High dimensional space is the biggest problem when classification process is carried out, because it takes longer time for computation, so that the costs involved are also expensive. In this research, the facial space generated from homogeneous and non-homogeneous polynomial was proposed to extract the facial image features. The homogeneous and non-homogeneous polynomial-based eigenspaces are t...

We consider the stabilization problem for three dimensional homogeneous polynomial systems, and derive an intrinsic suucient condition for stablizability. We show that this condition is satissed by an open set in the space of homogeneous systems of a xed degree.

Let W be a weight–homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this result to a particular family of planar polynomial systems having a nilpotent center without meromorphic first integral. 2000 AMS Subject Classification: 34C07, ...