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SHARP CONDITIONS FOR THE EXISTENCE OF AN EVEN [a, b]-FACTOR IN A GRAPH

  • Cho, Eun-Kyung;Hyun, Jong Yoon;O, Suil;Park, Jeong Rye
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.31-46
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    • 2021
  • Let a and b be positive integers, and let V (G), ��(G), and ��2(G) be the vertex set of a graph G, the minimum degree of G, and the minimum degree sum of two non-adjacent vertices in V (G), respectively. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), dH(v) is even and a ≤ dH(v) ≤ b, where dH(v) is the degree of v in H. Matsuda conjectured that if G is an n-vertex 2-edge-connected graph such that $n{\geq}2a+b+{\frac{a^2-3a}{b}}-2$, ��(G) ≥ a, and ${\sigma}_2(G){\geq}{\frac{2an}{a+b}}$, then G has an even [a, b]-factor. In this paper, we provide counterexamples, which are highly connected. Furthermore, we give sharp sufficient conditions for a graph to have an even [a, b]-factor. For even an, we conjecture a lower bound for the largest eigenvalue in an n-vertex graph to have an [a, b]-factor.

Effect of Operating Parameters on Electrochemical Degradation of Rhodamine B by Three-dimensional Electrode (3차원 전극을 사용한 Rhodamine B의 전기분해에 미치는 운전인자의 영향)

  • Kim, Dong-Seog;Park, Young-Seek
    • Journal of Environmental Health Sciences
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    • v.35 no.4
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    • pp.295-303
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    • 2009
  • A simulated wastewater containing the dye Rhodamine B (RhB) was electrolytically treated using a three-dimensional electrode reactor equipped with granular activated carbon (GAC) as particle electrode. The effect of type of packing material (GAC, ACF, Nonwoven fabric fiber coated with activated carbon), amounts of GAC packing (25-100 g), current (0.5-3 A) and electrolyte concentration (0.5-3 g/l) was evaluated. Experimental results showed that performance for RhB decolorization of the 3 three-dimensional electrodes lie in: GAC > Nonwoven fabric fiber > ACF. When considered RhB decolorization, oxidants concentration and electric power, optimum GAC dosage was 50 g. Generated concentration of 3 oxidants ($ClO_2$, free Cl, $H_2O_2$) was increased with increase of applied current, however optimum current for RhB degradation was 2.5 A. The oxidants concentration was increased with increase of NaCl concentration and optimum NaCl dosage for RhB degradation was 1.5 g/l.

Antioxidative Activity and Component Analysis of Broussonetia kazinoki SIEB Extracts (닥나무 추출물의 항산화 활성 및 성분 분석)

  • Park, Su Ah;Ha, Ji Hoon;Park, Soo Nam
    • Applied Chemistry for Engineering
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    • v.24 no.2
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    • pp.177-183
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    • 2013
  • In this study, the antioxidative activities and component analysis of Broussonetia kazinoki SIEB (B. kazinoki). extracts were investigated. B. kazinoki extract showed the effective free radical (1,1-diphenyl-2-picrylhydrazyl, DPPH) scavenging activity ($FSC_{50}=8.53{\mu}g/mL$). Reactive oxygen species (ROS) scavenging activity ($OSC_{50}$) of the ethyl acetate fraction of B. kazinoki. extracts in the luminol-dependent $Fe^{3+}-EDTA/H_2O_2$ system was $1.69{\mu}g/mL$. The ethyl acetate fraction of B. kazinoki. extracts also exhibited more prominent cellular protective effects (${\tau}_{50}$, 183.3 min at $10{\mu}g/mL$) than that of typical antioxidant $\alpha$-tocopherol (${\tau}_{50}$ = 38.00 min) in the $^1O_2$-induced photohemolysis of human erythrocytes. Components of the ethyl acetate fraction obtained from B. kazinoki extracts were analyzed by TLC, HPLC chromatogram, LC/ESI-MS/MS and $^1H$-NMR. Consequently, Components, components were identified as the kazinol J of kazinol series and luteolin (2-(3,4-dihydroxyphenyl)-5,7-dihydroxy-4-chromenone) of flavonoid series having antioxidant activities. These results indicate that extract/ fraction of B. kazinoki can be used as antioxidants in biological systems, particularly skins exposed to UV radiation by quenching and/or scavenging $^1O_2$ and other ROS, and protecting cellular membranes against ROS. Thus, the extract/fraction of B. kazinoki could be applicable to new cosmeceuticals.

Electromagnetic Wave Scattering of the Perfect Conducting Body of Revolution (회전형 완전도체의 전자파 산란특성)

  • Kim, Jung-Ki
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.25 no.2
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    • pp.130-138
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    • 1988
  • The method of conjugate gradient (C.G.M.) is applied to the solution of current distribution from body of revolution(B.O.R.). Using the C.G.M., it is possible to analyze electrically large arbitratily oriented B.O.R.. The fundamental differencess between C.G.M. and moment are outlined. This method converge for any initial guess, and this techniqe guarantees a monotonic convegence. Numerical resulsts are presented for electromagnetic case which shows good agreements with moment solution.

