• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.921-936
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• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• Korean Journal of Agricultural Science
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• v.3 no.2
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• pp.160-169
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• 1976

Monotupenes of the oleoresin of P. densiflora S. et Z., P. densi-thunber gii Uyeki, P. thunbergii Parl., and P. densiflora for. erecta Uyeki of the subgenus Diploxylon of the genus Pinus in Korea were analysed by means of gas liquid chromatography, and following results were obtained. Monoterpene of P. densiflora, P. densi-thunbergii, P. thunbergii, and P. densiflora for. erecta consisted of ${\alpha}$-pinene, camphene, ${\beta}$-pinene, myrcene, limonene, ${\beta}$-phellandrene, terpinolene and two unknown components. Major monoterpene components of P. densiflora and it's for. erecta were ${\alpha}$-pinene, ${\beta}$-phellandrene, myrcene, and terpinolene. Major monoterpene components of P. densi-thunbergii were ${\beta}$-pinene, ${\beta}$-phellandrene, ${\alpha}$-pinene, and terpinolene. Major monoterpene components of P. thunbergii were ${\beta}$-pinene, ${\alpha}$-pinene, ${\beta}$-phellandre, and limonene. Monoterpene components in P. densiflora, P. densi-thunbergii, P. thundergii, and P.densiflora for, erecta showed a range of variation by the individual trees. Monoterpene contents of P. densi-thunbergii were intermediate between those of P. densiflora and P. thunbergii. ${\alpha}$-pinene, ${\beta}$-pinene, and myrcene appeared to be the best taxonomio characteristics for separating P. densiflora from P. thunbergii, and the former had higher content of ${\alpha}$-pinene than ${\beta}$-pinene while those of the latter were vise versa. There was a significant difference of ${\alpha}$-pinene components of P. densiflora between that of Anmyun Island and Mt. Chiak, but it seemed to be caused by the difference of the individual trees rather than provenancial difference.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.285-297
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• 2008

For an endomorphism ${\alpha}$ of a ring R, the endomorphism ${\alpha}$ is called semicommutative if ab=0 implies $aR{\alpha}(b)$=0 for a ${\in}$ R. A ring R is called ${\alpha}$-semicommutative if there exists a semicommutative endomorphism ${\alpha}$ of R. In this paper, various results of semicommutative rings are extended to ${\alpha}$-semicommutative rings. In addition, we introduce the notion of an ${\alpha}$-skew power series Armendariz ring which is an extension of Armendariz property in a ring R by considering the polynomials in the skew power series ring $R[[x;\;{\alpha}]]$. We show that a number of interesting properties of a ring R transfer to its the skew power series ring $R[[x;\;{\alpha}]]$ and vice-versa such as the Baer property and the p.p.-property, when R is ${\alpha}$-skew power series Armendariz. Several known results relating to ${\alpha}$-rigid rings can be obtained as corollaries of our results.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.1
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• pp.253-262
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• 2016

This paper proposes a balance-swap method for the dynamic economic load dispatch problem. Based on the premise that all generators shall be operated at valve-points, the proposed algorithm initially sets the maximum generation power at $P_i{\leftarrow}P_i^{max}$. As for generator i with $_{max}c_i$, which is the maximum operating cost $c_i=\frac{F(P_i)-F(P_{iv_k})}{(P_i-P_{iv_k})}$ produced when the generation power of each generator is reduced to the valve-point $v_k$, the algorithm reduces i's generation power down to $P_{iv_k}$, the valve-point operating cost. When ${\Sigma}P_i-P_d$ > 0, it reduces the generation power of a generator with $_{max}c_i$ of $c_i=F(P_i)-F(P_i-1)$ to $P_i{\leftarrow}P_i-1$ so as to restore the equilibrium ${\Sigma}P_i=P_d$. The algorithm subsequently optimizes by employing an adult-step method in which power in the range of $_{min}\{_{max}(P_i-P_i^{min}),\;_{max}(P_i^{max}-P_i)\}$>${\alpha}{\geq}10$ is reduced by 10; a baby step method in which power in the range of 10>${\alpha}{\geq}1$ is reduced by 1; and a swap method for $_{max}[F(P_i)-F(P_i-{\alpha})]$>$_{min}[F(P_j+{\alpha})-F(P_j)]$, $i{\neq}j$ of $P_i=P_i{\pm}{\alpha}$, in which power is swapped to $P_i=P_i-{\alpha}$, $P_j=P_j+{\alpha}$. It finally executes minute swap process for ${\alpha}=\text{0.1, 0.01, 0.001, 0.0001}$. When applied to various experimental cases of the dynamic economic load dispatch problems, the proposed algorithm has proved to maximize economic benefits by significantly reducing the optimal operating cost of the extant Heuristic algorithm.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.44 no.4
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• pp.389-397
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• 2018

