• Honam Mathematical Journal
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• v.27 no.3
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• pp.389-397
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• 2005

Let K be an absolutely real abelian number field with $G=Gal(K/{\mathbb{Q}})$. Let E be a subfield of K and ${\Delta}=Gal(K/E)$. Let $C_K$ and $C_E$ be the group of circular units of K and E respectively. In [G], Greither has shown that if G is cyclic then $C_K^{\Delta}=C_E$. In this paper we show that the same result holds in function field case.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1489-1493
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• 2015

For a subset $E{\subseteq}\mathbb{R}^d$ and $x{\in}\mathbb{R}^d$, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by $$dim_{H,loc}(x,E)=\lim_{r{\searrow}0}dim_H(E{\cap}B(x,r))$$, $$dim_{P,loc}(x,E)=\lim_{r{\searrow}0}dim_P(E{\cap}B(x,r))$$, where $dim_H$ and $dim_P$ denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions $f,g:\mathbb{R}^d{\rightarrow}[0,d]$ with $f{\leq}g$, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.395-404
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• 2005

Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.425-437
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• 2008

Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function $X_{G(P)}$ which generalizes the chromatic polynomial ${\chi}_G$ of G, and showed all coefficients are nonnegative in the e-expansion of $X_{G(P)}$ for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.

• Journal of Nutrition and Health
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• v.32 no.3
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• pp.239-247
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• 1999

With the increasing elderly population in Korea, dementia has become a mojor health problem in Korea. Several studies have been conducted on the association between dementia and dietary intake, especially vitamin E and vitamin C. The purpose of this study was to investigate the effect of vitamin E and vitamin C supplementation on the decrease in cognitive function induced by scopolamine(300mg/kg) in rats. Rats were divided into three groups : control, vitamin C, and vitamin E supplementation(2.4g Vit C or Vit E /100g diet) and fed the diets for 6 weeks. There were significant decreases in active avoidance response and brain acetylcholinesterase activity in the control group, but no significant differences were observed in the vitamin E and C groups after scopolamine treatment. Brain dopamine concentration of vitamin E and C groups was significantly higher than those of control group after scopolamine injection. The concentrations of brain norepinephrine also showed similar tendence, even though it was not statistically significant. These results indicate that vitamin E and vitamin C may protect against the cognitive function decrease induced by scopolamine. However, it is still unclear how vitamin E and C influence brain neurotransmitters and improve cognitive function. Further study is need to elucidate the role of vitamin E and C supplementation in the prevention of dementia.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.221-238
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• 2020

Let G = (V (G), E(G)) be a graph and let g : V (G) → S₃ be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S₃ cordial remainder labeling of G if |v_g(i)-v_g(j)| ≤ 1 and |e_g(1)-e_g(0)| ≤ 1, where v_g(j) denotes the number of vertices labeled with j and e_g(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S₃ cordial remainder labeling is called a group S₃ cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S₃ cordial remainder labeling.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.39-49
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• 2010

This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.5
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• pp.1936-1942
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• 2010

To examine the effect of overdosed functional food in liver-injured patients, we tried to investigate the dose effect of Allium sativum L. (also called garlic) extract on rats with CCl4-induced liver damage, by comparatively examinating the hepatic function of each group. 42 male Sprague-Dawley rats were selected and divided equally (n=7) into normal, control, positive control, and three experimental subgroups (E1, E2 and E3), respectively. For each kg of body weight, hepatic injury was induced by intraperitoneal administration of $0.5\;m{\ell}$ (0.20 g/kg/day) $CCl_4$, which was diluted in equal amount of olive oil, once a day on every other day for total 5 times. Hot water extraction was performed using domestically cultivated organic garlics, and the obtained extract was injected by sonde, once daily during 4 weeks, to each experimental subgroups by different dosage of 0.35 g/kg(E1), 0.70 g/kg(E2), 1.40 g/kg(E3), respectively. Results showed that the injection of garlic extract positively influenced the physiological activation which lowered the oxidative stress, changed the toxicity, and functionally improved the hepatic condition. Comparing the dose effect between the three experimental subgroups (E1, E2, E3), results of the maximal-dosed subgroup (E3) showed less significance compared with the lower-dosed subgroups(E1 and E2), which seems to resulted from the (increased) toxicity of garlic.

• Preventive Nutrition and Food Science
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• v.15 no.3
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• pp.196-205
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• 2010

This study evaluated the effects of carnitine and/or GABA supplementation on immune function, lipid profiles and some vitamins in mice chronically administered alcohol. BALB/c mice were fed with either AIN-76 diet (N), control diet plus alcohol (4 g/kg bw, E), E plus 0.5 g/kg bw carnitine (EC), E plus 0.5 g/kg bw GABA (EG), or E plus 0.5 g/kg bw carnitine plus 0.5 g/kg bw GABA (ECG) for 6 weeks. Administrations of the carnitine and/or GABA prevented alcohol-induced increases in triglyceride concentrations in serum and liver. However, there was no difference among the supplemented groups. Serum vitamin E concentration was higher in mice supplemented with EC and EG, but not in mice given ECG. Phagocytic activity of peritoneal macrophages was increased in EG group compared with E group. The subpopulations of murine splenocyte's TH cells were increased significantly in EC and ECG groups. These data suggest that immune function, lipid profiles and some immune-related lipid soluble vitamins were positively changed by supplementation of carnitine or GABA, but do not show any synergistic effect of mixed supplementation.

• Proceedings of the Optical Society of Korea Conference
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• 2000.08a
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• pp.64-66
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• 2000

Theoretical foundations of atom dynamics in laser fields are reviewed in relation with applications to laser spectroscopy, control of atomic motion, atom traps and frequency standards. Quasiclassical kinetic equations are applied to multilevel atomic schemes interacting with counter-propagating laser waves to describe the properties of atomic populations and coherence and the time evolution of atomic distribution function. Basic types of the dipole radiation forces on atoms are discussed for the realistic cases of multilevel dipole interaction schemes such as 3(g)＋5(e), 3(g)＋3(e), 5(g)＋3(e), 5(g)＋7(e), 3(g)＋3(e)＋5(e) and 1(g)＋3(g)＋3(e)＋5(e).