v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

In this paper we analyze the problem of partitioning a continuous curve into n parts with equal successive chords, the curve EquiPartition problem (EP). The goal is to locate n− 1 consecutive curve points, so that the curve can be divided into n segments with equal chords under a distance function. We adopt a level set approach to prove that for any continuous injective curve in a metric space ...

The modular curve X1(N) parametrizes elliptic curves with a point of order N . For N ≤ 50 we obtain plane models for X1(N) that have been optimized for fast computation, and provide explicit birational maps to transform a point on our model of X1(N) to an elliptic curve. Over a finite field Fq, these allow us to quickly construct elliptic curves containing a point of order N , and can accelerat...

The available resources such as memory buuer and network bandwidth are limited and varying for diierent application systems. Given a VBR stream, we have already proposed an algorithm to construct a transmission schedule with minimum buuer, minimum workahead and maximum network utilization for the given transmission rate. Notably, there is a trade-oo between the allocated buuer size and the obta...

The critical nitrogen (N) dilution curve is a suitable analytical tool for in-season estimation of N status to implement precision N management. This study was undertaken for a comprehensive comparison of N dilution curves in Japonica and Indica rice to investigate, whether a single curve can be used for both rice ecotypes and to determine the most robust plant index for assessing N status in r...

Given a minimal model of an elliptic curve, $E/K$, over finite extension, $K$, ${\mathbb Q}_{p}$ for any rational prime, $p$, and point $P \in E(K)$ infinite order, we determine precisely $\min \left( v \phi_{n}(P) \right), \psi_{n}^{2}(P) \right) \right)$, where $v$ is normalised valuation on $K$ $\phi_{n}(P)$ $\psi_{n}(P)$ are polynomials arising from multiplication by $n$ this the curve.

‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

We consider simple cube-curves in the orthogonal 3D grid. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve’s length is defined to be that of the minimum-length polygonal curve (MLP) fully contained and complete in the tube of the curve. So far no provable general algorithm is known for the approximative calculation of...

i=0 Pn n=0 bijB m i (u)B n j (v) of bi-degree (m;n) has total degree m + n, however, the class of Gmn(u; v) is a subset of polynomials of total degree m + n. G (resp G) continuity implies curve segments share the same tangent(curvature) at join points(knots). In each of the G and G constructions, we develop a spline curve family whose member satis es given interpolation conditions. Each family ...

We study a generalization of the von Koch Curve, which has two parameters, an integer n and a real number c on the interval (0, 1). This von Koch type curve is constructed as the limit of a recursive process that starts with a regular n-gon (or line segment) and repeatedly replaces the middle c portion of an interval by the n− 1 other sides of a regular n-gon placed contiguous to the interval. ...