a r t i c l e i n f o a b s t r a c t Keywords: Valuation independence Generalized series fields Fields of Puiseux series Restricted exponential function We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed or algebraically closed field F with subfield K , we give a sufficient condition for a valued subfield of the field of gene...

Extending work of Puninski, Puninskaya and Toffalori in [PPT07], we show that if V is an effectively given valuation domain then the theory of all V -modules is decidable if and only if there exists an algorithm which, given a, b ∈ V , answers whether a ∈ rad(bV ). This was conjectured in [PPT07] for valuation domains with dense value group where it was proved for valuation domains with dense a...

For any Lagrangean Kähler submanifold M ⊂ T Cn, there exists a canonical hyper Kähler metric on T ∗M . A Kähler potential for this metric is given by the generalized Calabi Ansatz of the theoretical physicists Cecotti, Ferrara and Girardello. This correspondence provides a method for the construction of (pseudo) hyper Kähler manifolds with large automorphism group. Using it, a class of pseudo h...

Let S = Sg,n be an orientable surface with genus g and n marked points. The mapping class group of S is defined to be the group of homotopy classes of orientation preserving homeomorphisms of S. We denote it by Mod(S). Given a pseudo-Anosov element f ∈ Mod(S), let λ(f ) denote the dilatation of f (see section 2.1). We define L(Sg,n) := {log λ(f )|f ∈ Mod(Sg,n) pseudo-Anosov}. This is precisely ...

The pseudo-angle characterizes the pseudo-conformal group G." Let S2m be a fixed 2m dimensional manifold contained in 2;2 so that m . n. LetP be an arbitrary point of S2m. Suppose that S2,1n is an arbitrary (2n 1) dimensional manifold in Z2., which contains P, and let the intersection of S2m and S2,-1 be an S2m-j. Thus S2m is not contained in S2,1. The pseudo-angle between any curve C, in S2m, ...

In this paper we study the static Einstein–Maxwell space when it is conformal to an n-dimensional pseudo-Euclidean space, which invariant under action of $$(n-1)$$ -dimensional translation group. We also provide a complete classification such space.