The formal definition of valuation was firstly given by the Hungarian mathematician J. Kürschák in 1912 supported with ideas of Hensel. Valuation theory, based on this concept, has been developed by a large number of contributors (some of them distinguished mathematicians as Krull or Zariski) and it has a wide range of applications in different context and research areas as, for instance, algeb...

let $f$ be a finite extension of $bbb q$‎, ‎${bbb q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $e/f$ be a galois extension‎. ‎we study the realization fields of‎ ‎finite subgroups $g$ of $gl_n(e)$ stable under the natural‎ ‎operation of the galois group of $e/f$‎. ‎though for sufficiently large $n$ and a fixed‎ algebraic number field $f$ every its finite extension $e$ is‎ ‎re...

algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

The χ language is a hybrid language for modeling, simulation and verification. As a result of the recently completed formal semantics, the language now consists of a number of orthogonal operators that operate on all process terms, including differential algebraic equations. The same χ model can be used for simulation and verification. Verification is possible after a straightforward syntactica...