Asymptotes, Cubic Curves, and the Projective Plane

Locus Curves in Triangle Families

“…Now one can use results from [11] and [13] regarding asymptotes of algebraic curves and their relations to the equation of the curve. In [11] we find relations between linear factors of the highest degree homogeneous part of the equation and equations of asymptotes as follows in our case of degree 3 polynomial P:…”

Compositional flow in porous media: Riemann problem for three alkanes

“…2(b3), the discriminant becomes negative close to 0 and sx , therefore some gaps on the evaporation branch arise. The following lemma is based on [18] and establishes the existence of four possible asymptotes to the evaporation Hugoniot. Proof of Lemma 4.10.…”

“…Acknowledgments. We thank Ricardo Barros for pointing us to the paper of J. Nunemacher, [18], and Nuno Luzia for some suggestions for simplifying the analysis.…”