Displaying similar documents to “The growth rates of digits in the Oppenheim series expansions”

The growth rate and dimension theory of beta-expansions

Simon Baker (2012)

Fundamenta Mathematicae

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In a recent paper of Feng and Sidorov they show that for β ∈ (1,(1+√5)/2) the set of β-expansions grows exponentially for every x ∈ (0,1/(β-1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

On the maximal run-length function in the Lüroth expansion

Yu Sun, Jian Xu (2018)

Czechoslovak Mathematical Journal

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We obtain a metrical property on the asymptotic behaviour of the maximal run-length function in the Lüroth expansion. We also determine the Hausdorff dimension of a class of exceptional sets of points whose maximal run-length function has sub-linear growth rate.

On the growth of an algebroid function with radially distributed values

Nan Wu, Jian Hua Zheng (2015)

Annales Polonici Mathematici

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We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.

Growth induced buckling instability of anisotropic tube and its application in wound edge instability

Le Yang, Tarynn M. Witten, Ramana M. Pidaparti (2017)

Curved and Layered Structures

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Fiber reinforced anisotropic material abounds in biological world. It has been demonstrated in previous theoretical and experimental works that growth of biological soft tubular tissue plays a significant role in morphogenesis and pathology. Here we investigate growth-induced buckling of anisotropic cylindrical tissue, focusing on the effects of type of growth(constraint/unconstraint, isotropic/anisotropic), fiber property(orientation, density and strength), geometry and any interaction...

Growth Functions of Fr-sets

Lomond, Jonny (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 05C30, 20E08, 20F65. In this paper we consider an open problem from [1], regarding the description of the growth functions of the free group acts. Using the language of graphs, we solve this problem by providing the necessary and sufficient conditions for a function to be a growth function for a free group act.