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The Lambert W function is deened to be the multivalued inverse of the function w 7 ! we w. It has many applications in pure and applied mathematics, some of which are brieey described here. We present a new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an eecient numerical procedure for evaluating the function to(More)
An investigation ts made of the expected value of the maximum number of accesses needed to locate any element m a hashing file under various colhston resoluuon schemes This differs from usual worst-case considerations winch, for hashmg, would be the largest sequence of accesses for the worst possible file Asymptotic expressxons of these expected values are(More)
MOTIVATION We announce the availability of the second release of Darwin v. 2.0, an interpreted computer language especially tailored to researchers in the biosciences. The system is a general tool applicable to a wide range of problems. RESULTS This second release improves Darwin version 1.6 in several ways: it now contains (1) a larger set of libraries(More)
Ageing and the mortality that ensues are sustainable for the species only if age is reset in newborns. In budding yeast, buds are made young whereas ageing factors, such as carbonylated proteins and DNA circles, remain confined to the ageing mother cell. The mechanisms of this confinement and their relevance are poorly understood. Here we show that a(More)
Quadtrees constitute a hierarchical data structure which permits fast access to multidimensional data. This paper presents the analysis of the expected cost of various types of searches in quadtrees|fully speciied and partial match queries. The data model assumes random points with independently drawn coordinate values. The analysis leads to a class of(More)