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Currently displaying 1 – 4 of 4

Order by Relevance | Title | Year of publication

On the central limit theorem for random variables related to the continued fraction expansion

C. Faivre — 1996

Colloquium Mathematicae

On decimal and continued fraction expansions of a real number

C. Faivre — 1997

Acta Arithmetica

Sur la somme des quotients partiels du développement en fraction continue

D. Barbolosi; C. Faivre — 2001

Colloquium Mathematicae

Let [0;a₁(x),a₂(x),…] be the regular continued fraction expansion of an irrational x ∈ [0,1]. We prove mainly that, for α > 0, β ≥ 0 and for almost all x ∈ [0,1], $l i m_{n \to \infty} (a ⁿ ₁ (x) + \dots + a ⁿ ₙ (x)) / n l o g n = α / l o g 2$ if α < 1 and β ≥ 0, $l i m_{n \to \infty} (a ⁿ ₁ (x) + \dots + a ⁿ ₙ (x)) / n l o g n = 1 / l o g 2$ if α = 1 and β < 1, and, if α > 1 or α = 1 and β >1, $l i m i n f_{n \to \infty} (a ⁿ ₁ (x) + \dots + a ⁿ ₙ (x)) / n l o g n = 1 / l o g 2$ , $l i m s u p_{n \to \infty} (a ⁿ ₁ (x) + \dots + a ⁿ ₙ (x)) / n l o g n = \infty$ , where $a ⁿ_{i} (x) = a_{i} (x)$ if $a_{i} (x) \leq n^{α} l o g^{β} n$ and $a ⁿ_{i} (x) = 0$ otherwise, for all i ∈ 1,…,n.

Modeling the Impact of Anticancer Agents on Metastatic Spreading

S. Benzekry; N. André; A. Benabdallah; J. Ciccolini; C. Faivre; F. Hubert; D. Barbolosi — 2012

Mathematical Modelling of Natural Phenomena

Treating cancer patients with metastatic disease remains an ultimate challenge in clinical oncology. Because invasive cancer precludes or limits the use of surgery, metastatic setting is often associated with (poor) survival, rather than sustained remission, in patients with common cancers like lung, digestive or breast carcinomas. Mathematical modeling may help us better identify non detectable metastatic status to in turn optimize treatment for...

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