Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2018, Volume 222, Issue 7, pp. 1810 - 1826

Let K be the algebraic closure of a finite field Fq of odd characteristic p. For a positive integer m prime to p, let F=K(x,y) be the transcendence degree 1...

MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAIC-CURVES

MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAIC-CURVES

Journal Article

Turkish Journal of Mathematics, ISSN 1300-0098, 2018, Volume 42, Issue 4, pp. 2018 - 2034

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2018, Volume 370, Issue 1, pp. 131 - 196

From a topological viewpoint, a rational curve in the real projective plane is generically a smoothly immersed circle and a finite collection of isolated...

TOPOLOGY | MATHEMATICS | ALGEBRAIC-CURVES | Mathematics - Algebraic Geometry

TOPOLOGY | MATHEMATICS | ALGEBRAIC-CURVES | Mathematics - Algebraic Geometry

Journal Article

Journal of Number Theory, ISSN 0022-314X, 05/2018, Volume 186, pp. 259 - 268

Given a curve C over a field K, the period of C/K is the gcd of degrees of K-rational divisor classes, while the index is the gcd of degrees of K-rational...

Period | Index | Algebraic curves | MATHEMATICS | FIELDS

Period | Index | Algebraic curves | MATHEMATICS | FIELDS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2015, Volume 430, Issue 1, pp. 354 - 380

We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of...

Curve with only one place at infinity | Reduction of singularities | Planar polynomial vector field | Invariant algebraic curve | Polynomial first integral | Blow-up | MATHEMATICS, APPLIED | FOLIATIONS | SINGULARITIES | NEWTON-PUISEUX EXPANSION | HYPERSURFACE SOLUTIONS | INVARIANT ALGEBRAIC-CURVES | POINCARE PROBLEM | MATHEMATICS | BOUNDS | LIMIT-CYCLES | LINE BUNDLES | SURFACES | Algorithms

Curve with only one place at infinity | Reduction of singularities | Planar polynomial vector field | Invariant algebraic curve | Polynomial first integral | Blow-up | MATHEMATICS, APPLIED | FOLIATIONS | SINGULARITIES | NEWTON-PUISEUX EXPANSION | HYPERSURFACE SOLUTIONS | INVARIANT ALGEBRAIC-CURVES | POINCARE PROBLEM | MATHEMATICS | BOUNDS | LIMIT-CYCLES | LINE BUNDLES | SURFACES | Algorithms

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2019, Volume 526, pp. 30 - 50

Let X be a (projective, non-singular, irreducible) curve of even genus g(X)≥2 defined over an algebraically closed field K of characteristic p. If the p-rank...

Automorphism groups | p-Rank | Algebraic curves | MATHEMATICS | FUNCTION-FIELDS

Automorphism groups | p-Rank | Algebraic curves | MATHEMATICS | FUNCTION-FIELDS

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 03/2010, Volume 32, Issue 3, pp. 561 - 568

Representing 2D and 3D data sets with implicit polynomials (IPs) has been attractive because of its applicability to various computer vision issues. Therefore,...

Computer vision | Image recognition | Smoothing methods | Stability | Shape | implicit shape representation | Spline | implicit polynomial (IP) | Surface fitting | Polynomials | Computational efficiency | Curve fitting | Fitting algebraic curves and surfaces | Surfaces | Implicit polynomial (IP) | Implicit shape representation | Fitting algebraic curves | POSE ESTIMATION | PARAMETRIC CURVES | RECOGNITION | ALGEBRAIC-CURVES | REPRESENTATION | OBJECTS | 3D SURFACES | 2D CURVES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Machine vision | Analysis | Data compression | Pattern recognition | Object recognition (Computers) | Studies | Methods | Accuracy | Fittings | IP (Internet Protocol) | Decomposition | Ridges | Three dimensional

Computer vision | Image recognition | Smoothing methods | Stability | Shape | implicit shape representation | Spline | implicit polynomial (IP) | Surface fitting | Polynomials | Computational efficiency | Curve fitting | Fitting algebraic curves and surfaces | Surfaces | Implicit polynomial (IP) | Implicit shape representation | Fitting algebraic curves | POSE ESTIMATION | PARAMETRIC CURVES | RECOGNITION | ALGEBRAIC-CURVES | REPRESENTATION | OBJECTS | 3D SURFACES | 2D CURVES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Machine vision | Analysis | Data compression | Pattern recognition | Object recognition (Computers) | Studies | Methods | Accuracy | Fittings | IP (Internet Protocol) | Decomposition | Ridges | Three dimensional

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 06/2017, Volume 108, Issue 6, pp. 593 - 600

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 09/2019, Volume 357, pp. 302 - 318

We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not...

Similarity | Harmonic polynomials | Dihedral groups | Planar algebraic curves | Symmetry detection | MATHEMATICS, APPLIED | Analysis | Algorithms

Similarity | Harmonic polynomials | Dihedral groups | Planar algebraic curves | Symmetry detection | MATHEMATICS, APPLIED | Analysis | Algorithms

Journal Article

2008, STU - Student edition, Princeton series in applied mathematics, ISBN 9780691096797, xx, 696

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental...

