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[增长函数\(w = e^{(\sin(\frac{\pi}{2}(\frac{t}{t_e})^p))^{2q}}\)及其性质(作者译)]

[The growth function w = e (sin (pi/2(t/te)(p))) (2q) and its properties (author's transl)].

作者信息

Sager G

出版信息

Anat Anz. 1979;145(4):369-79.

PMID:507368
Abstract

Preceding investigations into increase functions of organic growth and their integration to growth functions have repeatedly shown curves looking like axially deformed harmonic functions. Arising from this experience the function W = E (sin (pi/2)t/tE)(p)))(2q) is considered and shown to be settled between growth functions of the increase types dW/dt = ktp(E--W)n and dW/dt = kWm(tE--t)q respectively. After gaining relations of the parameters to the basic values of growth and time graphs are given for the growth and increase functions in general and for 1 = 1 and p = 1 as special cases.

摘要

先前对有机生长增加函数及其与生长函数整合的研究反复表明,曲线看起来像轴向变形的调和函数。基于这一经验,考虑了函数(W = E (\sin (\frac{\pi}{2}\frac{t}{t_E}))^{2q}),并表明它分别介于增长类型为(\frac{dW}{dt} = kt^p(E - W)^n)和(\frac{dW}{dt} = kW^m(t_E - t)^q)的增长函数之间。在得到参数与生长基本值的关系后,给出了一般生长和增加函数以及(l = 1)和(p = 1)特殊情况下的生长和时间图。

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