BACKGROUND Continuity of care has long been considered a benefit to patients of family physicians, but quantifying these benefits has been problematic. Previous studies focused on patient preferences and relationship issues, whereas evidence regarding clinical endpoints has been lacking. This study reports differences in obstetric and neonatal outcomes related to continuity in prenatal care. ...

Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can also be applied to non regular meshes. For example, midpoint subdivision of degree 2 is a specific Doo-Sabin algorithm and midpoint subdivision of degree 3 is a specific Catmull-Clark algorithm. In 2001, Zorin and Schröder were able to prove C1-continuity for midpoint subdivision surfaces a...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

1. H. M. Elliott, On approximation to functions satisfying a generalized continuity condition, Trans. Amer. Math. Soc. vol. 71 (1951) pp. 1-23. 2. W. E. Sewell, Continuity and degree of approximation by rational functions, Revista de Ciencias vol. 41 (1939) pp. 435-451. 3. J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloquium Publi...

We present a sufficient condition for weak continuity in the method of compensated compactness. The condition links weak continuity to the structure of the wave cone and the characteristic set for polynomials of degree greater than two. The condition applies to all the classical examples of weakly continuous functions and generalizes the Quadratic Theorem and the Wedge Product Theorem. In fact,...

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X → Y , which satisfies the inequality ||∆xf(y)− n!f(x)|| ≤ φ(x, y) for suitable control function φ, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of t 7→ f(tx) and t 7→ φ(tx, ty) imply the continuity of t 7→ M(tx).

Three methods are proposed to construct a piecewise Hermite interpolation surface (PHIS), which is a piecewise algebraic surface interpolating a set of given points with associated normal directions. The surface is obtained by blending together some low-degree surface patches. Both the first and the second methods are completely local and give a surface with G-continuity. In the third construct...

General features of finite-time-stable (FTS) homogeneous differential inclusions (DIs) are investigated in the context of slidingmode control (SMC). The continuity features of the settling-time functions of FTS homogeneous DIs are considered, and the system asymptotic accuracy is calculated in the presence of disturbances, noises and delays. Performance of output-feedback multi-input multi-outp...

In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order [Formula: see text] that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applica...