• 제목/요약/키워드: Omega Methods

검색결과 261건 처리시간 0.025초

ENLARGING THE BALL OF CONVERGENCE OF SECANT-LIKE METHODS FOR NON-DIFFERENTIABLE OPERATORS

  • Argyros, Ioannis K.;Ren, Hongmin
    • 대한수학회지
    • /
    • 제55권1호
    • /
    • pp.17-28
    • /
    • 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.

지구 중력장에 기인한 원궤도에 가까운 인공위성의 평균 궤도요소 (Mean Orbital Elements of a Near-Circular Orbiting Artificial Satellite due to the Earth's Zonal Potentials)

  • 박필호;최규홍
    • Journal of Astronomy and Space Sciences
    • /
    • 제5권2호
    • /
    • pp.111-122
    • /
    • 1988
  • 지구의 비대칭 중력장 $J_2$$J_3$가 원궤도에 가까운 인공위성의 궤도요소에 미치는 장, 단주기 섭동과 영년섭동을 해석적 방법으로 구하였다. 이 때 궤도의 이심률이 작은 경우에 섭동방정식에서 발생하는 특이점은 Taff(1985)가 제시한 방법중 궤도요소 e, $\omega$, M을 $e_s$=$esin\omega$, $e_c=e\;cos\;\omega$, $\ell=\omega+M$으로 치환하는 방법을 사용하여 제거시켰다. Walter(1967)의 방법을 이용하여 기상위성 NOAA-10호의 평균궤도요소를 결정하였고 이를 NASA의 Brouwer 평균 궤도요소와 비교하였다. 평균 궤도요소 a, i, $\Omega$는 TBUS의 결과와 거의 일치하나 평균 궤도요소 e, $\omega$, M은 약간의 차이를 보였다. 그리고 특이점을 제거하기 위한 Taff의 방법 중 e, $\omega$, M 대신에 $e_s=e\;sin(\Omega+\omega)$, $e_c=e\;cos(\Omega+\omega)$, $L=\Omega+\omega+M$으로 치환하는 방법이 극궤도위성에는 부적합한 것으로 나타났다.

  • PDF

Association between Omega Fatty Acid Intake and Suicidality : Sex Differences in the General Korean Population

  • Hur, Yang-Im;Lee, Jung Hyun
    • 정신신체의학
    • /
    • 제27권2호
    • /
    • pp.181-190
    • /
    • 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.

${\omega}$-피리딜 알켄산의 형태와 활성간의 상관관계 (The Correlation Between Conformations and Activities of ${\omega}$-Pyridylalkenoic Acids)

  • 이종달;도성탁
    • 약학회지
    • /
    • 제41권3호
    • /
    • pp.298-304
    • /
    • 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.

  • PDF

Singular Representation and Finite Element Methods

  • 김석찬
    • 한국전산응용수학회:학술대회논문집
    • /
    • 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
    • /
    • pp.9-9
    • /
    • 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.

  • PDF

The effect of long-term supplementation with different dietary ${\omega}-6/{\omega}-3$ ratios on mineral content and ex vivo prostaglandin E2 release in bone of growing rabbits

  • Alnouri, Doha Mustafa;El-Din, Mohamed Fekry Serag;Al-Khalifa, Abdulrhman Salih
    • Nutrition Research and Practice
    • /
    • 제8권4호
    • /
    • pp.360-367
    • /
    • 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.

Association between dietary omega-3 fatty acid intake and depression in postmenopausal women

  • Chae, Minjeong;Park, Kyong
    • Nutrition Research and Practice
    • /
    • 제15권4호
    • /
    • pp.468-478
    • /
    • 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.

The Third-Order Nonlinear Optical Susceptibilities of Long-Chained Organic Molecules

  • Cho, Chang-Ho;Ko, Do-Kyeong;Lee, Jai-Hyung;Chang, Joon-Sung
    • 한국광학회지
    • /
    • 제2권1호
    • /
    • pp.31-35
    • /
    • 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.

  • PDF

ON A CLASS OF QUASILINEAR ELLIPTIC EQUATION WITH INDEFINITE WEIGHTS ON GRAPHS

  • Man, Shoudong;Zhang, Guoqing
    • 대한수학회지
    • /
    • 제56권4호
    • /
    • pp.857-867
    • /
    • 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.

EXISTENCE OF SOLUTIONS FOR FRACTIONAL p&q-KIRCHHOFF SYSTEM IN UNBOUNDED DOMAIN

  • Bao, Jinfeng;Chen, Caisheng
    • 대한수학회보
    • /
    • 제55권5호
    • /
    • pp.1441-1462
    • /
    • 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.