• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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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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• v.28 no.3_4
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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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• v.11 no.3
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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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• v.15 no.2
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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.

• Polymer(Korea)
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• v.38 no.4
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• pp.411-416
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• 2014

Due to the polar characteristics of silica compared to carbon black, the degree of silica dispersion, which affects the mechanical properties of rubber compounds, is an important issue. Wolff first introduced the in-rubber structure of particles (${\alpha}_F$) to express the structure development in the compounds; however, with the introduction of bifunctional silanes, his theory could not explain the 3-dimensional network structure of the compounds. Later his theory was expanded to express the composite interaction parameter (in-rubber structure of the compound) (${\alpha}_C$), which included Wolff's filler-filler interaction parameter (${\alpha}_F$), however, there was no reported experimental result proving the theory. This research first experimentally expressed the in-rubber structure of the compound ${\alpha}_C$ (= ${\alpha}_F+{\alpha}_{FP}$(filler-silane-rubber interaction parameter) + ${\alpha}_P$ (rubber-rubber interaction parameter)) upon mono- and bifunctional silane treated silica filled natural rubber (NR) compounds. Using different structure silanes, i.e. PTES, OTES, TESPD, and TESPT, the ${\alpha}_C$ value of each compound was measured and calculated. The ${\alpha}_C$ value of TESPT treated silica filled compound was 1.64, which composed of ${\alpha}_F$ (0.99), ${\alpha}_{FP}$ (0.31), and ${\alpha}_P$ (0.34).

• Fisheries and Aquatic Sciences
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• v.11 no.4
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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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• v.18 no.2
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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.

• Korean Journal of Microbiology
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• v.50 no.4
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• pp.381-383
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• 2014

In the course of screening for ${\alpha}$-glucosidase inhibitor produced by microorganism, the active compound was isolated from the culture filtrate of Bacillus sp. SKU31-1 using a series of chromatography procedures. The structure of the active compound was elucidated as 5-amino-1-hydroxymethyl-1, 2, 3, 4-cyclohexanetetrol on the basis of spectroscopic evidence obtained and comparison with data from the literature. The active compound showed potent inhibitory activity against ${\alpha}$-glucosidase with an $IC_{50}$ value of $1.9{\mu}M$ for maltose and 4.9 mM for sucrose. A Lineweaver-Burk plot indicated that its inhibition of ${\alpha}$-glucosidase was competitive, with a $K_i$ value of 0.15 mM.

• Journal of Applied Biological Chemistry
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• v.49 no.1
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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.