Interpolation of parameterized curves differs from classical interpolation in that we interpolate each spatial variable separately. A difficult challenge arises from the option of reparameterization: ...a presumably good interpolation (e.g., at the Gauss points) of a given parameterization does not necessarily give the best approximation of the curve, as there may exist a reparameterization better suited for polynomial interpolation. The reparameterization can be done implicitly by choosing different sets of interpolation points along the exact curve. We present common interpolation methods, and propose a new method, based on choosing the interpolation points in such a way that the interpolant is tangential to the exact (reparameterized) curve at these points. The new method is compared to the traditional ones in a series of numerical examples, and results show that classical interpolation is sometimes far from optimal in the sense of the Kolmogorov n-width, i.e., the best approximation using n degrees-of-freedom.
Este texto analisa dois movimentos de internacionalização de propostas para o ensino de matemática. O primeiro deles, no início do século XX, com a criação da Comissão Internacional do Ensino de ...Matemática, em 1908; o segundo, ocorrido em meados desse mesmo século, que ficou conhecido como Movimento da Matemática Moderna. A análise tem por objetivo mostrar que o tema da internacionalização remete à necessidade de uma abordagem histórico-comparativa como forma de produção de conhecimento da educação matemática.This text analyzes two movements toward the internationalization of proposals for the teaching of mathematics. The first of them, in the early nineteenth century, was the setting-up, in 1908, of the International Committee on Mathematical Instruction; the second, in the mid-twentieth century, became known as the Modern Mathematics Movement. The analysis aims to show that the issue of internationalization points to the need for a historic-comparative approach as a way of producing mathematical education.
► In Korea and Hong Kong, gender gap in maths was associated with single-sex schooling. ► Benefits for attending girls’ schools were found only in Korea. ► Gendered curriculum counteracted the ...advantage of girls’ schools in Hong Kong. ► Gendered social structure is associated with gender gap in maths achievement.
In many industrialised societies, women remain underrepresented in the sciences, which can be predicted by the gender gap in math achievement at school. Using PISA 2006 data, we explore the role of family background and single-sex schooling in girls’ disadvantage in maths in South Korea and Hong Kong. This disadvantage is found to be associated with single-sex schooling, but not with family background. Attending a girls’ school confers a benefit only in South Korea, whereas the gendered curriculum counteracts the selectivity advantage of girls’ schools in Hong Kong. We find that a gendered social structure prevalent in both societies.
This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various ...modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.
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