Some quantitative results in singularity theory

On some problems in singularity theory

On Some Constructions in Quantitative Domain Theory

Domains introduced by Dana Scott [11] and independently by Yuri L. Ershov [3] are a structure modelling the notion of approximation and of computation. A computation performed using an algorithm proceeds in discrete steps. After each step there is more information available about the result of the computation. In this way the result obtained after each step can be seen as an approximation of th...

Singularity in signal theory

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Some results of number theory

This is a collection of formalized proofs of many results of number theory. The proofs of the Chinese Remainder Theorem and Wilson’s Theorem are due to Rasmussen. The proof of Gauss’s law of quadratic reciprocity is due to Avigad, Gray and Kramer. Proofs can be found in most introductory number theory textbooks; Goldman’s The Queen of Mathematics: a Historically Motivated Guide to Number Theory...

Some Results on Fuzzy Theory

The apparition of Fuzzy Logic [10] has had a double repercussion on scientific research, and has provoked two types of reactions. From a theoretical point of view, it is indeed a very useful generalization of the classical Set Theory proposed by Boole and Cantor, in this way making possible our analysis of uncertainty. But unfortunately, in his first steps it had to avoid the assaults of routin...