  In this paper, we prove several theorems on systems of polynomials with at
least one positive real zero based on the theory of conceive polynomials. These
theorems provide sufficient conditions for systems of multivariate polynomials
admitting at least one positive real zero in terms of their Newton polytopes
and combinatorial structure. Moreover, a class of polynomials attaining their
global minimums in the first quadrant are given, which is useful in polynomial
optimization.