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Production of Cathepsin B Inhibitor by Steptomyces luteogriseus KT-10 (Streptomyces luteogriseus KT-10에 의한 Cathepsin B 저해물질의 발효생산)

  • 한길환;김상달
    • Microbiology and Biotechnology Letters
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    • v.27 no.6
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    • pp.458-465
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    • 1999
  • Streptomyces luteogriseus KT-10 isolated from Korean farm soil produced a strong cathepsin B inhibitor. Optimal conditions for the cathepsin B inhibitor production by s. luteogriseus KT-10 were evaluated. The cathepsin B inhibitor was produced with maximal yield in the cultural condition of pH 7.0 and $25^{\circ}C$ for 4 days. Optimal medium for the cathepsin B inhibitor production was determined to be a medium containing 20g, peptone 3g, yeast extract 1g, K2HPO4 0.5g, MgSO4.7H2O 0.5g, NaNO3 0.5g, NaCl 0.5g per l. The cathepsin B inhibitor produced by S. luteogriseus KT-10 could also inhibit the other proteinases such as trypsin, papain, and cathepsin D.

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SHARP ORE-TYPE CONDITIONS FOR THE EXISTENCE OF AN EVEN [4, b]-FACTOR IN A GRAPH

  • Cho, Eun-Kyung;Kwon, Su-Ah;O, Suil
    • Journal of the Korean Mathematical Society
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    • v.59 no.4
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    • pp.757-774
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    • 2022
  • Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), dH(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ2(G) = minuv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ2(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ2(G) is sharp.

A Study on Microwave Dielectric Properties of Low-Temperature Sintered (Zn0.8Mg0.2)TiO3 Ceramics (저온소결 (Zn0.8Mg0.2)TiO3 세라믹의 마이크로파 유전특성에 관한 연구)

  • 방재철;심우성
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.16 no.7
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    • pp.604-610
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    • 2003
  • The effects of sintering additives such as B $i_2$ $O_3$ and $V_2$ $O_{5}$ on the microwave dielectric and sintering properties of (Z $n_1$$_{-xM}$ $g_{x}$)Ti $O_3$ system were investigated. Highly dense samples were obtained for (Z $n_{0.8}$M $g_{0.2}$)Ti $O_3$ at the sintering temperature range of 870~90$0^{\circ}C$ with B $i_2$ $O_3$ and $V_2$ $O_{5}$ additions of 〈1 wt.%, respectively. The microwave dielectric properties of (Z $n_{0.8}$M $g_{0.2}$)Ti $O_3$ with 0.45 wt.%B $i_2$ $O_3$ and 0.55 wt.% $V_2$ $O_{5}$ sintered at 90$0^{\circ}C$ were as follows : Q$\times$ $f_{o}$ = 50,800 GHz, $\varepsilon$$_{r}$ = 22, and $\tau$$_{f}$ = -53 ppm/$^{\circ}C$. In order to improve temperature coefficient of resonant frequency, Ti $O_2$ was added to the above system. The optimum amount of Ti $O_2$ was 15 moi.% when sintered at 87$0^{\circ}C$, at which we could obtain following results: Q$\times$ $f_{o}$ = 32,800 GHz, $\varepsilon$$_{r}$ = 26, and$\tau$$_{f}$ = 0 ppm/$^{\circ}C$.EX>.EX>.EX>.EX>.EX>.EX>.EX>.

Growth Ingibiton Effect of E. coli O157:H7 and Salmonella typhimurium by Lactic Fermented Milk Products Administrated Orally in Rabbit (토끼에서 유산 발효유제품 급여에 의한 Escherichia coli O157:H7 및 Salmonella typhimurium의 증균억제효과)

