Abstract In present paper, an analysis of the stability behaviour ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for existence locally perturbed and their nearness a given reference value provided by refining recent results on theory parameterized set-valued inclusions. More precisely, Lipschitz lower semicontinuity property solution ma...

We study solutions of the relativistic hydrodynamical equations, which describe spherical or cylindrical expansion of ideal fluid. We derived approximate solutions involving two arbitrary functions, which describe asymptotic behavior of expanding fireballs in ultra-relativistic limit. In case of a linear equation of state p(ε) = κε − c 1 , (0 < κ < 1) we show that the solution may be represente...

We describe a method for searching for ideal symmetric solutions to the Prouhet-Tarry-Escott Problem. We report results of extensive searches for solutions of sizes up to 12. We found two solutions of size 10 that are smaller by two orders of magnitude than the solution found by A. Letac in the 1940s, which was the smallest size 10 solution known before our search. 1. The Prouhet-Tarry-Escott P...

Solutions of recursive program schemes over a given signature Σ were characterized by Bruno Courcelle as precisely the context-free (or algebraic) Σ-trees. These are the finite and infinite Σ-trees yielding, via labelling of paths, context-free languages. Our aim is to generalize this to finitary endofunctors H of general categories: we construct a monad C “generated” by solutions of recursive ...

In this work, the parallelization of some Multi-Objective Ant Colony Optimization (MOACO) algorithms has been performed. The aim is to get a better performance, not only in running time (usually the main objective when a distributed approach is implemented), but also improving the spread of solutions over the Pareto front (the ideal set of solutions). In order to do this, colony-level (coarsegr...

Solutions of recursive program schemes over a given signature Σ were characterized by Bruno Courcelle as precisely the context-free (or algebraic) Σ-trees. These are the finite and infinite Σ-trees yielding, via labelling of paths, context-free languages. Our aim is to generalize this to finitary endofunctors H of general categories: we construct a monad CH “generated” by solutions of recursive...

In Blind Source Separation problems it is assumed that the approximate diagonalization of a matrix set achieves more robust solutions than the simultaneous diagonalization of a matrix pencil. In this work we will analyse approximate diagonalization methods using a generalized eigendecomposition (GED) of any pair of a given matrix set. The constraints of GED solutions provide a criterion to choo...