Title: Generation of new knowledge and optimisation of systems and processes through meaningful interpretation of algebraic inequalities

Authors: Michael Todinov

Addresses: School of Engineering, Computing and Mathematics, Oxford Brookes University, Oxford, UK

Abstract: The paper introduces a method for increasing the impact of additive quantities by meaningful interpretation of multivariate sub-additive and super-additive functions. The paper demonstrates that the segmentation of additive quantities through sub-additive and super-additive functions can be used to generate new knowledge and optimise systems and processes and the presented algebraic inequalities are applicable to any area of science and technology. The meaningful interpretation of the modified Cauchy-Schwarz inequality, led to a method for increasing of the power output from a voltage source and to a method for increasing the capacity for absorbing strain energy of loaded mechanical components. It was found that the existence of asymmetry is essential to increasing the strain energy absorbing capacity and the power output. Loaded elements experiencing the same displacement do not yield an increase of the absorbed strain energy. Similarly, loaded resistances experiencing the same current do not yield an increase of the power output. Finally, the meaningful interpretation of an algebraic inequality in terms of potential energy resulted in a general necessary condition for minimising the sum of powers of distances to a fixed number of points in space.

Keywords: algebraic inequalities; sub-additive multivariate functions; super-additive multivariate functions; extensive quantities; segmentation.

DOI: 10.1504/IJMMNO.2021.118409

International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.4, pp.428 - 449

Received: 10 Aug 2020
Accepted: 17 Feb 2021
Published online: 25 Oct 2021 *

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