In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.

Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through recurrence relation. This paper gives explicit solution of by mapping it bijectively to two-fold nested combinatorial structure each counted Catalan numbers. These `nested tables' have description as diagrams non-crossing chords and threads.

This paper presents results on generalized public key cryptography with exponentials modulo primes and composite numbers where the mapping is not one-to-one and the uniqueness is achieved by additional side information. Such transformations may be used for oblivious transfer and generate events of specific probabilities. Introduction This paper presents generalized public key transformations th...

In this paper we present a method of circular arc approximation by quartic Bézier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvaturecontinuous quartic spline under the su...

The simplest quartic field was introduced by M. Gras and studied by A. J. Lazarus. In this paper, we will evaluate the values of the Dedekind zeta functions at s = −1 of the simplest quartic fields. We first introduce Siegel’s formula for the values of the Dedekind zeta function of a totally real number field at negative odd integers, and will apply Siegel’s formula to the simplest quartic fiel...

The Q-factoriality of a nodal quartic 3-fold implies its non-rationality. We prove that a nodal quartic 3-fold with at most 8 nodes is Q-factorial, and we show that a nodal quartic 3-fold with 9 nodes is not Q-factorial if and only if it contains a plane. However, there are non-rational non-Q-factorial nodal quartic 3-folds in P. In particular, we prove the non-rationality of a general non-Q-fa...

This paper proposes explicit formulae for the addition step and doubling step in Miller’s algorithm to compute Tate pairing on Jacobi quartic curves. We present a geometric interpretation of the group law on Jacobi quartic curves, which leads to formulae for Miller’s algorithm. The doubling step formula is competitive with that for Weierstrass curves and Edwards curves. Moreover, by carefully c...

A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous q...

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...