In this paper, weighted G-multi-degree reduction of Bézier curves is considered. The degree reduction of a given Bézier curve of degree n is used to write it as a Bézier curve of degree m,m < n. Exact degree reduction is not possible, and, therefore, approximation methods are used. The weight function w(t) = 2t(1 − t), t ∈ [0, 1] is used with the L2-norm in multidegree reduction with G-continui...

Let pm/qm denote the m-th convergent (m ≥ 0) from the continued fraction expansion of some real number α. We continue our work on error sum functions defined by E(α) := ∑m≥0 |qmα − pm| and E∗(α) := ∑ m≥0(qmα − pm) by proving a new density result for the values of E and E∗. Moreover, we study the function E with respect to continuity and compute the integral ∫ 1 0 E(α) dα. We also consider gener...

It is shown that, if a, b are recursively enumerable degrees such that 0 < a < 0 0 and a b = 0 0 , then there exists a recursively enumerable degree c such that c < a and c b = 0 0 .

In most knowledge-based systems, the experts' uncertainty is described by a real number from the interval 0; 1] (this number is called subjective probability, degree of certainty, etc.). However, experts usually use a small nite set of words to describe their degree of unecratinty; thus, to adequately describe the expert's optinion, it is desirable to use a nite (granular) logic. If all we know...

We assemble triangular patches of total degree at most eight to form a curvature continuous surface. The construction illustrates how separation of local shape from representation and formal continuity yields an effective construction paradigm in partly underconstrained scenarios. The approach localizes the technical challenges and applies the spline approach, i.e. keeping the degree fixed but ...

A degree of parallelism is an equivalence class of Scott-continuous functions which are relatively deenable each other with respect to the language PCF (a paradigmatic sequential language). We introduce an innnite (\bi-dimensional") hierarchy of degrees. This hierarchy is inspired by a representation of rst order continuous functions by means of a class of hypergraphs. We assume some familiarit...

Background In recent decades in Italy, there has been a progressive aging of the population with a consequent increase in chronic degenerative diseases which has caused a substantial increase in demand for long-lasting social-health performance for patients with different degrees of disability and low self-sufficiency levels [1]. Comorbidity is therefore becoming the most common clinical situat...

Lipschitz continuity is used as a tool for analyzing the relationship between incomputability and randomness. Having presented a simpler proof of one of the major results in this area—the theorem of Yu and Ding that there exists no cl-complete c.e. real—we go on to consider the global theory. The existential theory of the cl degrees is decidable but this does not follow immediately by the stand...

During the development of subdivision surface methods one of the important questions has been the degree of continuity of the limit surface. In particular whether continuity of curvature can be achieved at the extraordinary points. However, there are several different curvature behaviours, not just two, and this note demonstrates them by examples. q 2003 Elsevier Science Ltd. All rights reserved.

BACKGROUND AND OBJECTIVES Although continuity of care has been found to be associated with improved health outcomes in children, little is known about what factors predict having consistent contact with a pediatric provider. This study explored what patient, family, provider, and system factors are associated with high continuity of both total and well-child care. METHODS This cross-sectional...