A Class of Exceptional Sets in Oppenheim Series Expansion
一类Oppenheim展式的例外关系集(英文)
摘要
In this paper, we investigate the Hansdorff dimension of a class of exceptional sets occurring in Oppenheim series expansion. As an application, we get the exact Hansdorff dimension of the set in Liiroth series expansion. Moreover, we give an estimate of such dimensional number.
本文研究了Oppenheim展式中一类例外关系集的Hausdorff维数,作为其应用,我们得到了Lüroth级数展式中一些集合的Hausdorff维数的确切值。
参考文献8
-
1GALAMBOS J.Further ergodic results on the Oppenheim series[J].Quart.J.Math Oxford Ser.,1974,25(2):135-141.
-
2GALAMBOS J.On the speed of convergence of the Oppenheim series[J].Acta Arith.,1971,19:335-342.
-
3GALAMBOS J.Representations of Real Numbers by Infinite Series[M].Lecture Notes in Mathematics,Vol.502.Springer-Verlag,Berlin-New York,1976.
-
4GALAMBOS J.Further metric results on series expansions[J].Publ.Math.-Debrecen,1998,52(3-4):377-384.
-
5OPPENHEIM A.The representation of real numbers by infinite series of rationals[J].Acta Arith.,1972,21:391-398.
-
6SCHWEIGER F.Ergodic Theory of Fibred Systems and Metric Number Theory[M].Oxford Science Publications.The Clarendon Press,Oxford University Press,New York,1995.
-
7VERVAAT W.Success Epochs in Bernoulli Triails[M].Mathematical Centre Tracts,No.42.Mathematisch Centrum,Amsterdam,1972.
-
8WU Jun.On the distribution of denominators in Sylvester expansions[J].Bull London Math.Soc.,2002,34(1):16-20.
-
1邱建军.模糊(S,θ)-系的直积、上积和张量积[J].内江师范学院学报,2008,23(12):24-26.
-
2E．博罗维茨卡亚,M．S．舒尔,李国栋.量子点[J].国外科技新书评介,2005(4):6-7.
-
3焦争鸣,刘保才,宋文彦.Oppenheim不等式的进一步改进[J].河南师范大学学报（自然科学版）,1994,22(2):25-27. 被引量：2
-
4RazvanA.Satnoianu 陆昱 姚景齐.三角形中的Erdǒs-Mordell型不等式[J].数学译林,2005,24(1):95-96.
-
5陈计,王振.Oppenheim不等式推广的简单证明[J].Journal of Mathematical Research and Exposition,1996,16(1):62-64.
-
6王庚.两个高维Oppenheim不等式的简单证明[J].工科数学,1997,13(2):104-106. 被引量：1
-
7杨世国.一个几何不等式的高维推广及其应用[J].烟台师范学院学报（自然科学版）,1996,12(4):267-271.
-
8杨晋,杨礼泉.Oppenheim不等式的E^n推广[J].巢湖师专学报,1999,1(3):38-40.
-
9江胜华,宏宇.试论关系运算的守恒性[J].嘉应大学学报,1999,17(6):3-6.
-
10申一平.Pedoe不等式与Oppenheim不等式的推广[J].数学教学研究,1989(1):9-11. 被引量：1
