摘要
This paper mainly discuss the convergence of the complex plane compact series of sets, and there are a lot of good properties in the Hausdorff distance. We extend one-dimensional Gauss Test to the series of sets on the complex plane by these properties. In fact, we can extend the part of convergence to Banach space, but the part of divergence must be on the Euclidean space or the complex plane. There is a detailed introduction in this paper.
並列摘要
本篇論文主要討論複數平面緊緻集合級數之收斂性, 而在豪斯多夫距離下有很多好的性質, 我們利用此性質把一維度的高斯審斂法推廣到複數平面的集合級數, 其實在收斂部份, 其空間可推廣到Banach space, 但在發散部份則要在歐氏空間或複數平面, 此篇論文都有詳細的介紹.
參考文獻
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延伸閱讀
- Zhou, X. (2017). 大規模線性分類資料低階多項式映射中雜湊函數之應用 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU201701597
- 劉榆婕（2013）。歐氏空間在豪斯多夫距離下集合級數托普利茲審斂法〔碩士論文，中原大學〕。華藝線上圖書館。https://doi.org/10.6840/CYCU.2013.00427
- Chung, T. H. (2018). 緊複曲面的小平邦彥分類之探討 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU201803920
- Rao, K. P. R., Altun, I., & Bindu, S. H. (2011). Common Coupled Fixed-Point Theorems in Generalized Fuzzy Metric Spaces. Advances in Fuzzy Systems, 2011(), 169-174. https://doi.org/10.1155/2011/986748
- Han, Z., Wang, J., Jing, J., & Zhang, H. (2014). A Simple Gaussian Measurement Bound for Exact Recovery of Block-Sparse Signals. Discrete Dynamics in Nature and Society, 2014(), 19-26-002. https://doi.org/10.1155/2014/104709