  • 신광순;김용환;손원근;석주명;김상현
    • Journal of Food Hygiene and Safety
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    • v.12 no.3
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    • pp.188-194
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    • 1997
  • The growth inhibition effect of Orally administrated yogurt ACE and Metchnikoffupon E. coli O157:H7 and S. typhimurium inoculated into gastric lumen of rabbits was in vestigated. The rabbits challenged with each 1 $m\ell$ of suspension containing 108 CFU/$m\ell$ of the pathogens were divided into 4 groups by the interval of yogurt administration: A group; preadministrated 7 days before inoculation of the pathogens and fed daily; B group; administrated daily after inocjlation of the pathogens, C group; administrated every 3 days after inoculation of the pathogens; Control group, not fed after inoculation of the pathogens. Each 3 $m\ell$ of yogurt containing 109 CFU/$m\ell$ was orally administrated into rabbits. All yogurt administrated groups (A, B, c) chowed growth ingibition effect on E. coli O157:H7 in one day after inoculation of the pathogen by the level of 0.8~1.0 log CFU/g, compared with the result differences between the control group and the yogurt administrated groups. In the control group after 5 days of inoculation, the number of colonized pathogens was 105~106 CFU/g, whereas 103~104 CFU/g was detected in the yogurt administrated groups. After 10 days of inoculation, the viable pathogen number per gram (g) of the rabbit feces was 103 CFU/g in the control group, whereas the number below 101 CFU/g was detected in the group A, and 102 CFU/g in the control group, B and C. The growth inhibition effect of yogurt administration on E. coli O157:H7 was highly increased in the order of A, B, and C group. The same effect on S. typhimurium was observed at the level of 2 log CFU/g in the Metchnikoff yogurt administrated groups, compared with the control group result in one day after inoculation of the pathogen. In 7 days after inoculation of the pathogen, the viable number was increasingly decreased, and finally after 15 days no viable cell of S. typhimurium was discharged into the fecal samples in the group A, and the mean level of 10* CFU/g was detected in the group B, but there was no growth inhibition effect in the group C. The growth inhibition effect on S. typhimurium was observed at the same level of viable cell number between the yogurt ACE administrated groups and the control group in 5 days after inoculation. But, after 10 days of inoclation the viable cell number was started to decrease, and the viable cell of S. typhimurium was not discharged from rabbit intestinal contents after 15 days of inoculation in the yogurt ACE administrated groups. In such a case that yogurt was administrated in order to prevent the pathogens, pre-administration on a daily basis one week before inoculation of the pathogens exerted considerable effect in growth inhibition. In comparison with two kinds of yogurt tested in this study, the growth inhibition effect on two kinds of pathogens was observed more highly in the Metchnikoff administated group than the ACE administrated group.

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Color and COD Removal of Rhodamine B Using Ozone, Photocatalyst and Ozone-Complex Process (오존, 광촉매 및 오존-복합 공정을 이용한 Rhodamine B의 색도와 COD 제거)

  • Kim, Dong-Seog;Park, Young-Seek
    • Journal of Korean Society of Environmental Engineers
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    • v.29 no.6
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    • pp.662-669
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    • 2007
  • The effect of advanced oxidation processes such as $O_3$, $UV/TiO_2$, $O_3/UV$ and $O_3/UV/TiO_2$ on decolorization and COD removal of Rhodamine B(RhB) wastewater were considered. The results showed that the higher the $O_3$ concentration was, the higher the decolorization observed and the optimum $TiO_2$ dosage was 0.4 g/L in $UV/TiO_2$ and $O_3/UV/TiO_2$ process. $O_3/UV$ process showed the higher initial decolorization rate constant and the shorter termination time for decolorization than those of the $O_3$ process. The decolorization rate constants in various systems followed the order of $O_3/UV/TiO_2>O_3/UV>O_3{\gg}UV/TiO_2$. The decolorization rate of the RhB solution in every processes was more rapid than the mineralization rate identified by COD removal. The latter took longer time for further oxidation. The COD removal rate constants in four systems followed the order of $O_3/UV/TiO_2>O_3/UV>UV/TiO_2{\geqq}O_3$. Among four processes, combined photocatalysis and ozonation$(O_3/UV/TiO_2)$ was the most prospective process for removing color and COD such as dye wastewater.

The Effects of Bee Venom on iNOS, TNF-α and NF-kB in RAW 264.7 Cells (봉약침액(蜂藥鍼液)이 RAW 264.7 세포의 iNOS, TNF-α 및 NF-kB에 미치는 영향(影響 ))

  • Kim, Goon-Joong;Sim, Sung-Yong;Lee, Seong-No;Kim, Kee-Hyun
    • Journal of Pharmacopuncture
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    • v.6 no.2
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    • pp.45-56
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    • 2003
  • Objective : The purpose of this study was to investigate the effects of Bee Venom on the lipopolysaccharide(LPS), sodium nitroprusside(SNP), hydrogen peroxide$(H_2O_2)$-induced expression inducilble nitric oxide synthetase(iNOS), tumor necrosis factor-${\alpha}$(TNF-${\alpha}$) and nuclear factor kappa B(NF-kB) in RAW 264.7 cells, a murine macrophage cell line. Method : The expressions of expression iNOS and TNF-${\alpha}$ were determined by western blotting with corresponding antibodies. The expressions of expression NF-kB was assayed by EMSA method. Results : 1. The 0.5, 1 and $5{\mu}g/mg$ of bee venom on LPS-induced expression of iNOS, the $5{\mu}g/mg$ of bee venom on SNP-induced expression of iNOS and the $1{\mu}g/mg$ of bee venom on $H_2O_2$-induced expression of iNOS compared with control were inhibited significantly. 2. The 0.5, 1 and $5{\mu}g/mg$ of bee venom inhibited significantly LPS and $H_2O_2$-induced expression of TNF-${\alpha}$ compared with control, respectively. The $0.5{\mu}g/mg$ of bee venom increased significantly SNP-induced expression of TNF-${\alpha}$ compared with control. 3. The $5{\mu}g/mg$ of bee venom on LPS-induced expression of NF-kB, the $0.5{\mu}g/mg$ of bee venom on SNP-induced expression of NF-kB and the 0.5, $5{\mu}g/mg$ of bee venom on $H_2O_2$-induced expression of NF-kB were inhibited significantly compared with control, respectively.