We prove optimal radially weighted L2-norm inequalities for the Fourier extension operator associated to the unit sphere in Rn . Such inequalities valid at all scales are well understood. The purpose of this short paper is to establish certain more delicate single-scale versions of these. 2000 Mathematics subject classification: 42B10.

Recently Hadamard-type inequalities for nonnegative, evenly quasiconvex functions which attain their minimum have been established. We show that these inequalities remain valid for the larger class containing all nonnegative quasiconvex functions, and show equality of the corresponding Hadamard constants in case of a symmetric domain.

We present some recent developments involving inequalities for the ADM-mass and capacity of asymptotically flat manifolds with boundary. New, more general proofs of classic Euclidean estimates are also included. The inequalities are rigid and valid in all dimensions, and constitute a step towards proving the Riemannian Penrose inequality in arbitrary dimensions.

We extend the work of Letchford (2000) by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the most well-known multiple-handle constraints, including clique-tree, bipartition, path, and star inequalities. ...

This paper seeks to solve the long-term transmission expansion planning problem in power systems more effectively by reducing solution search space and computational effort. The proposed methodology finds adds cutting planes based on structural insights about bus angle differences along paths. Two lemmas a theorem are which formally establish validity of these onto underlying mathematical formu...

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit ine...

The cut polytope P,(G) of a graph G is the convex hull of the incidence vectors of all cuts of G; the cut cone C(G) of G is the cone generated by the incidence vectors of all cuts of G. We introduce the operation of collapsing an inequality valid over the cut cone C(K,) of the complete graph with n vertices: it consists of identifying vertices and adding the weights of the corresponding inciden...

In this paper, we study the set of 0−1 integer solutions to a single knapsack constraint and a set of non-overlapping cardinality constraints (MCKP). This set is a generalization of the traditional 0− 1 knapsack polytope and the 0− 1 knapsack polytope with generalized upper bounds. We derive strong valid inequalities for the convex hull of its feasible solutions by lifting the generalized cover...