scholarly journals Helical polynomial curves and double Pythagorean hodographs I. Quaternion and Hopf map representations

2009 ◽  
Vol 44 (2) ◽  
pp. 161-179 ◽  
Author(s):  
Rida T. Farouki ◽  
Carlotta Giannelli ◽  
Alessandra Sestini
Keyword(s):  
Polynomial Curves ◽  
Hopf Map ◽  
Pythagorean Hodographs

scholarly journals Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves

2009 ◽  
Vol 44 (4) ◽  
pp. 307-332 ◽  
Author(s):  
Rida T. Farouki ◽  
Carlotta Giannelli ◽  
Alessandra Sestini
Keyword(s):  
Polynomial Curves ◽  
Low Degree ◽  
Pythagorean Hodographs

scholarly journals On pencils of polynomial curves

1996 ◽  
Vol 111 (1-3) ◽  
pp. 51-57
Author(s):  
D. Daigle
Keyword(s):  
Polynomial Curves

scholarly journals Fourier restriction to polynomial curves I: a geometric inequality

2010 ◽  
Vol 132 (4) ◽  
pp. 1031-1076 ◽  
Author(s):  
Spyridon Dendrinos ◽  
James Wright
Keyword(s):  
Geometric Inequality ◽  
Polynomial Curves ◽  
Fourier Restriction

scholarly journals Vertical Shift and Simultaneous Diophantine Approximation on Polynomial Curves

2014 ◽  
Vol 58 (1) ◽  
pp. 1-26
Author(s):  
Faustin Adiceam
Keyword(s):  
Hausdorff Dimension ◽  
Diophantine Approximation ◽  
Rational Approximations ◽  
Vertical Shift ◽  
Polynomial Curves ◽  
Integer Coefficients ◽  
Simultaneous Diophantine Approximation ◽  
First Results

AbstractThe Hausdorff dimension of the set of simultaneously τ-well-approximable points lying on a curve defined by a polynomial P(X) + α, where P(X) ∈ ℤ[X] and α ∈ ℝ, is studied when τ is larger than the degree of P(X). This provides the first results related to the computation of the Hausdorff dimension of the set of well-approximable points lying on a curve that is not defined by a polynomial with integer coefficients. The proofs of the results also include the study of problems in Diophantine approximation in the case where the numerators and the denominators of the rational approximations are related by some congruential constraint.

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