Let K be an algebraically closed field of characteristic 0 and let ƒ ϵ K[[X]] [Y] be monic. Using the properties of approximate roots given in [J. Algebra 343 (2011), pp. 143-159] we propose some necessary conditions for ...

We present a survey of results concerning p-bases of rings of constants with respect to polynomial derivations in characteristic p > 0. We discuss characterizations of rings of constants, properties of their generators and ...

We reprove some results about affine complete intersections.

The paper is devoted to the investigation of the notion of sufficiency in quantum statistics. Three kinds of this notion are considered: plain sufficiency (called simply: sufficiency), Petz’s sufficiency, and Umegaki’s ...

We consider the algebroid plane curves de ned by formal power series of two variables with coe cients in an algebraically closed eld. Using quadratic transformations we prove the local normalization theorem. Then we study ...

The multiple zeta values ζ(d1, . . . , dr ) are natural generalizations of the values ζ(d) of the Riemann zeta functions at integers d. They have many applications, e.g. in knot theory and in quantum physics. It turns ...

The non-degenerate jump of the Milnor number of an isolated singularity f0 is the minimal non-zero difference between the Milnor numbers of f0 and one of its non-degenerate deformations (fs). In the paper the results by ...

Recently A.R.Chouikha gave a new characterization of isochronicity of center at the origin for the equation x'' + g(x) = 0, where g is a real smooth function de_ned in some neighborhood of 0 ϵ R. We present some new ...

The paper presents some details of the proofs by Kuiper and Kuo, and Bochnak and Łojasiewicz that refer to the impact of the Łojasiewicz exponent of gradient mappings on C0-sufficiency of jets.