• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.65-74
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• 2007

Suppose that $\mu$ is a finite positive Borel measure on bounded symmetric domain $\Omega{\subset}\mathbb{C}^n\;and\;\nu$ is the Euclidean volume measure such that $\nu(\Omega)=1$. Suppose 1 < p < $\infty$ and r > 0. In this paper, we will show that the norms $sup\{\int_\Omega{\mid}k_z(w)\mid^2d\mu(w)\;:\;z\in\Omega\}$, $sup\{\int_\Omega{\mid}h(w)\mid^pd\mu(w)/\int_\Omega{\mid}h(w)^pd\nu(w)\;:\;h{\in}L_a^p(\Omega,d\nu),\;h\neq0\}$ and $$sup\{\frac{\mu(E(z,r))}{\nu(E(z,r))}\;:\;z\in\Omega\}$$ are are all equivalent. We will also show that the inclusion mapping $ip\;:\;L_a^p(\Omega,d\nu){\rightarrow}L^p(\Omega,d\mu)$ is compact if and only if lim $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• East Asian mathematical journal
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• v.27 no.3
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• pp.373-380
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• 2011

In this paper L-fuzzy ${\omega}$-closed and L-fuzzy ${\omega}$-open sets are introduced. Also a new class of L-fuzzy topological space called L-fuzzy ${\omega}$-basically disconnected space is introduced. Several characterizations and some interesting properties are also given.

• 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 CROP SCIENCE
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• v.38 no.6
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• pp.560-565
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• 1993

This study was conducted to obtain basic information for breeding materials on the oil quality improvement of perilla seeds. Oil contents and omega(${\omega}$)fatty acid compositions of seeds were investigated to 317 varieties of domestic perillas. Oil contents of 317 perilla varieties ranged from 35.6 to 55.3 with 44.5% of varietal mean. The major omega fatty acids contained in the oil were oleic acid(${\omega}$-9) 15.2%, linoleic acid(${\omega}$-36) 13.9% and linolenic acid(${\omega}$-3) 63.1% in the mean value. Varietal variation of $\omega$-9, 6 and 3 fatty acids ranged of 9.5～21.4%, 9.1～20.4% and 50.6～70.5% respectively. Unsaturated fatty acid were averaged 92.2% of seed oil in fatty acid composition. The ratios of ${\omega}$-6 to ${\omega}$-3 ranged of 0.13～0.34%(0.22% in mean value). The highest linolenic acid variety was Yecheonjong being 70.5%. The lowest variety in rations of ${\omega}$-6 to ${\omega}$-3 was Goseongjong being 0.13%. Oil content showed positive correlation with stearic acid and linolenic acid, while the negative correlation with oil content and linoleic acid. On the other hand, A significant negative correlation were showed between lionolenic acid and the ratios ${\omega}$-6 / ${\omega}$-3 fatty acid, saturated fatty acid. Saturated fatty acid was highly correlated with unsaturated fatty acid negatively being r=-0.723$^{**}$

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.467-489
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• 1994

Let $\Omega$ be a closed and bounded polygonal domain in R$^2$, or a closed line segment in R$^1$ with boundary $\Gamma$, such that there exists an invertible mapping T : $\Omega$ \longrightarrow $\Omega$ with the following correspondence: x$\in$$\Omega$ ↔ x = T(x) $\in$$\Omega$, (1.1) and (1.2) t $\in$ U$\sub$p/($\Omega$) ↔ t = to T$\^$-1/ $\in$ U$\sub$p/($\Omega$), where $\Omega$ denotes the corresponding reference elements I = [-1,1] and I ${\times}$ I in R$^1$ and R$^2$ respectively, (1.3) U$\sub$p/($\Omega$) = {t : t is a polynomial of degree $\leq$ p in each variable on $\Omega$}, and (1.4) U$\sub$p/($\Omega$) = {t : t = to T $\in$ U$\sub$p/($\Omega$)}.(omitted)

• Journal of Nutrition and Health
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• v.29 no.8
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• pp.849-860
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• 1996

