The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve
The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve
The “generalized logistic growth curve” or the “5-point sigmoid” is a typical example for sigmoidal curves without symmetry and it is commonly used for non-linear regression. The “critical point” of a sigmoidal curve is defined as the limit, if it exists, of the points where its derivatives reach their absolute extreme values. The existence and the location of the critical point of a sigmoidal curve is expressed in terms of its Fourier transform. In this work, we obtain the Fourier transform of the first derivative of the generalized logistic growth curve in terms of Gamma functions and we discuss special cases.
___
- [1] Abramowitz, M., Stegun, I. A., (1972). Handbook of Mathe-matical Functions, Dover, New York, USA.
- [2] Beukers, F., (2007). Gauss’ Hypergeometric Function. Prog-ress in Mathematics. 260, 23–42.
- [3] Bilge, A.H., Pekcan, O., Gurol, M.V., (2012). Application of epidemic models to phase transitions. Phase Transitions. 85(11), 1009–1017.
- [4] Bilge, A.H., Pekcan, O., (2013). A Mathematical Description of the Critical Point in Phase Transitions. Int. J. Mod. Phys. C. 24.
- [5] Bilge, A.H., Pekcan, O., (2015). A mathematical characteri-zation of the gel point in sol-gel transition, Edited by: Va-genas, EC; Vlachos, DS; Bastos, C; et al., 3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014) August 28-31, 2014, Madrid, SPAIN, Journal of Physics Conference Series. 574.
- [6] Bilge, A.H., Ozdemir, Y., (2016). Determining the Critical Point of a Sigmoidal Curve via its Fourier Transform, Edited by Vagenas, E.C. and Vlachos, D.S., 5th International Confe-rence on Mathematical Modeling in Physical Sciences(IC-M-SQUARE 2016) May 23-26, 2016, Athens, GREECE, Jour-nal of Physics Conference Series. 738.
- [7] Bilge, A.H., Pekcan, O., Kara, S., Ogrenci, S., (2017). Epi-demic models for phase transitions: Application to a physical gel, 4th Polish-Lithuanian-Ukrainian Meeting on Ferroelect-rics Physics Location: Palanga, LITHUANIA, 05-09 Septem-ber 2016, Phase Transitions. 90(9), 905–913.
- [8] [Gradshteyn, I.S., Ryzhik I.M., (2007). Table of Integrals, Series, and Products. A. Jeffrey, D. Zwillinger (ed.), Elsevier Inc., USA.
- [9] Papoulis, A., (1962). The Fourier Integral and its Applicati-ons. McGraw-Hill Co., New York, USA.
- [10] Pearson J., (2009). Computation of Hypergeometric Functi-ons. MSc Thesis, Oxford University, UK
- Yayın Aralığı: Yılda 4 Sayı
- Yayıncı: Marmara Üniversitesi
Sayıdaki Diğer Makaleler
The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve
Yunus ÖZDEMİR, Ayşe Hümeyra BİLGE
Comparison of Hole Quality of Polyamide Materials Produced by Traditional and Additive Manufacturing