Introducing complex numbers into basic growth functions - (VI) hypothetic breakdown of '1' into complex numbers and application to definite integral of exp(t) expanded into infinite series

Masataka Shimojo, Kentarou Ikeda, Yoki Asano, Reiko Ishiwaka, Hiroyuki Sato, Yutaka Nakano, Manabu Tobisa, Noriko Ohba, Minako Eguchi, Yasuhisa Masuda

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The definite integral of exp(t) expanded into infinite series included two sets of '1+(-1)' in the calculation of growth, and each of '1' and '-1' was described using the product of eight complex numbers. The present study was designed under hypotheses to leave complex numbers by the breakdown of product form in the complex representation of '1', where a minus sign was given to each of even-numbered pieces of complex number out of eight in order to conserve the value of '1'. This was followed by inserting them into the calculation of growth using exp(t). The results obtained were as follows. The value of '1' was constructed by the product of complex numbers that were different in part from those used in the primary description, which was caused by giving a minus sign to each of even-numbered (2, 4, 6, 8) pieces of complex number. The hypothetic breakdown of product form in the complex representation of '1' left zero, two or four sorts of complex numbers. The complex numbers were left in more pieces when a minus sign was given to each of the four pieces of complex number than when given to each of the two, six or eight pieces. Inserting complex numbers that were left into exp(t) did not influence the calculation of growth, suggesting that the definite integral of exp(t) expanded into infinite series was accompanied hypothetically by pair appearances and pair disappearances of complex numbers with their opposites.

Original languageEnglish
Pages (from-to)407-414
Number of pages8
JournalJournal of the Faculty of Agriculture, Kyushu University
Volume50
Issue number2
Publication statusPublished - Oct 1 2005

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Growth

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Agronomy and Crop Science

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Introducing complex numbers into basic growth functions - (VI) hypothetic breakdown of '1' into complex numbers and application to definite integral of exp(t) expanded into infinite series. / Shimojo, Masataka; Ikeda, Kentarou; Asano, Yoki; Ishiwaka, Reiko; Sato, Hiroyuki; Nakano, Yutaka; Tobisa, Manabu; Ohba, Noriko; Eguchi, Minako; Masuda, Yasuhisa.

In: Journal of the Faculty of Agriculture, Kyushu University, Vol. 50, No. 2, 01.10.2005, p. 407-414.

Research output: Contribution to journalArticle

Shimojo, Masataka ; Ikeda, Kentarou ; Asano, Yoki ; Ishiwaka, Reiko ; Sato, Hiroyuki ; Nakano, Yutaka ; Tobisa, Manabu ; Ohba, Noriko ; Eguchi, Minako ; Masuda, Yasuhisa. / Introducing complex numbers into basic growth functions - (VI) hypothetic breakdown of '1' into complex numbers and application to definite integral of exp(t) expanded into infinite series. In: Journal of the Faculty of Agriculture, Kyushu University. 2005 ; Vol. 50, No. 2. pp. 407-414.
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