The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve
Yıl: 2020 Cilt: 32 Sayı: 1 Sayfa Aralığı: 52 - 56 Metin Dili: İngilizce DOI: 10.7240/jeps.598861 İndeks Tarihi: 22-12-2020
The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve
Öz: 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.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [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
APA | Bilge A, OZDEMIR Y (2020). The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. , 52 - 56. 10.7240/jeps.598861 |
Chicago | Bilge Ayse Humeyra,OZDEMIR YUNUS The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. (2020): 52 - 56. 10.7240/jeps.598861 |
MLA | Bilge Ayse Humeyra,OZDEMIR YUNUS The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. , 2020, ss.52 - 56. 10.7240/jeps.598861 |
AMA | Bilge A,OZDEMIR Y The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. . 2020; 52 - 56. 10.7240/jeps.598861 |
Vancouver | Bilge A,OZDEMIR Y The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. . 2020; 52 - 56. 10.7240/jeps.598861 |
IEEE | Bilge A,OZDEMIR Y "The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve." , ss.52 - 56, 2020. 10.7240/jeps.598861 |
ISNAD | Bilge, Ayse Humeyra - OZDEMIR, YUNUS. "The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve". (2020), 52-56. https://doi.org/10.7240/jeps.598861 |
APA | Bilge A, OZDEMIR Y (2020). The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. International journal of advances in engineering and pure sciences (Online), 32(1), 52 - 56. 10.7240/jeps.598861 |
Chicago | Bilge Ayse Humeyra,OZDEMIR YUNUS The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. International journal of advances in engineering and pure sciences (Online) 32, no.1 (2020): 52 - 56. 10.7240/jeps.598861 |
MLA | Bilge Ayse Humeyra,OZDEMIR YUNUS The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. International journal of advances in engineering and pure sciences (Online), vol.32, no.1, 2020, ss.52 - 56. 10.7240/jeps.598861 |
AMA | Bilge A,OZDEMIR Y The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. International journal of advances in engineering and pure sciences (Online). 2020; 32(1): 52 - 56. 10.7240/jeps.598861 |
Vancouver | Bilge A,OZDEMIR Y The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve. International journal of advances in engineering and pure sciences (Online). 2020; 32(1): 52 - 56. 10.7240/jeps.598861 |
IEEE | Bilge A,OZDEMIR Y "The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve." International journal of advances in engineering and pure sciences (Online), 32, ss.52 - 56, 2020. 10.7240/jeps.598861 |
ISNAD | Bilge, Ayse Humeyra - OZDEMIR, YUNUS. "The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve". International journal of advances in engineering and pure sciences (Online) 32/1 (2020), 52-56. https://doi.org/10.7240/jeps.598861 |