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Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 11/2017, Volume 86, Issue 308, pp. 2877 - 2888
A smooth curve of degree d in the real projective plane is hyperbolic if its ovals are maximally nested, i.e., its real points contain [d/2] nested ovals. By... 
MATHEMATICS, APPLIED | PLANE-CURVES
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2020, Volume 364, p. 112350
In this paper, we summarize two algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. The... 
Parametric plane curve | Approaching curves | Asymptotes | Infinity branches | Implicit algebraic plane curve | Perfect curves | MATHEMATICS, APPLIED
Journal Article
KODAI MATHEMATICAL JOURNAL, ISSN 0386-5991, 06/2019, Volume 42, Issue 2, pp. 308 - 331
The author classifies finite groups acting on smooth plane curves of degree at least four. Furthermore, he gives an upper bound for the order of automorphism... 
MATHEMATICS | automorphism groups | plane curves
Journal Article
2011, MAA guides, ISBN 9780883853535, Volume no. forty-six, xv, 193
Book
Journal fur die Reine und Angewandte Mathematik, ISSN 0075-4102, 04/2011, Volume 653, Issue 653, pp. 179 - 187
A new isoperimetric estimate is proved for embedded closed curves evolving by curve shortening flow, normalized to have total length 2 pi. The estimate bounds... 
MATHEMATICS | SINGULARITIES | PLANE-CURVES
Journal Article
Communications in Analysis and Geometry, ISSN 1019-8385, 2013, Volume 21, Issue 2, pp. 355 - 363
Huisken and Sinestrari [9] have recently defined a surgery process for mean curvature flow when the initial data are a two-convex hypersurface in Rn+1 (n >=... 
MATHEMATICS | SETS | PLANE-CURVES
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2010, Volume 17, Issue 4, pp. 625 - 636
We completely carry out the log minimal model program for the moduli space of stable curves of genus three with respect to the total boundary delta : We give a... 
MATHEMATICS | PLANE-CURVES
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 07/2018, Volume 29, Issue 8, p. 1850053
This paper deals with the curvature bound for a nonlocal curve flow with a prescribed rate of change in enclosed area via Andrews–Bryan’s distance comparison.... 
distance comparison principle | curvature bound | Convex plane curve | NONLOCAL FLOW | MATHEMATICS | PRESERVING EVOLUTION | CONVEX PLANE-CURVES | THEOREM
Journal Article
Journal of Number Theory, ISSN 0022-314X, 01/2020
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 06/2018, Volume 2018, Issue 739, pp. 121 - 158
Ardila and Block used tropical results of Brugallé and Mikhalkin to count nodal curves on a certain family of toric surfaces. Building on a linearity result of... 
ENUMERATIVE GEOMETRY | POLYNOMIALS | MATHEMATICS | PROOF | FORMULA | PLANE-CURVES | GRAPHS
Journal Article
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 12/2018, Volume 303, Issue S1, pp. 213 - 215
An error bound for the approximation of the curvature of graphs of periodic functions from the class W r for r ≥ 3 in the uniform metric is obtained with the... 
uniform metric | Mathematics, general | Mathematics | curvature approximation | plane curves from the class W r | plane curves from the class W | MATHEMATICS | MATHEMATICS, APPLIED | plane curves from the class W-r
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2017, Volume 145, Issue 10, pp. 4503 - 4516
We study curve shortening flows in two types of warped product manifolds. These manifolds are \mathbb{S}^1 \times N with two types of warped metrics where... 
MATHEMATICS | MATHEMATICS, APPLIED | MEAN-CURVATURE FLOW | HYPERSURFACES | PLANE-CURVES | SURFACES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 11/2017, Volume 320, pp. 1269 - 1317
In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine... 
Approximate roots | Maximal divisorial set | Nash problem | Plane curve singularities | Arc spaces | Adjacency of singularities | MATHEMATICS | SURFACE SINGULARITIES | SPACES | FAMILIES | MAP | ARCS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 06/2017, Volume 340, Issue 6, pp. 1327 - 1334
In Homma and Kim (2010), an upper bound of the number of rational points on a plane curve of degree d over Fq is found. Some examples attaining the bound are... 
Finite field | Plane curve | Rational point | MATHEMATICS | FINITE-FIELDS
Journal Article
Canadian Journal of Mathematics, ISSN 0008-414X, 12/2014, Volume 66, Issue 6, pp. 1225 - 1249
AbstractWe exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated with the ideal of three bivariate homogeneous polynomials... 
Minimal generators | Rational plane curves | Rees algebras
Journal Article
Journal of Singularities, ISSN 1949-2006, 01/2018, Volume 17, pp. 70 - 80
Journal Article
2010, ISBN 9789814291286, xxi, 210
Book
Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2014, Volume 366, Issue 2, pp. 857 - 874
The Hilbert function of the union of n-fold points in the plane is maximal if n\ge 4e^2 is a square. The Hilbert function of a union of A, E. The proofs use a... 
Integers | Linear systems | Morphisms | Staircases | Mathematical theorems | Algebra | Plane curves | Polynomials | Residual claimancy | Smooth curves | POLYNOMIALS | MATHEMATICS | POINTS | PLANE-CURVES
Journal Article
Topology and its Applications, ISSN 0166-8641, 02/2018, Volume 234, pp. 269 - 284
We consider in this paper the orthogonal projection of space curves. A vertex is a point on the projected plane curve where there exists a circle which has at... 
Orthogonal projection | Evolute | Vertex | Plane curve | Contact | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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