A "blend" is a two-point Hermite interpolational polynomial, typically of quite high degree. This note shows that implementing them in double Horner evaluation scheme has good backward error, and also the Lebesgue constant for balanced blend or nearly on interval [0,1] bounded by 2, independently grade degree approximation. On [-1,1], which more natural comparison, it course unbounded, but grow...

We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We introduce a new Datalog fragment with stratified negation, intensional-clique-guarded Datalog (ICG-Datalog), with linear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular co...

This paper is concerned with homeomorphisms of Euclidean spaces onto themselves, with bounded orbits. The following results are obtained. (1) A homeomorphism of E onto itself has both bounded orbits and an equicontinuous family of iterates iff it is a conjugate of either a rotation or a reflection; (2) An example of Bing is modified to produce a fixed point free, orientation preserving homeomor...

We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to two-dimensional disc. Our analysis is based on the mean field bounded vortices in microcanonical ensemble. The are specified by inverse temperature $\beta$ and rotation frequency $\omega$, which conjugate variables energy $E$ angular momentum $L$, respectively. formation (azimuthal angle independent) i...

This article describes a novel method for image-based, minimally invasive registration of the femur, for application to computer-assisted unicompartmental knee arthroplasty. The method is adapted from the well-known iterative closest point algorithm. By utilising an estimate of the hip centre on both the preoperative model and intraoperative patient anatomy, the proposed 'bounded' iterative clo...

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...