Given a compact semialgebraic set S ⊆ R, a polynomial map f : S → R, we consider the problem of approximating the image set F = f(S). This includes in particular the projections of S on R, for n ≥ m. Assuming that F ⊆ B, with B ⊆ R being a “simple” set (box or ellipsoid), we provide two methods (called Method 1 and Method 2) to compute certified outer approximations of F : — The first approach ...

In this paper, weak defining hyperplanes and the anchor points in DEA, as an important subset of the set of extreme efficient points of the Production Possibility Set (PPS), are used to construct unobserved DMUs and in the long run to improve the envelopment of all observed DMUs. There has been a surge of articles on improving envelopment in recent years. What has been done first is in Constant...

We prove theorems of the following form: if A ⊆ R is a “big set”, then there exists a “big set” P ⊆ R and a perfect set Q ⊆ R such that P × Q ⊆ A. We discuss cases where “big set” means: set of positive Lebesgue measure, set of full Lebesgue measure, Baire measurable set of second Baire category and comeagre set. In the first case (set of positive measure) we obtain the theorem due to Eggleston...

With a brief review of the studies on the industry in Data Envelopment Analysis (DEA) framework, the present paper proposes inner and outer technologies when only some basic information is available about the technology. Furthermore, applying Linear Programming techniques, it also determines lower and upper bounds for directional distance function (DDF) measure, overall and allocative efficienc...

Di Crescenzo and Longobardi (2002) has been proposed a measure of uncertainty related to past life namely past entropy. The present paper addresses the question of extending this concept to bivariate set-up and study some properties of the proposed measure. It is shown that the proposed measure uniquely determines the distribution function. Characterizations for some bivariate lifetime models a...

In the present research, data extracted from the stress analysis of 46 finite element models, verified using test results obtained from an experimental investigation, were used to study the effect of geometrical parameters on the chord-side stress concentration factors (SCFs) of central and outer braces in uniplanar tubular KT-joints of offshore structures subjected to four different types of i...