Galois theory on the line in nonzero characteristic

The author surveys Galois theory of function fields with non-zero caracteristic and its relation to the structure of finite permutation groups and matrix groups.Comment: 66 pages. Abstract added in migration

Multiobjective optimization of cluster measures in Microarray Cancer data using Genetic Algorithm Based Fuzzy Clustering

The field of biological and biomedical research has been changed rapidly with the invention of microarray technology, which facilitates simultaneously monitoring of large number of genes across different experimental conditions. In this report a multi objective genetic algorithm technique called Non-Dominated Sorting Genetic Algorithm (NSGA) - II based approach has been proposed for fuzzy clustering of microarray cancer expression dataset that encodes the cluster modes and simultaneously optimizes the two factors called fuzzy compactness and fuzzy separation of the clusters. The multiobjective technique produces a set of non-dominated solutions. This approach identifies the solution i.e. the individual chromosome which gives the optimal value of the parameters

On the uniqueness of the coefficient ring in a polynomial ring

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