We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these inequalities are already known, but new or more general proofs are given, whereas other inequalities are new. We also supply cases of equality to show that all ine...

In this paper we introduce a new class of facet-inducing inequalities for the Windy Rural Postman Problem and the Windy General Routing Problem. These inequalities are called Zigzag inequalities because they cut off fractional solutions containing a zigzag associated with variables with 0.5 value. Two different types of inequalities, the Odd Zigzag and the Even Zigzag inequalities, are presente...

We study a special case of a structured mixed integer programming model that arises in production planning. For the most general case of the model, called PI, we have earlier identified three families of facet–defining valid inequalities: (l, S) inequalities (introduced for the uncapacitated lot–sizing problem by Barany, Van Roy, and Wolsey), cover inequalities, and reverse cover inequalities. ...

Abstract. We derive the sharp constants for the inequalities on the Heisenberg group H whose analogues on Euclidean space R are the well known Hardy-Littlewood-Sobolev inequalities. Only one special case had been known previously, due to Jerison-Lee more than twenty years ago. From these inequalities we obtain the sharp constants for their duals, which are the Sobolev inequalities for the Lapla...

We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of valid inequalities, called cycle inequalities, valid for the problem and show that this inequalities together with the so-called cut inequalities yield an integ...

A new class of system of generalized parametric nonlinear quasivariational inequalities involving various classes of mappings is introduced and studied. With the properties of maximal monotone mappings, the equivalence between the class of system of generalized parametric nonlinear quasivariational inequalities and a class of fixed point problems is proved and an iterative algorithm with errors...

MOSER-TRUDINGER AND ADAMS TYPE INEQUALITIES AND THEIRAPPLICATIONSbyNGUYEN LAMAugust 2014Advisor: Dr. Guozhen LuMajor: MathematicsDegree: Doctor of PhilosophyIn this dissertation, we study some variants of the Moser-Trudinger inequalities and Adamsinequalities. The proofs of these inequalities relied crucially on the symmetrization arguments inthe lite...

We study mixed integer conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone or the positive semidefinite cone. In a unified framework, we introduce K-minimal inequalities and show that under mild assumptions, these inequalities together with the trivial cone-implied inequalities are sufficient to describe...

BACKGROUND The magnitude of educational inequalities in mortality avoidable by medical care in 16 European populations was compared, and the contribution of inequalities in avoidable mortality to educational inequalities in life expectancy in Europe was determined. METHODS Mortality data were obtained for people aged 30-64 years. For each country, the association between level of education an...

In this paper, we establish a one-to-one correspondence between information inequalities and group inequalities. The major implication of our result is that we can prove information inequalities by proving the corresponding group inequalities, and vice versa. By giving a group-theoretic proof for all Shannon-type inequalities, we suggest that new inequalities could be discovered by making use o...