Multihomogeneous resultant formulae for systems with scaled support

Multihomogeneous resultant matrices for systems with scaled support

Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose Newton polytopes are scaled copies of one polytope, thus taking a step towards systems with arbitrary supports. First, we specify matrices whose determinant equa...

Multihomogeneous resultant formulae by means of complexes

The first step in the generalization of the classical theory of homogeneous equations to the case of arbitrary support is to consider algebraic systems with multihomogeneous structure. We propose constructive methods for resultant matrices in the entire spectrum of resultant formulae, ranging from pure Sylvester to pure Bézout types, and including matrices of hybrid type of these two. Our appro...

Study of multihomogeneous polynomial systems via resultant matrices

Resultants provide conditions for the solvability of polynomial equations and allow reducing polynomial system solving to linear algebra computations. Sparse resultants depend on the Newton polytopes of the input equations. This polytope is the convex hull of the exponent vectors corresponding to the nonzero monomials of the equations (viewed as lattice points in the Cartesian space of dimensio...

Scaled Support Vector Machine

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...