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Journal article
Specific Mathematical Aspects of Dynamics Generated by Coherence Functions
Mathematical problems in engineering, Vol.2011, 436198
01/01/2011
Web of Science ID: WOS:000285604600001
Abstract
This study presents specific aspects of dynamics generated by the coherence function (acting in an integral manner). It is considered that an oscillating system starting to work from initial nonzero conditions is commanded by the coherence function between the output of the system and an alternating function of a certain frequency. For different initial conditions, the evolution of the system is analyzed. The equivalence between integrodifferential equations and integral equations implying the same number of state variables is investigated; it is shown that integro-differential equations of second order are far more restrictive regarding the initial conditions for the state variables. Then, the analysis is extended to equations of evolution where the coherence function is acting under the form of a multiple integral. It is shown that for the coherence function represented under the form of an nth integral, some specific aspects as multiscale behaviour suitable for modelling transitions in complex systems (e.g., quantum physics) could be noticed when n equals 4, 5, or 6.
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- Title
- Specific Mathematical Aspects of Dynamics Generated by Coherence Functions
- Publication Details
- Mathematical problems in engineering, Vol.2011, 436198
- Resource Type
- Journal article
- Publisher
- Hindawi Publishing Group
- Format
- link
- Number of pages
- 10
- Copyright
- Copyright © 2011 Ezzat G. Bakhoum and Cristian Toma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Identifiers
- WOS:000285604600001; 99380175880606600
- Academic Unit
- Hal Marcus College of Science and Engineering ; Dr. Muhammad Harunur Rashid Department of Electrical and Computer Engineering
- Language
- English