The starfish, Asterina pectinifera Muller and Troschel (Asterinidae) is an indigenous species commonly found in all coasts of Korea causes damages to shellfish farms. In order to exterminate A. pectinifera, they are dried and used as fertilizer. Although various studies have been conducted to create high added value from the retrieved A. pectinifera, their actual utilization is relatively low. Accordingly, this study aimed to find new practical uses of starfish by identifying useful ingredients for skin anti-aging. Two polyhydroxysteroids and one asterosaponin were isolated from the A. pectinifera. The structures of these compounds were identified as $5{\alpha}$-cholestane-$3{\beta},6{\alpha},7{\alpha},8,15{\alpha},16{\beta},26$-heptol, $5{\alpha}$-cholestane-$3{\beta},4{\beta},6{\alpha},7{\alpha},8,15{\beta},16{\beta},2$6-octol, and asterosaponin $P_1$ on the basis of chemical and spectroscopic analysis. Among these compounds, we have found that asterosaponin $P_1$ increased epidermal stem cell proliferation and the expression of hyaluronan synthase-2 and hyaluronan synthase-3 gene, which are enzymes that synthesize water-binding matrix hyaluronic acids in keratinocytes. In addition, asterosaponin $P_1$ increased synthesis of pro-collagen type I, a major dermal collagen in fibroblasts. As a result, asterosaponin $P_1$ isolated from A. pectinifera could be used as a useful cosmetic ingredient that improves skin symptoms accompanying skin aging.

• Asian-Australasian Journal of Animal Sciences
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• v.23 no.10
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• pp.1340-1347
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• 2010

To study the effects of ${\alpha}$-galactosidase (${\alpha}$-Gal) supplementation on performance and energy metabolism, 216 Arbor Acres male broilers were placed in 36 cages of 6 birds each and allotted to 4 diets for 42 d, with 0-21 d as starter period and 22-42 d as grower period. The 4 diets were based on corn non-dehulled soybean meal in a $2{\times}2$ factorial arrangement, with 2 levels of ${\alpha}$-Gal (0 vs. 60 U/kg feed) and 2 levels of ME (normal metabolizable energy (NME) and low metabolizable energy (LME)). Bird performance was obtained at 21 and 42 d of age with samples of feces collected for nutrient digestibility from 19-21 d and 40-42 d. At 21 and 42 d, 1 bird from 6 cages of each treatment was killed to determine liver weight, intestinal pH and chyme viscosity. With the addition of ${\alpha}$-Gal the 42 d body weight (BW) and 0-42 d average daily gain (ADG) were significantly improved (p<0.05). Average daily feed intake (ADFI) of birds fed the LME diet was significantly increased compared to those fed the NME diet during starter (p<0.01) and grower (p<0.05) periods and overall (p<0.01). There was an interaction of ${\alpha}-Gal{\times}ME$ on 0-21 d ADFI (p<0.01). Supplementation of ${\alpha}$-Gal significantly improved (p<0.01) feed efficiency during the grower period and overall. Feed efficiency of birds fed the LME diet was significantly decreased (p<0.05) compared to those fed the NME diet during the starter period and overall. With the addition of ${\alpha}$-Gal apparent metabolizable energy (AME) was improved (p<0.01) by 2.1% and 1.8% during starter and grower periods, respectively. There was a main effect (p<0.05) of ${\alpha}$-Gal on the digestion of neutral detergent fiber (NDF) during the starter period and crude protein (CP), NDF and acid detergent fiber (ADF) during the grower period. With the addition of ${\alpha}$-Gal, the relative weight of liver was reduced (p<0.01) during the two phases. The duodenal and jejunal pH were significantly decreased (p<0.01) with the supplementation of ${\alpha}$at the two phases. ${\alpha}$-Gal addition reduced (p<0.01) chyme viscosity of the ileum during the starter and grower periods. Overall, ${\alpha}$-Gal showed a major effect on nutrient efficiency, improved ADG and feed efficiency, whereas LME decreased feed efficiency. The incorporation of ${\alpha}$-Gal into a LME diet could at least partially offset ME deficiency of non-dehulled soybean meal.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.659-668
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• 2000

