Elliptic curves as an area of mathematical study are initially simple to understand, but reveal startling complexity when considered over different fields. This paper discusses the general properties and characteristics of projective space, elliptic curves, and the group structure that arises with certain binary operations on the curve. We discuss elliptic curves over Q, including the topic of ...

The Pythagorean hodograph (PH) curves are polynomial parametric curves whose hodograph (derivative) components satisfy the Pythagorean condition. Lots of research works had been done with PH curves relevant topics due that PH curves own many remarkable properties, e.g., its offset curves have exact rational representations. In this paper, ball curves with rational polynomial offset are studied....

We show that S. Saito’s fixed point formula serves as a powerful tool for counting the number of isolated periodic points of an area-preserving surface map admitting periodic curves. His notion of periodic curves of types I and II plays a central role in our discussion. We establish a Shub-Sullivan type result on the stability of local indices under iterations of the map, the finiteness of the ...

Finding suitable non-supersingular elliptic curves becomes an important issue for the growing area of pairing-based cryptosystems. For this purpose, many methods have been proposed when embedding degree k and cofactor h are taken different values. In this paper we propose a new method to find pairing-friendly elliptic curves without restrictions on embedding degree k and cofactor h. We propose ...

In 1956, Shiffman [Sh] proved that any compact minimal annulus with two convex boundary curves (resp. circles) in parallel planes is foliated by convex planar curves (resp. circles) in the intermediate planes. In 1978, Meeks conjectured that the assumption the minimal surface is an annulus is unnecessary [M]; that is, he conjectured that any compact connected minimal surface with two planar con...

‎in this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in lorentzian plane $mathbb{l}^{2}.$ then the‎ ‎special curves mentioned above are studied in lorentzian plane $mathbb{l}%‎‎^{2}.$ finally some characterizations of these special curves are given in‎ ‎$mathbb{l}^{2}.$‎

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both...

The aim of this paper is to provide an overview for the research that has been done so far on elliptic curves cryptography role in information security area. The elliptic curves cryptosystem is the newest public-key cryptographic system and represents a mathematically richer procedure then the traditional cryptosystem based on public-key, like RSA, Diffie-Hellman, ElGamal and Digital Signature ...

In 1931, Jesse Douglas showed that in Rn, every set of k rectifiable Jordan curves, with k ≥ 2, bounds an area-minimizing minimal surface with prescribed topological type if a “condition of cohesion” is satisfied. In this paper, it is established that under similar conditions, this result can be extended to non-Jordan curves.

Area-proportional Venn diagrams are a popular way of visualizing the relationships between data sets, where the set intersections have a specified numerical value. In these diagrams, the areas of the regions are in proportion to the given values. Venn-3, the Venn diagram consisting of three intersecting curves, has been used in many applications, including marketing, ecology and medicine. Whils...