منابع مشابه
Generalized Continued Logarithms and Related Continued Fractions
We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base b. We show that all of our so-called type III continued logarithms converge and all rational numbers have fin...
متن کاملContinued Fractions and Generalized Patterns
Babson and Steingrimsson (2000, Séminaire Lotharingien de Combinatoire, B44b, 18) introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Let fτ ;r (n) be the number of 1-3-2-avoiding permutations on n letters that contain exactly r occurrences of τ , where τ is a generalized pattern on k letters. Let Fτ ...
متن کاملVector continued fractions using a generalized inverse
A real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued ...
متن کاملContinued Fractions, Statistics, And Generalized Patterns
Recently, Babson and Steingrimsson (see [BS]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Following [BCS], let ekπ (respectively; fkπ) be the number of the occurrences of the generalized pattern 12-3. . . -k (respectively; 21-3. . . -k) in π. In the present note, we study the distribution of ...
متن کاملGeneralized Brjuno functions associated to α-continued fractions
For 0 ≤ α ≤ 1 given, we consider the α-continued fraction expansion of a real number obtained by iterating the map Aα(x) = ̨̨ x − ˆ x + 1− α ̃ ̨̨ defined on the interval Iα = (0, ᾱ), with ᾱ = max(α, 1− α). These maps generalize the classical (Gauss) continued fraction map which corresponds to the choice α = 1, and include the nearest integer (α = 1/2) and byexcess (α = 0) continued fraction expansio...
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ژورنال
عنوان ژورنال: New Trends in Mathematical Science
سال: 2019
ISSN: 2147-5520
DOI: 10.20852/ntmsci.2019.378