• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.1-11
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• 2000

The non-commutative torus $A_{\omega}=C^*(\mathbb{Z}^n,{\omega})$ may be realized as the $C^*$-algebra of sections of a locally trivial $C^*$-algebra bundle over $\widehat{S_{\omega}}$ with fibres $C^*(\mathbb{Z}^n/S_{\omega},{\omega}_1)$ for some totally skew multiplier ${\omega}_1$ on $\mathbb{Z}^n/S_{\omega}$. It is shown that $A_{\omega}{\otimes}M_l(\mathbb{C})$ has the trivial bundle structure if and only if $\mathbb{Z}^n/S_{\omega}$ is torsion-free.

• Journal of electromagnetic engineering and science
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• v.10 no.3
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• pp.186-189
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• 2010

Reflection(R($\omega$)), transmission(T($\omega$)) and loss(L($\omega$)) characteristics of multi-layer metamaterials are investigated experimentally in free space with the incident EM waves perpendicular to the substrate plane. The sample is made of split-ring resonators(SRRs) and wires which are the typical model of metamaterials. The R($\omega$) and T($\omega$) of multi-layer metamaterials have been calculated from the measured S-parameters. In this paper, we got the impedance-matched result according to the curves of R($\omega$), meanwhile the T($\omega$) decreased with increasing number of layers. At last, we attained the result that the L($\omega$) gets to nearly 98% around 8 GHz, with R($\omega$)=T($\omega$)=0. The design presented in this paper achieves experimented loss near unity.

• Nutrition Research and Practice
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• v.8 no.4
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• pp.360-367
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• 2014

BACKGROUND/OBJECTIVES: The aim of this research was to study the different long term effects of consumption of dietary oil sources with varying omega-6/omega-3 (${\omega}-6/{\omega}-3$) polyunsaturated fatty acids (PUFAs) ratios on bone marrow fatty acid level, ex vivo prostaglandin $E_2$ ($PGE_2$) release, and mineral content of bone in rabbits. MATERIALS/METHODS: For this purpose, weaning and female New Zealand white rabbits were purchased and randomly divided into five groups and offered ad libitum diets containing 70 g/kg of added oil for 100 days. The dietary lipid treatments were formulated to provide the following ratios of ${\omega}-6/{\omega}-3$ fatty acids: 8.68 soy bean oil (SBO control), 21.75 sesame oil (SO), 0.39 fish oil (FO), 0.63 algae oil (DHA), and 0.68 algae oils (DHA/ARA). DHA and ARA are two types of marine microalgae of the genus Crypthecodinium cohnii. RESULTS: The dietary treatments had significant effects on the bone marrow fatty acids of rabbits. Rabbits fed the FO diet, containing the highest ${\omega}-3$ PUFA concentration, and those fed the SBO diet showed the highest ${\omega}-6$ PUFA. On the other hand, a positive correlation was observed between Ex vivo $PGE_2$ level and the ${\omega}-6/{\omega}-3$ dietary ratio. Significant effects of dietary treatment on femur Ca, P, Mg, and Zn contents were observed in both genders. CONCLUSIONS: Findings of the current study clearly demonstrated that dietary PUFA, particularly ${\omega}-6/{\omega}-3$ and ARA/EPA ratios are important factors in determining bone marrow fatty acid profile, and this in turn determines the capacity of bone for synthesis of $PGE_2$, thereby reducing bone resorption and improving bone mass during growth.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.29-40
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• 2015

By using a set ${\Omega}$, we introduce the concept of ${\Omega}$-fuzzy subsemigroups and study some of it's properties. Also, we show that the homomorphic images and preimages of ${\Omega}$-fuzzy subsemigroups become ${\Omega}$-fuzzy subsemigroups.

• Journal of the Korean Applied Science and Technology
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• v.34 no.2
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• pp.315-326
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• 2017

