We determine the absolute differential Galois group of field C(x) rational functions: It is free proalgebraic on a set cardinality |C|. This solves longstanding open problem posed by B.H. Matzat. For proof we develop new characterization groups in terms split embedding problems, and use patching techniques order to solve very general class problems. Our result about also applies function fields...

A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If FRF varies significantly over resolution experiment (= reciprocal time), then these transients (leakage) cause important bias and variance estimate. To decrease errors, several local modeling techniques have been proposed literature. This ar...

This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certain r_r matrix are less than 2, where r is the degree of the rational function (or curve), and where the e...

A hyperelliptic function field can be always be represented as a real quadratic extension of the rational function field. If at least one of the rational prime divisors is rational over the field of constants, then it also can be represented as an imaginary quadratic extension of the rational function field. The arithmetic in the divisor class group can be realized in the second case by Cantor’...

The transfer function of IIR all-pass filters is a rational function of ω. However, the optimization of such a rational function using the successive projections method, which has a wider range of application than the Remez algorithm, has not been presented. In this paper, we propose designing IIR allpass filters using the successive projections method. key words: successive projections method,...

in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function which is the ratio of two polynomials (i.e., a rational function). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sums of squares certificates and hence such a Lyapunov fun...