Let's $S_n(p,\alpha)(p,n\in\ N={1,2,3,\cdots},0\leq\ \alpha<1)$ denote tje c;ass pf fimctopms $f(z)=z^p+a_{p+z}z^{p+n}+\cdots$ which are $\rho$-valently starlike of order $\alpha$ in the unit disk.Some criteria for a function f(z) to be in the class $S_n(\rho,\alpha)$ are given.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.87-101
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• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

• Tunnel and Underground Space
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• v.7 no.4
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• pp.293-298
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• 1997

Permeability was not represented as a simple function of the difference between confining pressure($P_c$) and pore pressure($P_p$). The effective pressure($P_e$) for measurements of the permeability is shown to be $P_c-{\alpha}P_p$, where $\alpha$ is a coefficient of effective pressure. Local values of $\alpha$ were determined at intervals along the pressure path which range 25MPa to 55MPa. The values of $\alpha$ ranged 0.65 to 1.09 for Pocheon granite and 1.20 to 1.43 for Wonju granite. Also, the value of $\alpha$ calculated by the cross-plotting method was 0.90 for Pocheon granite, 1.59 for Wonju granite and 4.35 for jointed Pocheon granite. $\alpha$ was found to be stress-history dependent.

• Journal of Microbiology and Biotechnology
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• v.20 no.12
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• pp.1711-1716
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• 2010

A gene encoding the ${\beta}$-xylosidase/${\alpha}$-arabinofuranosidase (XylC) of Paenibacillus woosongensis was cloned into Escherichia coli. This xylC gene consisted of 1,425 nucleotides, encoding a polypeptide of 474 amino acid residues. The deduced amino acid sequence exhibited an 80% similarity with those of both Clostridium stercorarium ${\beta}$-xylosidase/${\alpha}$-N-arabinosidase and Bacillus cellulosilyticus ${\alpha}$-arabinofuranosidase, belonging to the glycosyl hydrolase family 43. The structural gene was subcloned with a C-terminal His-tag into a pET23a(+) expression vector. The His-tagged XylC, purified from a cell-free extract of a recombinant E. coli BL21(DE3) Codon Plus carrying a xylC gene by affinity chromatography, was active on para-nitrophenyl-${\alpha}$-arabinofuranoside (pNPA) as well as para-nitrophenyl-${\beta}$-xylopyranoside (pNPX). However, the enzymatic activities for the substrates were somewhat incongruously influenced by reaction pHs and temperatures. The enzyme was also affected by various chemicals at different levels. SDS (5 mM) inhibited the enzymatic activity for pNPX, while enhancing the enzymatic activity for pNPA. Enzyme activity was also found to be inhibited by addition of pentose or hexose. The Michaelis constant and maximum velocity of the purified enzyme were determined for hydrolysis of pNPX and pNPA, respectively.