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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 $\emptyset \neq L_{ℱ} \neq 𝕊^{1}$ .

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Displaying 801 – 820 of 2647

Fuzzy stability of an additive-quadratic-quartic functional equation.

Fuzzy stability of Jensen-type quadratic functional equations.

Fuzzy stability of quadratic functional equations.

Fuzzy stability of the pexiderized quadratic functional equation: A fixed point approach.

$G$ - $n$ -quasigroups.

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

Galois theory of fuchsian q-difference equations

Galois theory of $q$ -difference equations

Gauss-Manin connections of Schläfli type for hypersphere arrangements

Gehring theory for time-discrete hyperbolic differential equations

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

General continuous solution of a linear homogeneous functional equation

General inequalities for quasideviation means.

General solution of a system of functional equations satisfied by sums of powers on arithmetic progressions.

General theory of the translation equation.

Generalization of sum representation functional equations. I.

Generalization of sum representation functional equations. II: Generalized directed divergence

Generalized Associativity on Grupoids

Generalized Cauchy functional equation and characterizations of inner product spaces.

Generalized Cauchy functional equation and characterizations of inner product spaces. (Summary).

Currently displaying 801 – 820 of 2647