To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...

O. Ismail, Senior Member, IEEE Abstract— This paper presents an efficient method for degree elevation of interval B-spline curves. The four fixed Kharitonov's polynomials (four fixed B-spline curves) associated with the original interval B-spline curve are obtained. The method is based on the matrix identity. The B-spline basis functions are represented as linear combinations of the B-splines o...

Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...

We bound the dimension of xed degree real algebraic interpolatory spline spaces. For a given planar triangulation T real algebraic splines interpolate speciied zi values at the vertices vi = (xi; yi) of T. For a three dimensional simplicial complex ST , real algebraic splines interpolate the boundary vertices vj = (xj; yj; zj) of ST. The main results of this paper are lower bounds on the dimens...

Abstract In this paper, we present a new form of density based topology optimization where the design space is restricted to the B-spline space. An arbitrarily shaped design domain is embedded into a rectangular domain in which tensor-product B-splines are used to represent the density field. We show that, with proper choice of B-spline degrees and knot spans, the B-spline design space is free ...

In this paper a rational cubic algebraic spline with two shape parameters is developed to create a high-order smoothness interpolation using function values and derivative values which are being interpolated. This is a kind of rational cubic interpolation with quadratic denominator. This rational spline interpolant is monotonic interpolant to given monotonic data. The more important achievement...

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “...