Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Design and Development of an Adaptable Frame -Based System for Dravidian Language Processing

This work is aimed at building an adaptable frame-based system for processing Dravidian languages. There are about 17 languages in this family and they are spoken by the people of South India.Karaka relations are one of the most important features of Indian languages. They are the semabtuco-syntactic relations between verbs and other related constituents in a sentence. The karaka relations and surface case endings are analyzed for meaning extraction. This approach is comparable with the borad class of case based grammars.The efficiency of this approach is put into test in two applications. One is machine translation and the other is a natural language interface (NLI) for information retrieval from databases. The system mainly consists of a morphological analyzer, local word grouper, a parser for the source language and a sentence generator for the target language. This work make contributios like, it gives an elegant account of the relation between vibhakthi and karaka roles in Dravidian languages. This mapping is elegant and compact. The same basic thing also explains simple and complex sentence in these languages. This suggests that the solution is not just ad hoc but has a deeper underlying unity. This methodology could be extended to other free word order languages. Since the frame designed for meaning representation is general, they are adaptable to other languages coming in this group and to other applications.