Results 21 to 30 of about 15,074 (239)
Fractal and FractionalThe paper deals with the problem of representing special functions by branched continued fractions, particularly multidimensional A- and J-fractions with independent variables, which are generalizations of associated continued fractions and Jacobi ...
Roman Dmytryshyn, Serhii Sharyn
doaj +1 more source
Continued Fractions and Generalized Patterns
European Journal of Combinatorics, 2002 In [BS] Babson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Let $f_{ ;r}(n)$ be the number of $1\mn3\mn2$-avoiding permutations on $n$ letters that contain exactly $r$ occurrences of $ $, where $ $ a generalized pattern on $k ...
openaire +2 more sources
Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution. The simplest examples which correspond to algebraic parameters, are related to the iteration of one substitution, but we
Arnoux, Pierre +3 more
openaire +4 more sources
Convergence criteria of branched continued fractions
Researches in MathematicsThe convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed.
I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak
doaj +1 more source
A special case of rational θs for terminating θ-expansions [PDF]
Surveys in Mathematics and its Applications, 2013 There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A ...
Santanu Chaktaborty
doaj
, 2013 We consider a family $\{\tau_m:m\geq 2\}$ of interval maps introduced by Hei-Chi Chan [5] as generalizations of the Gauss transformation. For the continued fraction expansion arising from $\tau_m$, we solve its Gauss-Kuzmin-type problem by applying the ...
Lascu, Dan
core +2 more sources
Convergence of continued fraction type algorithms and generators
Monatshefte f�r Mathematik, 1998 Continued fraction expansions and multidimensional generalizations (including the so-called Jacobi-Perron algorithm) or the ordinary binary expansion give various examples of number-expansion algorithms governed by dynamical systems. This paper exhibits a general setup which generalizes all the above situations.
Kraaikamp, Cor, Meester, Ronald
openaire +3 more sources
A short proof of the simple continued fraction expansion of e
, 2006 This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.Comment: 6 pages; only change from published version is that
Cohn, Henry
core +1 more source
Vertex topological indices and tree expressions, generalizations of continued fractions [PDF]
Journal of Mathematical Chemistry, 2009 We expand on the work of Hosoya to describe a generalization of continued fractions called "tree expressions." Each rooted tree will be shown to correspond to a unique tree expression which can be evaluated as a rational number (not necessarily in lowest terms) whose numerator is equal to the Hosoya index of the entire tree and whose denominator is ...
openaire +3 more sources
Математичні СтудіїIn this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions.
R. Dmytryshyn +3 more
doaj +1 more source