In this paper we approach the Compact Linear Operators Theory by the methods of Nonstandard Analysis. We present new proofs of several known results and some new results as well. AMS Mathematics Subject Classification (2000): 26E35, 47B07

The physical foundation of the main mathematical concepts in the nonstandard analysis theory of turbulence are presented and discussed. The basic fact is that there does not exist the absolute zero fluid-volume. Therefore, the corresponding physical object to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-partic...

Inspired by nonstandard analysis, we define and study internal subsets and internal functions in algebras of Colombeau generalized functions. We prove a saturation principle for internal sets and provide applications to Colombeau algebras.

It is shown that Dirichlet's theorem on primes in an arithmetic progression is equivalent to the statement that every unit of a certain quotient ring Z of the nonstandard integers is the image of an infinite prime. The ring Z is the completion of Z relative to the "natural" topology on Z. 1. Notation. Throughout this note A shall denote the natural numbers, Z the rational integers, and P the po...

We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice, Springer, 1995, pp. 195–204). Those trends, which might coexist with some a...