Mathematics | Curves, Algebraic | Finite fields (Algebra)

Mathematics | Curves, Algebraic | Finite fields (Algebra)

Book

Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2018, Volume 2018, Issue 32, pp. 1 - 18

In this paper we study the existence and uniqueness of limit cycles for socalled quadratic systems with a symmetrical solution: dx(t)/dt = P-2(x,y) equivalent...

Ordinary differential equations | Algebraic curve | Limit cycle | EXISTENCE | MATHEMATICS | ordinary differential equations | MATHEMATICS, APPLIED | limit cycle | INVARIANT ALGEBRAIC-CURVES | algebraic curve | LIMIT-CYCLES | UNIQUENESS

Ordinary differential equations | Algebraic curve | Limit cycle | EXISTENCE | MATHEMATICS | ordinary differential equations | MATHEMATICS, APPLIED | limit cycle | INVARIANT ALGEBRAIC-CURVES | algebraic curve | LIMIT-CYCLES | UNIQUENESS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 162 - 211

Let X be a (projective, geometrically irreducible, non-singular) algebraic curve of genus g≥2 defined over an algebraically closed field K of odd...

Automorphism groups | Algebraic curves | Positive characteristic | FINITE SIMPLE-GROUPS | MATHEMATICS | NUMBER | SUBGROUPS

Automorphism groups | Algebraic curves | Positive characteristic | FINITE SIMPLE-GROUPS | MATHEMATICS | NUMBER | SUBGROUPS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 09/2015, Volume 154, pp. 278 - 291

Let M be the Artin–Mumford curve over the finite prime field Fp with p>2. By a result of Valentini and Madan, AutFp(M)≅H with H=(Cp×Cp)⋊Dp−1. We prove that if...

Automorphism groups | Finite fields | Algebraic curves | MATHEMATICS

Automorphism groups | Finite fields | Algebraic curves | MATHEMATICS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2019, Volume 372, Issue 7, pp. 4805 - 4827

Given a real hyperelliptic algebraic curve X with non-empty real part and a real effective divisor \mathcal {D} arising via pullback from \mathbb{P}^1 under...

MATHEMATICS | real linear series | real algebraic curves | tropical geometry | real inflection points | Real enumerative algebraic geometry

MATHEMATICS | real linear series | real algebraic curves | tropical geometry | real inflection points | Real enumerative algebraic geometry

Journal Article

Journal of Algebra, ISSN 0021-8693, 09/2017, Volume 485, pp. 310 - 331

Let Fq be the finite field of order q=ph with p>2 prime and h>1, and let Fq¯ be a subfield of Fq. From any two q¯-linearized polynomials L1,L2∈F‾q[T] of degree...

Finite fields | Automorphism groups | Algebraic curves | Algebraic function fields | MATHEMATICS

Finite fields | Automorphism groups | Algebraic curves | Algebraic function fields | MATHEMATICS

Journal Article

Journal of Algebra, ISSN 0021-8693, 12/2016, Volume 468, pp. 253 - 274

In this paper we investigate the space of R-places of an algebraic function field of one variable. We deal with the problem of determining when two orderings...

Real algebraic curve | Space of cuts | Space of orderings | [formula omitted]-places | Algebraic function field | R-places | MATHEMATICS | ALGEBRAIC-CURVES | REAL

Real algebraic curve | Space of cuts | Space of orderings | [formula omitted]-places | Algebraic function field | R-places | MATHEMATICS | ALGEBRAIC-CURVES | REAL

Journal Article

2016, Mathematical surveys and monographs, ISBN 1470424088, Volume 210, xiii, 280

Arithmetic algebraic geometry (Diophantine geometry) | Mordell conjecture | Varieties over global fields | Varieties over finite and local fields | Varieties and morphisms | Curves, Algebraic | Arithmetical algebraic geometry | Arithmetic and non-Archimedean dynamical systems | Polynomials; rational maps; entire and meromorphic functions | Research exposition (monographs, survey articles) | Foundations | Complex dynamical systems | Arithmetic dynamics on general algebraic varieties | Non-Archimedean local ground fields | Dynamical systems and ergodic theory | Algebraic geometry | Number theory | Geometry, Algebraic

Book

Journal of Mathematical Physics, ISSN 0022-2488, 03/2011, Volume 52, Issue 3, pp. 032703 - 032703-13

We give a complete characterization of the Darbouxian first integrals of a generalized Raychaudhuri equation which appears in modern string cosmology and which...

PHYSICS, MATHEMATICAL | INVARIANT ALGEBRAIC-CURVES

PHYSICS, MATHEMATICAL | INVARIANT ALGEBRAIC-CURVES

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2019, Volume 538, pp. 290 - 311

Two classical results in algebraic geometry are that the branch curve of a del Pezzo surface of degree 1 can be embedded as a space sextic curve in P3 and that...

Theta characteristics | Algebraic curves | Del Pezzo surfaces | Tritangents | Space sextic | MATHEMATICS | Buildings | Remodeling, restoration, etc | Algorithms

Theta characteristics | Algebraic curves | Del Pezzo surfaces | Tritangents | Space sextic | MATHEMATICS | Buildings | Remodeling, restoration, etc | Algorithms

Journal Article

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