Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

高等代数与解析几何一体化教学思考

本探讨了高等代数与解析几何进行一体化教学的必要性，研究了高等代数与解析几何进行一体化教学以后教学内容的协调性与教学手段的合理性，强调了数学实验在高等代数与解析几何一体化教学中的重要性。     

Synthesis and electrochemical properties of Zn3V3O8 as novel anode material

Zn₃V₃O₈ two-dimensional micro sheets are successfully synthesized by combination of solvothermal method and heat treatment. The Zn₃V₃O₈ has better electrochemical performances after calcinations.     

基于创新能力培养的化学专业本科实验教学新体系的构建与实践

课程体系是人才培养的载体。为了更好地培养拔尖创新人才,南京大学化学国家级实验教学示范中心依据化学学科的特点和发展趋势,以科学内容的内在联系和研究规律为主线构建了“化学实验基础?化学合成与表征+化学原理与测量?化学功能分子实验+化学生物学综合实验+基于项目的研究实验”实验课程新体系,按照一流课程建设要求(高阶性、创新性和挑战度)对实验教学内容进行了优化,并建立起与之相适应的实验教学平台。新课程体系综合考虑了化学一级学科的整体性和关联学科的交叉性,在南京大学化学化工学院“拔尖计划”和“强基计划”学生中实施,教学效果显著。     

线上线下混合式物理化学实验研究型教学改革

针对目前实验教学在创新型人才培养中存在的问题,介绍了北京航空航天大学化学学院物理化学实验教学的改革与实践情况。结合线上教学灵活、不受时空限制,以及线下教学培养学生动手操作能力和严谨求实的科学素养的特点,从递进式教学内容设计、个性化实验操作指导和训练、科研式论文报告总结、针对性展示和专题分析等方面进行了线上线下混合式研究型教学改革。将理论方法、虚拟操作、实际训练和总结提升等相结合,充分发挥教师指导和学生主体的优势,多维度培养和提升学生的科学素养、创新思维和综合创新能力,为提升实验教学质量和促进创新型人才培养提供了有益的借鉴。     

An overview of innovation in industrial drying: current status and R&D needs

Over the past three decades there has been nearly exponential growth in drying R&D on a global scale. Although thermal drying had always been the workhorse of almost all major industrial sectors, the need for and opportunities in basic as well as industrial research became clear only after the energy crisis of the early 1970s. Although the price of oil did drop subsequently the awareness of the significance of improving the drying operation to save energy, improve product quality as well as reduce environmental effect remained and indeed has flourished over recent years. New drying technologies, better operational strategies and control of industrial dryers, as well as improved and more reliable scale-up methodologies have contributed to better cost-effectiveness and better quality dried products. Yet there is no universally or even widely applicable drying theory on the horizon. Most mathematical models of drying remain product-equipment specific for a variety of reasons. In this paper, we examine the role of innovation in drying in various industrial sectors, e.g. paper, wood, foods, agriculture, waste management, etc. Progress made over the past three decades and the challenges ahead are outlined. Some areas in need of further research are identified. Examples of intensification of innovation in dryer designs via mathematical modeling are discussed. Finally, the need for closer interaction between academia and industry is stressed as the key to successful drying R&D in the coming decade.     

Scaling of Prosocial Behavior in Cities

Previous research has examined how various behaviors scale in cities in relation to their population sizes. Behavior related to innovation and productivity has been found to increase per capita as the size of the city increases, a phenomenon known as superlinear scaling. Criminal behavior has also been found to scale superlinearly. Here we examine a variety of prosocial behaviors (e.g., voting and organ donation), which also would be presumed to be categorized into a single class of scaling with population. We find that, unlike productivity and innovation, prosocial behaviors do not scale in a unified manner. We argue how this might be due to the nature of interactions that are distinct for different prosocial behaviors.     

贯通中学和大学数学教与学 集成造就学生数学素养和创新实践能力

针对如何破解我国从应试教育向素质教育转变步履维艰的难题,本文详细介绍了如何贯通中学和大学数学教与学,集成培养学生数学素养和创新实践能力的具体做法和成效.