• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.685-697
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• 2015

For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.469-497
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• 2016

In this research, we develop a systematic learning the materials on constructibility of cubic roots. We propose two sets of materials: one is based on concepts of field, vector space, minimal polynomial in abstract algebra, another based on properties of cubic roots in elementary algebra. We assess the validity, applicability, defects and merits of developed materials through prospective teachers, in-service teachers, and professionals. It could be expected that materials be used for advanced secondary students, mathematics majoring college students and mathematics teachers. Furthermore, we may expect the materials be useful for understanding and solving the (un)constructibility problems.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.2
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• pp.149-159
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• 2001

The conventional block-based motion prediction suffers, especially in low bit-rate video application, from shortcomings such as blocking artifacts of motion field and unstable motion estimation. To overcome the deficiency, this paper proposes one method of adopting a new motion compensation scheme based on the irregular triangular mesh structure while keeping the current block-based DCT coding structure of H.263 as much as possible. To represent the reconstructed previous frame using minimal number of control points, the proposed method designs content-adaptive irregular triangular meshes, and then, estimate the motion vector of each control point using the affine transformation-based matching. The predicted current frame is obtained by applying the affine transformation to each triangular mesh. Experiment with the several real video sequences shows improvement both in objective and subjective picture quality over the conventional block-based H.263 method.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.643-702
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• 2021

Fix ℤ/2 is the prime field of two elements and write 𝒜₂ for the mod 2 Steenrod algebra. Denote by GL_d := GL(d, ℤ/2) the general linear group of rank d over ℤ/2 and by ${\mathfrak{P}}_d$ the polynomial algebra ℤ/2[x₁, x₂, …, x_d] as a connected unstable 𝒜₂-module on d generators of degree one. We study the Peterson "hit problem" of finding the minimal set of 𝒜₂-generators for ${\mathfrak{P}}_d$. Equivalently, we need to determine a basis for the ℤ/2-vector space $$Q{\mathfrak{P}}_d:={\mathbb{Z}}/2{\otimes}_{\mathcal{A}_2}\;{\mathfrak{P}}_d{\sim_=}{\mathfrak{P}}_d/{\mathcal{A}}^+_2{\mathfrak{P}}_d$$ in each degree n ≥ 1. Note that this space is a representation of GL_d over ℤ/2. The problem for d = 5 is not yet completely solved, and unknown in general. In this work, we give an explicit solution to the hit problem of five variables in the generic degree n = r(2^t - 1) + 2^ts with r = d = 5, s = 8 and t an arbitrary non-negative integer. An application of this study to the cases t = 0 and t = 1 shows that the Singer algebraic transfer of rank 5 is an isomorphism in the bidegrees (5, 5 + (13.2⁰ - 5)) and (5, 5 + (13.2¹ - 5)). Moreover, the result when t ≥ 2 was also discussed. Here, the Singer transfer of rank d is a ℤ/2-algebra homomorphism from GL_d-coinvariants of certain subspaces of $Q{\mathfrak{P}}_d$ to the cohomology groups of the Steenrod algebra, $Ext^{d,d+*}_{\mathcal{A}_2}$ (ℤ/2, ℤ/2). It is one of the useful tools for studying these mysterious Ext groups.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.4
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• pp.354-359
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• 2013

In this paper, we suggested the method for implementation of unsupervised nonlinear classification using Binary Harmony Search (BHS) algorithm, which is known as a optimization algorithm. Various algorithms have been suggested for classification of feature vectors from the process of machine learning for pattern recognition or EEG signal analysis processing. Supervised learning based support vector machine or fuzzy c-mean (FCM) based on unsupervised learning have been used for classification in the field. However, conventional methods were hard to apply nonlinear dataset classification or required prior information for supervised learning. We solved this problems with proposed classification method using heuristic approach which took the minimal Euclidean distance between vectors, then we assumed them as same class and the others were another class. For the comparison, we used FCM, self-organizing map (SOM) based on artificial neural network (ANN). KEEL machine learning datset was used for simulation. We concluded that proposed method was superior than other algorithms.

• Korean Journal of Remote Sensing
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• v.39 no.6_2
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• pp.1591-1604
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• 2023

In ocean color remote sensing, atmospheric correction is a vital process for ensuring the accuracy and reliability of ocean color products. Furthermore, in recent years, the remote sensing community has intensified its requirements for understanding errors in satellite data. Accordingly, research is currently addressing errors in remote sensing reflectance (R_rs) resulting from inaccuracies in meteorological variables (total ozone, pressure, wind field, and total precipitable water) used as auxiliary data for atmospheric correction. However, there has been no investigation into the error in R_rs caused by the variability of the water vapor profile, despite it being a recognized error source. In this study, we used the Second Simulation of a Satellite Signal Vector version 2.1 simulation to compute errors in water vapor transmittance arising from variations in the water vapor profile within the GOCI-II observation area. Subsequently, we conducted an analysis of the associated errors in ocean color products. The observed water vapor profile not only exhibited a complex shape but also showed significant variations near the surface, leading to differences of up to 0.007 compared to the US standard 62 water vapor profile used in the GOCI-II atmospheric correction. The resulting variation in water vapor transmittance led to a difference in aerosol reflectance estimation, consequently introducing errors in R_rs across all GOCI-II bands. However, the error of R_rs in the 412-555 nm due to the difference in the water vapor profile band was found to be below 2%, which is lower than the required accuracy. Also, similar errors were shown in other ocean color products such as chlorophyll-a concentration, colored dissolved organic matter, and total suspended matter concentration. The results of this study indicate that the variability in water vapor profiles has minimal impact on the accuracy of atmospheric correction and ocean color products. Therefore, improving the accuracy of the input data related to the water vapor column concentration is even more critical for enhancing the accuracy of ocean color products in terms of water vapor absorption correction.