Results 231 to 240 of about 180,889 (278)

Invariant Curves by Vector Fields on Algebraic Varieties

Journal of the London Mathematical Society, 2000
Summary: If \(C\) is a reduced curve which is invariant by a one-dimensional foliation \(\mathcal F\) of degree \(d_{\mathcal F}\) on the projective space then it is shown that \(d_{\mathcal F} -1+a\) is a bound for the quotient of the two coefficients of the Hilbert-Samuel polynomial for \(C\), where \(a\) is an integer obtained from a concrete ...
A. Campillo, M. M. Carnicer, J. García de la Fuente   +2 more
semanticscholar   +3 more sources

Projectively invariant representations using implicit algebraic curves

Image and Vision Computing, 1990
Abstract We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.’ We achieve this by using
D. Forsyth, J. Mundy, Andrew Zisserman, Christopherm . Brown   +3 more
semanticscholar   +2 more sources

A New Affine Invariant Fitting Algorithm for Algebraic Curves

Lecture Notes in Computer Science, 2004
In this paper, we present a new affine invariant curve fitting technique. Our method is based on the affine invariant Fourier descriptors and implicitization of them by matrix annihilation. Experimental results are presented to assess the stability and robustness of our fitting method under data perturbations.
Mustafa Unel
exaly   +2 more sources

Liénard systems for quadratic systems with invariant algebraic curves

Differential Equations, 2011
L. Cherkas
exaly   +2 more sources

The classification of the refined Humbert invariant for curves of genus 2

International Journal of Number Theory, 2022
The refined Humbert invariant is a positive definite quadratic form intrinsically attached to a curve $C$ of genus 2. This invariant is an algebraic generalization of the (usual) Humbert invariant.
Harun Kir
semanticscholar   +1 more source

Invariant Algebraic Curves of Polynomial Dynamical Systems

Differential Equations, 2003
The authors consider two-dimensional polynomial dynamical systems and study when their limit cycles are invariant algebraic curves. This problem goes back to Darboux, Poincaré, Erugin. The authors present some new interesting results.
Dolov, M. V., Pavlyuk, Yu. V.
openaire   +2 more sources

Semidifferential Invariants for Tactile Recognition of Algebraic Curves

The International Journal of Robotics Research, 2005
In this paper we study the recognition of low-degree polynomial curves based on minimal tactile data. Euclidean differential and semidifferential invariants have been derived for quadratic curves and special cubic curves that are found in applications.
Rinat Ibrayev, Yan-Bin Jia
openaire   +1 more source

Characterization of the Riccati and Abel Polynomial Differential Systems Having Invariant Algebraic Curves

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
The Riccati polynomial differential systems are differential systems of the form [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] for [Formula: see text] are polynomial functions. We characterize all the Riccati
Jaume Giné, J. Llibre
semanticscholar   +1 more source

Invariant singular points of algebraic curves

Mathematical Notes of the Academy of Sciences of the USSR, 1983
Let \(F\subset {\mathbb{C}}P^ 2\) be a plane curve and \(p\in F\) a singular point of F. The author establishes the following equality of local numerical invariants of the singularity (F,p): \(h(p)=2{\mathcal H}(p)+2g(p)+s^*(p),\) where \({\mathcal H}(p)\) is the intersection number p of the curve F and a generic curve whose equation is of the form: \(\
openaire   +2 more sources

Invariant Algebraic Curves and Hyperelliptic Limit Cycles of Liénard Systems

Qualitative Theory of Dynamical Systems, 2021
The paper under review studies Liénard systems of the form \[ \dot x=y, \quad \dot y=-f_m(x)y-g_n(x) \] with the focus on the following two aspects: the existence of invariant algebraic curves and hyperelliptic limit cycles of the systems. The functions \(f_m(x)\) and \(g_n(x)\) involved are real polynomials of degree \(m\) and \(n\), respectively. One
Qian, Xinjie, Shen, Yang, Yang, Jiazhong
openaire   +2 more sources