@article{oai:mie-u.repo.nii.ac.jp:00005710,
 author = {林, 拙郎 and Hayashi, Setuo},
 journal = {三重大学生物資源学部紀要 = The bulletin of the Faculty of Bioresources, Mie University},
 month = {Jan},
 note = {application/pdf, A discussion on a υ-ρ trajectory before reaching a full-density curve is given.This υ-ρ trajectory is derived from υ-t and ρ-t curves. First, the following equation is assumed for the decreasing process of stand density from the initial condition: (1/ρ) dρ/ dt=-λmρ/ρ0, λm=m{t^(m- 1)}/α. Here, ρ is the stand density, ρ₀ the initial stand density, t the time, and m and α the constants. The solution of this equation is : ρ₀ /ρ= 1 ＋(t^ m)/α. Second, the following equation is assumed for the growth process of the stand from the imitial condition; (1/υ₀) dυ/dt= λ₀ m{t^(m - 1)}/α. Here, υ is the mean stem-volume and υ₀ the initial value of υ.The solution of this equation is given as: υ/υ₀ = 1 +λ₀ (t^m)/α. Here, m and α are the same values  in the case of formula ρ(t). The results of the fitting above formula for the stand density and time data of SPURR et al. yield the each coefficients of formula ρ(t). Thus, m value is given as: m=3. The results of eliminating (t^m/α) from these ρ(t) and υ(t) equations yield the following formula: 1/ρ=Aυ+B, A=1/(λ₀ρ₀υ₀), B=(λ₀-1)/(λ₀ρ₀). This equation is simplest in equations of υ-ρ trajectry before reaching the full-density curve. and it is a kind of TADAKI type equation. In addition, the υ-t, ρ-t and υ-ρ equations are derived too in case of consideration of goal values (V) and (ρ). ρ(t) equation is related to equation υ(t) except for the growth coefficient in the following way :ρ∝1/υ(symbol z^x/α represents zx /αin the avobe formula).},
 pages = {9--22},
 title = {同種・同齢林の成長関係 : 自然枯死線},
 volume = {5},
 year = {1991}
}