TY - JOUR

T1 - 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

AU - Shimojo, Masataka

AU - Ikeda, Kentaro

AU - Ishiwaka, Reiko

AU - Sato, Hiroyuki

AU - Asano, Yoki

AU - Tobisa, Manabu

AU - Nakano, Yutaka

AU - Ohba, Noriko

AU - Eguchi, Minako

AU - Masuda, Yasuhisa

PY - 2004/10

Y1 - 2004/10

N2 - 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.

AB - 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.

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U2 - 10.5109/4593

DO - 10.5109/4593

M3 - Article

AN - SCOPUS:10044285840

SN - 0023-6152

VL - 49

SP - 331

EP - 335

JO - Journal of the Faculty of Agriculture, Kyushu University

JF - Journal of the Faculty of Agriculture, Kyushu University

IS - 2

ER -