Density effects on the growth and self-thinning of Eucalyptus urophylla stands were examined for 7 years.The reciprocal equation of the competition-density(C–D)effect was used to describe the C–D effect in even-aged...Density effects on the growth and self-thinning of Eucalyptus urophylla stands were examined for 7 years.The reciprocal equation of the competition-density(C–D)effect was used to describe the C–D effect in even-aged pure stands of E. urophylla during course of self-thinning and showed a good fit to the data. The time trajectories of mean stem volume-density nearly paralleled the y-axis during early growth stages of stands, and then began to curve left. Finally, the mean stem volume-density trajectories of the low-, middle-and high-density stands tended to follow the self-thinning lines with slopes of-2.01,-1.90 and-1.99, respectively. With increasing physical time t, the biological time s increased rapidly during early growth stages and became slow gradually during later growth stages. Realized density-initial density curves tended to become more or less flat with increasing initial density, indicating the existence of an asymptotic value for density at a given time. The coefficient e, the reciprocal of which represents the asymptotic density at a given time,increased with increasing biological time s, indicating that the asymptotic density decreased with increasing stand age.Final yield Y(t) increased gradually with increasing stand age.展开更多
The bending of the thin elastic semicircular plates, because of its complicated boundary conditions, brings some difficulties for us to obtain its solution. This paper applies the reciprocal theorem to propose a gener...The bending of the thin elastic semicircular plates, because of its complicated boundary conditions, brings some difficulties for us to obtain its solution. This paper applies the reciprocal theorem to propose a general simple convenient method to obtain the transverse deflectional equations of the plates.展开更多
Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact sol...Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.展开更多
基金partially supported by the Forestry Technology Popularization Demonstration Project of the Central Government of China(No.[2015]GDTK-07)
文摘Density effects on the growth and self-thinning of Eucalyptus urophylla stands were examined for 7 years.The reciprocal equation of the competition-density(C–D)effect was used to describe the C–D effect in even-aged pure stands of E. urophylla during course of self-thinning and showed a good fit to the data. The time trajectories of mean stem volume-density nearly paralleled the y-axis during early growth stages of stands, and then began to curve left. Finally, the mean stem volume-density trajectories of the low-, middle-and high-density stands tended to follow the self-thinning lines with slopes of-2.01,-1.90 and-1.99, respectively. With increasing physical time t, the biological time s increased rapidly during early growth stages and became slow gradually during later growth stages. Realized density-initial density curves tended to become more or less flat with increasing initial density, indicating the existence of an asymptotic value for density at a given time. The coefficient e, the reciprocal of which represents the asymptotic density at a given time,increased with increasing biological time s, indicating that the asymptotic density decreased with increasing stand age.Final yield Y(t) increased gradually with increasing stand age.
文摘The bending of the thin elastic semicircular plates, because of its complicated boundary conditions, brings some difficulties for us to obtain its solution. This paper applies the reciprocal theorem to propose a general simple convenient method to obtain the transverse deflectional equations of the plates.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11875040 and 12171308)
文摘Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.
