This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 = dX +Z. We improve the doubling and addition steps in Miller’s algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific point representation to obtain the best resu...

This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 D dX C Z. We improve the doubling and addition steps in Miller’s algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific point representation to obtain the best res...

Klein’s quartic curve may be described as the Riemann surface obtained by taking the quotient of H by the (principal congruence) subgroup Γ(7) = ker {PSL2(Z) → PSL2(Z/7Z)}, and filling points in the cusps (punctures) to get a closed surface (although the punctured surface is sometimes also referred to as Klein’s quartic). It has a cell decomposition by 24 heptagons, centered at each cusp coming...

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates...

For a fixed prime p ≡ 1 (mod 4), we define the corresponding quartic residue graph and determine the number of triangles contained in such a graph. Our computation requires us to compute the number of pairs of consecutive quartic residues modulo p via the evaluation of certain quartic Jacobi sums.

We prove that a nodal quartic threefold X containing no planes is Q-factorial provided that it has not more than 12 singular points, with the exception of a quartic with exactly 12 sin-gularities containing a quadric surface. We give some geometrical constructions related to the latter quartic.

Copyright q 2010 Dongseung Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function f...

We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimiz...

Wewill define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam– Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, co...