Results 11 to 20 of about 46,451 (125)
, 2021 We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aimed to compare the efficiency by describing the rate at which the digits of one
Lascu, Dan, Sebe, Gabriela Ileana
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Continued fractions built from convex sets and convex functions [PDF]
, 2014 In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions with deterministic terms are provided.
Molchanov, Ilya
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Partial sums of excursions along random geodesics and volume asymptotics for thin parts of moduli spaces of quadratic differentials [PDF]
, 2017 For a non-uniform lattice in SL(2, R), we consider excursions of a random geodesic in cusp neighborhoods of the quotient finite area hyperbolic surface or orbifold. We prove a strong law for a certain partial sum involving these excursions.
Gadre, Vaibhav
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2+1 gravity, chaos and time machines [PDF]
, 2000 2+1 gravity for spacetimes with topology RxT^2 has been much studied. We add a description of how to extend these spacetimes across a Cauchy horizon into a region where the torus becomes Lorentzian. The result is a one parameter family of tori given by a
Bengtsson, Ingemar, Braennlund, Johan
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Intermediate convergents and a metric theorem of Khinchin
, 2009 A landmark theorem in the metric theory of continued fractions begins this way: Select a non-negative real function $f$ defined on the positive integers and a real number $x$, and form the partial sums $s_n$ of $f$ evaluated at the partial quotients $a_1,
Haynes, Alan K.
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The Ostrogradsky series and related probability measures
, 2006 We develop a metric and probabilistic theory for the Ostrogradsky representation of real numbers, i.e., the expansion of a real number $x$ in the following form: \begin{align*} x&= \sum_n\frac{(-1)^{n-1}}{q_1q_2... q_n}= &=\sum_n\frac{(-1)^{n-1}}{g_1(g_1+
Albeverio, S. +3 more
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On the finiteness and periodicity of the $p$--adic Jacobi--Perron algorithm [PDF]
, 2019 Multidimensional continued fractions (MCFs) were introduced by Jacobi and Perron in order to obtain periodic representations for algebraic irrationals, as it is for continued fractions and quadratic irrationals.
Murru, Nadir, Terracini, Lea
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On the metric theory of the optimal continued fraction expansion [PDF]
Bulletin of the Australian Mathematical Society, 1997 Suppose kn denotes either φ(n) or φ(rn) (n = 1, 2, …) where the polynomial φ maps the natural numbers to themselves and rk denotes the kth rational prime. Let denote the sequence of convergents to a real numbers x for the optimal continued fraction expansion. Define the sequence of approximation constants byIn this paper we study the behaviour of the
openaire +2 more sources
Metrical Diophantine approximation for quaternions [PDF]
, 2014 Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.Comment: 30 pages.
Beresnevich +27 more
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, 2017 Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. L\"u, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett.
Kokkotas, K. +2 more
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