Reversible Equivariant Linear Systems

Reversible Equivariant Linear Systems

In this paper we classify the structure of linear reversible systems (vector elds) on R n that are equivariant with respect to a linear representation of a compact Lie group H. We assume the time-reversal symmetry R also acts linearly and is such that the group G that is generated by H and R is again a compact Lie group. The main tool for the classiication is the representation theory of compac...

Bifurcation and branching of equilibria in reversible equivariant vector fields

We study steady-state bifurcation in reversible equivariant vector fields. We assume an action on the phase space of a compact Lie group G with a normal subgroup H of index two, and study vector fields that are H-equivariant and have all elements of the complement G \ H as time-reversal symmetries. We focus on separable bifurcation problems that can be reduced to equivariant steady-state bifurc...

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

Complex fuzzy linear systems

FUZZY INCLUSION LINEAR SYSTEMS

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...