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[r, s, t; f]-COLORING OF GRAPHS

  • Yu, Yong;Liu, Guizhen
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.105-115
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    • 2011
  • Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

The Effects of Chungganhaeju-tang(Qingganjiejiu-tang) on Alcohol induced Cytotoxicity in CYP2E1-transfected HepG2 cells (청간해주탕(淸肝解酒湯)이 CYP2E1-transfected HepG2 cell에서 알코올유발 세포독성에 미치는 영향)

  • Lee, Ji-Eun;Kim, Young-Chul;Woo, Hong-Jung;Lee, Jang-Hoon
    • The Journal of Internal Korean Medicine
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    • v.27 no.1
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    • pp.27-39
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    • 2006
  • Objectives : Induction of CYP2E1 by ethanol is believed to be one of the major mechanism by which ethanol generate a state of oxidative stress. Previous studies showed that treatment with Chungganhaeju-tang prevents hepatic inflammation and apoptosis in alcoholic liver disease. The purpose of our study is to determine if Chungganhaeju-tang can also protect against alcohol-induced cytotoxicity in CYP2E1-transfected HepG2 cells. Materials and Methods : CYP2E1-transfected HepG2 cells and control vector-transfected HepG2 cells were exposed for isx hours to Chungganhaeju-tang, and then 50 mM of ethanol was added and left for two days. Results : Ethanol significantly decreased cell viability in CYP2E1-transfected HepG2 cells and increased apoptosis. These alterations were attenuated by Chungganhaeju-tang. This was accompanied by an improvement of NF-${\kappa}B$ and Akt activation. Conclusion : These results suggest that Chungganhaeju-tang exerts inhibitory effect against the cytotoxicity induced by alcohol in CYP2E1-transfected HepG2 cells, and that this is a protective action due, at least in part, to an activation of NF-${\kappa}B$ that plays a key role in the protection mechanism, and in reducing hepatotoxic cytokine gene expression.

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Effect of Chamomile German Oil Application of IgG1 and IgE 1 to Atopic Dermatitis in NC/Nga Mice Model (Chamomile German 오일도포가 아토피성 피부염을 가진 NC/Nga 생쥐모델의 혈청 IgE와 IgG1양 변동에 미치는 영향)

  • Shin, Gil-Ran;Kim, Yang-Weon
    • Korean Journal of Human Ecology
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    • v.18 no.2
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    • pp.501-507
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    • 2009
  • Atopic dermatitis is one of the most common skin disease in children and a characteristic chronically recurrent form of dermatitis with a hereditary tendency, affecting infants and may extend to the childhood or th the adult age. Environmental factors, stress, and foodstuffs such as milk, egg may cause atopic dermatitis. Nc/Nga mice were used as an animal model for human atopic dermatitis. The divided by 4group such as normal group, BMAC group, FK506 group, MR group for this study raised in conventional conditions. To investigate effect of Chamomile German on atopic dermatitis in NC/Nga mice, the serum IgE and IgG1 level were measured while the severity degree of the skin lesion was examined by the naked eyes of two volunteers who were unaware of the treatment status. The results were the followings. 1. The score on the severity degree of skin dermatitis in FK 506 and MR group was lower than that in control group. 2. The serum IgE level in control group was higher 25% than that in normal group. 3. The serum level of IgE in FK506 and MR group compares to control group was decreased. 4. The serum IgG1 level was decreased more than 3.5 times in FK506 compared to control group while MR group had significantly less the serum IgG1 than control group. From the above results, treatment of Chamomile German oil had the effect on atopic dermatitis in NC/Nga mice. If scientific researches on aroma oil are performed in various way, aroma oil will be used to cure skin dermatitis as a alternative therapy in the future.

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED SPACES OF VECTOR-VALUED ANALYTIC FUNCTIONS

  • Manhas, Jasbir Singh
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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    • pp.1203-1220
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    • 2008
  • Let V be an arbitrary system of weights on an open connected subset G of ${\mathbb{C}}^N(N{\geq}1)$ and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let $HV_b$ (G, E) and $HV_0$ (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings ${\phi}:G{\rightarrow}G$ and operator-valued analytic mappings ${\Psi}:G{\rightarrow}B(E)$ which generate weighted composition operators and invertible weighted composition operators on the spaces $HV_b$ (G, E) and $HV_0$ (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

Effect of Growth Hormone and Androgen on Vitellogenin and Estrogen Receptor Gene Expression in the Japanese eel, Anguilla japonica (뱀장어 Vitellogenin과 Estrogen 수용체 유전자 발현에 대한 성장호르몬 및 웅성호르몬의 영향)