This study was investigated the biochemical mechanism on reducing blood lipids in second-generation rats fed diet with different omega 6 to omega 3 fatty acid ratio. The experiment treatment groups were classified into the groups with the omega 6 to omega 3 ratios of 0 (control group), 1:1, 8:1, and 19:1, respectively. The levels of the blood triglyceride, total cholesterol, low density lipoprotein-cholesterol (LDL-C), aspartate aminotransferase (AST), alanine aminotransferase (ALT) and glucose were lowest in the group with the omega 6 to omega 3 ration of 1:1. The levels of high density lipoprotein-cholesterol and phospholipid were highest in the group with the omega 6 to omega 3 ration of 1:1. The HMG-CoA reductase activity was suppressed in the groups with the omega 6 to omega 3 ratio of 1:1 and 8:1 compared with that in the control group, but the excretion of sterol through feces was promoted. The blood omega 6 to omega 3 ratio decreased in a concentration-dependent manner depending on the increase in the omega 6 to omega 3 ratio within the ingested diet. The results of this study demonstrated a new finding that when the parent generation and second-generation rats ingested the diet with the omega 6 to omega 3 ratio of below 8:1, harmful lipids in the blood were reduced, the liver functions were maintained, and the growth was promoted due to the nutrient metabolism activation mechanism.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1291-1302
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• 2012

In this paper, we introduce a new elliptic PDE: $$\{{\nabla}{\cdot}\(\frac{|{\gamma}^{\omega}(r)|^2}{\sigma}{\nabla}v_{\omega}(r)\)=0,\;r{\in}{\Omega},\\v_{\omega}(r)=f(r),\;r{\in}{\partial}{\Omega},$$ where ${\gamma}^{\omega}={\sigma}+i{\omega}{\epsilon}$ is the admittivity distribution of the conducting material ${\Omega}$ and it is shown that the introduced elliptic PDE can replace the standard elliptic PDE with conductivity coefficient in EIT imaging. Indeed, letting $v_0$ be the solution to the standard elliptic PDE with conductivity coefficient, the solution $v_{\omega}$ is quite close to the solution $v_0$ and can show spectroscopic properties of the conducting object ${\Omega}$ unlike $v_0$. In particular, the potential $v_{\omega}$ can be used in detecting a thin low-conducting anomaly located in ${\Omega}$ since the spectroscopic change of the Neumann data of $v_{\omega}$ is inversely proportional to thickness of the thin anomaly.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.15-24
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• 2008

Let $N{\geq}1$ and p > 1. Let ${\Omega}$ be a domain of $\mathbb{R}^N$. In this article we shall establish Kato's inequalities for quasilinear degenerate elliptic operators of the form $A_pu$ = divA(x,$\nabla$u) for $u{\in}K_p({\Omega})$, ), where $K_p({\Omega})$ is an admissible class and $A(x,\xi)\;:\;{\Omega}{\times}\mathbb{R}^N{\rightarrow}\mathbb{R}^N$ is a mapping satisfying some structural conditions. If p = 2 for example, then we have $K_2({\Omega})\;= \;\{u\;{\in}\;L_{loc}^1({\Omega})\;:\;\partial_ju,\;\partial_{j,k}^2u\;{\in}\;L_{loc}^1({\Omega})\;for\;j,k\;=\;1,2,{\cdots},N\}$. Then we shall prove that $A_p{\mid}u{\mid}\;\geq$ (sgn u) $A_pu$ and $A_pu^+\;\geq\;(sgn^+u)^{p-1}\;A_pu$ in D'(${\Omega}$) with $u\;\in\;K_p({\Omega})$. These inequalities are called Kato's inequalities provided that p = 2. The class of operators $A_p$ contains the so-called p-harmonic operators $L_p\;=\;div(\mid{{\nabla}u{\mid}^{p-2}{\nabla}u)$ for $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• Journal of the Korean Applied Science and Technology
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• v.14 no.1
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• pp.61-76
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• 1997

