we find a minimal differential graded (dg) operad whose generic representations in ${\mathbb r}^n$ are in one-to-one correspondence with formal germs of those endomorphisms of the tangent bundle to ${\mathbb r}^n$ which satisfy the nijenhuis integrability condition. this operad is of a surprisingly simple origin: it is the cobar construction on the quadratic operad of homologically trivial dg lie algebras. as a by-product we obtain a strong-homotopy generalization of this geometric structure and show its homotopy equivalence to the structure of contractible dg manifolds.

One year after the invasion of Iraq, what lessons are to be drawn about the role of the Security Council in peace and security? This article looks at the issue by considering the nature of the Security Council in its dual functions as a forum for diplomacy and a corporate body for executive action. The idea of the Security Council's possessing a separate will in its executive function is developed. The article stresses the importance for the authority of the Council of that organ expressing its will within the legal parameters of the Charter and international law. It is argued that similar legal parameters are also applicable to the permanent members in exercising their power of veto and in interpreting resolutions. Further, when interpreting resolutions member states should not misconstrue the will of the Council. The Iraq crisis of 2003 raised all these issues and, further, necessitated a reappraisal of the rules of international law governing the use of force. This article considers the relationship between diminution in Council authority and erosion of the rules of the UN Charter governing the threat or use of force in international relations.

The goal of this paper is to study the Koszul property and the property of having a Gröbner basis of quadrics for classical varieties and algebras as canonical curves, finite sets of points and Artinian Gorenstein algebras with socle in low degree. Our approach is based on the notion of Gröbner flags and Koszul filtrations. The main results are the existence of a Gröbner basis of quadrics for the ideal of the canonical curve whenever it is defined by quadrics, the existence of a Gröbner basis of quadrics for the defining ideal of s [les ] 2n points in general linear position in Pn, and the Koszul property of the ‘generic’ Artinian Gorenstein algebra of socle degree 3.

Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees.