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ON UNBOUNDED SUBNOMAL OPERATORS

  • Jin, Kyung-Hee
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.65-70
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    • 1993
  • In this paper we will extend some notions of bounded linear operators to some unbounded linear operators. Let H be a complex separable Hilbert space and let B(H) denote the algebra of bounded linear operators. A closed densely defind linear operator S in H, with domain domS, is called subnormal if there is a Hilbert space K containing H and a normal operator N in K(i.e., $N^{*}$N=N $N^*/)such that domS .subeq. domN and Sf=Nf for f .mem. domS. we will show that the Radjavi and Rosenthal theorem holds for some unbounded subnormal operators; if $S_{1}$ and $S_{2}$ are unbounded subnormal operators on H with dom $S_{1}$= dom $S^{*}$$_{1}$ and dom $S_{2}$=dom $S^{*}$$_{2}$ and A .mem. B(H) is injective, has dense range and $S_{1}$A .coneq. A $S^{*}$$_{2}$, then $S_{1}$ and $S_{2}$ are normal and $S_{1}$.iden. $S^{*}$$_{2}$.2}$.X>.

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A Study on the Quantitative Process Facility Standards that Require H2S Toxic Gas Detectors and Location Selection for Emergency Safety (H2S 독성가스감지기가 필요한 정량적 공정설비 기준 및 비상시 안전을 위한 위치선정 방안에 대한 연구)

  • Choi, Jae-Young;Kwon, Jung-Hwan
    • Journal of the Korean Institute of Gas
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    • v.22 no.2
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    • pp.90-96
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    • 2018
  • Design techniques for minimizing the damage caused by leakage of $H_2S$ gas, contained in natural gas and petroleum, have been widely studied abroad in chemical plants that purify and process natural gas and petroleum. However, there is no domestic engineering practice and regulation of $H_2S$. In accordance with the circumstances, this study proposes the quantitative criteria of process equipment to install $H_2S$ toxic gas detector as 500 ppm and explains the valid basis. The $H_2S$ gas dispersion radius up to IDLH 100 ppm is calculated by ALOHA under previous $H_2S$ gas leak accident scenario. The weather conditions of modeling include the conditions of Ulsan, Yeosu and Daesan, the three major petrochemical complexes in Korea. The long radius up to 100 ppm was derived in order of Ulsan, Daesan, Yeosu. For emergency safety the dispersion radius up to 100 ppm of the $H_2S$ gas obtained in this study should be extended to apply the additional $H_2S$ toxic gas detector, and local climate conditions should be considered.

The Solvolysis of Benzoyl Chloride in Water-Acetone Mixtures Under High Pressure

  • Jee, Jong-Gi;Ree, Taik-Yue
    • Bulletin of the Korean Chemical Society
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    • v.8 no.1
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    • pp.31-39
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    • 1987
  • By using a complete rate constant($k_e$) which treats a solvent (water) as a reactant, and a conventional rate constant($k_c$), which ignores the solvent in describing the rate, the parameters ${\Delta}V^{\neq}_s,\;{\Delta}H^{\neq}_s\;and\;{\Delta}S^{\neq}_s$ were introduced. These quantities represent the volume change, the enthalpy change, and the entropy change accompanying the electrostriction which occurs when solvent molecules condense on the activated complex. The authors measured the rates of the solvolysis of benzoyl chloride in water-acetone mixtures at $15^{\circ}$ to $30^{\circ}C$ and 1 bar to 2500 bars. Applying the authors' theory to the experimental results, the parameters, ${\Delta}V^{\neq}_s,\;{\Delta}H^{\neq}_s\;and\;{\Delta}S^{\neq}_s$ were evaluated, and it was found that they are all negative, indicating that water dipoles condense on the activated complex. They also proposed the following equations: ${\Delta}H^{\neq}_c\;=\;{\Delta}H^{\neq}_e\;+\;{\Delta}H^{\neq}_s\;and\; {\Delta}S^{\neq}_c\;=\;{\Delta}S^{\neq}_e\;+{\Delta}S^{\neq}_s\;,\;where\;{\Delta}H^{\neq}_c\;and\;{\Delta}H^{\neq}_c\;and\;{\Delta}S^{\neq}_s $are the activation enthalpy change and the activation entropy change for the conventional reaction rate, respectively, and ${\Delta}H^{\neq}_e$ and ${\Delta}S^{\neq}_e$ are the corresponding quantities for the complete reaction rate. The authors proposed that for the $SN_1$ type, all the quantities, ${\Delta}V^{\neq}_s,\;{\Delta}S^{\neq}_s\;,{\Delta}H^{\neq}_s\;and\;{\Delta}S^{\neq}_s$ are comparatively large, and for the $SN_2$ type, these quantities are smaller than for the $SN_1$ type, and occasionally the case ${\Delta}S^{\neq}_e$ < 0 occurs. Using these criteria, the authors concluded that at high temperature, high pressure and for a high water content solvent, the SN_1$ type mechanism predominates whereas in the reversed case the $SN_2$M type predominates.

