A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper defines singular evolutoids and uses them to derive an integral equality.
Inspired by the concept of evolutoids of planar curves, we present the concept of evolutoids for regular surfaces as an envelope of a two-parameter family of lines in Euclidean 3-space. We give an explicit parametrization for such evolutoids. Besides, we used the theory of singularities to study the local behavior of r…
Study circle families' envelopes and related curves.
Study of evolutoids and involutoids of convex curves in 2D space forms.
The envelope of straight lines affine normal to a plane curve C is its affine evolute; the envelope of the affine lines tangent to C is the original curve, together with the entire affine tangent line at each inflexion of C. In this paper, we consider plane curves without inflexions. We use some techniques of singulari…
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
The study examines Bertrand Legendre curves in the unit tangent bundle over Euclidean plane.