• 호남수학학술지
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• 제27권3호
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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.

• 대한수학회보
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• 제52권5호
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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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• 제45권3호
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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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• 제16권3호
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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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• 제32권3호
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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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• 제38권3_4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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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.

• 한국산학기술학회논문지
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• 제11권5호
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• pp.1936-1942
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• 2010

본 논문은 기능식품의 과용에 따른 간질환 환자에게 미치는 영향을 알아보기 위해, 마늘열수추출물의 용량을 달리하여, 사염화탄소에 의한 랫드의 간 손상을 유발하여 기능학적검사를 통해 간장에 미치는 용량의 중요성을 알아보았다. 실험동물은 Sprague-Dawley 종 웅성 랫드로 하여 정상군, 대조군, 양성대조군, 실험군 E1, E2, E3 군으로 나누어 각 군당 7마리씩 총 42마리를 이용하였고, 실험동물은 체중 당 사염화탄소 $0.5\;m{\ell}$ (0.20 g/kg/day)를 olive oil에 동량 희석하여 1일 1회 격일 간격으로 총 5회 복강 내 투여하여 간 손상 유발한 후 국내에서 유기농 재배한 마늘을 열수 추출하여 각 실험군에 체중 당 0.35 g/kg(E1), 0.70 g/kg(E2), 1.40 g/kg(E3)를 일일 1회, 주 5일, 4주간 위존데를 사용하여 투여하였다. 실험의 결과로 마늘추출물의 투여가 생리적 기능 활성에 긍정적인 작용을 하여 간장에서 산화스트레스를 감소시키고 독성 증감작용 및 기능학적 변화를 확인하였고, 용량에 따른 실험군(E1, E2, E3) 간의 비교에서 고농도 투여군(E3)에서는 마늘독성의 영향 때문에 E1, E2보다 긍정적인 효과를 덜 보였다.

• Preventive Nutrition and Food Science
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• 제15권3호
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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.

• 한국광학회:학술대회논문집
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• 한국광학회 2000년도 하계학술발표회
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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).