Pure and Applied Mathematics Journal
Volume 4, Issue 2-1, March 2015, Pages: 7-13
Received: Nov. 22, 2014;
Accepted: Dec. 2, 2014;
Published: Dec. 27, 2014
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Keiichi Takahashi, Department Information and Computer Sciences, Faculty of Humanity-Oriented Science and Engineering, Kinki University, Iizuka, Fukuoka, Japan
Takayasu Kaida, Department Information and Computer Sciences, Faculty of Humanity-Oriented Science and Engineering, Kinki University, Iizuka, Fukuoka, Japan
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 ,  and . In , 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  that the stability is preserved by the Cartesian product of many copies of the attractor, we may conceive of the nested PSO.
Descartes’ Dream: Cartesian Products, Pure and Applied Mathematics Journal. Special Issue: Abridging over Troubled Water---Scientific Foundation of Engineering Subjects.
Vol. 4, No. 2-1,
2015, pp. 7-13.
R. C. Blei, Fractional Cartesian products of sets, Ann. Inst. Fourier (Grenoble) 29 (1979), 79-105.
C. Bonfiglio and W. Roessler, A cost optimized battery management system with active cell balancing for Lithium ion battery stacks, IEEE 2009.
A. Carbone and M. Gromov, A mathematical slices of molecular biology, Supplement to volume 88 of Gazette des Mathématiciens, French Math. Soc. (SMF), Paris 2001?
J. -Y. Cao and B. -G. Cao, Design of fractional order controllers based on particle swarm optimization, 2006.
P. J. Davis and R. Hersh, Descartes’ dream—The world according to mathematics, Harcourt Brace Jovanovich Publ., San Diego etc. 1986.
L. Jiang, S. Kanemitsu and H. Kitajima, Circulants, linear recurrences and codes, Ann. Univ. Sci. Budapest. Eötvös Sect. Comput.,to appear.
J. Justesen and T. Hoholdt, A course in error correcting codes, European Math. Soc. 2004.
S. Kanemitsu and M. Waldschmidt, Matrices of finite Abelian groups, finite Fourier transforms and codes, Proc. 6th China-Japan Sem. Number Theory, World Sci. London-Singapore-New Jersey, 2013, 90-106.
J. Kotre, White gloves—How we create ourselves from our memory, The Free Press, New York etc. 1995.
[NTA] F.-H. Li, N.-L. Wang and S. Kanemitsu, Number Theory and its Applications, World Scientific, Singapore etc. 2013.
J. L. Massey, Shift-register synthesis and BCH decoding, IEEE Trans. on Info. Th. IT-15 (1969), 122-127.
J. L. Massey, The discrete Fourier transform in coding and cryptography, IEEE Inform. Theory Workshop ITW 98, San Diego (1998), 9-11.
Y. Hayakawa, Systems and their control, Ohmsha, Tokyo 2008 (in Japanese).
J. W. Helon and O. Merino, Classical control using H^∞ method, Theory, optimization, and design, SIAM. Philadelphia 1998.
J. Kennedy and R. C. Eberhart, Particle swarm optimization, Proc. IEEE Intern. Conf. Neural Networks, 1942-1948, Piscateway, New Jersey 1995.
H. Kimura, Chain scattering approach to H^∞-control, Birkhäuser, Boston/Basel/Berlin 1997.
I. Podlubny, Fractional-order systems and PI^λ D^δ controllers, IEEE Trans. Autom. Control, 44, No.1 (1999), 208-213.
I. Podlubny, Geometric and physical interpretation of fractional integration and fraction differentiation, Fractional calculus and applied analysis, 5, No. 4 (2002), 367-386.
V.Pless, Introduction to the Theory of Error-Correcting Codes, 2nd ed., Wiley, New York etc.1989.
R. Shoenheimer, The dynamic state of body constituents, Harvard Univ. Press. Massachusetts, 1942.
K. Takahashi, G. Hirano, T. Kaida, S. Kanemitsu, H. Tsukada and T. Matsuzaki, Record of the second and the third interdisciplinary seminars, Kayanomori 14 (2011), 64-72.
K. Takahashi, G. Hirano, T. Kaida, S. Kanemitsu, H. Tsukada and T. Matsuzaki, Fluctuations in science and music, Kayanomori 25 (2014), to appear.
Sh.-Ch. Wang and Y.-H. Liu, PSO-based Fuzzy logic optimization of dual performance characteristic indices for fast charging of Lithium-ion batteries, MS.
Z.-Y. Zou, PSO optimization for cell-balancing charge of Lithium ion batteries, MS.