Die Lehre von den Kettenbrüchen

Perron, Oskar

doi:10.1007/978-3-663-12289-0

Cited by 123 publications

(185 citation statements)

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“…Theorem 1 and Theorem 2 of this paper extend and deepen the related results of Perron [1]. Theorem 3 gives a necessary condition on the solvability of kx2-l y2=1,2 by using D-invariants.…”

supporting

confidence: 59%

D-invariants and the solvability of kx2-ly2=1, 2

Yuan

1996

Jpn. j. math

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“…Theorem 1 and Theorem 2 of this paper extend and deepen the related results of Perron [1]. Theorem 3 gives a necessary condition on the solvability of kx2-l y2=1,2 by using D-invariants.…”

supporting

confidence: 59%

D-invariants and the solvability of kx2-ly2=1, 2

Yuan

1996

Jpn. j. math

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“…10], [12], and [13]. In this paper, we only discuss the case where a i is a positive integer for i ≥ 0, i.e., α is greater than or equal to 1.…”

Section: Continued Fraction Expansions Sturmian Words and Sturmian Gmentioning

confidence: 99%

On Lazy Representations and Sturmian Graphs

Epifanio

Frougny

Gabriele

et al. 2011

Implementation and Application of Automata

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Abstract. In this paper we establish a strong relationship between the set of lazy representations and the set of paths in a Sturmian graph associated with a real number α. We prove that for any non-negative integer i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α. Moreover, we provide several properties of the representations of the natural integers in this numeration system.

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“…Two continued fractions are called equivalent if they have the same approximants. The continued fraction (7) is equivalent to the following simple continued fraction (Perron, 1954;Jones and Thron, 1980):…”

Section: Preliminariesmentioning

confidence: 99%

On closure methods in nonlinear stochastic dynamics

Bobryk

2010

Statistics & Probability Letters

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Please cite this article as: Bobryk, R.V., On closure methods in nonlinear stochastic dynamics. Statistics and Probability Letters (2010Letters ( ), doi:10.1016Letters ( /j.spl.2010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTOn closure methods in nonlinear stochastic dynamics Roman V. BobrykInstitute of Mathematics, Jan Kochanowski University, 25406 Kielce, Poland AbstractThe paper discusses some problems in applications of closure techniques to moment hierarchies by considering equation of overdamped oscillator with cubic nonlinearity and additive Gaussian white noise. It is rigorously shown that some closure schemes can be inconsistent in spite of they good convergence properties.

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Die Lehre von den Kettenbrüchen

Cited by 123 publications

References 0 publications

<i>D</i>-invariants and the solvability of kx<sup>2</sup>-ly<sup>2</sup>=1, 2

<i>D</i>-invariants and the solvability of kx<sup>2</sup>-ly<sup>2</sup>=1, 2

On Lazy Representations and Sturmian Graphs

On closure methods in nonlinear stochastic dynamics

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