An interpolatory subdivision algorithm for surfaces over arbitrary triangulations

In this paper, an interpolatory subdivision algorithm for surfaces over ar-bitrary triangulations is introduced and its convergence properties over nonuni-form triangulations studied. The so called Butterfly Scheme (interpolatory) is a special case of this algorithm. In our analysis of the algorithm over uniform triangulations, a matrix approach is employed and the idea, of "Cross Differ-ence of Directional Divided Difference" analysis is presented. This method is a generalization of the technique used by Dyn, Gregory and Levin etc. to analyse univariate subdivision algorithms. While for nonuniform data, an extraordi-nary point analysis is introduced and the local subdivision matrix analysis is presented. It is proved that the algorithm produces smooth surfaces over ar-bitrary triangular networks provided the shape parameters are kept within an appropriate range

Effective website for educational institution

This paper examines the current status of a New Zealand educational institution’s website and makes a comparison among 44 samples. Two main sections have been contained in this research, secondary resource collection and observation. The aim of this research is to raise the awareness of this organisation and to attract potential students from the Chinese market by improve the organisation’s official website. This is desk research which has made use of qualitative methods. The results of the secondary resource collection mainly illustrate the general concepts of website design, the key factors of the education website, and Chinese web page preferences. The results from observation of 44 samples have been divided into two aspects, functionality and content. Most educational institution website pages are functional, while their online communication channels are basically limited to social media links; from the content point of view, school websites with Chinese versions generally have poor translations, and existing educational institution website samples can provide the information that the viewer needs through different presentation methods. These differences are explained in the discussion section. In conclusion, it suggested that in the current stage, educational institution websites could gain development by diversifying their communication channels and information presentation

Dobrushin ergodicity coefficient for Markov operators on cones, and beyond

The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, which include the unital completely positive maps (Kraus operators) arising in quantum information theory. In particular, we show that the contraction rate of such operators, with respect to the Hopf oscillation seminorm, is given by an analogue of Dobrushin's ergodicity coefficient. We derive from this result a characterization of the contraction rate of a non-linear flow, with respect to Hopf's oscillation seminorm and to Hilbert's projective metric

From a Chinese kindergarten: A personal journey

How do Chinese kindergarten teachers understand their teaching practices? How are these influenced by cultural, political and economic forces? What do their classrooms look like from the perspective of a Chinese New Zealander