In this brief note, we prove the following two Artin-Schreier curves are supersin-gular.

We study Bezier surfaces defined over triangular domains. We have seen how spaces of bivariate polynomials can be constructed as tensor-products of the univariate ones. An alternative choice of polynomial space is, for each n ≥ 0, the space of polynomials of the form p(x, y) = 0≤i+j≤n a i,j x i y j , where we understand that i ≥ 0 and j ≥ 0 in the summation. As in the univariate case, we denote...

In this article, we introduce a novel shape from focus method to compute 3D shape of microscopic objects, based on modified-pixel intensities and Bezier surface approximations. A new and simple but effective focus measure is proposed. In our focus measure, the original intensities of a sequence of small neighborhood are modified by subtracting the maximum of the values of first and last frames....

This paper presents a fast lane changing algorithm for Intelligent Vehicle Highway Systems. The algorithm is based on the use of polinomial approximation of clothoids by using s-series. A new and accurate method that permits to obtain a polinomial with a low degree. Using this approximation we build an elementary path. We introduce a trigonometric approximation of elementary paths for the calcu...

Abstract—A novel scheme of combining non-uniform rational Bsplines (NURBS) model with higher-order moment method (HOMM) is presented. The mesh precision of conforming to practical object is a major factor for HOMM to yield accurate results. In the present paper, NURBS technique is employed to model complex objects accurately with large curved Bezier patches and no factitious geometric discontin...

We propose a new kind of models, which are called Nonlinear Deformable Superquadric (NDS) models, for representing and reconstructing 3D objects. Instead of linear tapering deformation, a piecewise cubic Bezier spline is used to deform superquadrics. By changing the control points of the spline, the shape of the model is deformed as if it was made of a flexible material. In this manner, we can ...

In this paper, we give a ‘direct’ construction of the endomorphism ring of supersingular elliptic curves over a prime field Fp from ‘ideal classes’ of Q( √−p). We use the result to prove that the result of Kaneko on ‘minimal’ CM liftings of such supersingular elliptic curves is a best possible result. We also prove that the result of Elkies on ‘minimal’ CM liftings of all supersingular elliptic...