• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.709-715
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• 2008

We construct certain ring class fields over an imaginary quadratic field by making use of Shimura's canonical models and extend the result of Chen-Yui ([1] Theorem 3.7.5(2)) to the case where (a, b, N) $\neq$ N or (a/N, N) $\neq$ 1 for a positive integer N > 1.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.715-723
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• 2023

In this paper, we construct explicitly an infinite family of primes P with h^±_P ≡ 0 (mod q^{deg P}), where h^±_P are the plus and minus parts of the divisor class number of the P-th cyclotomic function field over 𝔽_q(T). By using this result and Dirichlet's theorem, we give a condition of A, M ∈ 𝔽_q[T] such that there are infinitely many primes P satisfying with h^±_P ≡ 0 (mod p^e) and P ≡ A (mod M).

• Communications of Mathematical Education
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• v.35 no.4
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• pp.475-504
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• 2021

This study is a study that developed class materials that can be applied directly to classes by field teachers in consideration of ' research on the development is valuable as a field support study.', 'In material development, organizing data centering on the knowledge composition and inquiry activities of characters related to the mathematics concept can help develop class materials', and 'The fact that the development of subject data for has been insufficient'. To this end, this study went through the procedure of 'establishing a data development plan, data development, verifying field teachers on development data, verifying subject experts on development data, and developing final data reflecting verification opinions.' Therefore, based on the 1st 50 minutes reflecting the task exploration model, it was possible to develop class materials for the 3rd time. In this study, development data were presented with a 17-week curriculum plan, a class guidance plan that presents teacher-student interaction, and a task development form that students fill out and submit in class. This study was developed with the developed data in mind to be applied to actual classes. Therefore, a follow-up study is needed to apply the developed data to actual classes and analyze the results.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.177-183
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• 2011

Hidden Markov random eld(HMRF) is one of the most common model for image segmentation which is an important preprocessing in many imaging devices. The HMRF has unknown hyper-parameters on Markov random field to be estimated in segmenting testing images. However, in practice, due to computational complexity, it is often assumed to be a fixed constant. In this paper, we numerically show that the segmentation results very depending on the fixed hyper-parameter, and, if the parameter is misspecified, they further depend on the choice of the class-labelling algorithm. In contrast, the HMRF with estimated hyper-parameter provides consistent segmentation results regardless of the choice of class labelling and the estimation method. Thus, we recommend practitioners estimate the hyper-parameter even though it is computationally complex.

• Journal of Korean Library and Information Science Society
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• v.30 no.4
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• pp.27-57
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• 1999

Standardization is a prerequisite of quality control in any field. Library field is not an exception. The bibliographic control structures of AACR2R, MARC, DDC, LCC, LCSH, ISBD are highly standardized and dependent on rigorous authority work, so that libraries and bibliographic utilities using these tools could provide effective quality services. In order to emphasize the importance of standardization in the field of bibliographic control structures, this study focuses on inconsistencies in transliterated foreign personal and geographic names in headings, used as the caption of a given class as well as in notes describing what is found in a class or clarifying the notation hierarchy in the 4th edition of KDC. This study also examines Korean transliteration of loan words in the schedule as well as the transliterated entries of the Relative Index.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.379-383
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• 2007

We show that the modular equation ${\phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${\Gamma}_0$(n) gives an affine model of the modular curve $X_0$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $T_n(z)\;and\;T_n$(mz).

• Honam Mathematical Journal
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• v.34 no.2
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.21-59
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• 2020

Let L_K denote the hypothetical automorphic Langlands group of a number field K. In our recent study, we briefly introduced a certain unconditional non-commutative topological group ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$, called the Weil-Arthur idèle group of K, which, assuming the existence of L_K, comes equipped with a natural topological group homomorphism $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K that we called the "Langlands form" of the global nonabelian norm-residue symbol of K. In this work, we present a detailed construction of ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ and $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K, and discuss their basic properties.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.125.1-125.1
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• 2011

After a short description of the observatory, this presentation will highlight some of the most recent scientific achievements based on CFHT observations and how they benefit from the current instrumentation and novel observing modes proposed to the CFHT users. We will then move to the mid-term future with the development of new spectroscopic capabilities (visible wide-field FTS or near-IR spectro-polarimetry) and the study of a novel wide-field imager in the visible using Ground-Layer AO to provide unprecedented image quality on a large field of view. As an option for the long-term future, the concept of a next generation 10-m class telescope to replace the current CFHT 3.6-m will be described. An emphasis will be given on how CFHT is slowly morphing into an Asia-Pacific Rim observatory and on the role the Korean community could play in such an endeavor, from immediate access to first-class astronomical data to partnering with other nations in exciting developments.

• Journal of IKEEE
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• v.17 no.2
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• pp.129-134
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• 2013

For the conventional power metal-oxide semiconductor field-effect transistor (MOSFET) device structure, there exists a tradeoff relationship between specific on-resistance ($R_{ON.SP}$) and breakdown voltage ($V_{BR}$). In order to overcome the tradeoff relationship, a uniform super-junction (SJ) trench metal-oxide semiconductor field-effect transistor (TMOSFET) structure is studied and designed. The structure modeling considering doping concentrations is performed, and the distributions at breakdown voltages and the electric fields in a SJ TMOSFET are analyzed. The simulations are successfully optimized by the using of the SILVACO TCAD 2D device simulator, Atlas. In this paper, the specific on-resistance of the SJ TMOSFET is successfully obtained 0.96 $m{\Omega}{\cdot}cm^2$, which is of lesser value than the required one of 1.2 $m{\Omega}{\cdot}cm^2$ at the class of 100 V and 100 A for BLDC motor.