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Uniform distribution modulo one and binary search trees

Michel Dekking, Peter Van der Wal (2002)

Journal de théorie des nombres de Bordeaux

Any sequence x = ( x k ) k = 1 of distinct numbers from [0,1] generates a binary tree by storing the numbers consecutively at the nodes according to a left-right algorithm (or equivalently by sorting the numbers according to the Quicksort algorithm). Let H n ( x ) be the height of the tree generated by x 1 , , x n . Obviously log n log 2 - 1 H n ( x ) n - 1 . If the sequences x are generated by independent random variables having the uniform distribution on [0, 1], then it is well known that there exists c > 0 such that H n ( x ) c log n as n for almost all sequences x . Recently...

Using fuzzy relational databases to represent agricultural and environmental information. An example within the scope of olive cultivation in Granada.

Juan Manuel Serrano, M.ª Amparo Vila, Víctor Aranda, Gabriel Delgado (2001)

Mathware and Soft Computing

A query system for several types of users and for information retrieval about olive cultivation and its environmental support in the province of Granada (Spain) is introduced. The system is based on fuzzy data and is flexible. The main problems which this model solves are those relating to uncertain and imprecise data processing (as in the case of environmental and cultivation information), spatial and punctual data representation, and fusion of cultivation-resulting and scientific-experimental...

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