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Title: The critical point of a sigmoidal curve
Authors: Bilge, Ayşe Hümeyra
Özdemir, Yunus
Keywords: Sigmoidal curve
critical point
Fourier transform
Hilbert transform
Issue Date: 2020
Publisher: Univ Babes-Bolyai
Abstract: Let y(t) be a monotone increasing curve with lim(t ->+/-infinity) y((n))(t) = 0 for all n and let t(n) be the location of the global extremum of the nth derivative y((n))(t). Under certain assumptions on the Fourier and Hilbert transforms of y(t), we prove that the sequence {t(n)} is convergent. This implies in particular a preferred choice of the origin of the time axis and an intrinsic definition of the even and odd components of a sigmoidal function. In the context of phase transitions, the limit point has the interpretation of the critical point of the transition as discussed in previous work [3].
ISSN: 0252-1938
Appears in Collections:Fizik Bölümü Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu
WoS İndeksli Yayınlar Koleksiyonu

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