A note on pair-formation functions

A Note on Conjugate Functions

1. Statement of results. The purpose of this note is to discuss as simply as possible a generalization of the classical theorem of M. Riesz2 on the integrability of the conjugate functions of functions in LP, and to point out some of the consequences for Fourier series. Suppose that(t) is a non-negative, convex function defined for t^O with (2t) ̂K<p(t) ior some constant K. Th...

A Note on Convex Functions

In this paper, we give twoweak conditions for a lower semi-continuous function on the n-dimensional Euclidean space Rn to be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.

A Note on SpanP Functions

A Note on Recursive Functions

In this paper, we propose a new and elegant deenition of the class of recursive functions, analogous to Kleene's deenition but diiering in the primitives taken, thus demonstrating the computational power of the concurrent programming language in-The deenition can be immediately rephrased for any distributive graph in a count-ably extensive category with products, thus allowing a wide, natural g...

A note on “Supplier selection by the pair of nondiscretionary factors-imprecise data envelopment analysis models”

   Recently, Farzipoor Saen [Journal of the Operational Research Society, 60(11), 1575–1582 (2009)] proposed a method based on data envelopment analysis to identify optimistic efficient suppliers in the presence of nondiscretionary factors-imprecise data. This short communication aims at showing a computational error in computing the value of preference intensity parameter in Farzipoor Saen’s [...