TY - JOUR

T1 - 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

AU - Shimojo, Masataka

AU - Ikeda, Kentarou

AU - Asano, Yoki

AU - Ishiwaka, Reiko

AU - Sato, Hiroyuki

AU - Nakano, Yutaka

AU - Tobisa, Manabu

AU - Ohba, Noriko

AU - Eguchi, Minako

AU - Masuda, Yasuhisa

PY - 2005/10/1

Y1 - 2005/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=27744462351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27744462351&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:27744462351

VL - 50

SP - 407

EP - 414

JO - Journal of the Faculty of Agriculture, Kyushu University

JF - Journal of the Faculty of Agriculture, Kyushu University

SN - 0023-6152

IS - 2

ER -