• Journal of the Korean Statistical Society
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• 제3권1호
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• pp.13-16
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• 1974

In my former paper [3] I defined an almost periodicity of weakly sationary random processes (a.p.w.s.p.) and presented some basic results of it. In this paper I shall present some notes on the Fourier series of an a.p.w.s.p., resulting from [3]. All the conditions at the introduction of [3] are assumed to hold without repreating them here. The essential facts are as follows : The weakly stationary process $X(t,\omega), t\in(-\infty,\infty), \omega\in\Omega$, defined on a probability space $(\Omega,a,P)$, has a spectral representation $$X(t,\omega)=\int_{-\infty}^{infty}{e^{it\lambda\xi}(d\lambda,\omega)},$$ where $\xi(\lambda)$ is a random measure. Then, the continuous covariance $\rho(\mu) = E(X(t+u) X(t))$ has the form $$\rho(u)=\int_{-\infty}^{infty}{e^{iu\lambda}F(d\lambda)},$$ $E$\mid$\xi(\lambda+0)-\xi(\lambda-0)$\mid$^2 = F(\lambda+0) - F(\lambda-0) \lambda\in(-\infty,\infty)$, assumimg that $\rho(u)$ is a uniformly almost periodic function.

• Annals of Clinical Neurophysiology
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• 제17권2호
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• pp.68-72
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• 2015

Background: The effects of omega-3 polyunsaturated fatty acids (PUFAs) on cerebral vessels have not been clarified until now. Thus we investigated the efficacy of omega-3 PUFAs supplementation on cerebral blood flow velocity and vascular resistance via transcranial doppler (TCD). Methods: Consecutive twenty patients (13 male and 7 female) with at least 1 cerebrovascular risk factor or a known cerebrovascular disease were enrolled. Patients were treated with omega-3 PUFAs (1 g, two times per day) for 12 weeks. Cerebral blood flow velocity, resistance index, and pulsatile index were checked before and after 12 weeks of treatment using TCD. Results: The change of resistance index in right MCA (from $0.58{\pm}0.07$ to $0.55{\pm}0.07$, p = 0.042) and left PCA (from $0.56{\pm}0.07$ to $0.53{\pm}0.06$, p = 0.037) showed significant improvement after 12 weeks of omega-3 PUFAs treatment. The changes in other vessels, however, failed to show any significant changes compared to the baseline. Conclusions: Omega-3 PUFAs treatment showed feasible efficacies for cerebral vascular resistances in this open label trial. To confirm these results, larger samples of patients and longer period of follow-up is warranted.

• Nutritional Sciences
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• 제5권2호
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• pp.68-74
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• 2002

Studies of the relationship between the composition of serum fatty acids and blood pressure are complex and controversial. Fatty acids, important constituents of biological membranes, could potentially affect vasoreactivities including blood pressure. In this study the compositions of fatty acids in serum phospholipids were compared between three types of hypertensive subjects (men, pre-menopausal women, and post-menopausal women) and their respective nrmotensive controls. Serum lipids were extracted and phospholipids were separated by thin layer chromatography. The percentage of palmitic acid (16 : 0) in serum phospholipids was significantly higher and the percentage of stearic acid (18 : 0) was significantly lower in all three hypertensive groups, compared with their corresponding control groups. Only in the group of post-menopausal women, palmitic acid was closely associated wish increases in both systolic (SBP) and diastolic blood pressure (DBP), while stearic acid was associated with decreases in both SBP and DBP. The polyunsaturated fatty acids in serum phospholipids behaved differently from saturated fatty acids. The ratios of products / precursor fatty acids, such as $\sumLCPUFA\omega6/18 : 2\omega$6, 20 : 4$\omega$6/18 : 2$\omega$6, ∑LCPUFA$\omega$3/18 : 3$\omega$3 and 22 : 6$\omega$3/20 : 5$\omega$3, were all clearly associated with both SBP and DBP in hypertensive, post-menopausal women. Desaturation and elongation in fatty acid metabolism could affect the bioavailability of eicosanoid precursors. Changes in the constituent fatty acids of phospholipids and eicosanoid precursors may also influence fluidity, ionic transport, hormone receptors and enzyme activities in biological membranes. In conclusion, both systolic and diastolic blood pressure in post-menopausal women was positively associated with the level of palmitic acid, and negatively associated with the level of stearic acid, in serum phospholipids. The relationships between serum phospholipid-$\omega$6 and $\omega$3 series fatty acids and blood pressure in women, especially in post-menopausal women, require further investigation by taking into consideration hormonal status and eicosanoid metabolism. Funker study is needed to determine the value of dietary manipulation of fatty acid constituents of serum phospholipids, relating to hypertension in women.

