| Issue |
MATEC Web Conf.
Volume 175, 2018
2018 International Forum on Construction, Aviation and Environmental Engineering-Internet of Things (IFCAE-IOT 2018)
|
|
|---|---|---|
| Article Number | 03036 | |
| Number of page(s) | 5 | |
| Section | Computer Simulation and Design | |
| DOI | https://doi.org/10.1051/matecconf/201817503036 | |
| Published online | 02 July 2018 | |
An elementary proof that real roots nonexistence of nonlinear equations and its optimal solutions
1
School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing Jiangsu 211800, China
2
Office of Information Construction and Management, Nanjing Institute of Technology, Nanjing Jiangsu 211167, China
a Corresponding author: lujinguin@163.com, lilanyou@163.com
In this paper, we give an elementary proof that the real roots nonexistence of nonlinear equation such as: xn+yn+zn=n,where n =1,2,3,(x,y,z)∈ℝ by contradiction. Thus, when n takes all positive integers between 4 and 1981, the value of function f= xn+yn+zn based on the exact solution of the above equations is still real. Finally, numerical experiments presents a set of approximate numerical solutions by using standard genetic algorithm(SGA), adaptive particle swarm optimization algorithm(APSO) and artificial fish swarm algorithm(AFSA).
© The Authors, published by EDP Sciences 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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