Sergeı̆ Sergeev

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The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is that of strict visualization scaling, defined as, for a given nonnegative matrix A, a diagonal matrix X such that all(More)
(2012): Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings, Linear and Multilinear Algebra, This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is(More)
Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring: it is known that one can separate a vector from a closed subsemimodule that does not contain it. We establish here a(More)
The Analytic Hierarchy Process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche [10, 11] introduced a max-algebraic approach to the single criterion AHP. We extend this to the multi-criteria AHP, by considering multi-objective generalisations of the single objective optimisation problem solved in these(More)
The subject of this paper is the consecutive procedure of discretization and quantization of two similar classical integrable systems in three-dimensional space-time: the standard three-wave equations and less known modified three-wave equations. The quantized systems in discrete space-time may be understood as the regularized integrable quantum field(More)
Investigated is the relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl's q we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six vertex R-matrix. Both independent Baxter's Q-operators are constructed explicitly as seria over local(More)