We study the existence theory for parabolic variational inequalities in weighted L spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L setting allows us to cover some singular cases...

In this paper we develop a characterisation of minimal non-planarity of level graphs. We show that a level minimal non-planar (LMNP) graph is completely characterised by either a tree, a level non-planar cycle or a level planar cycle with certain path augmentations. We discuss the usefulness of these characterisations in the context of an branch-and-cut Integer Linear Programming implementation...

in this paper‎, ‎making use of a new identity‎, ‎we establish new‎ ‎inequalities of ostrowski type for the class of preinvex functions and‎ ‎gave some midpoint type inequalities‎.

In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...

We give precise Gaussian upper and lower bound estimates on heat kernels on Riemannian manifolds with poles under assumptions that the Riemannian curvature tensor goes to 0 sufficiently fast at infinity. Under additional assumptions on the curvature, we give estimates on the logarithmic derivatives of the heat kernels. The proof relies on the Elworthy-Truman’s formula of heat kernels and Elwort...

Given monotone operators on the positive orthant in n-dimensional Euclidean space, we explore the relation between inequalities involving those operators, and induced monotone dynamical systems. Attractivity of the origin implies stability for these systems, as well as a certain inequality, the no-joint-increase condition. Under the right perspective the converse is also true. In addition we co...

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path const...

Although general methods led me to a complete solution, I soon saw that the result is obtained faster when the general procedure is left, and when one follows the path suggested by the particular problem at hand. S. Bernstein first lines of [6] Abstract. One establishes inequalities for the coefficients of orthogonal polynomials Φn(z) = z n + ξnz n−1 + · · · + Φn(0), n = 0, 1, . . . which are o...

This article studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to quality-of-service constraints that restrict the maximum number of intermediate routers along each communication path. Different possibilities to model the GHMSTP as an integer linear program and strengthening valid inequalities are studied. Th...

An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims on some amount of a scarce resource, but also by some exogenous ex-ante conditions (characteristics), different from claims (e.g., endowments, entitlements, wealth, obligations, assets). Inequalities in the ex-ante conditions induce compensations between agents which influence t...