  • Kwon, Hyuk-Chu;Choi, Seong-Hee;Kim, Eun-Hee;Kwon, Joon-Yeong
    • Development and Reproduction
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    • v.10 no.2
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    • pp.97-103
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    • 2006
  • Vitellogenin(Vg) is a sex specific serum protein present in sexually maturing female blood of oviparous vertebrates. Estrogen($E_2$) is a main inducer of hepatic Vg synthesis. We investigated the effects of androgen and growth hormone(GH) on regulation of Vg and estrogen receptor(ER) genes in Japanese eel. Immature eels($200{\sim}250\;g$) were given a single injection of $E_2(5{\sim}5,000\;{\mu}g/kg\;bw)$ alone, or in combination with eel recombinant GH(eGH, $1{\sim}10\;{\mu}g/kg$) or methyltestosterone(MT, $1{\sim}5\;mg/kg$) and sacrificed 10 days after the hormone treatments. Expression levels of ER and Vg genes from the liver were determined by means of reverse transcription and polymerase chain reaction(RT-PCR). Administration of $E_2$ stimulated Vg gene expression in a dose dependent manner. Levels of Vg mRNA after the injection of $E_2(500\;{\mu}g/kg)$ with MT(5mg/kg) or eGH($10\;{\mu}g/kg$) were much higher than in that of $E_2$ alone($500\;{\mu}g/kg$). Whereas, injection of either vehicle, eGH ($10\;{\mu}g/kg$) or MT(5mg/kg) alone did not induce the expression of Vg gene in the liver. ER mRNA was detected from the fish treated with vehicle alone. $E_2$ injection($5{\sim}500\;{\mu}g/kg\;bw$) increased this ER expression but dose dependent response was not clear. Addition of MT(5mg/kg) or eGH($10\;{\mu}g/kg$) did not affect $E_2-stimulated$ ER mRNA expression. This study confirms the necessity of $E_2$ as the primary factor for Vg gene expression and requirement of additional hormones such as MT or GH for the full expression of Vg mRNA, and suggests that the additive effect of MT or GH on Vg gene expression would be mediated by some unknown factors other than ER.

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Effect of Different Ethanol Treatments on the Oxidative Stress in Liver and Brain of SD Rats (알코올 투여 방법이 흰쥐의 간과 뇌에서 산화적 스트레스유발에 미치는 영향)

  • 박민경;이영재
    • Journal of Food Hygiene and Safety
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    • v.17 no.3
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    • pp.124-128
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    • 2002
  • The effect of different ethanol feeding protocols on the oxidative stress in liver and blain of rats was studied. The rats were fed 5%-ethanol solution in drinking water (5%-EtOH group) or 2.5g ethanol/kg body wt. once daily intragastrically (2.5g-EtOH group). The levels of thiobarbituric acid reactive substances (TRARS) and vitamin EI in the liver, cerebrum and cerebellum were measured. In the liver of 5%-EtOH group, the level of TBARS was not changed, whereas vitamin I was significantly increased compared to control group. In the liver of 2.5g-EtOH group, the level of TBARS was significantly increased compared to control group and the vitamin E concentration was not affected. The levels of TBARS were increased and the vitamin E concentrations were decreased significantly both in the cerebrum and cerebellum in 5%-EtOH group as well as in 2.5g-EtOH group. These results show that lipid peroxidation and vitamin E concentration in liver were varied according to the conditions of ethanol treatment, however, the vitamin E contents in cerebrum and cerebellum were affected by both ethanol intoxications used in this study.

Expression of Glypican-3 in Mouse Embryo Stem Cells and its Derived Hepatic Lineage Cells Treated with Diethylnitrosamine in vitro

