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A characterization of closed convex sets possessing a barrier cone with a nonempty interior is achieved. As a consequence, we describe all the proper extended-valued functionals for which the domain of their Fenchel conjugate has a nonempty interior. We end up the paper by giving an application to the study of the stability of the solution set of a(More)
We characterize in a reflexive Banach space all the closed convex sets ensures the closedness of the algebraic difference ¡ ¨ for all closed convex sets¨. We also answer a closely related problem: determine all the pairs ¡ , ¨ of closed convex sets containing no lines such that the algebraic difference of any sufficiently small uniform perturbation of ¢ ¡(More)
BACKGROUND A high body mass index (BMI) has been associated with reduced semen quality and male subfecundity, but no studies following obese men losing weight have yet been published. We examined semen quality and reproductive hormones among morbidly obese men and studied if weight loss improved the reproductive indicators. METHODS In this pilot cohort(More)
BACKGROUND Perfluorinated alkyl acids (PFAAs), persistent chemicals with unique water-, dirt-, and oil-repellent properties, are suspected of having endocrine-disrupting activity. The PFAA compounds perfluorooctanoic acid (PFOA) and perfluorooctane sulfonic acid (PFOS) are found globally in humans; because they readily cross the placental barrier, in utero(More)
When the subdifferential sum rule formula holds for the indicator functions ι C and ι D of two closed convex sets C and D of a locally convex space X, the pair (C, D) is said to have the strong conical hull intersection property (the strong CHIP). The specification of a well-known theorem due to Moreau to the case of the support functionals σ C and σ D(More)
The concept of continuous set has been used in finite dimension by Gale and Klee and recently by Auslender and Coutat. Here, we introduce the notion of slice-continuous set in a general reflexive Ba-nach space and we show that the class of such sets can be viewed as a subclass of the class of continuous sets. Further, we prove that every non constant(More)
Persistent organochlorine pollutants (POPs) are ubiquitous, bioaccumulative compounds with potential endocrine-disrupting effects. They cross the placental barrier thereby resulting in in utero exposure of the developing fetus. The objective of this study was to investigate whether maternal serum concentrations of polychlorinated biphenyls (PCBs) and(More)
This paper is devoted to studying boundedness criteria for extended-real-valued functions. The study is done in the framework of dual vector spaces, using new objects such as self-equilibrated sets and functions. We establish two boundedness new major criteria. The first one says that an extended-real-valued function is bounded below provided it is(More)
In this note we prove that an extended-real-valued lower semi-continuous convex function Φ defined on a reflexive Banach space X achieves its supremum on every nonempty bounded and closed convex set of its effective domain Dom Φ, if and only if the restriction of Φ to Dom Φ is sequentially continuous with respect to the weak topology on the underlying space(More)