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A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function [PDF]

Systems and Control Letters, 2018
We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.
Bachir El Khadir, Amir Ali Ahmadi
exaly   +5 more sources

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Polynomials with Irrational Coefficients

2001
Polynomials in one or several variables have a specific type in MAPLE, the type polynom. However, introducing such objects doesn’t require any specific declaration. The user simply enters the polynomials with the help of the usual arithmetic operators +, -, * and ^.
Jack-Michel Cornil, Philippe Testud
openaire   +1 more source

Computation of the Galois group of a polynomial with rational coefficients. II

Journal of Mathematical Sciences, 2006
Summary: A new method, which enables us to compute rather efficiently the Galois group of a polynomial over \(\mathbb Q\) or over \(\mathbb Z\), is presented. Reductions of this polynomial with respect to different prime modules are studied, and the information obtained is used for the calculation of the Galois group of the initial polynomial.
openaire   +3 more sources

Indicial rational functions of linear ordinary differential equations with polynomial coefficients

Journal of Mathematical Sciences, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S A Abramov
exaly   +2 more sources

On the Zeros of Linear Differential Polynomials with Small Rational Coefficients

Journal of the London Mathematical Society, 1987
We prove the following: Suppose that f(z) is transcendental and meromorphic of finite order in the plane, and that the linear differential polynomial F(z) is defined by \[ F(z)=f^{(k)}(z)+...+a_ 0(z)f(z) \] and is non-constant, where \(a_{k-1}(z),...,a_ 0(z)\) are rational functions vanishing at infinity. Then \[ N(r,1/(fFF'))=O(\log r) \] implies that
openaire   +1 more source

On the relative power of polynomials with real, rational, and integer coefficients in proofs of termination of rewriting

Applicable Algebra in Engineering, Communications and Computing, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Salvador Lucas
exaly   +4 more sources

Rational Polynomial Coefficients Modeling and Bias Correction by Using Iterative Polynomial Augmentation

Journal of the Indian Society of Remote Sensing, 2018
In this article, we establish an update procedure for rapid positioning coefficients or rational polynomial coefficients (RPCs) via iterative refinements using polynomial augmentation and reference images. RPCs are widely popular in establishing a ground-to-image relationship without using physical sensor model.
Bhaskar Dubey, B. Kartikeyan, Manthira Moorthi Subbiah   +2 more
openaire   +1 more source

Rational solutions of linear differential and difference equations with polynomial coefficients

USSR Computational Mathematics and Mathematical Physics, 1989
Linear differential and difference equations whose coefficients and right-hand sides are polynomials are considered. The problem of constructing all rational solutions of an equation is solved.
S A Abramov
exaly   +2 more sources

On the computation of rational solutions of linear integro-differential equations with polynomial coefficients

Journal of Symbolic Computation
The authors propose a ``direct'' algorithm for calculating rational solutions to scalar integro-differential equations with polynomial coefficients. In particular, an algorithm for calculating polynomial solutions previously developed by the authors in [``On polynomial solutions of linear integro-differential equations'', IFAC PapersOnLine 55, No.
Thomas Cluzeau
exaly   +3 more sources

Note on the coefficients of rational Ehrhart quasi-polynomials of Minkowski-sums

Online Journal of Analytic Combinatorics, 2015
By extending former results of Ehrhart, it was shown by Peter McMullen that the number of lattice points in the Minkowski-sum of dilated rational polytopes is a quasipolynomial function in the dilation factors. Here we take a closer look at the coefficients of these quasi-polynomials and show that they are piecewise polynomials themselves and that they
Henk, Martin, Link, Eva
openaire   +2 more sources