ファイル情報(添付) | |
タイトル |
生長曲線の検討(第2報) : テイラー級数展開とCrozier式
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タイトル |
Analysis of Growth Curve(2) : Taylor Series and the Crozier Equation
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タイトル 読み |
セチョウ キョクセン ノ ケントウ ダイ2ホウ テイラー キュウスウ テンカイ ト CROZIER シキ
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著者 |
山本 充男
安井 鈞
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収録物名 |
島根大学農学部研究報告
Bulletin of the Faculty of Agriculture, Shimane University
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巻 | 17 |
開始ページ | 34 |
終了ページ | 38 |
収録物識別子 |
ISSN 0370940X
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内容記述 |
抄録・要旨
The system of growth can be defined mathematically in various ways. Assuming that the system consists of only one measure y, the system is reduced to the single differential equation :
(dy)/(dt) = f(y) where f(y) is the function of y. Let us assume that f(y) can be developed into Taylor series : f(y) = a_0 + a_1y + a_2y_2 + a_3y_3 + . . . .. Retaining three trems, we have : (dy)/(dt) = a_0 + a_1y + a_2y_2 . This equation is almost the same as the Crozier (Crozier, 1926). Moreover, this equation comes to the Mitscherlich (when a_2 = 0) and the Logistic (when a_0 = 0). Denoting the Crozier by (dy)/(dt) = (K_1 + K_2y)(A - y), the solution of the Crozier is : y =( AB exp[(K_1 + K_2A)t] - K_1)/(B exp[(K_1 + K_2A)t] + K_2) where A. B. K_1 and K_2 are constants. To examine the applicability of the Crozier equation, it was applied to the observed height growth. The Crozier showed a good fit to the growth not only with a clear inflection but also without one, as compared with the Mitscherlich, the Logistic and the Gompertz. The applicability of the Crozier equation in the growthcurve- fitting was recognized. |
言語 |
日本語
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資源タイプ | 紀要論文 |
出版者 |
島根大学農学部
Shimane University, Faculty of Agriculture
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発行日 | 1983-12-20 |
アクセス権 | オープンアクセス |
関連情報 |
[NCID] AN00108015
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