A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

Temporal freedom in mathematical thought: A philosophical–empirical enquiry

This paper seeks to introduce and elaborate on the notion of ‘temporal freedom’ in the context of mathematical thinking.The intention is to merge a philosophical and empirical discussion on this topic, and findings will be presented from a qualitative study in which 29 high-school students were invited to explore the symmetry group of a square during clinical interviews. The data indicate how the interviewees – who were given the opportunity to freely explore an unseen mathematical system – repeatedly brought past and future together in a tangible present during their investigations. In doing so they were exceptionally successful in engaging with advanced abstract algebra, far beyond what might have been expected at the outset.By using empirical data to exemplify an otherwise highly philosophical discussion, I hope to draw explicit attention to the temporal aspect of the human mind in mathematical action which instructional methods frequently fail to recognise, value and utilise.     

The simultaneous elimination of arsenic and mercury ions via hollow fiber supported liquid membrane and their reaction mechanisms: Experimental and modeling based on DFT and generating function

This study investigates the simultaneous removal of low concentrations of arsenic and mercury ions from synthetic produced water via hollow fiber supported liquid membrane (HFSLM). Results show that HFSLM can remove both arsenic and mercury ions from synthetic produced water to less than 0.02 and 0.001 mg·L^-1, respectively. These final concentrations comply with the wastewater standard of Thailand. Percentages of extraction for arsenic and mercury ions proved to be about 100 %. Those of recovery for arsenic and mercury ions reached 70 % and 75 %, respectively. A quantum model based on density functional theory (DFT) is introduced to analyze the forming and breaking of supramolecular complex species in the processes of extraction and recovery, respectively. Furthermore, the concept of Generating Function is applied to construct a mathematical model for forecasting the potential of removing metal ions via HFSLM. The mathematical model conforms to the experimental data, having an average relative deviation of 5 %. The results of this study provide a better understanding of the transport mechanisms of arsenic and mercury ions.     

二种求算晶体平面间距d_(hkl)的数学方法

用数学方法推导出结构化学晶体学中晶面间距的一般通式,并在此基础上推导出其他晶系的晶面间距(d(hkl))的计算表达式。     

夹心法免疫层析试条的数学模型与仿真研究

基于夹心法免疫层析试条检测原理,结合对流扩散方程和流体动力学方程,建立了夹心法免疫层析试条动态反应过程的数学模型,并通过COMSOL软件对试条动态反应过程进行仿真.分别探究了目标待测物A浓度在0 ～ 20 mol/L,标记物P浓度在1×10-2～1×103 mol/L以及硝酸纤维素膜的孔隙率在0～1范围内变化时,检测线上夹心复合物浓度关于位置和时间的浓度变化情况,并分析了各物质初始浓度以及试条结构对于检测结果和检测时间的影响.结果表明,在一定浓度范围内,目标待测物A以及标记物P浓度的增加将提高试条的定量检测性能,而孔隙率通过影响混合液流速和混合液中各物质反应接触情况来影响检测结果.     

废水生物脱氮工艺中N2O排放数学模型研究进展

N_2O是一种重要的温室气体,而污水生物脱氮处理过程是N_2O的潜在产生源之一。随着污水处理量和处理程度的不断提高,N_2O的排放量也将不断增大。建立N_2O排放数学模型对污水生物脱氮系统中N_2O生成机制的深入研究和污水处理行业N_2O削减工艺技术的开发具有重大的理论及实践意义。本文归纳了生物脱氮工艺的原理,系统阐述了生物脱氮工艺中N_2O的生成机理和排放数学模型的类型、建立方法及应用情况。在此基础上,对生物脱氮工艺中N_2O排放数学模型的研究现状和研究方向进行了总结和展望,以期为N_2O排放数学模型的完善、N_2O排放量的削减、污水生物脱氮工艺的优化及污水处理行业的可持续发展提供理论基础和科学依据。     

The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.     

Modeling the depletion of dissolved oxygen in a water body located near a city

Water bodies located nearby cities are much prone to pollution, especially in the developing countries, where effluents treatment facilities are generally lacking. The main reason for this phenomenon is the increasing population in the cities, and the large number of industries located near them. This leads to generation of huge amounts of domestic and industrial sewage that is discharged into the water bodies, increasing their organic pollutant load and resulting in the depletion of dissolved oxygen. In this paper, we propose a mathematical model for this situation, focusing especially on the resulting quality of the water, determined by the level of dissolved oxygen. The model also accounts for resources needed for the population survival and for the industrial operations. In addition, we describe also the decomposition of organic pollutants by bacteria in the aquatic medium. Feasibility conditions and stability criteria of the system's equilibria are determined analytically. The results show that human population and industries are relevant influential factors responsible for the increase in organic pollutants and the decrease in dissolved oxygen in the water body, in the sense that they may exert a destabilizing effect on the system. The numerical simulations confirm the analytical results. Copyright © 2016 John Wiley & Sons, Ltd.     

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.