Introducing Viewpoints of Mechanics into Basic Growth Analysis : (XIV) Growth Dynamics and Related Problems based on Mathematical Properties of Modified Differential Equation for Growth
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This study was conducted to investigate growth dynamics and related problems by analyzing mathematical properties of whole solutions to modified differential equation for growth. This modified differential equation was obtained by relating basic growth function with its first and second derivatives. The results obtained were as follows. (1) Sixteen functions were whole solutions to the modified differential equation for growth. Each of weight, relative growth rate (RGR), time and exponential function with base e was given positive and negative signs, namely symmetries in them with respect to ± signs. Functions in which time was replaced with space were also taken up. (2) The conservation of positive weight, by avoiding negative weight, required the existence of the past and that of the environmental space. (3) There were time reversal and space inversion theoretically in functions. But actually there was a breakdown of those symmetries, because moving forward in time is the principle of information transmission and there is an effect of gravity determining the upper and lower sides. (4) The hypothesis that RGR in functions was a mixture of positive and negative RGRs was discussed in relation to metabolic turnover, compensatory growth and homeostasis. (5) The form of the modified differential equation for growth suggested analogies to laws of motion. It was suggested from the present study that growth dynamics and related problems resulted from conservation, symmetry and analogy in whole solutions to modified differential equation for growth.
- 2010-10-29
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