scholarly journals Line and rational curve arrangements, and Walther’s inequality

2019 ◽  
Vol 30 (3) ◽  
pp. 615-633 ◽  
Author(s):  
Alexandru Dimca ◽  
Gabriel Sticlaru
Keyword(s):  
Rational Curve

scholarly journals Zariski k-plets of rational curve arrangements and dihedral covers

2004 ◽  
Vol 142 (1-3) ◽  
pp. 227-233 ◽  
Author(s):  
Enrique Artal Bartolo ◽  
Hiro-o Tokunaga
Keyword(s):  
Rational Curve

Minimal Generators of the Defining Ideal of the Rees Algebra Associated with a Rational Plane Parametrization with μ = 2

2014 ◽  
Vol 66 (6) ◽  
pp. 1225-1249 ◽  
Author(s):  
Teresa Cortadellas Benítez ◽  
Carlos D'Andrea
Keyword(s):  
Projective Plane ◽  
Rational Curve ◽  
Rees Algebra ◽  
Homogeneous Polynomials ◽  
Rational Plane ◽  
Minimal Generators ◽  
The Ideal

AbstractWe exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated with the ideal of three bivariate homogeneous polynomials parametrizing a proper rational curve in projective plane, having a minimal syzygy of degree 2.

scholarly journals Bounds for the smallest integer point of a rational curve

2003 ◽  
Vol 107 (3) ◽  
pp. 251-268
Author(s):  
Dimitrios Poulakis
Keyword(s):  
Integer Point ◽  
Rational Curve

Dimensional Synthesis and Constrained Motion Interpolation for Planar and Spherical 6R Closed Chains

2008 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Qiaode Jeffrey Ge
Keyword(s):  
Rational Curve ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Initial Attempt ◽  
Kinematic Constraints ◽  
Constraint Manifold ◽  
Cartesian Space ◽  
Closed Chain ◽  
Kinematic Mapping ◽  
The Given

In the recent past, we have studied the problem of synthesizing rational interpolating motions under the kinematic constraints of any given planar and spherical 6R closed chain. This work presents some preliminary results on our initial attempt to solve the inverse problem, that is to determine the link lengths of planar and spherical 6R closed chains that follow a given smooth piecewise rational motion under the kinematic constraints. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of planar and spherical closed chains in the Cartesian space. By using kinematic mapping and a quaternions based approach to represent displacements of the coupler of the closed chains, the given smooth piecewise rational motion is mapped to a smooth piecewise rational curve in the space of quaternions. In this space, the aforementioned workspace constraints on the coupler of the closed chains define a constraint manifold representing all the positions available to the coupler. Thus the problem of dimensional synthesis may be solved by modifying the size, shape and location of the constraint manifolds such that the mapped rational curve is contained entirely inside the constraint manifolds. In this paper, two simple examples with preselected moving pivots on the coupler as well as fixed pivots are presented to illustrate the feasibility of this approach.

An elementary proof and an extension of Thas' theorem on k-arcs

1989 ◽  
Vol 105 (3) ◽  
pp. 459-462 ◽  
Author(s):  
Hitoshi Kaneta ◽  
Tatsuya Maruta
Keyword(s):  
Finite Field ◽  
Projective Space ◽  
Elementary Proof ◽  
Rational Curve ◽  
Image Position

Let q be the finite field of q elements. Denote by Sr q the projective space of dimension r over q. In Sr,q, where r ≥ 2, a k-arc is defined (see [4]) as a set of k points such that no j + 2 lie in a Sj,q, for j = 1,2,…, r−1. (For a k-arc with k > r, this last condition holds for all j when it holds for j = r−1.) A rational curve Cn of order n in Sr,q, is the set

Commutative differential operator and a class of solutions for the BKP equation on the singular rational curve

1991 ◽  
Vol 32 (12) ◽  
pp. 3473-3475 ◽  
Author(s):  
A. Roy Chowdhury ◽  
N. Das Gupta
Keyword(s):  
Differential Operator ◽  
Rational Curve ◽  
Bkp Equation

scholarly journals Matrices of integers associated with self-transformations of surfaces

1948 ◽  
Vol 193 (1032) ◽  
pp. 25-43
Keyword(s):  
Rational Curve ◽  
Pell Equation ◽  
Quartic Surface ◽  
Twisted Cubic ◽  
Cubic Curve ◽  
The Matrix ◽  
Quartic Surfaces ◽  
Infinite Sequences ◽  
Square Matrix

Let c = ( c 1 , . . . , c r ) be a set of curves forming a minimum base on a surface, which, under a self-transformation, T , of the surface, transforms into a set T c expressible by the equivalences T c = Tc, where T is a square matrix of integers. Further, let the numbers of common points of pairs of the curves, c i , c j , be written as a symmetrical square matrix Г. Then the matrix T satisfies the equation TГT' = Г. The significance of solutions of this equation for a given matrix Г is discussed, and the following special surfaces are investigated: §§4-7. Surfaces, in particular quartic surfaces, wìth only two base curves. Self-transformations of these depend on the solutions of the Pell equation u 2 - kv 2 = 1 (or 4). §8. The quartic surface specialized only by being made to contain a twisted cubic curve. This surface has an involutory transformation determined by chords of the cubic, and has only one other rational curve on it, namely, the transform of the cubic. The appropriate Pell equation is u 2 - 17 v 2 = 4. §9. The quartic surface specialized only by being made to contain a line and a rational curve of order m to which the line is ( m - 1)⋅secant (for m = 1 the surface is made to contain two skew lines). The surface has two infinite sequences of self-transformations, expressible in terms of two transformations R and S , namely, a sequence of involutory transformations R S n , and a sequence of non-involutory transformations S n .

Compact complex threefolds which are Kähler outside a smooth rational curve

1999 ◽  
Vol 207 (1) ◽  
pp. 21-59 ◽  
Author(s):  
Lucia Alessandrini ◽  
Giovanni Bassanelli
Keyword(s):  
Rational Curve

The envelope of the subspaces of the polyhedra of an involution on a rational curve

1937 ◽  
Vol 33 (2) ◽  
pp. 183-187 ◽  
Author(s):  
H. F. Baker
Keyword(s):  
General Theorem ◽  
Binomial Coefficient ◽  
Rational Curve ◽  
Interesting Paper ◽  
Analytical Proof ◽  
Image Position

The following note was suggested by an interesting paper written by F. P. White, where many references are given. It refers to a theorem given by W. F. Meyer, by whom the proof is indicated as possible by generalization of an intricate analytical proof given by him for a simple case. His result is that if on the rational curve of order r, in space [r], say the curve cr [r], there be an involution ∞k, of sets of m points, expressed, suppose, by an equationthen the spaces [r − 1], formed from r points of any one of the polyhedra of m points, are an aggregate ∞k of primes of this space [r], which is of class (m − k, m − r), the notation (p, q) meaning the binomial coefficient p! / q!(p − q)!. By Meyer, the conditions k < r ≤ m are supposed to be satisfied. But there is a theorem for r < k ≤ m − 1, relating to selected [r − 1], formed from r points of any one of the polyhedra of m points. The general theorem may be formulated thus: In a space [r], the equation of any prime may be expressed by λu + μv +... + ρw = 0, where u = 0, v = 0, …w = 0 are any r + 1 given independent primes, and λ, μ, …ρ are coefficients which may be described as prime coordinates of the [r].

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