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让学生经历真实的数学研究过程——“基本不等式”的教学实录与反思
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作者 龚亮亮 卓斌 《中学数学月刊》 2021年第3期48-51,共4页
“基本不等式”这节课让学生经历提出数学问题、作出数学猜想、得出数学命题、析出研究经验的研究过程,从而培养学生综合应用数学知识和思想方法进行数学探究的能力.让学生经历数学研究过程有四点建议:设计恰当的问题串,让研究有载体;... “基本不等式”这节课让学生经历提出数学问题、作出数学猜想、得出数学命题、析出研究经验的研究过程,从而培养学生综合应用数学知识和思想方法进行数学探究的能力.让学生经历数学研究过程有四点建议:设计恰当的问题串,让研究有载体;基于学情的修正完善,让研究有根基;逐步实现命题精致化,让研究有生长;运用现代教育技术,让研究有抓手. 展开更多
关键词 数学研究过程 基本不等式 实录与反思
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Experimental Research and Mathematical Modelling for Coal Reburning in Furnace
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作者 XIANG Jun SU Sheng +3 位作者 SUN Lu-shi SUN Xue-xi ZHANG Zhong-xiao ZHU Ji-mu 《Journal of China University of Mining and Technology》 EI 2006年第3期301-307,共7页
Reburning technology is one of the most cost-effective NOx reduction strategies for coal combustion systems. In this paper, a nitric oxide submodel incorporated into a comprehensive coal combustion model was developed... Reburning technology is one of the most cost-effective NOx reduction strategies for coal combustion systems. In this paper, a nitric oxide submodel incorporated into a comprehensive coal combustion model was developed for predicting NOx reduction in a 93 kW laboratory-scale coal combustion furnace by reburning. This NO submodel, including reburning mechanism, requires the solution of only two transport equations to model the behavior of NO reduction in the reburning process. A number of experiments have been performed in the same furnace, and the experimental data obtained from the optimized reburn configuration was used to validate the model. Measurements and predictions both show above 50% reduction of NO emissions for the optimized reburning process. Profile comparisons show that the predicted temperature and oxygen concentration match well with the measurements, and the general trend of predicted NO concentration is very similar to that measured. The results of this study show that the present nitric oxide submodel depicts quite well the observed behaviour of NO annihilation in the reburning process. It is expected that this usable and computationally economic model represents a useful tool to simulate the gaseous fuel reburning process for the researchers concerned with practical combustors. 展开更多
关键词 coal combustion nitric oxide REBURNING experimental research mathematical modeling
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Role of antibiotic therapy in bacterial disease:A mathematical study
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作者 Priti Kumar Roy Yanhui Zhang +2 位作者 Priyanka Ghosh Joydeep Pals Fahad Al Basir 《International Journal of Biomathematics》 SCIE 2018年第3期131-154,共24页
Pathogenic bacteria in human system mature through the bin-synthesis of protective layer known as cell wall. This bacterial cell wall growth occurs in the presence of enzyme released by it. After maturation by the cel... Pathogenic bacteria in human system mature through the bin-synthesis of protective layer known as cell wall. This bacterial cell wall growth occurs in the presence of enzyme released by it. After maturation by the cell wall formation, pathogenic bacteria become harmful for human body as they are responsible for different diseases. Antibiotics or drugs are employed for curing bacterial diseases through the inhibition of this maturation process and it occurs by the binding progression of antibiotics with the released enzyme. But nowadays, drugs or antibiotics like β-lactum family (Amoxcillin) which are generally used for inhibition of bin-synthesis of cell wall become ineffective due to evolution of antibiotic resistance by the bacteria. Antibiotic resistance occurs when an antibiotic has lost its ability to effectively control or kill bacterial growth. As a result, the bacteria becomes "resistant" and continue to multiply for the generation of robust pathogenic bacteria in spite of drug administration. This is due to the release of another type of enzyme by the resistant bacteria which binds with the active antibiotic or drug making it ineffective. Hence, another type of drug (Clauvanic acid) is combined to resist the activity of drug hydrolyzing enzyme so that the initial drug can act effectively. Hence a combination of drug therapy is applied to cure the bacterial diseases successfully. We developed a mathematical model based on the bacterial enzyme and bacterial cell wall proliferation mechanism and showed how we can reduce the bacterial infection in the resistant cases with application of combination drugs (Amoxcillin and Clauvanic acid) to restore normal health. Based on the enzymatic activity and individual drug dynamics we studied the overall system under the single drug and combinational drug administra- tion through our formulated model analysis. We also demonstrated the different dosing time interval and dosing concentration to evaluate the optimized drug administration for arresting the cell wall formation completely. Sensitivity of the different kinetic rate constant also has been performed with subject to drug hydrolyzing enzyme. Our analytical and numerical studies also confirm the efficiency of the combinational drug treatment compared to single drug treatment being more effective in drug resistant cases providing recovery from bacterial disease. 展开更多
关键词 BACTERIA cell wall resistance enzyme inhibition modeling impulsive drug dosing.
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