What does it mean to be straight? That the direction of the line does not change. In other words, the unit tangent vector to the curve remains constant. Note that the speed does not need to be constant; only the direction remains the same. However, if we are only interested in the shape of the line, and not in the particular manner in which we move along it, it is convenient to use a descriptio...

Navier–Stokes equilibrium solutions of a viscous fluid confined between two infinite parallel plates that can independently stretch or shrink in orthogonal directions are studied. It is assumed the admissible satisfy spatial self-similarity stretching shrinking perpendicular coordinates. The nonlinear steady boundary-value problem discretized using spectral Legendre method, and found tracked tw...

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

The principal contribution of this article is to determine the existence zones of the various periodic ferroresonant modes (fundamental, harmonic and subharmonic) intervening in the electrical power network. The bifurcation diagrams are used for this purpose. To be able to plot a bifurcation diagram of a particular solution, it is initially necessary to locate this solution and then to follow i...

The appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail. We focus on solutions in the twofold azimuthally-periodic subspace because of their special stability properties, but relate our findings to other solutions as well. Using timestepping, an adapted Krylov–Newton method and Arnoldi itera...

This paper presents a method that is able to continue periodic orbits in systems where only output of the evolution over a given time period is available, which is the typical situation in an experiment. The starting point of our paper is an analysis of time-delayed feedback control, a method to stabilize periodic orbits experimentally that is popular among physicists. We show that the well-kno...

Relative entropy with respect to normalized arclength on the circle is greater than or equal to the negative logarithmic energy (Voiculescu’s negative free entropy) and is greater than or equal to the modified relative free entropy. This note contains proofs of these inequalities and related consequences of the first Lebedev–Milin inequality.