where φ is the angle between the unit vortex line tangent vectors ξ(x−y, t) and ξ(x, t). Some degree of smoothness of the bundle of vortex lines near a potential singularity may result in averting blowup [3]. For simplicity, we’ll discuss Lipschitz continuous cases, although Hölder continuous cases may be analyzed in a similar fashion. We distinguish between the sine-Lipschitz case (i.e. sinφ i...

We prove that if there are consecutive gaps at a rational point on a smooth curve defined over a finite field, then one can improve the usual lower bound on the minimum distance of certain algebraic-geometric codes defined using a multiple of the point. A q-ary linear code of length n and dimension k is a vector subspace of dimension k of Fq , where Fq denotes the finite field with q elements. ...

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.

Scroll rings are three-dimensional spiral waves of excitation that rotate around circular filaments. In a modified Belousov-Zhabotinsky reaction, these filaments expand, buckle, and build up gradients in rotation phase. The instability is caused by negative filament tension (-4.3x10;{-4}cm;{2}s) . Initial deformations are strongest in the direction normal to the filament's osculating plane, and...

This paper presents an alternative way to calculate the next approximate point in marching techniques for the computation of the intersection of two parametric surfaces. Di ering from the classical methods, the algorithm is based on the approximate osculating circle instead of tangent vector to estimate the next point. It provides closer estimation and a larger marching step in each iteration w...

The nucleus of a Veronese variety is the intersection of all its osculating hyperplanes. Various authors have given necessary and sufficient conditions for the nucleus to be empty. We present an explicit formula for the dimension of this nucleus for arbitrary characteristic of the ground field. As a corollary, we obtain a dimension formula for that subspace in the t–th symmetric power of a fini...

Motion-trajectory (MT) curves are used to introduce Frenet oscillations. Time-varying orientation of the motion plane that contains absolute velocity and acceleration vectors is defined in terms three Frenet–Euler angles; curvature, vertical-development, bank angles, referred as angles for brevity. The angle associated super-elevation plane, which measure deviation centrifugal inertia force fro...