  • Kim, Young Hee;Kang, Jin Seok
    • Asian Pacific Journal of Cancer Prevention
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    • v.14 no.11
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    • pp.6341-6345
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    • 2013
  • To clarify the role of stem cells in hepatocarcinogenesis, glypican-3 (GPC-3) and E-cadherin expression was investigated in embryonic cell lineages. Mouse embryonic stem cells (ESCs), hepatic progenitor cells (HPCs) and hepatocyte like cells (HCs), representing 0, 22 and 40 days of differentiation, respectively, were treated in vitro with diethylnitrosamine (DEN) at four doses (0, 1, 5 and 15 mM; G1, G2, G3 and G4, respectively) for 24 h and GPC-3 and E-cadherin expression was examined by relative quantitative real-time PCR and immunocytochemistry. GPC-3 mRNA expression was significantly different for G4 at day 0 (p<0.001) and for G4 at day 22 (p<0.01) compared with the control (G1). E-cadherin mRNA expression was significantly different for G3 and G4 at day 0 (p<0.05 and p<0.001, respectively), for G2 and G4 (p<0.05 and p<0.001, respectively) at day 22 and for G2 and G4 (p<0.01 and p<0.001, respectively) at day 40 compared with G1. Immunofluorescence staining for GPC-3 showed a membranous and/or granular expression in cytoplasm of ESCs and HPCs and granular and/or diffuse expression in cytoplasm of HCs, which were also stained by E-cadherin. DEN treatment increased GPC-3 expression in ESCs, HPCs and HCs, with increase of E-cadherin expression. Taken together, the expression of GPC-3 was altered by DEN treatment. However, its expression pattern was different at the stage of embryo stem cells and its derived hepatic lineage cells. This suggests that GPC-3 expression may be modulated in the progeny of stem cells during their differentiation toward hepatocytes, associated with E-cadherin expression.

Production of Soluble Recombinant Human Granulocyte Colony Stimulating Factor in E. coli by Control of Growth Rate. (대장균에서 증식속도 조절에 의한 수용성 재조합 인간 과립구 콜로니 촉진인자의 생산)

  • 박세철;고인영;강희일
    • Microbiology and Biotechnology Letters
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    • v.32 no.2
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    • pp.135-141
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    • 2004
  • Human granulocyte colony-stimulating factor (hG-CSF) is a hematopoiesis agent that principally affects the differentiation of neutrophils in the bone marrow. At present, recombinant hG-CSF is used successfully in the treatment of chemotheraphy-induced neutropenia and its indication has been expanded to bone marrow transplantation and aplastic anemia. In this study, we have constructed rhG-CSF secretion plasmid pYRC1 in which OmpA signal sequence/hG-CSF gene was expressed under the control of the T7 promoter. rhG-CSF produced in E. coli BL21 (pYRC1) grown at $37{\circ}C$ was found in aggregates. However, 15% of the periplasmic protein was soluble rhG-CSF when the E. coli BL21 (pYRC1) was cultured at $25^{\circ}C$ for 7 h in the modified MBL medium containing 10 g/$\ell$ glucose with 10 $\mu$M IPTG induction. The production of soluble rhG-CSF in E. coli BL21 (pYRC1) using fed batch culture was also studied. In the fed batch culture system, the final yield of rhG-CSF produced from E. coli BL21 (pYRC1) was increased from 4.4 mg/$\ell$to 24 mg/$\ell$by controlling the specific growth rate from $0.43 h^{-1}$ to $0.14 h^{-1}$, and optimizing the time of induction.

Band Lineup Types Based on Ge1-xSnx/Ge1-ySny(001) (Ge1-xSnx/Ge1-ySny(001)의 band lineup 유형)

  • 박일수;전상국
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.15 no.9
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    • pp.770-775
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    • 2002
  • We present the band lineups of G $e_{1-}$x S $n_{x}$ G $e_{1-}$y S $n_{y(001)}$ heterostructures for the new devices. The energy gap of the bulk G $e_{1-}$x S $n_{x}$ alloy is calculated by taking into account the Vegard's law. The change of the energy gap due to the strain is understood in terms of the deformation Potential theory The valence band offset is obtained from the average bond energy model, where the changes of the band offset due to alloy compositions and strain are included. It is found that Ge/G $e_{1-}$y S $n_{y(001)}$ heterostructure has a staggered lineup type for 0$\leq$0.06 and a straddling one for 0.06$\leq$0.26. Meanwhile, Ge/G $e_{l-y}$ S $n_{y(001)}$ heterostructure has a staggered lineup type for 0$\leq$0.19 and a broken-gap one for 0.19$\leq$0.26. As a result, the various type of the G $e_{1-}$x S $n_{x}$ G $e_{1-}$y S $n_{y(001)}$ heterostructure can be applied for the useful device.evice.

Distance Eccentric Connectivity Index of Graphs

  • Alqesmah, Akram;Saleh, Anwar;Rangarajan, R.;Gunes, Aysun Yurttas;Cangul, Ismail Naci
    • Kyungpook Mathematical Journal
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    • v.61 no.1
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    • pp.61-74
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    • 2021
  • Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.