Geodesic
Schur-convex functions of the $2$nd order on $ \mathbb{R}^n$
Algebra i analiz, Tome 31 (2019) no. 5, pp. 184-205.

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In the author's earlier paper [Revyakov M., J. Multivariate Anal. 116 (2013) 25-34] concerning mathematical statistics, a need arose to employ functions called "Schur-convex functions of the $2$nd order with respect to two variables". In the present paper, the class of Schur-convex functions of the $2$nd order in $ n$ variables is introduced. Necessary and sufficient conditions (in the form of analogs of the Sylvester criterion) are established for a function to belong to this class. Examples are given of using Schur-convex functions of the $2$nd order for achieving maximal system reliability on the set of all possible allocations of elements into its subsystems.
Keywords: Schur-convex function, Hessian matrix, Sylvester criterion, system reliability, ordered allocation, majorization on a line. 
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M. I. Revyakov. Schur-convex functions of the $2$nd order on $ \mathbb{R}^n$. Algebra i analiz, Tome 31 (2019) no. 5, pp. 184-205. http://geodesic.mathdoc.fr/item/AA_2019_31_5_a5/

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