Introducing viewpoints of mechanics into basic growth analysis - (XI) negative weight problem in basic growth functions and its hypothetic avoidance by sign reversal of relative growth rate, space inversion and time reversal

This study was conducted to avoid negative weight problem hypothetically by applying sign reversal of relative growth rate, space inversion and time reversal to basic growth functions with negative weight. The negative weight occurred when ± signs are given to each of three terms including weight when the square root was taken to solve a differential equation for basic growth mechanics. The positive weight was the animal body weight and the negative weight was interpreted as the feed whose absolute value was expressed in terms of the animal body weight. The results obtained were as follows. Space inversion suggested that the feed was produced at the external space of the animal body. Time reversal suggested that the feed was produced before fed to the animal. The product of sign reversal of RGR and space inversion or time reversal gave positive weight to the feed. These mathematical operations were summarized by the transformation of coordinates from (r, x, y, z, t, -W_o) to (-r, -x, -y, -z, -t, W_o). Thus, the animal ate the feed with positive weight. It was suggested from the present study that the negative weight problem in basic growth functions was hypothetically avoided by applying sign reversal, space inversion and time reversal.