• Wind and Structures
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• 제15권5호
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• pp.409-421
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• 2012

In this paper, the method of introducing additional source/sink terms in the turbulence and momentum transport equations was applied to appropriately model the effect of the tree canopy. At first, the new additional source term for the turbulence frequency ${\omega}$ equation in the SST k-${\omega}$ model was proposed through theoretical analogy. Then the new source/sink term model for the SST k-${\omega}$ model was numerically verified. At last, the proposed source term model was adopted in the wind environment optimal design of the twin high-rise buildings of CABR (China Academy of Building Research). Based on the numerical simulations, the technical measure to ameliorate the wind environment was proposed. Using the new inflow boundary conditions developed in the previous studies, it was concluded that the theoretically reasonable source term model of the SST k-${\omega}$ model was applicable for modeling the tree canopy flow and accurate numerical results are obtained.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.217-231
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• 2010

We consider a class of elliptic problems of a logistic type $$-div(|{\nabla}_u|^{m-2}{\nabla}_u)\;=\;w(x)u^q\;-\;(a(x))^{\frac{m}{2}}\;f(u)$$ in a bounded domain of $\mathbf{R}^N$ with boundary $\partial\Omega$ of class $C^2$, $u|_{\partial\Omega}\;=\;+{\infty}$, $\omega\;\in\;L^{\infty}(\Omega)$, 0 < q < 1 and $a\;{\in}\;C^{\alpha}(\bar{\Omega})$, $\mathbf{R}^+$ is non-negative for some $\alpha\;\in$ (0,1), where $\mathbf{R}^+\;=\;[0,\;\infty)$. Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.

• Korean Journal of Mathematics
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• 제8권2호
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• pp.155-162
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• 2000

For a sequence $\{{\eta}_m\}_m$ of unit vectors in $\mathbb{C}^n$, we consider the associated linear functional ${\omega}$ on the Cuntz algebra $\mathcal{O}_n$. We show that the restriction ${\omega}{\mid}_{UHF_n}$ is the product pure state of a subalgebra $UHF_n$ of $\mathcal{O}_n$ such that ${\omega}{\mid}_{UHF_n}={\otimes}{\omega}_m$ with ${\omega}_m({\cdot})$ < ${\cdot}{\eta}_m,{\eta}_m$ >. We study product pure states of UHF and obtain a concrete description of them in terms of unit vectors. We also study states of $UHF_n$ which is the restriction of the linear functionals on $O_n$ associated to a fixed unit vector in $\mathbb{C}^n$.

• 대한수학회보
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• 제50권5호
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.

• 한국응용과학기술학회지
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• 제16권1호
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• pp.45-57
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• 1999

This study was designed to examine the effect of ${\omega}-3$ fatty acid, linlenic acid, EPA, DHA on serum lipid and cytokines of male rats(Sprague-Dawley). Animals of 3 groups were administrated perilla oil, salmoon oil, and tuna oil of 0.4 $m{\ell}/day$ for 8 weeks respectively. These oils were used for a source of linolenic acid, EPA and DHA. ${\omega}-3$ polyunsaturated fatty acid decreases significantly body weight, serum $PGE_2$ content and serum cytokines content of the rat, and increases internal organs weight, specially liver weight and serum HDL-cholesterol level of the rat. In the results, authors propose to use perilla oil for source of effective ${\omega}-3$ poly-unsaturated fatty acid(linolenic acid) to Prevent cardiovascular and immune diseases.

• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.195-202
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• 2009

This paper deals with very weak solutions of the A-harmonic equation $divA(x,{\nabla}u)$ = 0 (*) with the operator $A:{\Omega}{\times}R^n{\rightarrow}R^n$ satisfies some coercivity and controllable growth conditions with Muckenhoupt weight. By using the Hodge decomposition with weight, a regularity property is proved: There exists an integrable exponent $r_1=r_1({\lambda},n,p)$ < p, such that every very weak solution $u{\in}W_{loc}^{1,r}({\Omega},{\omega})$ with $r_1$ < r < p belongs to $W_{loc}^{1,p}({\Omega},{\omega})$. That is, u is a weak solution to (*) in the usual sense.

• 생명과학회지
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• 제20권4호
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• pp.561-571
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• 2010

대장암은 미국 등 서양 국가뿐만 아니라 국내에서도 2번째로 많이 발병이 되는 암으로 알려져 있다. 역학조사에 의하면 ${\omega}3$-PUFAs를 많이 섭취한 인종에서 대장암 발생빈도가 감소하고 최근 ${\omega}3$-PUFAs는 수종의 암에 대해 항암작용을 나타낸다고 한다. 이에 본 연구에서는 대장암에서 DHA 등 ${\omega}3$-PUFA의 항침윤 기전을 규명하여 다음과 같은 결과를 얻었다. DHA및 EPA는 대장암 세포주 SW480의 증식을 농도 의존적으로 억제하였으나 AA는 거의 영향이 없었으며 TUNEL assay로 apoptotic cell death가 확인 되었다. DHA는 $\beta$-catenin 단백 및 TCF/LEF luciferase 활성을 농도 의존적으로 억제 하였다. SW480 세포의 침윤능은 DHA의 농도에 의존적으로 억제되었다. DHA처리 후 MMP-9 및 MMP-2 mRNA양이 감소되었을 뿐만 아니라 그 promoter의 reporter 활성도 억제되었다. NF-kB 및 p-IkB 단백질양도 DHA의 처리농도에 의존적으로 감소하였으며 NF-kB promoter의 활성도 억제되었다. 이상의 결과로 ${\omega}3$-PUFA는 대장암에서 NF-kB 신호전달 차단에 의한 MMP-2 및 MMP-9 발현을 억제하여 침윤을 억제하여 항암작용을 나타낼 수 있음을 시사하며, 따라서 ${\omega}3$-PUFA는 대장암의 예방 및 치료에 유용하게 사용될 수 있으리라 생각된다.