A certain property of polynomials.
A certain property of polynomials. (Short Communication).
A Characterization of Linear Difference Equations Which are Solvable by Elementary Operations.
A characterization of locally compact fields II
A characterization of locally compact fields, III
A characterization of locally compact fields of zero characteristic
A Characterization of One-Element p-Bases of Rings of Constants
Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x₁,...,xₙ] be a polynomial not lying in . We prove that is the ring of constants of a K-derivation of K[x₁,...,xₙ] if and only if all the partial derivatives of f are relatively prime. The proof is based on a generalization of Freudenburg’s lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.
A characterization of the spherically complete normed spaces with a distinguished basis
A class of hyperrings and hyperfields.
A complete parametriziation of cyclic field extensions of 2-power degree.
A Concept of Bernoulli Numbers in Algebraic Function Fields (II).
A Condition for a Polynomial Map to be Invertible.
A conjecture in the arithmetic theory of differential equations
A constructive Approach to Noether's Problem.
A continuous, constructive solution to Hilbert's 17th problem.
A counterexample to a conjecture of multinomial degree
A criterion for rational places over local fields.
A duality based proof of the combinatorial nullstellensatz.
A fast numerical test of multivariate polynomial positiveness with applications
The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.
A Galois theory with stable units for simplicial sets.