public health interventions aimed at promoting healthy drinking habits by, for example, seeking to discourage the excessive consumption of alcohol or soft drinks with high sugar content. Dealing with drink is a much more solemn affair, the "morning after" perhaps to the Liquid pleasures earlier imbibed. None the less, it is an equally good book. Against the background of growing alcohol consump...

Abstract Grothendieck polynomials were introduced by Lascoux and Schützenberger play an important role in K-theoretic Schubert calculus. In this paper, we give a new definition of double stable based on iterated residue operation. We illustrate the power our calculating expansion Thom ${\mathcal {A}}_{2}$ singularities. present two versions: one displays its stabilization property, while other ...

Let (V,0)⊂(ℂ n ,0) be a quasi-homogeneous isolated hypersurface singularity. In this paper we prove under certain weight conditions relation between the property of (V,0) being Thom–Sebastiani type and dimension toral Lie subalgebras contained in Yau algebra L(V).

We show that there is an equivalence of categories between the orthogonal components for the slice filtration and the birational motivic stable homotopy categories which are constructed in this paper. Relying on this equivalence, we are able to describe the slices for projective spaces (including P), Thom spaces and blow ups. 2000 Mathematics Subject Classification: 14F42

Complex K-Theory is an extraordinary cohomology theory defined from the complex vector bundles on a space. This essay aims to provide a quick and accessible introduction to K-theory, including how to calculate with it, and some of its additional features such as characteristic classes, the Thom isomorphism and Gysin maps.