• 대한수학회보
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• 제47권1호
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• pp.81-87
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• 2010

In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem(BVP) $-D_0^{\alpha}+u(t)=\lambda[f(t, u(t))+q(t)]$, 0 < t < 1 u(0) = u(1) = 0, where $\lambda$ > 0 is a parameter, 1 < $\alpha$ $\leq$ 2, $D_{0+}^{\alpha}$ is the standard Riemann-Liouville differentiation, f : [0, 1] ${\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is continuous, and q(t) : (0, 1) $\rightarrow$ [0, $+\infty$] is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when $\lambda$ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.

• 대한수학회보
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• 제53권5호
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• pp.1585-1596
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• 2016

In this paper we investigate the existence of nontrivial solutions for the following fractional boundary value problem (FBVP) $$\{_tD_T^{\alpha}(_0D_t^{\alpha}u(t))={\nabla}W(t,u(t)),\;t{\in}[0,T],\\u(0)=u(T)=0,$$ where ${\alpha}{\in}(1/2,1)$, $u{\in}{\mathbb{R}}^n$, $W{\in}C^1([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ and ${\nabla}W(t,u)$ is the gradient of W(t, u) at u. The novelty of this paper is that, when the nonlinearity W(t, u) involves a combination of superquadratic and subquadratic terms, under some suitable assumptions we show that (FBVP) possesses at least two nontrivial solutions. Recent results in the literature are generalized and significantly improved.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.711-721
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• 2010

Values of the parameter $\lambda$ are determined for which there exist positive solutions of the system of boundary value problems, $u^{(n)}+{\lambda}p(t)f(\upsilon)=0$, $\upsilon^{(n)}+{\lambda}q(t)g(u)=0$, for $t\;{\in}\;[a,b]$, and satisfying, $u^{(i)}(a)=0$, $u^{(\alpha)}(b)=0$, $\upsilon^{(i)}(a)=0$, $\upsilon^{(\alpha)}(b)=0$, for $0\;{\leq}\;i\;{\leq}\;n-2$ and $1\;{\leq}\;\alpha\;\leq\;n-1$ (but fixed). A well-known Guo-Krasnosel'skii fixed point theorem is applied.

• Communications for Statistical Applications and Methods
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• 제11권3호
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• pp.631-641
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• 2004

In this paper, a model for an inventory whose stock decreases with time is considered. When a deliveryman arrives, if the level of the inventory exceeds a threshold $\alpha$, no stock is delivered, otherwise a delivery is made. It is assumed that the size of a delivery is a random variable Y which is exponentially distributed. After assigning various costs to the model, we calculate the long-run average cost and show that there exist unique value of arrival rate of deliveryman $\alpha$, unique value of threshold $\alpha$ and unique value of average delivery m which minimize the long-run average cost.

• International Journal of Industrial Entomology and Biomaterials
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• 제15권2호
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• pp.161-164
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• 2007

While searching for ${\alpha}$-glucosidase inhibitors, the active compound was found in a methanol extract of Burthus martensi Kirsch. The separation of the active compound was performed using various chromatography methods and the physico-chemical properties of the purified compound were characterized. The compound showed very potent inhibitory activity against ${\alpha}-glucosidase$ with an $IC_{50}$ value of $5.3\;{\mu}g/ml$. Lineweaver-Burk plot indicated that its inhibition of ${\alpha}-glucosidase$ was competitive.

• 폴리머
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• 제38권4호
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• pp.411-416
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• 2014

극성을 띠고있어 응집되는 성향이 카본블랙에 비해 강한 실리카의 분산도는 고무 복합소재의 물성을 좌우하는 중요한 요소이다. Wolff는 입자간 상호계수(${\alpha}_F$)를 도입하여 충전제간의 구조발달을 최초로 표현하였다. 하지만, 양기능성 실란의 도입에 따라 형성되는 3차원 구조발달은 표현할 수 없었다. 후에 이를 보완하기 위하여 Wolff의 표현은 복합소재 내 ${\alpha}_F$를 포함하는 구조발달 상호계수 ${\alpha}_C$로 확장되어 표현되었지만, 실험적으로 이 표현을 증명한 연구는 없었다. 이 논문은 구조발달 상호계수인 ${\alpha}_C$를 ${\alpha}_F$(실리카-실리카간 구조발달 상호계수), ${\alpha}_{FP}$(실리카-실란-고무간 구조발달 상호계수), ${\alpha}_P$(고무-고무간 구조발달 상호계수)로 고려하여 단기능성 및 양기능성 실란으로 처리된 실리카가 함유된 복합소재를 실험에 의해 최초로 표현하였다. 구조가 다른 실란들(PTES, OTES, TESPD, TESPT)을 이용하여 구조발달 상호계수 ${\alpha}_C$를 구성하는 ${\alpha}_F$, ${\alpha}_{FP}$, ${\alpha}_P$의 수치들을 측정하고 계산하였다. TESPT가 첨가된 복합소재의 ${\alpha}_C$의 값은 1.64이며, 이를 구성하고 있는 ${\alpha}_F$, ${\alpha}_{FP}$, ${\alpha}_P$는 각각 0.99, 0.31, 0.34로 나타났다.

