Let φ(x) be an Eisenstein polynomial of degree n over a local field and α be a root of φ(x). Our main tool is the ramification polygon of φ(x), that is the Newton polygon of ρ(x) = φ(αx+α)/(αx). We present a method for determining the Galois group of φ(x) in the case where the ramification polygon consists of one segment.

We present a new method for the rational parametrization of plane algebraic curves. The algorithm exploits the shape of the Newton polygon of the defining implicit equation and is based on methods of toric geometry.

Economic Model Predictive Control (EMPC) has recently become popular because of its ability to control constrained nonlinear systems while explicitly optimizing a prescribed performance criterion. Large gains have been reported for many applications and closed-loop stability investigated. However, computational still remains an open issue only few contributions proposed real-time algorithms tai...

In this paper operator pencils A(x,D, λ) are studied which act on a manifold with boundary and satisfy the condition of N-ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by Agmon and Agranovich–Vishik. Sobolev spaces corresponding to the Newton polygon are defined and investigated; in particular it is possible to describe their trace spaces...

In an extension of Newton’s method to generalized equations, we carry further the implicit function theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set of all associated sequences of Newton’s iterates as elements of a sequence space. An inverse function version of this result shows that the strong regularity of the mapping asso...

We compute a basis for the p-adic Dwork cohomology of a smooth complete intersection in projective space over a finite field and use it to give padic estimates for the action of Frobenius on this cohomology. In particular, we prove that the Newton polygon of the characteristic polynomial of Frobenius lies on or above the associated Hodge polygon. This result was first proved by B. Mazur using c...

The T -adic deformation of p-adic exponential sums is defined. It interpolates all classical p-power order exponential sums over a finite field. Its generating L-function is a T -adic entire function. We give a lower bound for its T -adic Newton polygon and show that the lower bound is often sharp. We also study the variation of this L-function in an algebraic family, in particular, the T -adic...