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Interactive Design of Cubic IPH Spline Curves
Indirect Pythagorean hodographs (IPH) spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a...
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On Triple Lines and Cubic Curves: The Orchard Problem Revisited
Planar point sets with many triple lines (which contain at least three distinct points of the set) have been studied for 180 years, started with...
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Orthogonal Polynomials on Planar Cubic Curves
Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a...
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Discriminants of cubic curves and determinantal representations
The discriminant of a smooth plane cubic curve over the complex numbers can be written as a product of theta functions. This provides an important...
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The Truncated Moment Problem on Reducible Cubic Curves I: Parabolic and Circular Type Relations
In this article we study the bivariate truncated moment problem (TMP) of degree 2 k on reducible cubic curves. First we show that every such TMP is...
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Constructing cubic curves with involutions
In 1888, Heinrich Schroeter provided a ruler construction for points on cubic curves based on line involutions. Using Chasles’ Theorem and the...
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Closed-form solution of a class of generalized cubic B-splines
Using the Blossom method in the quasi extended Chebyshev space, we first construct a class of generalized cubic Bernstein functions in the...
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Qualitative dynamics of five quadratic polynomial differential systems exhibiting five classical cubic algebraic curves
This article is devoted to classify the dynamics of five quadratic differential systems exhibiting five known different cubic invariant algebraic...
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Elliptic Curves over the Rationals
This chapter covers prerequisites on elliptic curves over $$\mathbb...
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Stable Ulrich bundles on cubic fourfolds
In this paper, we examine the presence of Ulrich bundles on cubic fourfolds. We establish necessary and sufficient conditions for the existence of...
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On Affine Real Cubic Surfaces
We prove that the space of affine, transversal at infinity, nonsingular real cubic surfaces has 15 connected components. We give a topological...
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Elliptic Curves Induced by Diophantine Triples
This chapter introduces elliptic curves induced by Diophantine triples and discusses their properties and applications. One of the main applications...
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A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints
Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new...
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Phase Portraits of a Class of Cubic Systems with an Ellipse and a Straight Line as Invariant Algebraic Curves
In this paper we classify the phase portraits in the Poincaré disc of a class of cubic polynomial differential systems having an invariant ellipse...
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On the saturation number for singular cubic surfaces
We investigate the distribution of rational points on singular cubic surfaces, whose coordinates have few prime factors. The key tools used are...