Triacylglycerols of the seeds of Ginkgo biloba have been resolved by high-performace liquid chromatography(HPLC} in the silver-ion and reverse-phase modes. The fatty acids were identified by a combination of capillary gas chromatography and gas-chromatography /mass spectrometry as the methyl and /or picolinyl ester. The main components are $C_{18:2{\omega}6}$(39.0mol%), $C_{18:1{\omega}7}$(asclepic acid 21.5mol%), and $C_{18:1{\omega}9}$(oleic acid, 13.8mol%). Considerable amounts of unusual acid such as $C_{20:3{\Delta}^{5,11,14}$ (5.7mol%), $C_{18:2{\Delta}^{5,9}$(2.8mol%), and $C_{18:3}{\Delta}^{5,9,12}$(1.6mol%), were checked. In addition, an anteiso-branched fatty acid, 14-methylhexadecanoic acid, was also present as a minor component(0.9 mol%). The triacylglycerols were separated into 17 fractions by reverse-phase HPLC, and the fractionation was achieved according to the partition numnber(PN) in which a ${\Delta}^5$-non methylene interrupted double bond($^5$-NMDB) showed different behaviour from a methylene interrupted double bond in a molecule with a given cahinlength. Silver-ion HPLC exhibited excellent resolution in which fractions(23 fractions) were resolved on the basis of the number and configuration of double bonds. In this instance, the strength of interaction of a ${\Delta}^5$-NMDB system with silver ions seemed to be weaker than a methylene interrupted double bond system. The principal triacylglycerol species are as follows ; $(C_{18:2{\omega}6)2}/C_{18:1{\omega}7}$, $C_{18:1{\omega}9}/C_{18:1{\omega}7}/C_{18:2{\omega}6}$, $(C_{18:1{\omega}7)2}/C_{18:2{\omega}6}$, $C_{16:1{\omega}7}/C_{18:1{\omega}9}/C_{20:3}{\Delta}^{5,11,14}$, $C_{16:1{\omega}7}/C_{18:1{\omega}7}/C_{20:3}{\Delta}^{5,11,14}$, $C_{18:1{\omega}9}/C_{18:1{\omega}7}/C_{18:2{\omega}6}$, $C_{18:1{\omega}9}/C_{18:2}{\Delta}^{5,5}/C_{20:3}{\Delta}^{5,11,14}$, $(C_{18:1{\omega}7)2}/C_{18:2{\omega}6}$ and $(C_{18:1{\omega}9)2}/C_{18:2{\omega}6}$, while simple triacylglycerols without $C_{18:2{\omega}6})_3$ were not present. Stereospecific analysis showed that fatty acids with ${\Delta}^5$-NMDB system and saturated chains were predominantly located at the site of sn-3 carbon of glycerol backbones. It is evident that there is asymmetry in the distribution of fatty acids in the TG molecules of Ginkgo nut oils.

• Korean Journal of Psychosomatic Medicine
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• v.27 no.2
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• pp.181-190
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• 2019

Objectives : Epidemiological studies in other countries show that a low intake of omega-3 fatty acids (FAs) increases the risk of depression or suicidality. However, no studies have investigated the associations of suicidality with omega-3 FAs in Korea. Hence, this cross-sectional study aimed to investigate the effects of omega FAs on suicidality in the general South Korean population. Methods : The data in this study were sourced from adults (n=215,860) who completed the Sixth Korea National Health and Nutrition Examination Survey (KNHANES VI), and the associations between omega FAs and suicidality were analyzed using multivariate logistic regressions. Results : Our results demonstrated that high omega-3 FA intake was associated with a decreased risk of suicide (OR=0.83, 95% CI : 0.71-0.98) and the high omega-6 to omega-3 FA ratio was associated with an increased risk of suicide (OR=1.25, 95% CI : 1.02-1.54). Additionally, a high intake of omega-3 FAs was associated with a decreased risk of suicide in men, but not in women (OR=0.72, 95% CI : 0.59-0.88). Conclusions : Overall, our findings suggest that a lower intake of omega-3 FA is associated with the increased risk of suicidality in the general Korean population, especially in men.

• Journal of Nutrition and Health
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• v.19 no.3
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• pp.135-145
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• 1986

식이 $\omega$3 지방산이 신장의 지질구성 및 기능에 미치는 영향을 조사하기 위해 젖뗀 55-60 g의 흰쥐에게 고등어유, 들깨유, 콩기름을식이의 10% (W/W)포함하는 먹이를 조제하여 24일간 섭취시켰다. 고등어유군의 신장 인지질 지방산에 C20~C22 $\omega$ 3 지방산의 함량이 월등히 많은 반면 들깨유군은 콩기름군에 비해 약간 높을 뿐이어서 C18 : 3 ($\omega$3) 지방산으로 단기간에 쉽게 전환되지 않음을 보였다. C18 : 2($\omega$6) 지방산은 고등어군만 낮았고 C20 : 4($\omega$6)는 들깨유군에서는 낮았지만 고등어유군은 콩기름군과 같은 수준이었다. 또한 고등어유군에서 C18 : 1($\omega$9)을 포함한 단일 불포화 지방산이 높고 포화지방산 함량이 낮은 것도 특징이었다 . 인지질 종류별 분석결과에서 고등어유군이 sphingomyelin 이 높고 phosphatidylethanol-amine이 낮았다. 반면 신장 Cholest대기 함량은 고등어유군이 높았으며, 이러한 지질구성 변화는 신장 Na-K-ATPase 활성감소시킨 것이다.