• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.529-541
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• 2013

We study 132 avoiding permutations that also avoid $(2r+1)(2r+2){\cdots}12$ but contain $(2r-1)(2r){\cdots}12$ pattern. We find an identity between the number of these permutations and the Narayana number. We also present relations between 132 avoiding permutations and polygon dissections. Finally, a generalization of these permutations is obtained.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.335-343
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• 2022

We show that valleys, high peaks, and modular ascents are statistics of Fuss-Catalan paths having a distribution given by the Fuss-Narayana number. We prove the results using the Cycle Lemma and provide bijections among them. We also show that relative peaks are independent of the base path. In particular, valleys and high peaks can be obtained from relative peaks by fixing the base path in certain ways.

• Journal of Astronomy and Space Sciences
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• v.33 no.2
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• pp.109-117
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• 2016

We explain the results of Yu et al. (2015b) of the novel sharpness angle measurement to a large number of spectra obtained from the Fermi gamma-ray burst monitor. The sharpness angle is compared to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. It is found that more than 91% of the high temporally and spectrally resolved spectra are inconsistent with any kind of optically thin synchrotron emission model alone. It is also found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to 58⁺²³₋₁₈% of the peak flux. These results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed spectra. Since any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.154-154
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• 2021

Since the development of Bubble Image Velocimetry (BIV) technique as the complementary technique of Particle Image Velocimetry (PIV), the application of digital imaging technique in the field of hydraulic and coastal engineering increased rapidly. BIV works very well in multi-phase flow (air-water) flows where the PIV technique doesn't. However, the velocity field obtained from BIV technique often resulted in a velocity vector on the outside of the flow (false velocity) since the Field of View (FOV) usually not only cover the air-water flow but also the area outside the flow. In this study, a simple technique of post processing velocity field was developed. This technique works based on the average of the pixel value in the interrogation area. An image of multi-phase flow of wave overtopping was obtained through physical experiment using BIV technique. The velocity calculation was performed based on the similar method in PIV. A velocity masking technique developed in this study then applied to remove the false velocity vector. Result from non-masking, manually removed and auto removed false velocity vector were presented. The masking technique show a similar result as manually removed velocity vector. This method could apply in a large number of velocity field which is could increase the velocity map post-processing time.