We consider certain classes of functions with a restriction on the fractality of their graphs.
Maxim L. Gridnev 2017, 'DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THEFRACTALITY OF THEIR GRAPHS', Ural Mathematical Journalhttps://umjuran.ru/index.php/umj/article/view/103. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The complex signal has several properties including a chaotic behavior, fractality or self-similarityproperty.
Rizal Achmad, Hidayat Risanuri, Nugroho Hanung Adi 2018, 'Fractality evaluation for pulmonary crackle sound using the Degree of Self-Similarity',MATEC Web of Conferenceshttps://doi.org/10.1051/matecconf/201815401038. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
As has been reported previously, these distributions exhibit complex statistical properties and fractality.
G. Michas, F. Vallianatos, P. Sammonds 2013, 'Non-extensivity and long-range correlations in the earthquake activity at the WestCorinth rift (Greece)', Nonlinear Processes in Geophysicshttp://www.nonlin-processes-geophys.net/20/713/2013/npg-20-713-2013.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The degree of fractality may be used for automatic keyword detection.
Elham Najafi, Amir H. Darooneh 2015, 'The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction',PLOS ONE10.1371/journal.pone.0130617. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
There are such properties as symmetry, asymmetry, self-similarity and fractality used in the modern architecture.
Mayatskaya Irina, Yazyev Batyr, Yazyeva Svetlana, Kulinich Polina 2017, 'Building constructions: architecture and nature', MATEC Web of Conferenceshttps://doi.org/10.1051/matecconf/201710601031. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Thus, secondary insults to the injured cord disrupt intraspinal pressure fractality.
Suliang Chen, Mathew J. Gallagher, Marios C. Papadopoulos, Samira Saadoun 2018, 'Non-linear Dynamical Analysis of Intraspinal Pressure Signal Predicts Outcome AfterSpinal Cord Injury', Frontiers in Neurologyhttps://www.frontiersin.org/article/10.3389/fneur.2018.00493/full. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
This review begins with information on fractality and statistical self-similar structure.
Gómez Herrera, C. 2004, 'Naturaleza fractal en redes de cristales de grasas', Grasas y Aceiteshttp://grasasyaceites.revistas.csic.es/index.php/grasasyaceites/article/view/165/165. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
There are many methods to study time series in terms of their fractality.
Puchalski Andrzej, Komorska Iwona 2019, 'Data-driven monitoring of the gearbox using multifractal analysis and machine learningmethods', MATEC Web of Conferenceshttps://doi.org/10.1051/matecconf/201925206006. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
These processes exhibit temporal fractality and non-local behaviors.
JE Escalante-Martínez, JF Gómez-Aguilar, C Calderón-Ramón, LJ Morales-Mendoza, I Cruz-Orduña,JR Laguna-Camacho 2016, 'Experimental evaluation of viscous damping coefficient in the fractional underdampedoscillator', Advances in Mechanical Engineeringhttp://ade.sagepub.com/content/8/4/1687814016643068.full.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Moreover, we found that images exhibited the highest fractality close to the global histogram threshold level.
Laura Maugeri, Mauro DiNuzzo, Marta Moraschi, Charles Nicaise, Inna Bukreeva, FabioMangini, Federico Giove, Alessia Cedola, Michela Fratini 2018, 'Fractal Dimension Analysis of High-Resolution X-Ray Phase Contrast Micro-TomographyImages at Different Threshold Levels in a Mouse Spinal Cord', Condensed Matterhttps://www.mdpi.com/2410-3896/3/4/48. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)