On Groebner bases and their use in solving some practical problemsMatej Mencinger
, 2013, original scientific article
Abstract: Groebner basis are an important theoretical building block of modern (polynomial) ring theory. The origin of Groebner basis theory goes back to solving some theoretical problems concerning the ideals in polynomial rings, as well as solving polynomial systems of equations. In this article four practical applications of Groebner basis theory are considered; we use Groebner basis to solve the systems of nonlinear polynomial equations, to solve an integer programming problem, to solve the problem of chromatic number of a graph, and finally we consider an original example from the theory of systems of ordinary (polynomial) differential equations. For practical computations we use systems MATHEMATICA and SINGULAR .
Keywords: polynomial system of (differential) equations, integer linear programming, chromatic number of a graph, polynomial rings, Groebner basis, CAS systems
Published in DKUM: 10.07.2015; Views: 1427; Downloads: 94
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Natural convection flows in complex cavities by BEMLeopold Škerget
, Matjaž Hriberšek
, Zoran Žunič
, 2003, original scientific article
Abstract: A numerical method for the solution of Navier-Stokes equations is developed using an integral representation of the conservation equations. The velocity- vorticity formulation is employed, where the kinematics is given with the Poisson equation for a velocity vector, while the kinetics is represented with the vorticity transport equation. The corresponding boundary-domain integral equations are presented along with discussions of the kinetics and kinematics of the fluid flow problem. THE BEM formulation is developed and tested for natural convection flows in closed cavities with complex geometries.
Keywords: fluid dynamics, natural convection, boundary element method, differential equations, closed cavity
Published in DKUM: 01.06.2012; Views: 1910; Downloads: 85
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