On the number of terms of a power of a polynomial
On the number of zero trace elements in polynomial bases for F2n.
Let Fq denote the finite field of q elements. O. Ahmadi and A. Menezes have recently considered the question about the possible number of elements with zero trace in polynomial bases of F2n over F2. Here we show that the Weil bound implies that there is such a basis with n + O(log n) zero-trace elements.
On the -adic continuation of the logarithmic derivative of certain hypergeometric functions
On the problem of Baer and Kolchin in the Picard-Vessiot theory
We present the history of the development of Picard-Vessiot theory for linear ordinary differential equations. We are especially concerned with the condition of not adding new constants, pointed out by R. Baer. We comment on Kolchin's condition of algebraic closedness of the subfield of constants of the given differential field over which the equation is defined. Some new results concerning existence of a Picard-Vessiot extension for a homogeneous linear ordinary differential equation defined over...
On the Pythagoras number of a real irreducible algebroid curve.
On the Pythagoras number of orders in totally real number fields.
On the Pythagorean hull of Q.
The purpose of this paper is to prove that the Pythagorean hull of Q is the splitting field in R of a special set of rational polynomials.
On the rank of semimodules over semirings.
On the real roots of generalized Thue-Morse polynomials
On the reducibility type of trinomials
On the representation of cyclotomic polynomials as sums of squares
On the roots of polynomials over division algebras.
On the semi-simplicity of Galois actions
On the seperation of basic semialgebraic sets by polynomials.
On the set of distances between two sets over finite fields.
On the Sharpness of Theorems Concerning Zero-Free Regions for Certain Sequences of Polynomials.
On the shifted QR iteration applied to companion matrices.
On the structure of compact subsets of ℂₚ
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.