We present randomized online algorithms for scheduling on m = 3; : : : ; 7 machines. For two machines, a randomized algorithm achieving a competitive ratio of 4 3 was found by Bartal, Fiat, Karloo and Vohra 3]. These same authors show a matching lower bound. Seiden has presented a randomized algorithm which achieves competitive ratios of 1. A barely random algorithm is one which a distribution ...

Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble — the ensemble realizing the entanglement of formation — is greater than the rank of the mixed state. We find examples for which the number of states in this optimal ensemble can be larger than the rank by an arbitrarily large factor. In one case the...

in this study, yield-water and profit function was used to obtain water demand function in agriculture sector. the results showed that the ratio of actual to potential evapotranspiration had positive, significant effecton the ratio of actual to potential yield for wheat and barley. also, square ratio of actual to potential evapotranspiration had negative, significant relationship. after estimat...

Background: Hyperbilirubinemia is a common problem in neonates that affects approximately 60% of term neonates and 80% of pre-term neonates in the first week of life. Newborns, due to prematurity of the liver and digestive tract, could not eliminate bilirubin quickly. This phenomenon leads to hyperbilirubinemia and jaundice during the first days of the birth. Because indirect bilirubin is toxi...