We prove that the first-order theory of any function field K of characteristic p > 2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.

The method of moments proposed by Carrasco and Florens (2000) permits to fully exploit the information contained in the characteristic function and yields an estimator which is asymptotically as effi cient as the maximum likelihood estimator. However, this estimation procedure depends on a regularization or tuning parameter α that needs to be selected. The aim of the present paper is to provide...

In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields F3n . Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special attention to the case where n is composite. This allows us to represent the function field over different base fields. Practical experiments appear to show t...

We determine the structure of the homology of the BeckerSchultz space SGiS1) ~ Q(CP^° AS1) of stable Sx-equivariant self-maps of spheres (with standard free S1 -action) as a Hopf algebra over the DyerLashof algebra. We use this to compute the homology of BSGiS1). Along the way, we give a fresh account of the partially framed transfer construction and the Becker-Schultz homotopy equivalence. We ...

The master equation of quantum optical density operator is transformed to the equation of characteristic function. The parametric amplification and amplitude damping as well as the phase damping are considered. The solution for the most general initial quantum state is obtained for parametric amplification and amplitude damping. The purity of one mode Gaussian system and the entanglement of two...

The paper is devoted to two real problems that generate a cooperative game model with a so-called k-convex characteristic function when certain conditions are fulfilled. Both a bankruptcy problem and an information trading problem are modelled as a cooperative game by constructing the corresponding bankruptcy game as well as the information market game. Firstly, it is established that the bankr...

The positive characteristic function-field Mordell-Lang conjecture for finite rank subgroups is resolved for curves as well as for subvarieties of semiabelian varieties defined over finite fields. In the latter case, the structure of the division points on such subvarieties is determined.

We consider Calderón’s inverse problem on planar domains Ω with conductivities in fractional Sobolev spaces. When Ω is Lipschitz, the problem was shown to be stable in the L–sense in [18]. We remove the Lipschitz condition on the boundary. To this end, we analyse the Sobolev regularity of the characteristic function of Ω. For Ω a quasiball, we compute ‖χΩ‖W s,p(Rd) in terms of the δ–neighbourho...

Finally we wish to indicate that a procedure analogous to those of [4] enables us to associate with every function/, meromorphic in 9JÎ, a characteristic function T(r, ƒ), r<\. Using the results of [5] and those of a work of Bers as well as the theorem of this paper it is possible to show that, under certain hypotheses, |jf| possesses boundary values almost everywhere on g, if the T(r, ƒ) is un...

In the unit ball B(0, 1), let u and Ω (a domain in RN ) solve the following overdetermined problem: ∆u = χΩ in B(0, 1), 0 ∈ ∂Ω, u = |∇u| = 0 in B(0, 1) \ Ω, where χΩ denotes the characteristic function, and the equation is satisfied in the sense of distributions. If the complement of Ω does not develop cusp singularities at the origin then we prove ∂Ω is analytic in some small neighborhood of t...