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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.

Physical and Sensory Characteristics of Korean Style Meat Products (한국형 육가공 제품류의 물리적 및 관능적 품질 특성)

  • Kim, I.S.;Jin, S.K.;Hah, K.H.;Lyou, H.J.;Park, K.H.
    • Journal of Animal Science and Technology
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    • v.47 no.1
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    • pp.49-56
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    • 2005
  • The Korean styled meat products such as grilled and/or roasted ham(Jikhwagui: J), Bulgogi ham(B), Kimbab ham(K) and sliced roasted ham(DDukgalbi: D) were obtained from different Korean meat processing companies and investigated for their salinity, saccharinity, pH, moisture and fat content, meat color and sensory evaluation. The results obtained were as follows; Percentage of saccharinity in J, B, K and D ranged 7.5 %(13) - 12.7% (J2), 5.3 0/«B2) -7.5 o/«BI), 5.2 0/«K4) - 6.6 o/«KI, K2, KS), and 6.60/«04) - 14.4o/«Dl), respectively. Percentage of salinity in J, B, K and D ranged 2.260/«13)- 2.38 0/«J4), 1.850/«B2) - 2.45 0/«B3), 1.94o/«KI) - 2.40% (K3), and 1.830/«02) - 2.19 o/«Dl), respectively. The pH value of J, B and K were ranged 6.30 - 6.44, 6.266.37 and 6.20 - 6.42, respectively, which are slightly higher than that of D(5.86 - 6.25). Content of average moisture were higher in B(61.0 %), K(59.94%) and J(59.63%) compared to the D(55.93%). In crude fat, B and D were ranged 14-21 %, which are very lower than those of K(59.94%) and J(59.63%). In meat color, $L^*$ value were above 50.0, except D2 and D3. $a^*$ value of B were slightly higher than those of other meat products. Compared to sensory evaluation, the overall acceptability of J is excellent in the range of saccharinity 12.7%, salinity 2.3 %, moisture 61 %, crude fat II - 12%, $L^*$ value 52 - 54, and $a^*$ value 12.3- 12.7. In the case of B, the overall acceptability is excellent in the range of saccharinity 6.6 - 7.5 %, salinity 1.90- 2.45 %, moisture 60 %, crude fat 15 %, $L^*$ value 56, and $a^*$ value 15. In the case of K, the overall acceptability is excellent in the range of saccharinity 6.5 %, salinity 2.4 %, moisture 61 %, crude fat 16%, $L^*$ value 53, and $a^*$ valuce 15. In the case of D, the overall acceptability is excellent in the range of saccharinity 14.0%, salinity 2.1 %, moisture 55%, crude fat 55%, $L^*$ value 50, and $a^*$ value 13.

Experiments for Forming Limit Diagram and Springback Characteristics of AZ31B Magnesium Alloy Sheet at Elevated Temperature (AZ31B 마그네슘 합금판재의 온간 성형한계도 및 스프링백 특성 시험)

  • Choi, C.S.;Lee, H.S.;Kim, H.J.;Lee, K.T.;Kim, H.Y.
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 2007.05a
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    • pp.289-293
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    • 2007
  • The effect of temperature on the forming limit diagram was investigated for AZ31B magnesium alloy sheet through the limit dome height test in the range from room temperature to $300^{\circ}C$. The formability of AZ31B sheet was improved significantly according to the increasing temperature. Also we studied the springback characteristics through the 2D draw bending test with different blank holding forces at elevated temperatures. Springback quantity was considerably reduced as temperature went up. The blank holding force in the range used, however, had little influence on springback. Experimental results obtained in this study may provide a material database for AZ31B sheet.

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Synthesis of (${\pm}$)-cis-8-amino-l-2,3,4,4a,5,10b-hexahydrothiazolo[4,5-f]indeno [1,2-b][1,4]oxazine ((${\pm}$)-cis-8-Amino-2,3,4,4a,5,10b-hexahydrothiazolo[4,5-f]indeno [1,2-b][1,4]oxazine의 합성)

  • Ma, Eun-Sook
    • YAKHAK HOEJI
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    • v.52 no.6
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    • pp.488-493
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    • 2008
  • 2-Aminothiazole ring as a bioisoster of catechol in dopamine has provided with good oral availability and lipophilic property. 2-Aminoindan, is a rigid form of dopamine, was evaluated as a dopamine D3 agonist with low neurotoxicity. Dopamine D3 agonist was evaluated as selective for the treatment of Parkinson's disease. In order to develop a novel dopamine D3 agonist, we tried to synthesize the aminothiazoloindenoxazine derivative that is a hybrid structure of aminoindenoxazine and thiazole ring. cis-2-Amino-1-indanol (2) was synthesized from 1,2-indandione-2-oxime by catalytic hydrogenation and it was treated with chloroacetyl chloride and NaH in benzene solution to give (${\pm}$)-cis-4,4a,5,9b-tetrahydroindeno[1,2-b][1,4]oxazin-3(2H)-one (6). Nitration of 6 by the mixed acid gave 8-nitro compound (7) and the carbonyl group of 7 was reduced with $LiAlH_4$ to afford compound (8). 8 was reduced to form (${\pm}$)-cis-8-amino-2,3,4,4a,5,9b-hexahydroindeno[1,2-b][1,4]oxazine (9) and finally it was cyclized with KSCN in glacial acetic acid to yield (${\pm}$)-cis-8-amino-2,3,4,4a,5,10b-hexahydrothiazolo[4,5-f]indeno[1,2-b][1,4]oxazine (10).

