where is the output signal associated with the case of an uninfected system. The set of all -admissible disturbances is the admissible set. The characterization of is investigated...