Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 8

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

A problem of Galambos on Engel expansions

100%
Wu J.
Acta Arithmetica
|
2000
|
tom 92
|
nr 4
383-386
EN
1. Introduction. Given x in (0,1], let x = [d₁(x),d₂(x),...] denote the Engel expansion of x, that is, (1) $x =1/d₁(x) + 1/(d₁(x)d₂(x)) + ... + 1/(d₁(x)d₂(x)...d_n(x)) + ... $, where ${d_{j}(x), j ≥ 1}$ is a sequence of positive integers satisfying d₁(x) ≥ 2 and $d_{j+1}(x) ≥ d_{j}(x)$ for j ≥ 1. (See [3].) In [3], János Galambos proved that for almost all x ∈ (0,1], (2) $lim_{n→∞} d_{n}^{1/n}(x) =e. He conjectured ([3], P132) that the Hausdorff dimension of the set where (2) fails is one. In this paper, we prove this conjecture: Theorem. $dim_H{x ∈ (0,1]: (2) fails} = 1$. We use L¹ to denote the one-dimensional Lebesgue measure on (0,1] and $dim_{H}$ to denote the Hausdorff dimension.
2
Content available remote

The Oppenheim series expansions and Hausdorff dimensions

88%
Wu J.
Acta Arithmetica
|
2003
|
tom 107
|
nr 4
345-355
3
Content available remote

Metric properties for p-adic Oppenheim series expansions

88%
Wu J.
Acta Arithmetica
|
2004
|
tom 112
|
nr 3
247-261
4
Content available remote

Hausdorff dimensions in Engel expansions

64%
Liu Y.-Y., Wu J.
Acta Arithmetica
|
2001
|
tom 99
|
nr 1
79-83
5
Content available remote

The growth rates of digits in the Oppenheim series expansions

64%
Wang B.-W., Wu J.
Acta Arithmetica
|
2006
|
tom 121
|
nr 2
175-192
6
Content available remote

Continued fractions with sequences of partial quotients over the field of Laurent series

64%
Hu X., Wu J.
Acta Arithmetica
|
2009
|
tom 136
|
nr 3
201-211
7
Content available remote

The growth speed of digits in infinite iterated function systems

51%
Cao C.-Y., Wang B.-W., Wu J.
Studia Mathematica
|
2013
|
tom 217
|
nr 2
139-158
EN
Let ${fₙ}_{n≥1}$ be an infinite iterated function system on [0,1] satisfying the open set condition with the open set (0,1) and let Λ be its attractor. Then to any x ∈ Λ (except at most countably many points) corresponds a unique sequence ${aₙ(x)}_{n≥1}$ of integers, called the digit sequence of x, such that $x = lim_{n→∞} f_{a₁(x)}∘ ⋯ ∘ f_{aₙ(x)}(1)$. We investigate the growth speed of the digits in a general infinite iterated function system. More precisely, we determine the dimension of the set ${x ∈ Λ: aₙ(x) ∈ B (∀ n ≥ 1), lim_{n→∞} aₙ(x) = ∞}$ for any infinite subset B ⊂ ℕ, a question posed by Hirst for continued fractions. Also we generalize Łuczak's work on the dimension of the set {x ∈ Λ: $aₙ(x) ≥ a^{bⁿ}$ for infinitely many n ∈ ℕ} with a,b > 1. We will see that the dimension of the sets above is tightly connected with the convergence exponent of the contraction ratios of the sequence ${fₙ}_{n≥1}$.
8
Content available remote

Univoque sets for real numbers

51%
Lü F., Tan B., Wu J.
Fundamenta Mathematicae
|
2014
|
tom 227
|
nr 1
69-83
EN
For x ∈ (0,1), the univoque set for x, denoted 𝒰(x), is defined to be the set of β ∈ (1,2) such that x has only one representation of the form x = x₁/β + x₂/β² + ⋯ with $x_{i} ∈ {0,1}$. We prove that for any x ∈ (0,1), 𝒰(x) contains a sequence ${β_{k}}_{k ≥ 1}$ increasing to 2. Moreover, 𝒰(x) is a Lebesgue null set of Hausdorff dimension 1; both 𝒰(x) and its closure $\overline {𝒰(x)}$ are nowhere dense.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.