Zobrazeno 1 - 10
of 97
pro vyhledávání: '"Allaart, Pieter C."'
Autor:
Allaart, Pieter C.
Publikováno v:
Discrete Contin. Dyn. Syst. A 39, no. 11, 6507--6522 (2019)
For a positive integer $M$ and a real base $q\in(1,M+1]$, let $\mathcal{U}_q$ denote the set of numbers having a unique expansion in base $q$ over the alphabet $\{0,1,\dots,M\}$, and let $\mathbf{U}_q$ denote the corresponding set of sequences in $\{
Externí odkaz:
http://arxiv.org/abs/1812.09446
Autor:
Allaart, Pieter C., Allen, Andrew
Publikováno v:
Math. Appl. 47, no. 2, 293-312 (2019)
In Robbins' problem of minimizing the expected rank, a finite sequence of $n$ independent, identically distributed random variables are observed sequentially and the objective is to stop at such a time that the expected rank of the selected variable
Externí odkaz:
http://arxiv.org/abs/1811.07096
Autor:
Allaart, Pieter C.
Publikováno v:
Adv. Math. 328 (2018), 1-39
This paper studies a large class of continuous functions $f:[0,1]\to\mathbb{R}^d$ whose range is the attractor of an iterated function system $\{S_1,\dots,S_{m}\}$ consisting of similitudes. This class includes such classical examples as P\'olya's sp
Externí odkaz:
http://arxiv.org/abs/1707.07376
Autor:
Allaart, Pieter C.
Publikováno v:
J. Math. Anal. Appl. 450 (2017), no. 2, 954-968
This paper highlights an unexpected connection between expansions of real numbers to noninteger bases (so-called {\em $\beta$-expansions}) and the infinite derivatives of a class of self-affine functions. Precisely, we extend Okamoto's function (itse
Externí odkaz:
http://arxiv.org/abs/1606.07838
Autor:
Allaart, Pieter C.
Publikováno v:
Adv. Math. 308 (2017), 575-598
Much has been written about expansions of real numbers in noninteger bases. Particularly, for a finite alphabet $\{0,1,\dots,\alpha\}$ and a real number (base) $1<\beta<\alpha+1$, the so-called {\em univoque set} of numbers which have a unique expans
Externí odkaz:
http://arxiv.org/abs/1601.04680
Autor:
Allaart, Pieter C., Islas, Jose A.
Publikováno v:
J. Appl. Prob. 53 (2016), no. 4, 1041-1051
This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win probability. Pr
Externí odkaz:
http://arxiv.org/abs/1511.02211
Autor:
Allaart, Pieter C.
Publikováno v:
J. Fractal Geom. 3 (2016), no. 1, 1-31
Externí odkaz:
http://arxiv.org/abs/1502.03374
Autor:
Allaart, Pieter C.
Publikováno v:
J. Math. Anal. Appl. 419, 1168-1180 (2014)
This paper examines the level sets of the continuous but nowhere differentiable functions \begin{equation*} f_r(x)=\sum_{n=0}^\infty r^{-n}\phi(r^n x), \end{equation*} where $\phi(x)$ is the distance from $x$ to the nearest integer, and $r$ is an int
Externí odkaz:
http://arxiv.org/abs/1312.2119
Autor:
Allaart, Pieter C.
Publikováno v:
Monatsh. Math. 175, no. 2, 313-318 (2014)
The purpose of this note is to correct an error in an earlier paper by the author about the level sets of the Takagi function [Monatsh. Math. 167 (2012), 311-331 and arXiv:1102.1616], and to prove a stronger form of one of the main results of that pa
Externí odkaz:
http://arxiv.org/abs/1306.0167
Autor:
Allaart, Pieter C.
Publikováno v:
Math. Proc. Camb. Phil. Soc. 157 (2014) 253-278
This paper examines level sets of two families of continuous, nowhere differentiable functions (one a subfamily of the other) defined in terms of the "tent map". The well-known Takagi function is a special case. Sharp upper bounds are given for the H
Externí odkaz:
http://arxiv.org/abs/1301.4747