• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.261-267
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• 2007

We show the existence of the positive solution for the system of the following nonlinear wave equations with Dirichlet boundary conditions $$u_{tt}-u_{xx}+av^+=s{\phi}_{00}+f$$, $$v_{tt}-v_{xx}+bu^+=t{\phi}_{00}+g$$, $$u({\pm}\frac{\pi}{2},t)=v({\pm}\frac{\pi}{2},t)=0$$, where $u_+=max\{u,0\}$, s, $t{\in}R$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}=1$ of the eigenvalue problem $u_{tt}-u_{xx}={\lambda}_{mn}u$ with $u({\pm}\frac{\pi}{2},t)=0$, $u(x,t+{\pi})=u(x,t)=u(-x,t)=u(x,-t)$ and f, g are ${\pi}$-periodic, even in x and t and bounded functions in $[-\frac{\pi}{2},\frac{\pi}{2}]{\times}[-\frac{\pi}{2},\frac{\pi}{2}]$ with $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}f{\phi}_{00}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g{\phi}_{00}=0$.

• Journal of Life Science
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• v.32 no.2
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• pp.86-93
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• 2022

Lupeol is a type of pentacyclic triterpene and has been reported to have pharmacological activities against various diseases; however, the effect of lupeol on glucose absorption has not been elucidated yet. This study aimed to investigate the effect of lupeol on glucose uptake in 3T3-L1 adipocytes. Lupeol significantly facilitated glucose uptake by translocating glucose transporter type 4 (GLUT4) to the plasma membrane of the 3T3-L1 adipocytes, which was related to activation of the phosphoinositide 3-kinase (PI3K)/protein kinase B (AKT) and 5 'adenosine monophosphate-activated protein kinase (AMPK) pathways. In the PI3K/AKT pathway, lupeol stimulates the phosphorylation of insulin receptor substrate 1 (IRS-1), which activates PI3K. Its activation by lupeol promotes the phosphorylation of AKT, but not the atypical protein kinase C isoforms ζ and λ. Lupeol also promoted the phosphorylation of AMPK. The activation of AMPK increased the expressions of the plasma membrane GLUT4 and the intracellular glucose uptake. The increase in the glucose uptake by lupeol was suppressed by wortmannin (PI3K inhibitor) and compound C (AMPK inhibitor) in the 3T3-L1 adipocytes. The results indicate that lupeol can facilitate glucose uptake by increasing insulin sensitivity through the stimulation of the expression of plasma membrane glucose transporter type 4 via the PI3K/AKT and AMPK pathways in the 3T3-L1 adipocytes.

• Honam Mathematical Journal
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• v.28 no.2
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• pp.261-277
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• 2006

In this paper a new class of sets called ${\pi}gs$-closed sets is introduced and its properties are studied. Further the notions of ${\pi}gs$-$T_{1/2}$ spaces and ${\pi}gs$-continuity are introduced.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.22 no.5
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• pp.281-290
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• 1989

Growth of the Korean pomfret, Pampus echinogaster, captured in the East China Sea from January to December 1987, was estimated by annual rings on the vertebral centrum. The time of annual ring formation was approximately during September and October. Von Ber-talanffy growth equations derived from the mean back-calculated fork length(cm) at each age were as follows: for females, $L_{t}=29.17(1-e xp(-0.3213(t+0.7601)))$, for males, $L_t=28.21(1-e xp(-0.3169(t+0.8284)))$, and for sexes combined, $L_t=29.00(1-e xp(-0.3228(t+0.7361)))$, Seasonal growth equations derived from the mean observed fork length (cm) at age by month were as follows: for females, $L_t=29.2(1-e xp(-0.3458(t+0.8182)+(0.3458/2\pi)sin2\pi(t+0.027)))$, and for males, $L_t=28.2(1-e xp(-0.2789(t+1.5913)+(0.2789/2\pi)sin2\pi(t-0.1062)))$.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.339-345
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• 2008

We prove the existence of the positive solution for the nonlinear system of suspension bridge equations with Dirichlet boundary condition and periodic condition $$\{u_{tt}+u_{xxxx}+av^+=1+{\epsilon}_1h_1(x,t)\text{ in }(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\v_{tt}+v_{xxxx}+bu^+=1+{\epsilon}_2h_2(x,t)\text{ in }(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small numbers and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel}h_1{\parallel}={\parallel}h_2{\parallel}=1$.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• Journal of Life Science
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• v.31 no.1
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• pp.1-9
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• 2021

