• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.17-28
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• 2018

In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.

• Journal of Astronomy and Space Sciences
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• v.5 no.2
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• pp.111-122
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• 1988

The short and long periodic perturbations and secular perturbation due to the geopotentials of degree $J_2$ and $J_3$ which affect orbital elements of a near-circular orbiting satellite are obtained by the analytical method. The singular points due to a small denominator e in the perturbation equations can be excluded using one of the methods introduced by Taff(1985), which substitutes $e_s=esin\omega,\;e_c=ecos\omega\;and\;\ell=\omega+M$ for the orbital elements e, $\omega$ and M. We determined the mean orbital elements of the meteorological satellite NOAA-10 using the Walter (1967)'s iterative procedure and compared with Brouwer's mean orbital elements determined at NASA. The mean orbital elements a, ⅰand $\Omega$ are consistent with those of NASA but the mean orgital elements e, $\omega$ and M have some deviations from those of NASA. According to the our results, it is not suitable for the polar orbiting satellites to use the Taff's proposal for excluding the singular points, which substitutes e, $\omega$ and M by $e_s=esin(\Omega+\omega),\;e_c=ecos(\Omega+\omega)\;and\;L=\Omega+\omega+M$.

• 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.

• YAKHAK HOEJI
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• v.41 no.3
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• pp.298-304
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• 1997

Molecular mechanics and conformation search methods were carried oyt to investigate the relationship between conformations and thromboxane synthetase ingibitory activities of om ega-pyridylalkenoic acids. The initial geometries of ${\omega}$-pyridylalkenoic acids and heme part of cytochrome P-450 were obtained from MM+ geometry optimization. The bond lenths and angles were not varied by step during the conformation searching. Stable conformers of some ${\omega}$-pyridylalkenoic acids were obtained by comformational search method. The distances were 8.5~10.8 ${\AA}$- between N atom at 3-position of pyridine ring and C atom at carboxylic group of stable ${\omega}$-pyridylalkenoic acids. The conformations of ${\omega}$-pyridylalkenoic acids and heme part complex were determined by same method. In theses structures, benzene ring and ethylene group in ${\omega}$-pyridylalkenoic acids are making the structure more rigid and increase inhbitory activity. The electron donating groups in C atom shich is connected to pyridine ring also increase activity.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.9-9
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• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• 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.

• Nutrition Research and Practice
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• v.15 no.4
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• pp.468-478
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• 2021

BACKGROUND/OBJECTIVES: This study aimed to analyze the association between dietary omega-3 fatty acid intake and depression in postmenopausal women using data from the Korea National Health and Nutrition Examination Survey (KNHANES) VI. SUBJECTS/METHODS: The KNHANES is a cross-sectional nationwide health and nutrition survey. Dietary data, including omega-3 fatty acids, were assessed using the 24-h recall method. Depression was evaluated using a survey questionnaire. The association between dietary omega-3 fatty acids and depression was evaluated using multivariate logistic regression analysis. Depression, according to the dietary omega-3 fatty acid intake, was expressed as the odds ratio (OR) with a 95% confidence interval (CI). A total of 4,150 postmenopausal women were included in the analysis. RESULTS: In the fully-adjusted model, the group with the highest dietary omega-3 fatty acid intake significantly showed lower prevalence of depression than the group with the lowest intake (OR, 0.52; 95% CI, 0.33-0.83); a significant linear trend was detected (P for trend = 0.04). According to the dose-response analysis using cubic restricted spline regression, this association was linear and monotonic (P for non-linearity = 0.32). CONCLUSIONS: In this study, the dietary omega-3 fatty acid intake in postmenopausal women was inversely proportional to depression in a dose-response manner. Large cohort studies are needed to verify the causality between omega-3 fatty acids and depression in Korean postmenopausal women.

• Korean Journal of Optics and Photonics
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• v.2 no.1
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• pp.31-35
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• 1991

The third-order nonlinear optical susceptibilities of $\beta$-carotene, retinal and retinol have been measured using self-induced ellipse rotation and dc-Kerr effects. The strengths of $\chi$1221(-$\omega$, $\omega$, -$\omega$, $\omega$) and $\chi$1221(-$\omega$, $\omega$, 0, 0) measured by the two different methods are not different each other significantly. And it is observed that the strength of the third order nonlinear optical susceptibility is relatively insensitive to the conformational difference between retinal and retinol. It is also demonstrated that the third order nonlinear optical susceptibility of long-chained organic molecules is dependent upon the number of the double-bonds.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1441-1462
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• 2018

In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.