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...

Abstract We present a generalization of the notion neighborliness to non-polyhedral convex cones. Although definition is available in case literature, it fairly restrictive as requires all low-dimensional faces be polyhedral. Our approach more flexible and includes, for example, cone positive-semidefinite matrices special (this not neighborly general). term our Terracini convexity due its conce...

Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in [4].

Many combinatorial numbers can be placed in the following generalized triangular array [ T n , k ] ? 0 satisfying recurrence relation: = ? ( a + 1 2 ) ? b d with and unless ? for suitable . For denote by q generating function of -th row. In this paper, we develop various criteria x -Stieltjes moment property 3- -log-convexity based on Jacobi continued fraction expression ? t where is set indete...

We consider the problem of computing the outer-radii of point sets. In this problem, we are given integers n, d, k where k ≤ d, and a set P of n points in R. The goal is to compute the outer k-radius of P , denoted by Rk(P ), which is the minimum, over all (d−k)-dimensional flats F , of maxp∈P d(p, F ), where d(p, F ) is the Euclidean distance between the point p and flat F . Computing the radi...

We introduce a notion of fractional convexity that extends naturally the usual in Euclidean space to setting. With this convexity, we study convex envelope inside domain an exterior datum (the largest possible function is below outside) and show characterized as viscosity solution non-local equation given by infimum among all directions 1-dimensional laplacian. For prove existence, uniqueness c...