Search results for "Invariant polynomial"
showing 3 items of 3 documents
Some topological invariants for three-dimensional flows
2001
We deal here with vector fields on three manifolds. For a system with a homoclinic orbit to a saddle-focus point, we show that the imaginary part of the complex eigenvalues is a conjugacy invariant. We show also that the ratio of the real part of the complex eigenvalue over the real one is invariant under topological equivalence. For a system with two saddle-focus points and an orbit connecting the one-dimensional invariant manifold of those points, we compute a conjugacy invariant related to the eigenvalues of the vector field at the singularities. (c) 2001 American Institute of Physics.
A Leibniz variety with almost polynomial growth
2005
Abstract Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras V ˜ 1 defined by the identity y 1 ( y 2 y 3 ) ( y 4 y 5 ) ≡ 0 . We give a complete description of the space of multilinear identities in the language of Young diagrams through the representation theory of the symmetric group. As an outcome we show that the variety V ˜ 1 has almost polynomial growth, i.e., the sequence of codimensions of V ˜ 1 cannot be bounded by any polynomial function but any proper subvariety of V ˜ 1 as polynomial growth.
A new hyperelastic model for anisotropic hyperelastic materials with one fiber family
2016
International audience; The main goal of this study is to propose a practical application of a new family of transverse anisotropic invariants by designing a strain energy function (SEF) for incompressible fiber-reinforced materials. In order to validate the usability and creativeness of the proposed model, two different fiber-reinforced rubber materials under uniaxial and shear testing are considered. For each kind of material, numerical simulations based on the proposed model are consistent with experimental results and provide information about the effect of the new family of invariants in the construction of the SEF.