Longitudinal studies are those in which the same variable is repeatedly measured at different times. These studies are more likely than others to suffer from missing values. Since the presence of missing values may have an important impact on statistical analyses, it is important that they should be dealt with properly. In this paper, we present “Copy Mean”, a new method to impute intermittent ...

We investigate weighted L p mean convergence of Grünwald interpolation operators based on the zeros of orthogonal polynomials with respect to a general weight and generalized Jacobi weights. We give necessary and sufficient conditions for such convergence for all continuous functions. 1. Introduction. In this paper, we study weighted L p (0 < p < ∞) mean con

Interpolation is a fundamental process in solar resource assessment that glues consecutive components of the modeling chain. Most interpolation techniques assume interpolating function must go through points. However, this assumption does not fit with averaged datasets or variables be conserved across interpolation. Here I present mean-preserving splines method for one-dimensional data conserve...

Bernstein polynomials are a classical tool in Computer Aided Design to create smooth maps with a high degree of local control. They are used for the construction of Bézier surfaces, free-form deformations, and many other applications. However, classical Bernstein polynomials are only defined for simplices and parallelepipeds. These can in general not directly capture the shape of arbitrary obje...

In this article, we will discuss various issues concerning when a complete Riemannian manifold possesses a global mean value inequality for positive subsolutions of either the Laplace equation or the heat equation. This study is motivated by the recent result of the first author [L1]. In that paper, he proved estimates on the dimensions of spaces of harmonic functions of at most polynomial grow...

We derive a generalization of barycentric coordinates which allows a vertex in a planar triangulation to be expressed as a convex combination of its neighbouring vertices. The coordinates are motivated by the Mean Value Theorem for harmonic functions and can be used to simplify and improve methods for parameterization and morphing.  2003 Elsevier Science B.V. All rights reserved.

Bézier surfaces are an important design tool in Computer Aided Design. They are parameterized surfaces where the parameterization can be represented as a homogeneous polynomial in barycentric coordinates. Usually, Wachspress coordinates are used to obtain tensor product Bézier surfaces over rectangular domains. Recently, Floater introduced mean value coordinates as an alternative to Wachspress ...