In this note we study the distribution of real inflection points among the ovals of a real non-singular hyperbolic curve of even degree. Using Hilbert’s method we show that for any integers d and r such that 4 ≤ r ≤ 2d − 2d, there is a non-singular hyperbolic curve of degree 2d in R with exactly r line segments in the boundary of its convex hull. We also give a complete classification of possib...

This paper investigates the singular curves in the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

Given a sequence {Ek}k of almost-minimizing clusters in R which converges in L to a limit cluster E we prove the existence of C-diffeomorphisms fk between ∂E and ∂Ek which converge in C to the identity. Each of these boundaries is divided into C-surfaces of regular points, C-curves of points of type Y (where the boundary blows-up to three half-spaces meeting along a line at 120 degree) and isol...

In this paper, we construct a complete invariant for stably homeomorphic classes of curves on compact oriented surfaces without boundaries and show that this is a finite type invariant for curves. In knot theory, it is still unknown whether finite type invariants completely classify knots (the Vassiliev conjecture). We consider the analogy to this conjecture for generic immersed curves: do fini...

Non Uniform Rational B-splines (NURBs) are proved to be very promising for metamodeling in engineering problems, because they have unique properties such as local modification scheme, strong convex hull property, and infinitely differentiability, etc. Since NURBs are defined by control points, knot vector, and weights associated with control points, the precision of NURBs is influenced by all o...

We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.

We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.

We provide a new technique to detect the singularities of rational space curves. Given a rational parametrization of a space curve, we first compute a μ-basis for the parametrization. From this μ-basis we generate three planar algebraic curves of different bidegrees whose intersection points correspond to the parameters of the singularities. To find these intersection points, we construct a new...

Let M be a compact connected oriented surface. The surface M is called a translation surface if it is equipped with a translation structure, that is, an atlas of charts such that all transition functions are translations in R2. It is assumed that the chart domains cover all surface M except for finitely many points called singular. The translation structure induces the structure of a smooth man...