Chapter 6 On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method

A novel approach for solving the DEA linear programming problems using a primaldual interior-point method is presented. The solution found by this method satisfies the Strong Complementarity Slackness Condition (SCSC) and maximizes the product of the positive components among all SCSC solutions. The first property is critical in the use of DEA and the second one contributes significantly to the reliability of the solution.This research was partially supported by NSF Cooperative Agreement No. CCR-88-09615, ARO Grant 9DAAL03-90-G-0093, DOE Grant DEFG05-86-ER25017, and AFOSR Grant 89-0363.Partially supported by Fulbright/LASPAU.     

Norm-graphs and bipartite turán numbers

For everyt>1 and positiven we construct explicit examples of graphsG with |V (G)|=n, |E(G)|c _t ·n ^2–1/t which do not contain a complete bipartite graghK _t,t !+1 This establishes the exact order of magnitude of the Turán numbers ex (n, K _t,s ) for any fixedt and allst!+1, improving over the previous probabilistic lower bounds for such pairs (t, s). The construction relies on elementary facts from commutative algebra.Research supported in part by NSF Grants DMS-8707320 and DMS-9102866.Research supported in part by Hungarian National Foundation for Scientific Research Grant     

Strongly prime alternative pairs with minimal inner ideals

In this paper, we use the known classification of the finite capacity simple alternative pairs and the version of the Litoff Theorem for Jordan pairs to describe all the strongly prime alternative pairs with nonzero socle. We study the inheritance of some properties (primeness, nondegenerancy,…) when passing from the original alternative pair to the symmetrized pair. Thus, we can apply Jordan theoretical results to the alternative case. This work has been partially supported by 1) the “Plan Andaluz de Investigación y Desarrollo Tecnológico” with project no. 1027 and 2) the DGICYT with project no. PB93-0990     

Generating well-behaved utility functions for compromise programming

The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated through the application of the well-known operational research approach called compromise programming. It is shown that there are large families of utility functions satisfying this condition, thus reinforcing the value of compromise programming as a good surrogate of the traditional utility optimum.Thanks are due to the reviewers for their helpful suggestions. The English editing by Ms. Christine Méndez is appreciated. The authors have been supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT), Madrid, Spain.     

On lower bounds for theL 2-Wasserstein metric in a Hilbert space

We provide two families of lower bounds for theL ²-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02.     

Levels in160Yb from the radioactive decay of160Lu

Theγ-rays following the radioactive decay of¹⁶⁰Lu into¹⁶⁰Yb have been studied. The Lu source was produced in the¹⁴⁴Sm(¹⁹F, 3n) reaction at 85 MeV. Excitation functions, half-lives,γ-γ andγ-X-ray coincidences and conversion electrons were measured. Twoβ ⁺ decaying states in¹⁶⁰Lu were found with half-lives of 36.2(3) s and 40(1) s.¹⁶⁰Yb levels deduced from the decay of¹⁶⁰Lu are presented.