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The bounds of the general M and J sets and the estimations for the Hausdorff’s dimension of the general J set

✍ Scribed by Liu Xiang-dong; Yan De-jun; Zhu Wei-yong; Wang Guang-xing

Publisher
Springer
Year
2001
Tongue
English
Weight
288 KB
Volume
22
Category
Article
ISSN
0253-4827

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The Hausdorff Dimension of Sets Arising
The Hausdorff Dimension of Sets Arising from Diophantine Approximation with a General Error Function
✍ Bryan P. Rynne 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 204 KB

Let m, n be positive integers and let : Z n Ä R be a non-negative function. Let W(m, n; ) be the set { X # R mn : " : n j=1 x ij q j " < (q), 1 i m, for infinitely many q # Z n = . The Hausdorff dimension of W(m, n; ) is obtained for arbitrary non-negative functions , with no monotonicity assumpti