• 충청수학회지
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• 제26권1호
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• 충청수학회지
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• 제24권4호
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• 대한수학회논문집
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• 제37권3호
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• pp.635-648
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• 2022

In this paper, we establish an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_P)$ averaging over ℙ_2g+1 and over ℙ_2g+2 as g → ∞ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_u)$ averaging over 𝓘_g+1 and over 𝓕_g+1 as g → ∞ in even characteristic.

• 충청수학회지
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• 제23권4호
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• 충청수학회지
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• 제35권1호
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• pp.1-12
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• 2022

In this paper we prove an even characteristic analogue of the result of Andrade on lower bounds for moment of quadratic Dirichlet L-functions in odd characteristic. We establish lower bounds for the moments of Dirichlet L-functions of characters defined by Hasse symbols in even characteristic.

• 천문학회보
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• 제40권2호
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• pp.31.1-31.1
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• 2015

For probing magnetic fields in the universe, rotation measure (RM) have been often used. RM allows us to obtain the information of integrated (or averaged) magnetic fields along a line of sight (LOS). On the other hand, the new technique so-called Faraday tomography will be used in practical in the near future thanks to the wide-band polarimetry by Square kilometre Array and/or its precursors. The technique allows us to obtain so-called Faraday dispersion function (FDF). FDF is the distribution function of magnetic fields and polarized sources along a LOS. Because of this fact, it is expected that the studies of magnetic fields associated with various astronomical objects will progress dramatically. Since FDF also includes information of cosmic-rays and thermal electrons, the investigation of FDF may advance the studies of dynamics of external galaxies and/or the star formation activities. We have studied the potentials of Faraday tomography such as a tool to probe the intergalactic magnetic field associated with filaments of galaxies in the large scale structure. We have also studied the realistic FDFs of galaxies for understanding global magnetic field, cosmic-ray and thermal electrons of external galaxies. In the talk, we briefly introduce the Faraday tomography technique and report the results related to the Faraday tomography.

• 대한수학회보
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• 제37권2호
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• 대한수학회논문집
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• 제12권3호
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• pp.553-560
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• 1997

A class number formula over global function field, extending the formula obtained by Shu, is proved.

• 한국전산유체공학회지
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• 제4권2호
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• pp.47-56
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• 1999

We developed a computer program to simulate the flow field in the presence of electro-magnetic fields. The steady, two-dimensional conservation equations for mass and momentum were solved simultaneously with Maxwell equations for electro-magnetic fields. Using this program, a numerical analysis was carried out to analyze the fluid flow in the continuous casting mold with electromagnetic brake. The effects of magnetic fields size, nozzle angle and EMBR yoke position on the flow fields in the continuous casting were investigated in the present study. The flow fields with EMBR were compared with those without EMBR. We also investigated the distribution of tracer concentration as a function of time in order to calculate their residence time in the mold with EMBR. By controlling the flow fields properly using EMBR, we can prevent the direct flow impaction on the wall which can give a damage on the mold surface and reduce surface defects of stainless steel sheet products.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.419-427
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• 2014

Let $k=\mathbb{F}_q(T)$ be the rational function field over a finite field $\mathbb{F}_q$, where $q{\equiv}1$ mod 3. In this paper, we determine asymptotic values of average of ideal class numbers of some family of cubic Kummer extensions of k.