A Condition for a Polynomial Map to be Invertible.
A continuous, constructive solution to Hilbert's 17th problem.
A criterion for rational places over local fields.
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 generalization of the Gauss-Lucas theorem
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
A geometric maximization problem
A note on involutory automorphisms of and the use of algebraically independent numbers for the construction of diagonable matrices
A note on Robinson's non-negativity criterion
A note on the pp conjecture for sheaves of spaces of orderings
In this note we provide a direct and simple proof of a result previously obtained by Astier stating that the class of spaces of orderings for which the pp conjecture holds true is closed under sheaves over Boolean spaces.
A polynomial solution to regulation and tracking. II. Stochastic problem
A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.
Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning...
A really elementary proof of real Lüroth's theorem.
Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K is a subfield...
A remark on the Chebotarev theorem about roots of unity.
A Remark on the Multidimensional Moment Problem.
A simple counterexample to Kouchnirenko's conjecture.
A simple proof of the Fundamental Theorem of Algebra
In the paper an elementary and simple proof of the Fundamental Theorem of Algebra is given.
A way of Reducing the Factorization Problem in Z[x] to the Factorization Problem in Z
A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
Abelian varieties and a conjecture of R.M. Robinson.
Abstract Grothendieck rings