We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a smooth surface by parallel planes. More precisely we will trace the patterns of inf…
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8 results for “inflexion”
Evolving Affine Evolutoidsmath.DG
The paper explains how curves evolve from one envelope to another using singularity theory.
problem Understanding the evolution of curves from one envelope to another.
method Singularity theory applied to plane curves without inflexions.
result Existence of the first slope at which singularities occur in the discriminant surface.
In this paper we study global properties of the Wigner caustic of parameterized closed planar curves. We find new results on its geometry and singular points. In particular, we consider the Wigner caustic of rosettes, i.e. regular closed parameterized curves with non-vanishing curvature. We present a decomposition of a…
Paper tackles non-stationary bandits with various examples.
problem Non-stationary stochastic bandit problem with specific cases.
method Proposes a single algorithm for multiple non-stationary bandit problems.
result Unified solution for four different bandit problems.
Study on the geometry of secant caustic of planar curves.
problem Analyzing the secant caustic of planar curves.
method Investigating the geometrical properties of secant caustic, including number of branches, cusps, and inflexion points.
result Detailed investigation of secant caustic properties, especially for rosettes.
We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generalization of the I-invariant of line arrangements developed by the first author with Artal and Florens. We give two practical tools for computin…
With a new deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the `global' mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reductio…
New points detected on surfaces in 4D space, revealing symmetries.
problem Detecting symmetries and special points on surfaces in 4D space.
method Contact classification of symmetric maps from the plane to the plane.
result Special parabolic points detected and associated with sign changes.