• Fisheries and Aquatic Sciences
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• 제11권4호
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• pp.212-218
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• 2008

Time series changes in the chlorophyll $\alpha$ concentrations before and after the ship Prestige oil spill on 13 November 2002 were analyzed using NCEP wind data and ocean color data. Following the oil spill, southwesterly winds pushed the oil towards the Spanish coast. In addition, the daily chlorophyll $\alpha$ concentration decreased dramatically from the middle of November to the end of December 2002, with the minimum value being recorded in December. Additionally, the mean chlorophyll $\alpha$ concentration in November and December 2002 was lower than the average value recorded for the same months from 2000 to 2005; however, with the exception of 2000, the concentration was higher in October 2002 before the spill and in January-March 2003 after the spill during the same period from 2000 to 2005.

• Food Science and Biotechnology
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• 제18권2호
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• pp.526-532
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• 2009

Quenching mechanisms and kinetics of $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-tocopherol in photosensitized oxidation of lard were studied. Lard at 0.03, 0.07, 0.11, and 0.3 M in methylene chloride containing $4.4{\times}10^{-6}\;M$ chlorophyll and 0, 0.1, 0.3, and 0.6 mM $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-tocopherol were stored under light for 4 hr, respectively. Oxidation was determined by headspace oxygen and peroxide value. Tocopherols prevented the photosensitized oxidation of lard (p<0.05). Steady state kinetic study showed that $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-tocopherol prevented the photosensitized oxidation of lard by quenching singlet oxygen. Singlet oxygen quenching rates of $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-tocopherol by headspace oxygen depletion were 1.86, 2.39, 2.47, and $2.11{\times}10^7/M/sec$, respectively. The quenching rates of $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-tocopherol by peroxide value were 1.42, 1.11, 0.97, and $0.42{\times}10^7/M/sec$, respectively. The quenching rates of tocopherols were slightly different depending on the measurements of oxidation.

• 미생물학회지
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• 제50권4호
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• pp.381-383
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• 2014

미생물 기원의 ${\alpha}$-glucosidase 저해제를 탐색하는 과정에서 토양에서 분리한 균주인 Bacillus sp. SKU31-1 배양액에서 강력한 저해제 compound K을 일련의 크로마토그래피 방법에 의해 분리 정제하였고 $^1H$ NMR, $^{13}C$ NMR, $^1H-^1H$ COSY spectra 분석과 문헌조사를 통해 5-amino-1-hydroxymethyl-1,2,3,4-cyclohexanetetrol로 동정되었다. Compound K의 ${\alpha}$-glucosidase 저해 활성은 $IC_{50}$값이 maltose 기질에서는 $1.9{\mu}M$이고, sucrose 기질 사용시 4.9 mM이었다. Lineweaver Burk plot에 의해 $K_i$값이 0.15 mM 로 강력한 경쟁적 저해제 임이 밝혀졌다.

• Journal of Applied Biological Chemistry
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• 제49권1호
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• pp.24-27
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• 2006

Four ursane-type triterpenoids, 2${\alpha}$,3${\alpha}$,19${\alpha}$-trihydroxy-24-norurs-4(23),12-dien-28-oic acid (1), 4(R),23-epoxy-2${\alpha}$,3${\alpha}$,19${\alpha}$-trihydroxy-24-norurs-12-en-28-oic acid (2), myrianthic acid (3), and tormentic acid (4), and a phenolic compound, ethyl gallate (5), from an EtOAc-soluble extract of the stems of Rumex japonicus, were subjected to in vitro bioassays to evaluate advanced glycation end products (AGEs) and rat lens aldose reductase (RLAR) inhibitory activity. Compounds 1 and 5 exhibited a significant inhibitory activity on AGEs formation with $IC_{50}$ value of 87 ${\mu}M$ and on RLAR with $IC_{50}$ value of 14.3 ${\mu}M$, respectively. Ethyl gallate (5) was isolated for the first time from this plant.