The supply of different fatty acids during the development period has significant effects. This study examined the effects of dietary $\omega$3 and $\omega$6 fatty acid compositions on phospholipids (PLs) of RBC and rat brain subcellular fractions (synaptosome, microsome, mitochondria), and on learning ability of the 2nd generation rat. Rats were fed experimental diets 3-4 wks prior to the conception. Early in the lactation period, the feeding mothers were exchanged. Diets consisted of 10% fat(by weight), which was either safflower oil('S') poor in $\omega$3 fatty acids or computer-searched mixed oil('M') with P/M/S ratio, 1/1.4/1 and $\omega$6/$\omega$3 ratio, 6.1/1. The 'S' and 'M' rats were subdivided further into SS, SM, MS & MM rats according to their lactation stauts. At 3 (weaning) & 9 wks of age, the percentage of total $\omega$3 fatty acids to their lactation status. At 3 (weaning) & 9 wks of age, the percentage of total $\omega$3 fatty acids and the ratios of $\omega$3/$\omega$6 fatty acids in PLs of RBC and brain subcellular fractions in SM and MM groups fed milk from the mixed oil-fed mothers for 2 wks tended to be higher than those in SS and MS groups respectively. In contrast, the concentrations of $\omega$6 fatty acids, especially 22:5$\omega$6 in all fractions, were significantly lower in the SM & MM groups compared to those of the SS & MS groups respectively. In contrast, the concentration of $\omega$6 fatty acids, especially 22:5$\omega$6 in all fractions, were significantly lower in the SM & MM groups compared to those of the SS & MS groups, The values for the DHA$\omega$3/22:5$\omega$6 ratios after the lactation period were markedly higher in the groups (SM & MM) which were reared by mixed oil(MO) fed mothers. In carring out Y-water maze at 9th wk of age, the SM(4.2$\pm$0.5) & MM (5.3$\pm$0.5) groups made significantly less errors compared to the SS(6.2$\pm$0.6, p<0.05 compared with SM) & MM (7.2$\pm$0.5, p<0.05 compared with MM) groups which were lactated by the safflower oilfed mothers. Therefore, by feeding a balanced fatty acid diet from the lactation period up to 9 wks of age as compared with the groups fed $\omega$3 fatty acid-deficient diet regardless of mother's diet given before parturition. The levels of DHA(synaptosome) and 22:5$\omega$3 (mitochondria) were positively correlated not only with these values in RBC but also with visual discriminating ability. The levels of DHA and 22:5$\omega$3 in RBC can, therfore, reflect visual discriminatng ability in the rat.

• 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.

• 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 the Korean Applied Science and Technology
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• v.18 no.1
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• pp.67-77
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• 2001

In search for several fatty acid with unusual structure in vegetable oils, we have found that unknown peaks were shown on GLC in the analysis of fatty acids of the lipids from the pulp of ripened jujube (Zizypus jujuba var. inermis) fruits. These fatty acids were identified as a series of cis-monoenoic acids with ${\omega}-5$ double bond system such as $C_{14:1{\omega}5}$, $C_{16:1{\omega}5}$ and $C_{18:1{\omega}5}$, including ${\omega}-7$ fatty acid as $C_{16:1{\omega}7}$ and $C_{18:1{\omega}7}$, by GLC, solid-phase extraction silver ion-column chromatographic, GLC-mass spectrometric and IR techniques. First of all, total fatty acid methyl esters were resolved into saturated and branched fatty acid, monoenoic acid, dienoic acid, and trienoic acid fraction, respectively, with 100% dichloromethane (DCM), DCM/acetone (9:1, v/v) 100% acetone, and acetone/ acetonitrile (97:3, v/v) solvent system. Unknown fatty acids were included in the monoenoic fraction and were confirmed to have cis-configuration by IR. Picolinyl esters of monoenoic fatty acids gave distinct molecular ion peak and dominant diagnostic peaks, for example, m/z 317, 220 and 260 fragment for $cis-C_{14:1{\omega}5}$, m/z 345, m/z 248 and 288 fragment for $cis-C_{16:1{\omega}5}$ and m/z 373, m/z 276 and 316 fragment for $cis-C_{18:1{\omega}5}$. In this way the occurrence of $cis-C_{16:1{\omega}7}$ and $cis-C_{18:1{\omega}7}$ could be deduced from the appearance of prominent fragments as m/z 345, 220 and 260, and m/z 373, 248 and 280. Level of total ${\omega}-5$ fatty acids amounted to about 30% in the fatty acid composition with the predominance of $C_{16:1{\omega}5}$ $ (18.7{\sim}25.0%)$, in the semi-ripened and/or ripened samples collected in September 14 ($C_{16:1{\omega}5}$ ; 18.7%, $C_{14:1{\omega}5}$ ; 3.6% and $C_{18:1{\omega}5}$ ; 3.0%), September 22 ($C_{16:1{\omega}5}$ ; 25.0%, $C_{14:1{\omega}5}$ ; 1.4% and $C_{18:1{\omega}5}$ ; 2.6%), and October $7 (C_{16:1{\omega}5}$ ; 24.7%, $C_{14:1{\omega}5}$ ; 7.7% and $C_{18:1{\omega}5}$ ; 2.5%). However, the lipids extracted from unripened jujube in July and August contain these unusual fatty acids as low as negligible. It could be observed that the level of ${\omega}-5$ fatty acids in the pulps increased sharply with an elapse of ripening time of jujube fruits. Other monoenoic fatty acids with ${\omega}-7$ series, $C_{16:1{\omega}7}$ (palmitoleic acid) and $C_{18:1{\omega}7}$ (cis-vaccenic acid) could be detected. And in the lipids of the kernel and leaf of jujube, none of ${\omega}-5$ fatty acids could be detected.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.483-488
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• 2007

Given a set ${\Omega}$, the notion of ${\Omega}-fuzzy$ ideals in a near-ring is introduced, and related properties are investigated. Using fuzzy ideals, ${\Omega}-fuzzy$ ideals are described. Conversely, fuzzy ideals are constructed by using ${\Omega}-fuzzy$ ideals.