10,177 research outputs found
New and Old Results in Resultant Theory
Resultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical. Emphasis is made on explicit
formulas for resultants, which could be practically useful in a future physics
research.Comment: 50 pages, 15 figure
Integrability and explicit solutions in some Bianchi cosmological dynamical systems
The Einstein field equations for several cosmological models reduce to
polynomial systems of ordinary differential equations. In this paper we shall
concentrate our attention to the spatially homogeneous diagonal G_2
cosmologies. By using Darboux's theory in order to study ordinary differential
equations in the complex projective plane CP^2 we solve the Bianchi V models
totally. Moreover, we carry out a study of Bianchi VI models and first
integrals are given in particular cases
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