In the last century, especially in the last half of the century, there was the paradigm of sectionalism prevailing and sciences and engineering were divided into very small parts which are mutually independent. It was like in Babel where there was no common language to communicate. The purpose of this paper is to present one of the possible glues—the notion of Cartesian product—to stick some remotely separated parts of science and engineering together. This concept appears in various places and it will turn out that it can unify the scattered notions quite well. Our two main objectives are the interpretation of cyclic codes as polynomials and nested PSO. We make clear the meaning of polynomials through Cartesian product or rather as terminating formal power series. The latter, formal power series, is not touched in engineering disciplines but is quite useful in unifying and interpreting various notions. In particular, it will make clear the meaning of addition of polynomials. This reminds us of topologization of adéles. PSO (Particle Swarm Optimization), a developed form of genetic algorithm, has come to our attention through the papers [4], [23] and [24]. In [4], the PSO is used to find optimal choice of parameters in the FOPID. In other two papers, PSO algorithm is used in cell balancing in the Lithium-ion battery pack for EV’s. Motivated by the passage on [3] that the stability is preserved by the Cartesian product of many copies of the attractor, we may conceive of the nested PSO.
| Published in |
Pure and Applied Mathematics Journal (Volume 4, Issue 2-1)
This article belongs to the Special Issue Abridging over Troubled Water---Scientific Foundation of Engineering Subjects |
| DOI | 10.11648/j.pamj.s.2015040201.12 |
| Page(s) | 7-13 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Cartesian Product, Formal Power Series, Cyclic Codes, PSO Algorithm, Nested PSO
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APA Style
Keiichi Takahashi, Takayasu Kaida. (2014). Descartes’ Dream: Cartesian Products. Pure and Applied Mathematics Journal, 4(2-1), 7-13. https://doi.org/10.11648/j.pamj.s.2015040201.12
ACS Style
Keiichi Takahashi; Takayasu Kaida. Descartes’ Dream: Cartesian Products. Pure Appl. Math. J. 2014, 4(2-1), 7-13. doi: 10.11648/j.pamj.s.2015040201.12
AMA Style
Keiichi Takahashi, Takayasu Kaida. Descartes’ Dream: Cartesian Products. Pure Appl Math J. 2014;4(2-1):7-13. doi: 10.11648/j.pamj.s.2015040201.12
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Download@article{10.11648/j.pamj.s.2015040201.12,
author = {Keiichi Takahashi and Takayasu Kaida},
title = {Descartes’ Dream: Cartesian Products},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {2-1},
pages = {7-13},
doi = {10.11648/j.pamj.s.2015040201.12},
url = {https://doi.org/10.11648/j.pamj.s.2015040201.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040201.12},
abstract = {In the last century, especially in the last half of the century, there was the paradigm of sectionalism prevailing and sciences and engineering were divided into very small parts which are mutually independent. It was like in Babel where there was no common language to communicate. The purpose of this paper is to present one of the possible glues—the notion of Cartesian product—to stick some remotely separated parts of science and engineering together. This concept appears in various places and it will turn out that it can unify the scattered notions quite well. Our two main objectives are the interpretation of cyclic codes as polynomials and nested PSO. We make clear the meaning of polynomials through Cartesian product or rather as terminating formal power series. The latter, formal power series, is not touched in engineering disciplines but is quite useful in unifying and interpreting various notions. In particular, it will make clear the meaning of addition of polynomials. This reminds us of topologization of adéles. PSO (Particle Swarm Optimization), a developed form of genetic algorithm, has come to our attention through the papers [4], [23] and [24]. In [4], the PSO is used to find optimal choice of parameters in the FOPID. In other two papers, PSO algorithm is used in cell balancing in the Lithium-ion battery pack for EV’s. Motivated by the passage on [3] that the stability is preserved by the Cartesian product of many copies of the attractor, we may conceive of the nested PSO.},
year = {2014}
}
TY - JOUR T1 - Descartes’ Dream: Cartesian Products AU - Keiichi Takahashi AU - Takayasu Kaida Y1 - 2014/12/27 PY - 2014 N1 - https://doi.org/10.11648/j.pamj.s.2015040201.12 DO - 10.11648/j.pamj.s.2015040201.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 7 EP - 13 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040201.12 AB - In the last century, especially in the last half of the century, there was the paradigm of sectionalism prevailing and sciences and engineering were divided into very small parts which are mutually independent. It was like in Babel where there was no common language to communicate. The purpose of this paper is to present one of the possible glues—the notion of Cartesian product—to stick some remotely separated parts of science and engineering together. This concept appears in various places and it will turn out that it can unify the scattered notions quite well. Our two main objectives are the interpretation of cyclic codes as polynomials and nested PSO. We make clear the meaning of polynomials through Cartesian product or rather as terminating formal power series. The latter, formal power series, is not touched in engineering disciplines but is quite useful in unifying and interpreting various notions. In particular, it will make clear the meaning of addition of polynomials. This reminds us of topologization of adéles. PSO (Particle Swarm Optimization), a developed form of genetic algorithm, has come to our attention through the papers [4], [23] and [24]. In [4], the PSO is used to find optimal choice of parameters in the FOPID. In other two papers, PSO algorithm is used in cell balancing in the Lithium-ion battery pack for EV’s. Motivated by the passage on [3] that the stability is preserved by the Cartesian product of many copies of the attractor, we may conceive of the nested PSO. VL - 4 IS - 2-1 ER -
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