Brown seaweeds have been shown to decrease blood glucose levels and improve insulin sensitivity previously. In this study, we investigated the effect of fucoidan, a complex polysaccharide derived from brown seaweeds, on glucose uptake to improve insulin resistance, and examined its mechanism of action in 3T3-L1 adipocytes. We observed that fucoidan significantly increased glucose uptake and it was related to an increased expression of plasma membrane-glucose transporter 4 (PM-GLUT4) in 3T3-L1 adipocytes. Fucoidan treatment increased the activation of phosphatidylinositol-3-kinase (PI3K) and the phosphorylation of insulin receptor substrate 1 (IRS1tyr) compared with that of the control cells. Fucoidan also promoted the phosphorylation of Akt and protein kinase C (PKC)-λ/ζ compared to that of the control cells. Moreover, fucoidan significantly upregulated acetyl-CoA-carboxylase (ACC) and adenosine monophosphate - activated protein kinase (AMPK) phosphorylation. As a result, translocation of GLUT4 was significantly enhanced in 3T3-L1 adipocytes, which significantly promoted glucose uptake via the PI3K/AMPK pathways. The elevation of glucose uptake by fucoidan was blocked by inhibitor of PI3K and inhibitor of AMPK in 3T3-L1 adipocytes. These findings indicate that fucoidan might ameliorate glucose uptake through GLUT4 translocation to the plasma membrane by activating the PI3K/Akt and AMPK pathways in 3T3-L1 adipocytes. Fucoidan is thought to be of high material value to diabetes treatments and functional foods.

• Journal of Life Science
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• v.32 no.10
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• pp.762-770
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• 2022

Hyperglycemia in type 2 diabetes can be alleviated by promoting cellular glucose uptake. Betulinic acid (3β,-3-hydroxy-lup-20(29)-en-28-oic acid) is a pentacyclic lupane-type triterpenoid compound. Although there have been studies on the antidiabetic activity of betulinic acid, studies on cellular glucose uptake are lacking. We investigated the effects of betulinic acid on glucose uptake and its mechanism of action in 3T3-L1 adipocytes. Betulinic acid significantly stimulated glucose uptake in 3T3-L1 adipocytes by increasing the phosphorylation of the insulin receptor substrate 1-tyrosine (IRS-1tyr) in the insulin signaling pathway, which in turn stimulated the activation of phosphoinositide 3-kinase (PI3K) and the phosphorylation of protein kinase B (Akt). The activation of PI3K and Akt by betulinic acid translocated glucose transporter 4 to the plasma membrane (PM-GLUT4), thereby increasing the expression of PM-GLUT4 and thus stimulating cellular glucose uptake. Betulinic acid also significantly increased the phosphorylation/activation of AMP-activated protein kinase (AMPK) and acetyl-CoA carboxylase. The activation of PI3K and AMPK by betulinic acid was confirmed using the PI3K inhibitor wortmannin and the AMPK inhibitor compound C. The increase in glucose uptake induced by betulinic acid was significantly decreased by wortmannin and compound C in the 3T3-L1 adipocytes. These results suggest that betulinic acid stimulates glucose uptake by activating PI3K and AMPK in 3T3-L1 adipocytes.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.271-279
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• 1995

In 1986, Fabry, Mawhin and Nkashama [1] have considered periodic solutios for Lienard equation $$ (1_s) x" + f(x)x' + g(t,x) = s, $$ where s is a real parameter, f and g are continuous functions, and g is $2\pi$-periodic in t and have proved that if $$ (H) lim_{$\mid$x$\mid$\to\infty} g(t,x) = \infty uniformly in t \in [0,2\pi], $$ there exists $s_1 \in R$ such that $(1_s)$ has no $2\pi$periodic solution if $s< s_1$, and at least one $2\pi$-periodic solution if $s = s_1$, and at least two $2\pi$-periodic solutions if $s > s_1$.s_1$.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.17 no.3
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• pp.249-256
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• 1988

The purpose of this paper is to research the estimations of the indoor natural temperature in a case of the earth sheltered space and the 1st basement room in comparison with a conventional housing. The result of this study can be summerized as follows: The natural temperature of the earth sheltered house Summer : $${\theta}es=27.0+1.65sin(2{\pi}/24{\cdot}T-1.34)$$ Winter : $${\theta}ew=11.5+1.15sin(2{\pi}/24{\cdot}T-1.61)$$ The natural temperature of the 1st basement space Summer : $${\theta}us=25.5+1.00sin(2{\pi}/24{\cdot}T-1.72)$$ Winter : $${\theta}uw=13.9+1.10sin(2{\pi}/24{\cdot}T-2.29)$$ From the results of the stated above, we can calculate the cooling and heating load in the earth sheltered house and the underground space exactly and easily at Taejeon City.