Results 21 to 30 of about 436,402 (269)
Geodesic Rosen Continued Fractions [PDF]
, 2015 We describe how to represent Rosen continued fractions by paths in a class of graphs that arise naturally in hyperbolic geometry. This representation gives insight into Rosen's original work about words in Hecke groups, and it also helps us to identify ...
Short, Ian, Walker, Mairi
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The discrete logarithm problem modulo one: cryptanalysing the Ariffin–Abu cryptosystem
Journal of Mathematical Cryptology, 2010 The paper provides a cryptanalysis of the AAβ-cryptosystem recently proposed by Ariffin and Abu. The scheme is in essence a key agreement scheme whose security is based on a discrete logarithm problem in the infinite (additive) group ℝ/ℤ (the reals ...
Blackburn Simon R.
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$q$-DEFORMED RATIONALS AND $q$-CONTINUED FRACTIONS
Forum of Mathematics, Sigma, 2020 We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$-deformed Pascal
SOPHIE MORIER-GENOUD, VALENTIN OVSIENKO
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Continued fractions and class number two
International Journal of Mathematics and Mathematical Sciences, 2001 We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm-induced quadratic polynomial.
Richard A. Mollin
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Ramanujan and the Regular Continued Fraction Expansion of Real Numbers [PDF]
, 2004 In some recent papers, the authors considered regular continued fractions of the form \[ [a_{0};\underbrace{a,...,a}_{m}, \underbrace{a^{2},...,a^{2}}_{m}, \underbrace{a^{3},...,a^{3}}_{m}, ...
Laughlin, James Mc, Wyshinski, Nancy J.
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Formulas for the Number of Spanning Trees in a Chain of Cycles
Sultan Qaboos University Journal for Science, 2010 We give a formula for the number of spanning trees in a chain of cycles that have connected intersection of one edge but where the cycles have variable sizes. The formula uses basic properties of continued fractions.
Thomas Bier
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The Generating Functions for Special Pringsheim Continued Fractions
Communications in Advanced Mathematical Sciences, 2020 In previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs $\mathrm{\mathbf{F}}_{u,N}$ were investigated.
Ali Hikmet Değer, Ümmügülsün Akbaba
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Bounding differences in Jager Pairs [PDF]
, 2013 Symmetrical subdivisions in the space of Jager Pairs for continued fractions-like expansions will provide us with bounds on their difference. Results will also apply to the classical regular and backwards continued fractions expansions, which are ...
Bourla, Avraham
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Excursions of diffusion processes and continued fractions [PDF]
, 2010 It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process.
Comtet, Alain, Tourigny, Yves
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On the metrical theory of a non-regular continued fraction expansion
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 We introduced a new continued fraction expansions in our previous paper. For these expansions, we show the Brodén-Borel-Lévy type formula. Furthermore, we compute the transition probability function from this and the symbolic dynamical system of the ...
Lascu Dan, Cîrlig George
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