Maximum cut problem: new models

In the paper, we present the maximum cut problem as maximization of a non-smooth convex function over polytope which is the convex hull of bases of the polymatroid associated with a submodular function defined on the subsets of node set of a given graph. We also formulate other new models for this problem and give necessary and enough conditions on an optimal solution in terms of network flow.

On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space II

Let u be a smooth convex function in ℝn and the graph M∇u of ∇u be a space-like translating soliton in pseudo-Euclidean space [Formula: see text] with a translating vector [Formula: see text], then the function u satisfies [Formula: see text] where ai, bi and c are constants. The Bernstein type results are obtained in the course of the arguments.