Add to ORKGAbstract. We give an explicit upper bound for the number of isolated inter-sections between an integral curve of a polynomial vector field in Rn and an affine hyperplane. The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives. This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being eithe
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial v...
In this paper we give for any integer a numerical criterion ensuring the existence of a chain of len...
AbstractWe give a new upper bound on the number of isolated roots of a polynomial system. Unlike man...
We give an explicit upper bound for the number of isolated intersections between an integral curve o...
Abstract. We give an explicit upper bound for the number of isolated inter-sections between an integ...
this paper, concerns oscillatory properties of functions defined by polynomial ordinary differential...
Let ξ be a polynomial vector field on $^n$ with coefficients of degree d and P be a polynomial of de...
We show that gradient trajectories of a denable (in an o-minimal structure) family of functions are ...
Let X be a smooth affine surface, X \u2192 G2 m be a finite morphism. We study the affine curves on ...
We give a necessary and sufficient condition for the Jacobian conjecture, and if polynomials f(x,y) ...
We address the problem of {\em root isolation} for polynomial systems: for an affine, zero-dimension...
We obtain analogues of several recent bounds on the number of solutions of polynomial congruences mo...
AbstractWe give an upper bound for the maximum number N of algebraic limit cycles that a planar poly...
Abstract. Some improved bounds on the number of directions not determined by a point set in the affi...
For a Lipschitzian vector field in IRn, angular velocity of its trajectories with respect to any sta...
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial v...
In this paper we give for any integer a numerical criterion ensuring the existence of a chain of len...
AbstractWe give a new upper bound on the number of isolated roots of a polynomial system. Unlike man...
We give an explicit upper bound for the number of isolated intersections between an integral curve o...
Abstract. We give an explicit upper bound for the number of isolated inter-sections between an integ...
this paper, concerns oscillatory properties of functions defined by polynomial ordinary differential...
Let ξ be a polynomial vector field on $^n$ with coefficients of degree d and P be a polynomial of de...
We show that gradient trajectories of a denable (in an o-minimal structure) family of functions are ...
Let X be a smooth affine surface, X \u2192 G2 m be a finite morphism. We study the affine curves on ...
We give a necessary and sufficient condition for the Jacobian conjecture, and if polynomials f(x,y) ...
We address the problem of {\em root isolation} for polynomial systems: for an affine, zero-dimension...
We obtain analogues of several recent bounds on the number of solutions of polynomial congruences mo...
AbstractWe give an upper bound for the maximum number N of algebraic limit cycles that a planar poly...
Abstract. Some improved bounds on the number of directions not determined by a point set in the affi...
For a Lipschitzian vector field in IRn, angular velocity of its trajectories with respect to any sta...
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial v...
In this paper we give for any integer a numerical criterion ensuring the existence of a chain of len...
AbstractWe give a new upper bound on the number of isolated roots of a polynomial system. Unlike man...