If the absolute number of poor people goes up, but the fraction of people in poverty comes down, has poverty gone up or gone down? The economist’s instinct, framed by population replication axioms that undergird standard measures of poverty, is to say that in this case poverty has gone down. But this goes against the instinct of those who work directly with the poor, for whom the absolute numbe...

PURPOSE To retrospectively assess the clinical utility in ureteroscopy (URS) planning of cumulative stone diameter (CSD), which does not account for stone width or depth, as a predictor of URS outcome and compare it with stone volume. MATERIALS AND METHODS Patients with renal stones treated at a single institute by flexible URS were retrospectively evaluated. To assess the clinical utility of...

The existing topological representation of an orthocomplemented lattice via the clopen orthoregular subsets a Stone space depends upon Alexander’s Subbase Theorem, which asserts that X is compact if every subbasic open cover admits finite subcover. This easy consequence Ultrafilter Theorem—whose proof Zorn’s Lemma, well known to be equivalent Axiom Choice. Within this work, we give choice-free ...

In this paper we deal with the minimization of a convex function over the solution set of a range inclusion problem determined by a multivalued operator with convex graph. We attach a dual problem to it, provide regularity conditions guaranteeing strong duality and derive for the resulting primal-dual pair necessary and sufficient optimality conditions. We also discuss the existence of optimal ...

Abstract. We present some new Farkas-type results for inequality systems involving a finite as well as an infinite number of convex constraints. For this, we use two kinds of conjugate dual problems, namely an extended Fenchel-type dual problem and the recently introduced FenchelLagrange dual problem. For the latter, which is a ”combination” of the classical Fenchel and Lagrange duals, the stro...

We study in this paper the strong duality for discrete-time convex constrained portfolio selection problems when adopting a risk neutral computational approach. In contrast to the continuous-time models, there is no known result of the existence conditions in discrete-time models to ensure the strong duality. Investigating the relationship among the primal problem, the Lagrangian dual and the P...

We prove a duality theorem for graded algebras over a field that implies several known duality results: graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and Herzog-Rahimi bigraded duality.