Divergence-free polynomial derivations

In this paper we present some new and old properties of divergences and divergence-free derivations

The gloaming : narrative in contemporary painting

Also available online.The key to understanding my project lies in the assumption that the task of representation for contemporary painting is different from that of newer media such as photography and film. I see the role of painting as being the representation of the past; an engagement with history. Many of the painters who have inspired my way of seeing are artists who re-imagined the role of pre-modernist narrative painting and re-asserted it in contemporary practice. Contemporary narrative painting occupies a different role from that of its pre-modernist predecessors, such as Romantic painting. It also occupies a different role in relation to dominant narrative media of photography and film

A Note on the Jacobian Conjecture in Two Variables

Article信州大学理学部紀要 22(1): 11-12(1987)departmental bulletin pape

Generic polynomial vector fields are not integrable

AbstractWe study some generic aspects of polynomial vector fields or polynomial derivations with respect to their integration. In particular, using a well-suited presentation of Darboux polynomials at some Darboux point as power series in local Darboux coordinates, it is possible to show, by algebraic means only, that the Jouanolou derivation in four variables has no polynomial first integral for any integer value s ≥ 2 of the parameter.Using direct sums of derivations together with our previous results we show that, for all n ≥ 3 and s ≥ 2, the absence of polynomial first integrals, or even of Darboux polynomials, is generic for homogeneous polynomial vector fields of degree s in n variables