• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1529-1560
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• 2019

We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

• Applied Chemistry for Engineering
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• v.23 no.3
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• pp.279-283
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• 2012

Bio-ethanol production research using various material has been problemed for solving problems of environment pollution caused by fossil fuels. Red-algae consists of agar, carrageenan, and porphyran. If it is treated by acid, it is able to change useful bio-mass for bio-ethanol. In this study, we found an optimal condition for bio-ethanol production from acid hydrolysate in red-algae. To produce bio-ethanol, Saccharomyces cerevisiae KCCM1129 inoculated to acid hydrolysate of Gelidium amansii. The optimal condition for Gelidium amansii hydrolysis was found to be 30 min reaction at $H_2SO_4$ concentration of 1.5% and $121^{\circ}C$. At this condition, its produced to 7.04 g/L galactose and 1.94 g/L glucose. And acetic acid concentration of 2.0% in agar produced 0.75 g/L galactose. In contrast, Pachymeniopis elliptica was treated with $H_2SO_4$concentration of 1.5%, it produced 6.38 g/L galactose. And Pachymeniopis elliptica treated with acetic acid concentration of 2% produced 0.368 g/L galactose. The optimal condition of ethanol production was found to be 96 h reaction at $H_2SO_4$concentration of 1.0% and $30^{\circ}C$, which produced 3.77 g/L ethanol.

• Journal of environmental and Sanitary engineering
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• v.15 no.4
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• pp.91-97
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• 2000

The objective of this study was to evaluate the possiblity of Foodwaste and co-treatment with other waste for vermistabilization. The value of oxidation-reduction potential(Eh) of the dewaterized foodwaste by a plant of subatmospheric evaporation was a possitive(+) value indicating, but the values of pH, salinity was idicating an unfavorable condition for earthworm life. The paper mill mixing waste properties by ripening for 20days were changed into the favorable range for earthworm. The growth of earthworms in foodwaste and mixing waste of paper mill 30% was found to be 68%, 84% for the survival rate, 227%, 275% for the liveweight increasing rate, respectively. The ingestion rate of foodwaste and mixing waste of paper mill 30% indicate 0.72g/g·d, 0.81g/g·d, respectively. About 62∼75% of ingestion amount produce cast and characteristics of cast indicate pH 6.1∼6.5 organic component 34∼42%, salinity 0.35∼0.4, CEC 73∼94 me/100g, N, P, K concentration 0.8∼1.2%, 0.4∼1.6%, 0.43∼0.5% respectively. Therefore it can be evaluated that the casts are good soil condition and organic fertilizer.

• Journal of Korean Society of Water and Wastewater
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• v.21 no.6
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• pp.717-726
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• 2007

Fully-grown flocs in a mixing tank of membrane filtration with dead-end membrane are ruptured while passing through a pump and the ruptured flocs are aggregated again in a Membrane-Feed-Pipe (MFP). To look at more details, this study tries to relate the reaggregation to a parameter of mixing intensity in MFP, i.e., G-value. The G-value is a function of Reynolds number, pipe diameter, friction factor and average velocity in MFP. To deal with polydispersity condition, we develop a representative particle size called in this study EDPD (Effective Diameter for Polydispersity condition in Dead-end filtration). The experimental results show that as the G-value increases, the EDPD decreases and also the cake resistance increases. Through comparison between EDPD and cake resistance, these results show that cake resistances are controlled by reaggregation phenomenon in MFP. The effect of detention time in MFP, however, does not affect the reaggregation of the broken flocs as G-values are increased.

• Journal of the Korean Society of Food Science and Nutrition
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• v.27 no.4
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• pp.585-590
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• 1998

To renew interest in Chrysanthemum boreale as a traditional food material, response surface methodology was used for optimizing extraction conditions and monitoring physicochemical properties of ethanol extracts from Chrysanthemum petal. The phenolic compounds of ethanol extracts were minimized in 87ml/g(solvent per sample), 21%(ethanol concentration), and 15 hours(extraction time). The physicochemical properties of ethanol extracts were maximized in the conditions of 115ml/g, 98% and 16 hours on yellow color intensity, 143ml/g, 75% and 19 hours on carotenoid content, and 148ml/g, 53% and 18 hours on soluble solid content. Optimum ranges of extraction condition for physicochemical properties of Chrysanthemum boreale were 130~150ml/g, 70~85% and 20~28 hours, respectively. Predicted values at the optimum extraction condition were in good agreement with experimental values.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.949-961
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• 1995

Let f be a smooth G map from a nonsingular real algebraic G variety to an equivariant Grassmann variety. We use some G vector bundle theory to find a necessary and sufficient condition to approximate f by an entire rational G map. As an application we algebraically approximate a smooth G map between G spheres when G is an abelian group.

• 한국생물공학회:학술대회논문집
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• 2003.04a
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• pp.393-397
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• 2003

P. aeruginosa F722 produces biosurfactant (BS) while degrading hydrocarbons. BS production was 0.78 $g/{\ell}$ on the C-medium. However, BS production increased by 1.66 $g/{\ell}$ on the condition of 0.05% (w/v) $NH_4Cl+0.1%$ (w/v) yeast extract and 3.0% (w/v) glucose, which was proved to be advantageous to BS production. In the condition of aeration of 1.0 liter per minute (LPM), BS production was increased 20% (1.94 $g/{\ell}$)more than 1.66 $g/{\ell}$ produced when the air was not supplied. Moreover, the velocity of glucose degradation at both of log and stationary growth phases increased from 0.25 and 0.18 $h^{-1}$ to 0.33 and 0.29 $h^{-1}$ respectively when the air was supplied. Besides, BS activity was more stabilized on the condition of air supply.

• Food Science and Preservation
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• v.13 no.2
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• pp.252-258
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• 2006

To find the optimum extraction condition of dried omija, central composite experimental design having three independent variable (extraction temperature, extraction time and water ratio) with five levels was conducted for response surface analysis. The maximum of soluble solid was predicted to the extraction conditions of over 25 fold water ratio, $7{\sim}8hr$ and $75^{\circ}C$. Total acid, total phenol, reducing sugar and vitamin C were predicted to respectively 30 fold water ratio, 6 hr, $70^{\circ}C$, 30 fold water ratio, $6{\sim}7\;hrs,\;80^{\circ}C$ and 30 fold water ratio, $6{\sim}8\;hr,\;80^{\circ}C$, 25 fold water ratio, $5{\sim}6hr,\;80^{\circ}C$ extraction condition. Turbidity of extraction condition. Turbidity of extraction condition was 7 over 25 ford water ratio and over $60^{\circ}C$. From the superimposing results of response variables, the optimum extraction condition was predicted 25 folds water ratio, 6 hr and $65{\sim}70^{\circ}C$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.465-472
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• 2004

A group G is said to satisfy the maximal condition on infinite normal subgroups if there does not exist an infinite properly ascending chain of infinite normal subgroups. We characterize the structure of locally nilpotent groups satisfying this chain condition. We then show how to construct locally nilpotent groups with the maximal condition on infinite normal subgroups, but not the maximal condition on subgroups.