ABSTRACT
This chapter demonstrates that inequalities based on sub- and super-additive single- and multivariable functions can be interpreted meaningfully if their variables and terms can be interpreted as additive quantities. Subsequently, the generated new knowledge can be used for optimising systems and processes in all areas of science and technology. In mechanical engineering, the meaningful interpretation of inequalities based on a sub-additive multivariable function led to a method for developing light-weight designs, increasing the kinetic energy absorbing capacity during inelastic impact, increasing the stiffness of an assembly and minimising the drag force experienced by an object moving through fluid. In materials science, the meaningful interpretation of an inequality inequalities based on a super-additive function can be used for decreasing the quantity of undesirable second phase during solidification. In electrochemistry, the meaningful interpretation of a new inequality based on a sub-additive function can be used for maximising the mass of deposited substance during electrolysis. An alternative interpretation of the same inequality avoids overestimation of intensive quantities during measurements. Finally, in economics, an inequality based on a sub-additive function can be used for maximising the profit from an investment. Important properties have been established for a process described by the power law. If the power is smaller than unity, the segmentation of the controlling factor leads to a larger total yield from the process. If the power is non-negative and greater than unity, aggregation of the controlling factor leads to a smaller total yield from the process.
