一类集合的 3 因子个数研究
3-Factor Number Study of aClass of Sets
DOI: 10.12677/PM.2024.141018, PDF, 下载: 50  浏览: 93 
作者: 庄婷婷：福建师范大学，数学与统计学院，福建 福州
关键词: 3 因子；非 3 因子；因子个数；Factor 3； Non-3-Factor； Number of Factors
摘要: 本论文研究由任意非 3 因子元素组成的集合 其中D是一无穷整数子集，我们证明了对任意的k≥1，存在无穷多个𝛾1,𝛾2∈A，它们的差𝛾1−𝛾2至少有k个 3 因子。 分别讨论了集合A是整数集或有理数集下，利用数学归纳法以及集合之间的包含关系证得了上述结论是成立的。
Abstract: In this thesis, we study the set consisting of any non-3-factor element where D is an infinite subset of integers.We show that there are infinitely many 𝛾1,𝛾2∈A, and their difference 𝛾1−𝛾2 has at least 𝑘 factors of 3 for any k≥1. If A is set of integers or set of rational numbers, the above conclusion is proved by mathematical induction and the induction relation between sets.
文章引用：庄婷婷. 一类集合的 3 因子个数研究[J]. 理论数学, 2024, 14(1): 168-175. https://doi.org/10.12677/PM.2024.141018

参考文献

[1] Mandelbrot, B.B. (1975) Les Objets Fractals: Forme, Hasard et Dimension. Flammarion, Paris.
[2] Matilla, P. (1995) Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability. In: Cambridge Studies in Advanced Mathematics, Vol. 44, Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511623813
[3] Kigami, J. (2001) Analysis on Fractals. Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511470943
[4] Falconer, K. (2004) Fractal Geometry-Mathematical Foundations and Applications. 2nd Edition, John Wiley, New York.
https://doi.org/10.1002/0470013850
[5] Strichartz, R. (2006) Differential Equations on Fractals. Princeton University Press, Princeton and Oxford.
https://doi.org/10.1515/9780691186832
[6] Lund, J.P., Strichartz, R.S. and Vinson, J.P. (1998) Cauchy Transforms of Self-Similar Measures. Experimental Mathematics, 7, 177-190.
https://doi.org/10.1080/10586458.1998.10504368
[7] Dong, X.H. and Lau, K.S. (2003) Cauchy Transforms of Self-Similar Measures: The Laurent Coefficients. Journal of Functional Analysis, 202, 67-97.
https://doi.org/10.1016/S0022-1236(02)00069-1
[8] Dong, X.H. and Lau, K.S. (2004) An Integral Related to the Cauchy Transform on the Sierpinski Gasket. Experimental Mathematics, 13, 415-419.
https://doi.org/10.1080/10586458.2004.10504549
[9] Dong, X.H., Lau, K.S. and Liu, J.C. (2013) Cantor Boundary Behavior of Analytic Functions. Advances in Mathematics, 232, 543-570.
https://doi.org/10.1016/j.aim.2012.09.021
[10] Dong, X.H., Lau, K.S. and Wu, H.H. (2017) Cauchy Transforms of Self-Similar Measures: Starlikeness and Univalence. Transactions of the American Mathematical Society, 369, 4817- 4842.
https://doi.org/10.1090/tran/6819
[11] Strichartz, R.S. (2000) Mock Fourier Series and Transforms Associated with Certain Cantor Measures. Journal d’Analyse Math´ematique, 81, 209-238.
https://doi.org/10.1007/BF02788990
[12] Dai, X.R., He, X.G. and Lai, C.K. (2013) Spectral Property of Cantor Measures with Consecutive Digits. vAdvances in Mathematics, 242, 187-208.
https://doi.org/10.1016/j.aim.2013.04.016
[13] Hu, T.Y. and Lau, K.S. (2008) Spectral Property of the Bernoulli Convolutions. Advances in Mathematics, 219, 554-567.
https://doi.org/10.1016/j.aim.2008.05.004
[14] An, L.X., He, X.G. and Li, H.X. (2015) Spectrality of Infinite Bernoulli Convolutions. Journal of Functional Analysis, 269, 1571-1590.
https://doi.org/10.1016/j.jfa.2015.05.008
[15] Ting, X. (2023) Spectrality of Moran Measures with Three-Element Digit Sets. Acta Mathematica Scientia, 43A, 1-17.

为你推荐