Shrinkage in Ternary Mixes of Container Media

Abstract

43Based on functional relationships established for binary mixes of container media, a mathematical model is proposed for ternary component mixtures. Shrinkage values are generated for three-component mixtures based on mathematical equations. Empirically observed shrinkage values for corresponding three-component mixtures are determined and used as the basis for assessing the reliability of the proposed mathematical model for characterizing shrinkage in mixtures of container media. . Regression equations were developed and compared for both theoretical and empirical results.

Canonical reduction of second-order fitted models subject to linear restrictions

“…5. Three ingredients mixture example (Bures et al, 1992) We illustrate some of the details above via a three-ingredient (q = 3) example in the usual mixture space x 1 + x 2 + x 3 = 1 (m = 1), leading to a canonical reduction in q − m = 2 dimensions. Consider the ÿtted mixture model in three ingredients ŷ = −0:00658x 1 − 0:00243x 2 + 0:00367x 3 + 0:34265x 1 x 2 + 0:47074x 1 x 3 + 0:14115x 2 x 3 , derived fromselected data for the proportional shrinkage of a m ixture of three ingredients forming an artiÿcial medium for growing plants.…”