While many ancient individuals, known and unknown, contributed to the subject, none equaled the impact of Euclid and his Elements of geometry, a book now 2,300 years old and the object of as much painful and painstaking study as the Bible.
Later Mahfoud [3] essentially contributed to the subject and presented a very useful comparison technique for studying the properties of a delay differential equation from those of a differential equation without delay.
ME, MR, AR, SPF, LGL, RM and MC, ACA contributed to the study subject and design.
In addition to directly contributing to the subject, he later applied some of the ideas he developed in the 1930s with great effectiveness to probability theory, as detailed in Harmonic Analysis and the Theory of Probability (1956).
The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results.
AZ contributed to the study design, recruitment of subjects and data analysis, and drafting and editing of the manuscript.
Amir Al-Khami contributed to some of the ex vivo experiments/analysis. Matthew Lammi contributed to the human subjects' referral, assisted in the acquisition of human PBMCs, edited the manuscript and contributed to discussion.
PGF contributed to the initial study design, recruited subjects, collected data and reviewed drafts of the manuscript.
We thank all subjects for contributing to the study.
SB coordinated and contributed to the recruitment of subjects, carried out functional studies, interpreted results and wrote manuscript, PMK contributed to the recruitment of subjects and carried out functional studies, JS performed statistical analysis of data, SRR contributed to the recruitment of subjects and carried out functional studies.