Development of a Method to Measure Hydrogen Sulfide in Wine Fermentation

  • Park, Seung-Kook
    • Journal of Microbiology and Biotechnology
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    • v.18 no.9
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    • pp.1550-1554
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    • 2008
  • A hydrogen sulfide $(H_2S)$ detecting tube was developed for the quantitative determination of $H_2S$ produced by yeast during laboratory scale wine fermentations. The detecting tube consisted of a small transparent plastic tube packed with an $H_2S$-sensitive color-indicating medium. The packed medium changed color, with the color change progressing upward from the bottom of the tube, upon exposure to $H_2S$ produced by yeast during fermentation. A calibration study using a standard $H_2S$ gas showed that the length of the portion that darkened was directly related to the quantity of $H_2S$ (${\mu}g$) with a high correlation coefficient ($r^2$=0.9997). The reproducibility of the $H_2S$ detecting tubes was determined with five repetitive measurements using a standard $H_2S$ solution [5.6${\mu}g$/200 ml (28 ppb)], which resulted in a coefficient of variation of 3.6% at this level of $H_2S$. With the sulfide detecting tubes, the production of $H_2S$ was continuously monitored and quantified from laboratory scale wine fermentations with different yeast strains and with the addition of different levels of elemental sulfur to the grape juice. This sulfide detecting tube technology may allow winemakers to quantitatively measure $H_2S$ produced under different fermentation conditions, which will eventually lead winemakers to better understand the specific factors and conditions for the excessive production of $H_2S$ during wine fermentation in a large production scale.

Analysis of a Sphingosine 1-phosphate Receptor $hS1P_3$ in Rat Hepatoma Cells

  • Im, Dong-Soon
    • The Korean Journal of Physiology and Pharmacology
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    • v.6 no.3
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    • pp.139-142
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    • 2002
  • To examine intracellular signaling of human $S1P_3\;(hS1P_3),$ a sphingosine 1-phosphate (S1P) receptor in plasma membrane, $hS1P_3$ DNA was transfected into RH7777 rat hepatoma cell line, and the inhibition of forskolin-induced cAMP accumulation and activation of MAP kinases by S1P were tested. In $hS1P_3$ transformants, S1P inhibited forskolin-induced activation of adenylyl cyclase activity by about 80% and activated MAP kinases in dose-dependent and pertussis-toxin (PTX) sensitive manners. In oocytes expressing $hS1P_3$ receptor, S1P evoked $Cl^-$ conductance. These data suggested that PTX-sensitive G proteins are involved in $hS1P_3-mediated$ signaling, especially the positive action of S1P in cell proliferation. The potential advantages of rat hepatoma cells for the research of sphingosine 1-phosphate receptor are discussed.