• Korean Journal of Mathematics
• /
• v.20 no.4
• /
• pp.477-483
• /
• 2012

In this paper we study the infiniteness of the Hilbert ${\ell}$-class field tower of imaginary ${\ell}$-cyclic function fields when ${\ell}{\geq}5$.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.161-166
• /
• 2013

In this paper we study the infiniteness of the Hilbert 3-class field tower of imaginary cubic function fields.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.11a
• /
• pp.915-918
• /
• 2005

Acoustic holography uses Kirchhoff·Helmholtz integral equation and Green's function which satisfies Dirichlet boundary condition Applications of acoustic holography have been taken to the sound field neglecting the effect of flow. The uniform flow, however, changes sound field and the governing equation, Green's function and so on. Thus the conventional method of acoustic holography should be changed. In this research, one possibility to apply acoustic holography to the sound field with uniform flow is introduced through checking for the plane wave in a duct. Change of Green's function due to uniform flow and one method to derive modified form of Kirchhoff·Heimholtz integral is suggested for 1-dimensional sound field. Derivation results show that using Green's function satisfying Dirichlet boundary condition, we can predict sound pressure in a duct using boundary value.

• Communications of the Korean Mathematical Society
• /
• v.28 no.4
• /
• pp.735-740
• /
• 2013

In this paper, we will introduce the notion of the real quadratic function fields of minimal type, which is a function field analogue to Kawamoto and Tomita's notion of real quadratic fields of minimal type. As number field cases, we will show that there are exactly 6 real quadratic function fields of class number one that are not of minimal type.

• Journal of the Korean Society of Physical Medicine
• /
• v.16 no.1
• /
• pp.103-109
• /
• 2021

PURPOSE: This study examined the effects of the Visual Analog Scale (VAS) and knee function index on the knee strength and endurance in the national male field-hockey athletes. METHODS: Twenty-four male field-hockey athletes with a painful knee who trained at the national training center in 2019 were enrolled. The VAS and knee function index questionnaire were used to evaluate the degree of pain and functional state of the knee. The muscle strength and endurance of the knee were measured by Biodex (System 4, USA). The Pearson product moment correlation was performed to examine the effects of the VAS and knee function index the of knee on the strength and endurance. In addition, the VAS and knee function index and muscle strength and muscle endurance were examined to determine the relationship using Simple Linear Regression. The statistical significance level was α=.05. RESULTS: An analysis of the correlation between VAS and knee function index and muscle strength and muscle endurance revealed the VAS and knee function index to be statistically significant (r = .700). In addition, the extensor muscle strength, knee VAS (r = -.457), and knee function index (r = -.414) were also statistically significant. A 1-point increase in the VAS and knee function index was associated with an approximately 9.881 and 1.006 extensor muscle strength. CONCLUSION: The VAS and knee function index of field-hockey athletes are related to the strength of the knee extensors. Therefore, field-hockey athletes should develop a program to strengthen the extensor muscle strength of the knee.

• Korean Journal of Mathematics
• /
• v.22 no.3
• /
• pp.419-427
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.1
• /
• pp.17-23
• /
• 2009

Let F be a finite real abelian extension of a global function field k with G = Gal(F/k). Assume that F is an extension field of the Hilbert class field $K_e$ of k and is contained in a cyclotomic function field $K_n$. Let $\ell$ be any prime number not dividing $ph_k{\mid}G{\mid}$. In this paper, we show that if $\theta{\in}\mathbb{Z}[G]$ annihilates the Sylow $\ell$-subgroup of ${\mathcal{O}}^{\times}_F/{\mathcal{C}}_F$, then (q-1)$\theta$ annihilates the Sylow $\ell$-subgroup of ${\mathcal{Cl}}_F$.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.417-426
• /
• 2017

We explicitly determine fundamental units and regulators of an infinite family of cyclic quartic function fields $L_h$ of unit rank 3 with a parameter h in a polynomial ring $\mathbb{F}_q[t]$, where $\mathbb{F}_q$ is the finite field of order q with characteristic not equal to 2. This result resolves the second part of Lehmer's project for the function field case.

• Journal of the Korean Mathematical Society
• /
• v.39 no.5
• /
• pp.765-773
• /
• 2002

Let $textsc{k}$＝$F_{q}$(T) be a rational function field. Let $\ell$ be a prime number with ($\ell$, q-1) ＝ 1. Let K/$textsc{k}$ be an elmentary abelian $\ell$-extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$-divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.

• The Pure and Applied Mathematics
• /
• v.20 no.2
• /
• pp.79-87
• /
• 2013

In this paper we study the infniteness of Hilbert 2-class field towers of inert imaginary quadratic function fields over $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime number.