Effect of Fermentation Temperature on the Physicochemical Properties of Mustard Leaf(Brassica juncea) Kimchi during Various Storage Days (발효숙성온도를 달리한 갓 김치의 저장중 이화학적 특성 변화)

  • 박삼수;장명숙;이규환
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.24 no.5
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    • pp.752-757
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    • 1995
  • The effect of fermentation temperature on the changes of pH, acidity, salt content, color and vitamin C of mustard leaf kimchi during various storage days was investigated. The conditions of fermentation temperature were set at $4^{\circ}C$ (sample A) and $20^{\circ}C$ (sample B), and $4^{\circ}C$ after keeping at $20^{\circ}C$ for 12 hours(sample C) and $20^{\circ}C$ for 36 hours(sample D). As the fermentation proceeded, pH of sample stored at low temperature(sample A) was drop ped gradually from initial pH of 5.24 but there was great pH drop in the sample stored at high temperature(sample B, D). The salt content of the sample B at high temperature increased remarkably, and then the values showed D > A > C. The Humter values of L and a increased at the optimum ripening period, the higher the initial fermentation temperature(B) and the later the initial fermentation time at $20^{\circ}C$ those values, then decreased. The Hunter value of b constantly increased until day of 108. As fermentation time passed, the content of total vitamin C decreased to the range of 9.0mg% to 14.0mg% up to 24 days of fermentation, and at the optimum ripening period, it increased to the range of 14.0mg% to 22.0mg%, and at the fermentation period(until day 108), it decreased gradually.

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The Correlation between Holmberg's diameter and de Vaucouleurs' diameter of External Galaxies (Holmberg 은하 직경과 de Vaucoluleurs 은하 직경의 상관 관계)

  • 홍정호;천문석
    • Journal of Astronomy and Space Sciences
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    • v.2 no.2
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    • pp.117-129
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    • 1985
  • Holmberg's diameters of galaxies $D_{h}$ were obtained from Holmberg catalogue. The difference between Holmberg's diameter and de Vaucouleurs' face-on diameter is campared with the results of Heidmann et al. The difference obtained in this paper is smaller than that of Heidmann at al. Also, the correlation between $D_{h}$ and $D_{v}$ was obtained for each type in de Vaucouleurs' classification of galaxies. It shows that $D_{h}$ is overestimated that $D_{v}$.

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Design of Stacked Circular Microstrip Antenna for Mobile Communication Base Station (이동통신 기지국을 위한 적층된 원형 마이크로스트립 안테나 설계)

  • Kim, Nam-Hyeon;No, Gwang-Hyeon;Gang, Yeong-Jin
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.37 no.2
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    • pp.83-90
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    • 2000
  • In this paper, a stacked circular-disk microstrip 1${\times}$4 array antenna was designed and manufactured and tested to apply in next generation mobile communication, on IMT-2000 system(up-link: 1.885 GHz∼2.025 GHz, down-link: 2.11 GHz∼2.2 GHz) base station which has dual frequency, broadband and high-gain characteristics. The experimental results are as follows : resonant frequency of 1.885 GHz and 2.178 GHz VSWR (1.064 , 1.432), return loss (-30.19 dB , -24.99 dB), band width (VSWR<2) are 402 MHz, -3dB beam width at radiation pattern are ${\alpha}$E-16.8$^{\circ}$, ${\alpha}$H-69$^{\circ}$(1.885 GHz) and ${\alpha}$E-l5.2$^{\circ}$, ${\alpha}$H-51.5$^{\circ}$(2.178 GHz), gain(13.7 dBi∼15.21 dBi).

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Design and Fabrication of the Ka-band Waveguide to Microstrip Transition using Probe structure (프로브 구조를 이용한 Ka 대역 도파관-마이크로스트립 트랜지션의 설계 및 제작)

  • Kwon, Hyuk-Ja;Lee, Sung-Ju;Jang, Ho-Joon
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.45 no.7
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    • pp.67-71
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    • 2008
  • We report the waveguide to microstrip transition using probe structure for Ka-band transceiver. The waveguide to microstrip transition is composed of probe, inductive line, ${\lambda}/4$ impedance transformer, and $50{\Omega}$ microstrip line. For design of the transition, we optimized the characteristic impedances and the lengths of the component parts. The fabricated transition exhibits an insertion loss of 1.3 dB and the input/output return losses of below 14 dB between 30 and 40 GHz. The insertion loss of each transition is about $0.5{\sim}0.6dB$, considering the losses in the microstrip line and input/output waveguides.