• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.35-54
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• 2007

Let $M_c$ = M(2, 0, c) be the moduli space of O(l)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0\;and\;c_2=c$ on a K3 surface X, where O(1) is a generic ample line bundle on X. When $c=2n\geq4$ is even, $M_c$ is a singular projective variety equipped with a holomorphic symplectic structure on the smooth locus. In particular, $M_c$ has trivial canonical divisor. In [22], O'Grady asks if there is any symplectic desingularization of $M_{2n}$ for $n\geq3$. In this paper, we show that there is no crepant resolution of $M_{2n}$ for $n\geq3$. This obviously implies that there is no symplectic desingularization.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.433-438
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• 2007

Let $\mathbb{A}=\mathbb{F}_q[T]$ and $k=\mathbb{F}_q(T)$. Assume q is odd, and fix a prime divisor ${\ell}$ of q - 1. Let P be a monic irreducible polynomial in A whose degree d is divisible by ${\ell}$. In this paper we define a subgroup $\tilde{C}_F$ of $\mathcal{O}^*_F$ which is generated by $\mathbb{F}^*_q$ and $\{{\eta}^{{\tau}^i}:0{\leq}i{\leq}{\ell}-1\}$ in $F=k(\sqrt[{\ell}]{P})$ and calculate the unit-index $[\mathcal{O}^*_F:\tilde{C}_F]={\ell}^{\ell-2}h(\mathcal{O}_F)$. This is a generalization of [3, Theorem 16.15].

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.993-1002
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• 2017

Let ${\Omega}$ be a bounded, uniformly totally pseudoconvex domain in ${\mathbb{C}}^2$ with the smooth boundary b${\Omega}$. Assuming that ${\Omega}$ satisfies the negative ${\bar{\partial}}$ property. Let M be a positive, finite area divisor of ${\Omega}$. In this paper, we will prove that: if ${\Omega}$ admits a maximal type F and the ${\check{C}}eck$ cohomology class of the second order vanishes in ${\Omega}$, there is a bounded holomorphic function in ${\Omega}$ such that its zero set is M. The proof is based on the method given by Shaw [27].

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.181-195
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• 1999

This research is produced as a applet of learning materials, and is made with the internet languages HTML, Java, and NamoWebeditor. It contains "Greatest Common Divisor and Least Common Multiple", "Parallel translation of function of second order", "Pythagoras Theorem", which is the current middle school mathmatics textbook for third graders. The keynote of this research is that the students can study individually through logging into the internet on their own computers; the program is made using graphics and animation on order to develop the learners′ interest in mathematics. I hope that this research can supplement our currently insufficient internet educational data.

• Journal of the Korean Institute of Navigation
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• v.9 no.1
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• pp.41-81
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• 1985

Tidal phenomenon can be utilized by the wise and cautious mariner to safely perform his duties as pilot and navigator. It can be either a help or hindrance to the mariner. The principle of MULDAE which expresses the determination of the state of the tide based upon knowledge of the lunar date and it has been used in Korea since ancient times. The folk method of calculation was essentially based on an unsystematic division of the lunar month, traditionally using the numbers 7 or 8. As the lunar cycle is complete in 15 days the tidal cycle should also correspondence closely to the lunar date. This paper represents the first scientific attempt to systematically investigate this unique traditional method of tidal calculation and contains a comparison of the MULDAE and ordinary (solar based) tide calculation methods. MULDAE was compared with the standard tide table for standard and island ports in Korea from 1982 to 1985. This study concluded that MULDAE was indeed an accurate adn reliable predictor of tidal activity. Furthermore, the number 6 was found to be the correct divisor upon which to base MULDAE calculations Also a formula expressing MULDAE as a function was discovered. This research show that MULDAE can be applied nationwide and is a reliable and easy way to predict tides based upon mean figures for certain ports and island A calender showing MULDAE is presented here for the first time. A clear relationship between the MULDAE method of calculating tides and the use of ordinary tide tables is proven.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.753-782
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• 2016

In this paper we deduce the number of representations of a positive integer n by each of the six triangular forms as $${\frac{1}{2}}x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{1}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+3x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+3x_3(x_3+1)+3x_4(x_4+1).$$

• The Korean Journal of Applied Statistics
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• v.29 no.2
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• pp.291-299
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• 2016

This paper discusses how to establish estimable functions when there are fixed and random effects in design models. It proves that estimable functions of mixed models are not related to random effects. A fitting constants method is used to obtain sums of squares due to random effects and Hartley's synthesis is used to calculate coefficients of variance components. To test about the fixed effects the degrees of freedom associated with divisor are determined by means of the Satterthwaite approximation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.7
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• pp.640-650
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• 1991

In the paper, the threepoint search algorithm used direct search method for optimal design is proposed. Proposed algorithm is composed of two iteration procedure to determine the minimum value of performance index. The minumum value of three-point existing in the inner N-order searching is firstly determined and next searching space is then reduced by the result of first procedure. To compute performance index. 3N iteration for a searching is necessary. 3N searching method is also described and confirmed with exception of parameter included multiphicator and divisor. Proposed algorithm have good stability and reliability when performance index is linear or quadratic function.

• Journal of the Korea Computer Graphics Society
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• v.21 no.5
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• pp.1-10
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• 2015

This study proposes a method of developing authoring tool that can easily and intuitively generate diverse digital leaves that compose virtual landscape. The main system of the proposed authoring tool consists of deformation method for the contour of leaf blade based on image warping, procedural modeling of leaf vein and visualization method based on mathematical model that expresses the color and brightness of leaves. First, the proposed authoring tool receives leaf input image and searches for contour information on the leaf blades. It then designs leaf blade deformation method that can generate diverse shapes of leaf blades in an intuitive structure using feature-based image warping. Based on the computed leaf blade contour, the system implements the generalized procedural modeling method suitable for the authoring tool that generates natural vein patterns appropriate for the leaf blade shape. Finally, the system applies visualization function that can express color and brightness of leaves and their changes over time using a mathematical model based on convolution sums of divisor functions. This paper provides texture support function so that the digital leaves that were generated using the proposed authoring tool can be used in a variety of three-dimensional digital contents field.