Walton & Meek [13] obtained fair G Pythagorean hodograph (PH) quintic transition Sand C-shaped curves connecting two circles. It was shown that an S-shaped curve has no curvature extremum and a Cshaped curve has a single curvature extremum. We simplified and completed their analysis. A family of fair PH quintic transition curves between two circles has been derived. We presented an algorithm wi...

The purpose of this paper is to study some properties of the Newton maps associated to real quintic polynomials. First using the Tschirnhaus transformation, we reduce the study of Newton’s method for general quintic polynomials to the case f(x) = x − c x + 1. Then we use symbolic dynamics to consider this last case and construct a kneading sequences tree for Newton maps. Finally, we prove that ...

introduction 3d reconstruction of an object from its 2d cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. in order to perform 3d reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. mate...

We study the stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physical models are Gross-Pitaevskii (GP) equation and cubic-quintic equation. First, under a non-degeneracy condition we prove a sharp instability criterion for 3D traveling waves of (GP), which had been conjectured in the...

Let k be a field of characteristic 6= 2. We survey a general method of the field intersection problem of generic polynomials via formal Tschirnhausen transformation. We announce some of our recent results of cubic, quartic and quintic cases the details of which are to appear elsewhere. In this note, we give an explicit answer to the problem in the cases of cubic and dihedral quintic by using mu...

Abstract Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. The quintic Pythagorean hodograph (PH) curve discussed in this technical report is polynomial; it has the attractive properties that its arc-length is a polynomial of its parameter, a...

We study degenerations of Kummer surfaces associated to certain divisors in Nieto’s quintic threefold and show how they arise from boundary components of a suitable toroidal compactification of the corresponding Siegel modular threefold. The aim of this paper is to study the degenerations of an interesting class of Kummer surfaces in P in terms of degenerations of the corresponding abelian surf...

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of smal...

This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are p...