Narrow Results

The obvious current reversion to micro-scale investigations in basic chemical engineering, combined with the need, of a quite different nature, in the rapid growth of high added-value and small-lot functional materials, have been pointing to an area not yet sufficiently covered by the unit operations, transport phenomena and chemical reaction engineering. Although it is difficult to define accurately this area, a cursory scan of the activities already in progress has revealed a few common attributes: multi-phased (structured), multi-scaled, multi-disciplined, nonlinear, needs for resolution to reductionism-solvable subsystems, and pervasive in the process industry. From these activities, the present paper drafts a tentative scheme for studying the related problems: first to dissect a problem into various scales — spatial, temporal or otherwise as best suits the case in hand — in order to identify pertinent parameters which are then organized into model formulations. Together with inter-scale model formulations, a zoom-in/zoom-out process is carried out between the scales, by trial-and-error and through reasoning, to arrive at a global formulation of a quantitative solution, in order to derive, eventually, the general from the particular.

Mathematics education in eastern Asian countries emphasizes the importance of foundations, and in Mainland China the principle of "basic knowledge and basic skills" was explicitly put forward for the teaching of mathematics. This chapter analyzes in a detailed way the benefits and inadequacies of this principle and the practice arising from it from four aspects, namely, its historical roots and social environment, the goals of classroom teaching, teaching characteristics and underlying psychological principles, and education reforms and development in China. The different characteristics of Eastern and Western mathematics education can be complementary to each other, helping strike a balance between foundation and development concerning classroom teaching.