This note proves sharp affine Gagliardo-Nirenberg inequalities which are stronger than all known sharp Euclidean Gagliardo-Nirenberg inequalities and imply the affine L−Sobolev inequalities. The logarithmic version of affine L−Sobolev inequalities is verified. Moreover, An alternative proof of the affine Moser-Trudinger and Morrey-Sobolev inequalities is given. The main tools are the equimeasur...

In this paper, we present procedures to obtain facet-defining inequalities for the independence system polytope. These procedures are defined for inequalities which are not necessarily rank inequalities. We illustrate the use of these procedures by deriving strong valid inequalities for the acyclic induced subgraph, triangle free induced subgraph, bipartite induced subgraph, and knapsack polyto...

Despite the great success of quantum mechanics, questions regarding its application still exist and the boundary between quantum and classical mechanics remains unclear. Based on the philosophical assumptions of macrorealism and noninvasive measurability, Leggett and Garg devised a series of inequalities (LG inequalities) involving a single system with a set of measurements at different times. ...

In this glossary, the authors address eight key questions pertinent to health inequalities: (1) What is the distinction between health inequality and health inequity?; (2) Should we assess health inequalities themselves, or social group inequalities in health?; (3) Do health inequalities mainly reflect the effects of poverty, or are they generated by the socioeconomic gradient?; (4) Are health ...

Background Measuring health status by using standardized and validated instrument has become a growing concern over the past few decades throughout the developed and developing countries. The aim of the study was to investigate the overall self-reported health status along with potential inequalities by using EuroQol 5 dimensions (EQ-5D) instrument among low-income people of Bangladesh.   Metho...

in this paper, the finitely many constraints of a fuzzy relationinequalities problem are studied and the linear objective function on the regiondefined by a fuzzy max-average operator is optimized. a new simplificationtechnique which accelerates the resolution of the problem by removing thecomponents having no effect on the solution process is given together with analgorithm and a numerical exa...

model order reduction is known as the problem of minimizing the -norm of the difference between the transfer function of the original system and the reduced one. in many papers, linear matrix inequality (lmi) approach is utilized to address the minimization problem. this paper deals with defining an extra matrix inequality constraint to guarantee that the minimum phase characteristic of the sys...

We propose in this paper a tour of the symmetric traveling salesman polytope, focusing on inequalities that can be deened on sets. The most known inequalities are all of this type. Many papers have appeared which give more and more complex valid inequalities for this polytope, but no intuitive idea on why these inequalities are valid has ever been given. In order to help in understanding these ...

CONTEXT Substantive equity-focused policy changes in Ontario, Canada have yet to be realized and may be limited by a lack of widespread public support. An understanding of how the public attributes inequalities can be informative for developing widespread support. Therefore, the objectives of this study were to examine how Ontarians attribute income-related health inequalities. METHODS We con...

We consider two formulations for the uncapacitated hub location problem with single assignment (UHL) which use multicommodity flow variables. We project out the flow variables and determine some extreme rays of the projection cones. Then we investigate whether the corresponding inequalities define facets of the UHL polyhedron. We also present two families of facet defining inequalities that dom...