• Journal for History of Mathematics
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• v.32 no.1
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• pp.1-15
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• 2019

We divide the timeline of the history of Finsler geometry, which dates back to Riemann's inaugural lecture in 1854, into three periods (hibernation, hiatus, rebirth) and we study formation of Romanian Finsler school around Iasi, Romania during the hiatus period. We look for the history centered around Radu Miron who is a third generation geometer of Iasi University and the mathematical heritage there through five generations. We also investigate mathematical impact of T. Levi-Civita, D. Hilbert, ${\acute{E}}$ Cartan who are considered as top mathematicians at their time.

• Journal of Korea Water Resources Association
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• v.44 no.2
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• pp.109-123
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• 2011

In this study, 2D finite volume model, which can apply to the mixed meshes that is effective to treat the complicated topography such as a natural river, is developed. To do so, an algorithm for finding the neighbouring cell of a computational cell is introduced, and fluxes are computed using the HLLC approximate Riemann solver at each interface between a computational cell and it's neighbouring cells. Moreover, in order to numerically treat the bed slope which has important effect on the balance between flux gradients and sourte terms, different formula to compute the bed slope for rectangular and triangular mesh are applied. The developed model is applied to analyze dam-break in an experimental channel with $90^{\circ}$ bend and Malpasset dam-break in France. The two cases consist of mixed meshes and the suggested method is validated for the experimental channel and natural channel by comparison with the experimental data, field data and computed results.

• Journal of Digital Contents Society
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• v.9 no.1
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• pp.109-116
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• 2008

The variation of real phenomena and shape of nature in our world is so complicated that some mathematical tools using the traditional geometric methods based on the Euclidean geometry and analytical differential method may be irrelevant or insufficient in some problems. Recently, to deal with these circumstances, one can use the fractal geometric method. As another measures, in this paper we introduce the non-integral order derivative function for the analytical method and construct to facilitate their calculation.

• Journal of Wetlands Research
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• v.10 no.2
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• pp.67-79
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• 2008

The one-dimensional (1D) finite-difference method (FDM) with Abbott-Ionescu scheme and the two-dimensional (2D) finite-volume method (FVM) with an approximate Riemann solver (Osher scheme) for unsteady flow calculation in river are described. The two models have been applied to several problems including flow in a straight channel, flow in a slightly meandering channel and a flow in a meandering channel. The uniform rectangular channel was employed for the purpose of comparing results. A comparison is made between the results of computation on 1D and 2D flows including straight channel, slightly meandering channel and meandering channel application. The implementation of the finite-volume method allows complex boundary geometry represented. Agreement between FVM and FDM results regarding the discharge and stage is considered very satisfactory in straight channel application. It was concluded that a 1D analysis is sufficient if the channel is prismatic and remains straight. For curved (meandering) channels, a 2D or 3D model must be used in order to model the flow accurately.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1752-1756
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• 2008

A simple, accurate and efficient mesh generation technique, the cut-cell method, is able to represent an arbitrarily complex geometry. Both structured and unstructured grid meshes are used in this method. First, the numerical domain is constructed with regular Cartesian grids as a background grid and then the solid boundaries or bodies are cut out of the background Cartesian grids. As a result, some boundary cells can be contained two numerical conditions such as the flow and solid conditions, where the special treatment is needed to simulate such physical characteristics. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. Also, the TVD-WAF method is applied on the Cartesian cut-cell grids to stabilize numerical results. Present method is validated for the rectangular dam break problems. Initially, a conventional grid is constructed with the Cartesian regular mesh only and then applied to the dam-break flow simulation. As a comparative simulation, a cut-cell grids are applied to represent the flow domain rotated with arbitrary angles. Numerical results from this study are compared with the results from the case of the Cartesian regular mesh only. A good agreement is achieved with other numerical results presented in the literature.

• The Journal of the Korea Contents Association
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• v.22 no.10
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• pp.132-142
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• 2022

The purpose of this study is to interpret the MCU's universal worldview from the perspective of geometry and to storytell narrative elements with mathematical imagination. For storytelling, data from the Phase 3 series aired from 2016 to 2019 was used. The Phase 3 series stimulates the imagination of the public with the sense of reality shown in the narrative and images based on geometrical theory and various predictions about future technology. Imagination is the driving force for diverse and original thinking about the unexperienced, and the ability to find order in chaos and create new perceptions of matter. The power of imagination is very necessary not only in artistic activities, but also in the scientific field where logic and rationality are important. Bachelard's imagination aims for art, the primitive realm of human beings, and contains sincerity and passion for the wonders of nature and all things. By exploring the MCU's worldview and superhero narrative through geometrical logic and imagination-driven imagery, you can understand the cosmic messages and laws in the film. From a convergence point of view of art and science, various and original techniques based on mathematics and scientific imagination used in MCU video production will help to improve the quality of video analysis.