DSpace Collection: https://scholars.lib.ntu.edu.tw/handle/123456789/29389 2020-01-19T11:16:18Z Distance sets over arbitrary finite fields https://scholars.lib.ntu.edu.tw/handle/123456789/430738 Title: Distance sets over arbitrary finite fields Authors: Pham, Thang; Lee, Sujin; Koh, Doowon; CHUN-YEN SHEN Abstract: © 2019 by the University of Illinois at Urbana-Champaign. In this paper, we study the Erdős distinct distances problem for Cartesian product sets in the setting of arbitrary finite fields. More precisely, let Fq be an arbitrary finite field and A be a set in Fq. Suppose ǀAՈ (αG) ≤ ǀG ǀ1/2 for any subfield G and α ϵ F*q, then (Formula Presented) Using the same method, we also obtain some results on sum-product type problems. 2019-10-01T00:00:00Z A note on inner and reflexive inverses in semiprime rings https://scholars.lib.ntu.edu.tw/handle/123456789/430737 Title: A note on inner and reflexive inverses in semiprime rings Authors: TSIU-KWEN LEE Abstract: © 2020 World Scientific Publishing Company. Let R be a semiprime ring, not necessarily with unity, and a,b R. Let I(a) (respectively, Ref(a)) denote the set of inner (respectively, reflexive) inverses of a in R. It is proved that if I(a) â I(b)â‰ â then I(a) âŠ I(b) if and only if b = awb = bwa for all w I(a). As an immediate consequence, if ââ‰ I(a) = I(b), then a = b (see Theorem 7 in [A. Alahmadi, S. K. Jain and A. Leroy, Regular elements determined by generalized inverses, J. Algebra Appl. 18(7) (2019) 1950128] for rings with unity). We also give a generalization of Theorem 10 in [A. Alahmadi, S. K. Jain and A. Leroy, Regular elements determined by generalized inverses, J. Algebra Appl. 18(7) (2019) 1950128] by proving that if ââ‰ Ref(a) âŠRef(b) then a = b. 2019-01-01T00:00:00Z A correction to “the deformation of lagrangian minimal surfaces in kähler-einstein surfaces” https://scholars.lib.ntu.edu.tw/handle/123456789/428730 Title: A correction to “the deformation of lagrangian minimal surfaces in kähler-einstein surfaces” Authors: LEE, Y.-I.; YNG-ING LEE 1999-01-01T00:00:00Z Self-similar solutions and translating solutions https://scholars.lib.ntu.edu.tw/handle/123456789/428729 Title: Self-similar solutions and translating solutions Authors: Lee, Y.-I.; YNG-ING LEE 2011-01-01T00:00:00Z