The calculation of RTS amounts to measuring a relationship between inputs and outputs in a production structure. There are many methods to measure RTS in the primal space or the dual space. One of the main approaches is using the multiplier on the convexity constraint. But returns to scale measurements in DEA models are affected by the presence of regulatory constraints. These additional constr...

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X , KC(C) the family of all compact convex subsets of C, and T a nonexpansive mapping from C into KC(C). We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is a 1-χcontractive m...

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove this sort is inherited by the convex envelope, which key to obtain other remarkable properties such as coercivity. Our techniques allow retrieve Enflo's uniformly renorming super-reflexive Banach spaces regularization raw function built from trees. Among appl...

The main result is that, for any projective compact analytic subset Y of dimension q > 0 in a reduced complex space X , there is a neighborhood Ω of Y such that, for any covering space Υ: X̂ → X in which Ŷ ≡ Υ(Y ) has no noncompact connected analytic subsets of pure dimension q with only compact irreducible components, there exists a C∞ exhaustion function φ on X̂ which is strongly q-convex on Ω̂ ...

The interplay between topological hyperconvex spaces and sigma-finite measures in such gives rise to a set of analytical observations. This paper introduces the Noetherian class k-finite k-hyperconvex subspaces (NHCs) admitting countable finite covers. A measure is constructed sigma-semiring NHC under ordering NHCs. relation maintains irreflexive anti-symmetric algebraic properties while retain...

In this paper, we study the convexity of the integral operator

The aim of the present study was to obtain quantitative information concerning the three-dimensional (3D) arrangement of the facial soft tissues of subjects with Down's syndrome. The 3D co-ordinates of 50 soft tissue facial landmarks were recorded by an electromechanical digitizer in 17 male and 11 female subjects with Down's syndrome aged 12-45 years, and in 429 healthy individuals of the same...

Restricted-orientation convexity (O-convexity) is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected. The notion of O-convexity generalizes standard convexity, as well as several other types of nontraditional convexity. We introduce and study O-halfspaces, which are analogs of standard halfspaces in the theory of O-convexity,...

The classic Atiyah-Singer index theory of elliptic operators on compact manifolds has been vastly generalized to higher index theories of elliptic operators on noncompact spaces in the framework of noncommutative geometry [5] by Connes-Moscovici for covering spaces [8], Baum-Connes for spaces with proper and cocompact discrete group actions [2], Connes-Skandalis for foliated manifolds [9], and ...