BACKGROUND Previous studies have reported large socioeconomic inequalities in mortality from conditions amenable to medical intervention, but it is unclear whether these can be attributed to inequalities in access or quality of health care, or to confounding influences such as inequalities in background risk of diseases. We therefore studied whether inequalities in mortality from conditions ame...

As an essential substructure underlying a large class of chance-constrained programming problems with finite discrete distributions, the mixing set with 0 − 1 knapsack has received considerable attentions in recent literature. In this study, we present a family of strong inequalities that subsume known inequalities for this set. We also find many other inequalities that can be explained by lift...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...

We study the mixed–integer knapsack polyhedron, that is, the convex hull of the mixed–integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet–defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable. These inequalities strengthen and/or generalize known inequalit...

Bansal and Kianfar introduced continuous multi-mixing set where the coefficients satisfy the so-called n-step MIR conditions and developed facet-defining inequalities for this set. In this paper, we first generalize their inequalities for the continuous multi-mixing set with general coefficients (where no conditions are imposed on the coefficients) and show that they are facetdefining in many c...

In this paper, we consider a new class of quasi variational inequalities involving three operators, which is called the extended general quasi variational inequality. It is shown that the extended general quasi variational inequalities are equivalent to the fixed problems. This equivalence is used to suggest and analyze some iterative methods for solving the extended general quasi variational i...

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

OBJECTIVE To compare the trends in mortality inequalities by educational attainment with trends using area deprivation. SETTING Scotland and England & Wales (E&W). PARTICIPANTS All people resident in Scotland and E&W between 1981 and 2011 aged 35-79 years. PRIMARY OUTCOME MEASURES Absolute inequalities (measured using the Slope Index of Inequality (SII)) and relative inequalities (measure...

In this paper, we introduce a generalization of the continuous mixing set (which we refer to as the continuous n-mixing set) Qm,n := {(y, v, s) ∈ ( Z× Zn−1 + )m×Rm+1 + : ∑nt=1 αty t + vi + s ≥ βi, i = 1, . . . ,m}. This set is closely related to the feasible set of the multi-module capacitated lot-sizing (MML) problem with(out) backlogging. For each n′ ∈ {1, . . . , n}, we develop a class of va...

Flow cover inequalities are among the most effective valid inequalities for solving capacitated fixed-charge network flow problems. These valid inequalities are implications on the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be modeled b...