The non-proper value set of a nonsingular polynomial map from C 2 into itself, if non-empty, must be a curve with one point at infinity. 2000 Mathematical Subject Classification: 14 H07, 14R15.

The proper orientation number χ→(G) of a graph G is the minimum k such that there exists an edges with all vertex-outdegrees at most and for any adjacent vertices, outdegrees are different. Two major conjectures about resolved. First it shown, planar 14. Secondly, shown every graph, , where r=χ(G) usual chromatic maximum average degree taken over subgraphs G. Several other related results deriv...

Discretization of the harmonic map flow into spheres often uses a penalization or projection strategy, where the first suffers from the proper choice of an additional parameter, and the latter from the lack of a discrete energy law, and restrictive mesh-constraints. We propose an implicit scheme that preserves the sphere constraint at every node, enjoys a discrete energy law, and unconditionall...

We study an equivariant co-assembly map that is dual to the usual Baum–Connes assembly map and closely related to coarse geometry, equivariant Kasparov theory, and the existence of dual Dirac morphisms. As applications, we prove the existence of dual Dirac morphisms for groups with suitable compactifications, that is, satisfying the Carlsson–Pedersen condition, and we study a K–theoretic counte...

Using multiple point spaces some new examples of perverse sheaves on images of maps are described. Furthermore, suppose f : X ! Y is a nite and proper map of complex analytic manifolds of dimension n and n + 1 such that every multiple point space is non-singular and has the dimension expected of a generic map. Then we can describe the composition series for the constant sheaf on the image in th...

Different environmental stimuli often use the same set of signaling proteins to achieve very different physiological outcomes. The mating and invasive growth pathways in yeast each employ a mitogen-activated protein (MAP) kinase cascade that includes Ste20, Ste11, and Ste7. Whereas proper mating requires Ste7 activation of the MAP kinase Fus3, invasive growth requires activation of the alternat...

This paper studies the homotopy type of the configuration spaces Fn(X) by introducing the idea of configuration spaces of maps. For every map f : X → Y , the configuration space Fn(f) is the space of configurations in X that have distinct images in Y . We show that the natural maps Fn(X) ← Fn(f) → Fn(Y ) are homotopy equivalences when f is a proper cell-like map between d-manifolds. We also sho...

According to [LO], the Prym variety of any non-cyclic étale triple cover f : Y → X of a smooth curve X of genus 2 is a Jacobian variety of dimension 2. This gives a map from the moduli space of such covers to the moduli space of Jacobian varieties of dimension 2. We extend this map to a proper map Pr of a moduli space S3M̃2 of admissible S3-covers of genus 7 to the moduli space A2 of principally...

Almost every planner needs good heuristics to be efficient. Heuristic planning has experienced an impressive progress over the last years thanks to the emergence of more and more powerful estimators. However, this progress has not been translated to multi-agent planning (MAP) due to the difficulty of applying classical heuristics in distributed environments. The application of local search heur...