Introducing complex numbers into basic growth functions - (I) applying complex representation of '1' to differentiation of exponential function with base e expanded into infinite series

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

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The basic growth analysis using exponential function with base e is a primary factor in the management of forages and ruminants. The present study was conducted to investigate the application of complex representation of '1' and '0' to the differentiation of exp(t) expanded into infinite series. The results obtained were as follows. The differentiation of '1', resulting in '0', was replaced by pair disappearances of complex numbers with their opposites occurring after the hypothetic breakdown of multiplication form connecting them to construct '1'. The differentiation of (t/1!) with respect to t, resulting in '1', was replaced by the product of eight complex numbers constructing '1'. These results suggested that there were hypothetic pair appearances and disappearances of complex numbers according to the fluctuation between '1' and '0' occurring whenever the rate of growth was calculated.

Original languageEnglish
Pages (from-to)331-335
Number of pages5
JournalJournal of the Faculty of Agriculture, Kyushu University
Volume49
Issue number2
Publication statusPublished - Oct 1 2004

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range management
ruminants
Ruminants
Growth

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Agronomy and Crop Science

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Introducing complex numbers into basic growth functions - (I) applying complex representation of '1' to differentiation of exponential function with base e expanded into infinite series. / Shimojo, Masataka; Ikeda, Kentaro; Ishiwaka, Reiko; Sato, Hiroyuki; Asano, Yoki; Tobisa, Manabu; Nakano, Yutaka; Ohba, Noriko; Eguchi, Minako; Masuda, Yasuhisa.

In: Journal of the Faculty of Agriculture, Kyushu University, Vol. 49, No. 2, 01.10.2004, p. 331-335.

Research output: Contribution to journalArticle

Shimojo, Masataka ; Ikeda, Kentaro ; Ishiwaka, Reiko ; Sato, Hiroyuki ; Asano, Yoki ; Tobisa, Manabu ; Nakano, Yutaka ; Ohba, Noriko ; Eguchi, Minako ; Masuda, Yasuhisa. / Introducing complex numbers into basic growth functions - (I) applying complex representation of '1' to differentiation of exponential function with base e expanded into infinite series. In: Journal of the Faculty of Agriculture, Kyushu University. 2004 ; Vol. 49, No. 2. pp. 331-335.
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AU - Sato, Hiroyuki

AU - Asano, Yoki

AU - Tobisa, Manabu

AU - Nakano, Yutaka

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