On maps with nonnegative Jacobian.

Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian Conjecture

Real Divergence-free Jacobian Maps Are Shear Maps *

We show that divergence-free jacobian maps, recently considered in [11], [14], are actually shear maps.

Distributional Jacobian and singularities of Sobolev maps

– We review the definition and main properties of the distributional Jacobians, in particular for Sobolev maps u : R → R with values in the (k − 1)dimensional sphere S.

Unipotent Jacobian Matrices and Univalent Maps

The Jacobian Conjecture would follow if it were known that real polynomial maps with a unipotent Jacobian matrix are injective. The conjecture that this is true even for C maps is explored here. Some results known in the polynomial case are extended to the C context, and some special cases are resolved.

On Nonnegative Cosine Polynomials with Nonnegative Integral Coefficients

We show that there exist Po > 0 ar>d P\, ■■■ , Pn nonnegative integers, such that 0 < p(x) = Po + Pi cosx + • ■ • + Pn cos Nx and po -C s1/3 for .s = J2'J=oPj < improving on a result of Odlyzko who showed the existence of such a polynomial p that satisfies Po < (.slogs)1/3 . Our result implies an improvement of the best known estimate for a problem of Erdos and Szekeres. As our method is noncon...