• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1033-1046
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• 1999

This paper is devoted to the point wise error estimate up to boundary for the standard finite element solution of Poisson equation with Dirichlet boundary condition. Our new approach used the discrete maximum principle for the discrete harmonic solution. once the mesh in our domain satisfies the $\beta$-condition defined by us, the discrete harmonic solution with dirichlet boundary condition has the discrete maximum principle and the pointwise error should be bounded by L-errors newly obtained.

• Research in Mathematical Education
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• v.16 no.3
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• pp.177-194
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• 2012

What strategies are used to help students understand quadratic functions in mathematics classroom? In specific, how does Chinese teacher highlight a connection between algebraic representation and graphic representation? From October to November 2009, an experienced teacher classroom was observed. It was found that when students started learning a new type of quadratic function in lessons, the teacher used two different teaching strategies for their learning: (1) Eliciting students to plot the graphs of quadratic functions with pointwise approaches, and then construct the function image in their minds with global approaches; and (2) Presenting a specific mathematical problem, or introducing conception to elicit students to conjecture, and then encouraging them to verify it with appoint approaches.

• Smart Structures and Systems
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• v.31 no.5
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• pp.501-516
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• 2023

Dynamic irregularity and acceleration of bridges subjected to high-speed trains provide crucial information for comprehensive evaluation of the health state of under-track structures. This paper proposes a novel approach for real-time estimation of vertical track dynamic irregularity and bridge acceleration using deep generative adversarial network (GAN) and vibration data from in-service train. The vehicle-body and bogie acceleration responses are correlated with the two target variables by modeling train-bridge interaction (TBI) through least squares generative adversarial network (LSGAN). To realize supervised learning required in the present task, the conventional LSGAN is modified by implementing new loss function and linear activation function. The proposed approach can offer pointwise and accurate estimates of track dynamic irregularity and bridge acceleration, allowing frequent inspection of high-speed railway (HSR) bridges in an economical way. Thanks to its applicability in scenarios of high noise level and critical resonance condition, the proposed approach has a promising prospect in engineering applications.

• Journal of the Korean Association of Geographic Information Studies
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• v.19 no.4
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• pp.118-129
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• 2016

Many epidemiological studies, relying on administrative air pollution monitoring data, have reported the association between particulate matter ($PM_{10}$) air pollution and human health. These monitoring data were collected at a limited number of fixed sites, whereas government-generated health data are aggregated at the area level. To link these two data types for assessing health effects, it is necessary to estimate area-level concentrations of $PM_{10}$. In this study, we estimated district (Gu)-level $PM_{10}$ concentrations using a previously developed pointwise exposure prediction model for $PM_{10}$ and three types of point locations in Seoul, Korea. These points included 16,230 centroids of the largest census output residential areas, 422 community service centers, and 610 centroids on the 1km grid. After creating three types of points, we predicted $PM_{10}$ annual average concentrations at all locations and calculated Gu averages of predicted $PM_{10}$ concentrations as representative Gu-estimates. Then, we compared estimates to each other and to measurements. Prediction-based Gu-level estimates showed higher correlations with measurement-based estimates as prediction locations became more population representative ($R^2=0.06-0.59$). Among the three estimates, grid-based estimates gave lowest correlations compared to the other two(0.35-0.47). This study provides an approach for estimating area-level air pollution concentrations and assesses air pollution health effects using national-scale administrative health data.