Results 21 to 30 of about 1,648,333 (245)
Inhomogeneous and simultaneous Diophantine approximation in beta dynamical systems [PDF]
Journal of Mathematical Analysis and Applications, 2022 In this paper, we investigate inhomogeneous and simultaneous Diophantine approximation in beta dynamical systems. For $\beta>1$ let $T_{\beta}$ be the $\beta$-transformation on $[0,1]$. We determine the Lebesgue measure and Hausdorff dimension of the set
Yu-Feng Wu
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Intrinsic Diophantine approximation for overlapping iterated function systems [PDF]
Mathematische Annalen, 2021 In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine’s theorem for these sets.
S. Baker
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Mahler’s question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory [PDF]
Mathematische Zeitschrift, 2021 In this paper, we consider Mahler’s question for intrinsic Diophantine approximation on the triadic Cantor set K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
Bo Tan, Bao-Wei Wang, Jun Wu
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On the Approximation of Quasiperiodic Functions with Diophantine Frequencies by Periodic Functions [PDF]
SIAM Journal on Mathematical Analysis, 2023 We present an analysis of the approximation error for a $d$-dimensional quasiperiodic function $f$ with Diophantine frequencies, approximated by a periodic function with the fundamental domain $[0,L_1)\times [0,L_2)\times \cdots \times[0,L_d)$.
Kai Jiang, Shifeng Li, Pingwen Zhang
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On Hausdorff dimension in inhomogeneous Diophantine approximation over global function fields [PDF]
Journal of Number Theory, 2021 In this paper, we study inhomogeneous Diophantine approximation over the completion $K_v$ of a global function field $K$ (over a finite field) for a discrete valuation $v$, with affine algebra $R_v$.
Taehyeong Kim, Seonhee Lim, F. Paulin
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Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis
Axioms, 2022 Rough set (RS) and fuzzy set (FS) theories were developed to account for ambiguity in the data processing. The most persuasive and modernist abstraction of an FS is the linear Diophantine FS (LD-FS).
Saba Ayub +5 more
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Журнал Белорусского государственного университета: Математика, информатика, 2021 The article is devoted to the latest results in metric theory of Diophantine approximation. One of the first major result in area of number theory was a theorem by academician Jonas Kubilius. This paper is dedicated to centenary of his birth.
Victor V. Beresnevich +4 more
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Khintchine’s theorem and Diophantine approximation on manifolds
Acta Mathematica, 2023 holds for infinitely many (p1, ..., pn, q)∈Z×N. The set of ψ -approximable points in R will be denoted by Sn(ψ). In the special case of ψτ (q):=q−τ for some τ>0, we will also write Sn(τ) instead of Sn(ψτ ).
V. Beresnevich, Le-le Yang
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Forum of Mathematics, Pi, 2022 We present a framework for tame geometry on Henselian valued fields, which we call Hensel minimality. In the spirit of o-minimality, which is key to real geometry and several diophantine applications, we develop geometric results and applications for ...
Raf Cluckers +2 more
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Metric Diophantine Approximation: aspects of recent work [PDF]
, 2017 In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approximation; such as theorems of Khintchine, Jarnik, Duffin-Schaeffer and Gallagher.
Velani, Sanju +2 more
core +5 more sources