let r be a ring and v be a matrix valuation on r. it is shown that, there exists a correspondence between matrix valuations on r and some special subsets ?(mvpr) of the set of all square matrices over r, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. furthermore, based on malcolmson’s localization, an alternative proof for t...

This paper concerns the problem of output consensus in nonlinear non-minimum phase systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, an output redefinition method is proposed. The new outputs of agents are functions of original outputs and internal states and defined such that the dynamics of agents a...

In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian...