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$G$ - $n$ -quasigroups.

Petrescu, Adrian (2008)

Acta Universitatis Apulensis. Mathematics - Informatics

Galois groups and connection matrices for $q$ -difference equations.

Etingof, Pavel (1995)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Galois theory of fuchsian q-difference equations

Jacques Sauloy (2003)

Annales scientifiques de l'École Normale Supérieure

Galois theory of $q$ -difference equations

Marius van der Put, Marc Reversat (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Choose $q \in ℂ$ with $0 < | q | < 1$ . The main theme of this paper is the study of linear $q$ -difference equations over the field $K$ of germs of meromorphic functions at $0$ . A systematic treatment of classification and moduli is developed. It turns out that a difference module $M$ over $K$ induces in a functorial way a vector bundle $v (M)$ on the Tate curve $E_{q} : = ℂ^{*} / q^{ℤ}$ that was known for modules with ”integer slopes“, [Saul, 2]). As a corollary one rediscovers Atiyah’s classification $([A t])$ of the indecomposable vector bundles on the complex Tate...

Gauss-Manin connections of Schläfli type for hypersphere arrangements

Kazuhiko Aomoto (2003)

Annales de l’institut Fourier

The cohomological structure of hypersphere arragnements is given. The Gauss-Manin connections for related hypergeometrtic integrals are given in terms of invariant forms. They are used to get the explicit differential formula for the volume of a simplex whose faces are hyperspheres.

Gehring theory for time-discrete hyperbolic differential equations

Keisuke Hoshino, Norio Kikuchi (1998)

Commentationes Mathematicae Universitatis Carolinae

This paper is concerned with extending Gehring theory to be applicable to Rothe's approximate solutions to hyperbolic differential equations.

General construction of non-dense disjoint iteration groups on the circle

Krzysztof Ciepliński (2005)

Czechoslovak Mathematical Journal

Let $ℱ = {F^{v} 𝕊^{1} \to 𝕊^{1}, v \in V}$ be a disjoint iteration group on the unit circle $𝕊^{1}$ , that is a family of homeomorphisms such that $F^{v_{1}} \circ F^{v_{2}} = F^{v_{1} + v_{2}}$ for $v_{1}$ , $v_{2} \in V$ and each $F^{v}$ either is the identity mapping or has no fixed point ( $(V, +)$ is a $2$ -divisible nontrivial Abelian group). Denote by $L_{ℱ}$ the set of all cluster points of ${F^{v} (z)$ , $v \in V}$ for $z \in 𝕊^{1}$ . In this paper we give a general construction of disjoint iteration groups for which $\emptyset \neq L_{ℱ} \neq 𝕊^{1}$ .