• School Mathematics
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• v.13 no.1
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• pp.65-88
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• 2011

Epistemological development process of the Fundamental Theorem of Calculus is considered in a history of mathematical notions and the genetic process of the Fundamental Theorem is arranged by the order of geometric, algebraic and formalization steps. Based on this, we studied students' episte- mological obstacles and error and analyzed the content of textbooks related the Fundamental Theorem of Calculus. Then, We developed the "Folding Back Model" of the fundamental theorem of calculus for students to lead meaningful faithfully. The Folding Back Model consists of "the Framework of thou- ght"(figure V-1) and "the Model of genetic understanding of concept"(figure V-2). The framework of thought in the Folding Back Model is included steps of pedagogical intervention which is used "the Monitoring working questions"(table V-3) by the mathematics teacher. The Folding Back Model is applied the Pirie-Kieren Theory(1991), history of mathematical notions and students' epistemological obstacles to practical use of instructional design. The Folding Back Model will contribute the professional development of mathematics teachers and improvement of thinking skills of students when they learn the Fundamental Theorem of Calculus.

• Journal of Environmental Science International
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• v.11 no.5
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• pp.419-436
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• 2002

The current paper reports on the enhancement of O$_3$, CO, NO$_2$, and aerosols during the Asian dust event that occurred over Korea on 1 May 1999. To confirm the origin and net flux of the O$_3$, CO, NO$_2$, and aerosols, the meteorological parameters of the weather conditions were investigated using Mesoscale Meteorological Model 5(MM5) and the TOMS total ozone and aerosol index, the back trajectory was identified using the Hybrid Single-Particle Lagrangian Integrated Trajectory Model(HYSPLIT), and the ozone and ozone precursor concentrations were determined using the Urban Ashed Model(UAM). In the presence of sufficiently large concentrations of NO$\sub$x/, the oxidation of CO led to O$_3$ formation with OH, HO$_2$, NO, and NO$_2$ acting as catalysts. The sudden enhancement of O$_3$, CO, NO$_2$ and aerosols was also found to be associated with a deepening cut-off low connected with a surface cyclone and surface anticyclone located to the south of Korea during the Asian dust event. The wave pattern of the upper trough/cut-off low and total ozone level remained stationary when they came into contact with a surface cyclone during the Asian dust event. A typical example of a stratosphere-troposphere exchange(STE) of ozone was demonstrated by tropopause folding due to the jet stream. As such, the secondary maxima of ozone above 80 ppbv that occurred at night in Busan, Korea on 1 May 2001 were considered to result from vertical mixing and advection from a free troposphere-boundary layer exchange in connection with an STE in the upper troposphere. Whereas the sudden enhancement of ozone above 100 ppbv during the day was explained by the catalytic reaction of ozone precursors and transport of ozone from a slow-moving anticyclone area that included a high level of ozone and its precursors coming from China to the south of Korea. The aerosols identified in the free troposphere over Busan, Korea on 1 May 1999 originated from the Taklamakan and Gobi deserts across the Yellow River. In particular, the 1000m profile indicated that the source of the air parcels was from an anticyclone located to the south of Korea. The net flux due to the first invasion of ozone between 0000 LST and 0600 LST on 1 May 1999 agreed with the observed ground-based background concentration of ozone. From 0600 LST to 1200 LST, the net flux of the second invasion of ozone was twice as much as the day before. In this case, a change in the horizontal wind direction may have been responsible for the ozone increase.

• Steel and Composite Structures
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• v.46 no.3
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• pp.319-334
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• 2023

Localizing damages is an essential task to monitor the health of the structures since they may not be able to operate anymore. Among the damage detection techniques, non-destructive methods are considerably more preferred than destructive methods since damage can be located without affecting the structural integrity. However, these methods have several drawbacks in terms of detecting abilities, time consumption, cost, and hardware or software requirements. Employing artificial intelligence techniques could overcome such issues and could provide a powerful damage detection model if the technique is utilized correctly. In this study, the crack localization in flat and folded plate structures has been conducted by employing a Backpropagated Artificial Neural Network (BPANN). For this purpose, cracks with 18 different dimensions in thin, flat, and folded structures having 15⁰, 30⁰, 45⁰, and 60⁰ folding angle have been modeled and subjected to free vibration analysis by employing the Classical Plate Theory with Finite Element Method. A Four-nodded quadrilateral element having six degrees of freedom has been considered to represent those structures mathematically. The first ten natural frequencies have been obtained regarding healthy and cracked structures. To localize the crack, the ratios of the frequencies of the cracked flat and folded structures to those of healthy ones have been taken into account. Those ratios have been given to BPANN as the input variables, while the crack locations have been considered as the output variables. A total of 500 crack locations have been regarded within the dataset obtained from the results of the free vibration analysis. To build the best intelligent model, a feature search has been conducted for BAPNN regarding activation function, the number of hidden layers, and the number of hidden neurons. Regarding the analysis results, it is concluded that the BPANN is able to localize the cracks with an average accuracy of 95.12%.