This article is devoted to the rotation minimizing frames that are associated with spatial curves. Firstly we summarize some results concerning the differential geometry of the sweeping surfaces which are generated by these frames (the so–called profile or moulding surfaces). In the second part of the article we describe a rational approximation scheme. This scheme is based on the use of spatia...

Given four polynomial or rational Bézier curves defining a curvilinear rectangle, we consider the problem of constructing polynomial or rational tensor–product Bézier patches bounded by these curves, such that they are geodesics of the constructed surface. The existence conditions and interpolation scheme, developed in a general context in earlier studies, are adapted herein to ensure that the ...

The notion of rational exchange introduced by Syverson in 1998 is a particularly interesting alternative when an efficient scheme for fair exchange is required but the existence of a trusted third party simply cannot be assumed. A rational exchange protocol cannot provide true fairness, but it ensures that rational –i.e. self-interested– parties would have no reason to deviate from the protocol...

Two of the authors earlier suggested a method of calculating special grid steps for three point finite-difference schemes which yielded exponential superconvergence of the Neumann-to-Dirichlet map. We apply this approach to solve the two-dimensional timedomain wave problem and the 2.5-D elasticity system in cylindrical coordinates. Our numerical experiments exhibit exponential convergence at pr...

This paper gives an elementary deterministic algorithm for completely factoring any polynomial over GF(q), q = p , criteria for the identification of three types of primitive polynomials, an exponential representation for GF(<j) which permits direct rational calculations in GF(q) as opposed to modular arithmetic over GF[p, xl, and a matrix representation for GF(p) which admits computer computat...