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POSITIVE INTERPOLATION ON Ax = y AND AX = Y IN ALG$\mathcal{L}$

  • Kang, Joo-Ho
    • Honam Mathematical Journal
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    • v.31 no.2
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    • pp.259-265
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    • 2009
  • Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$. Let x and y be vectors in $\mathcal{H}$ and let $P_x$ be the projection onto sp(x). If $P_xE$ = $EP_x$ for each E ${\in}\;\mathcal{L}$, then the following are equivalent. (1) There exists an operator A in Alg$\mathcal{L}$ such that Ax = y, Af = 0 for all f in $sp(x)^{\perp}$ and A ${\geq}$ 0. (2) sup ${\frac{{\parallel}E^{\perp}y{\parallel}}{{\parallel}E^{\perp}x{\parallel}}:E{\in}\mathcal{L}}$ < ${\infty}$ < x, y > ${\geq}$ 0. Let X and Y be operators in $\mathcal{B}(\mathcal{H})$. Let P be the projection onto $\overline{rangeX}$. If PE = EP for each E ${\in}\;\mathcal{L}$, then the following are equivalent: (1) sup ${\frac{{\parallel}E^{\perp}Yf{\parallel}}{{\parallel}E^{\perp}Xf{\parallel}}:f{\in}\mathcal{H},E{\in}\mathcal{L}}$ < ${\infty}$ and < Xf, Yf > ${\geq}$ 0 for all f in H. (2) There exists a positive operator A in Alg$\mathcal{L}$ such that AX = Y.

Sensitivity of Escherichia coli to Seaweed (Ascophyllum nodosum) Phlorotannins and Terrestrial Tannins

  • Wang, Yuxi;Xu, Z.;Bach, S.J.;McAllister, T.A.
    • Asian-Australasian Journal of Animal Sciences
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    • v.22 no.2
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    • pp.238-245
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    • 2009
  • Pure culture experiments were conducted to assess the bacteriostatic and bactericidal effects of phlorotannins (PT) isolated from Ascophyllum nodosum (brown seaweed) on Escherichia coli O157:H7. In Exp. 1, one non-O157:H7 strain (25922) and three strains of E. coli O157:H7 (3081, EDL933 and E318N) were cultured in M9 medium with PT included at 0 (control), 25, 50 or $100{\mu}g/ml$ (n = 3). Bacterial growth was monitored by $OD_{600}$ at 0, 4, 6, 12 and 24 h, and by dilution plating at 0, 4, 6 and 24 h. All strains were inhibited (p<0.001) by PT to varying degrees. At 50 or $100{\mu}g/ml$, PT prevented growth of all four strains. At $25{\mu}g\;PT/ml$, growth of 25922, 3081, E318N and EDL933 was inhibited for 6, 12 and 24 h, respectively, but 25922 and 3081 resumed growth by 12 and 24 h. Direct plating confirmed bactericidal effects of PT on all four strains at $100{\mu}g/ml$, and on EDL933 and E318N at $50{\mu}g/ml$. In Exp. 2, strains 25922 and 3081 were incubated with no tannins or with $50{\mu}g/ml$ of PT, purified condensed tannins (CT) from Quebracho (Schinopsis balansaei), or purified tannic acid from Rhus semialata (Anacardiaceae) as hydrolysable tannins (HT). Strain 3081 was unaffected by HT or CT, but was completely inhibited (p<0.001) by PT at 4, 6 and 24 h. Strain 25922 was unaffected by HT, slightly inhibited by CT, and almost eradicated by PT at 4 and 6 h. Transmission electron microscopy revealed tannin-mediated alterations to bacterial cell walls. Phlorotannins from A. nodosum exhibit growth-inhibiting and bactericidal effects in vitro against the strains of E. coli O157:H7 investigated. Anti-E. coli efficacy of A. nodosum PT is superior to that of terrestrial tannins purified from Quebracho and from Rhus semialata.

Chemical Constituents of Pulicaria gnaphalodes

  • Ali, Muhammad Shaiq;Jahangir, Muhammad;Saleem, Muhammad;Ahmad, Viqar Uddin
    • Natural Product Sciences
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    • v.5 no.3
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    • pp.134-137
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    • 1999
  • The chloroform extract of Pulicaria gnaphalodes yielded flavonoids (1-2), sesquiterpenoid (3), sterol (4), benzoic acid derivative (5) and fatty acids (6-7). Their structures were elucidated with the aid of NMR spectroscopy. The described compounds have not been reported so far from this source.

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An Analysis on the Over-Potentially Deposited Hydrogen at the Polycrystalline $Ir/H_2SO_4$ Aqueous Electrolyte Interface Using the Phase-Shift Method (위상이동 방법에 의한 다결정 $Ir/H_2SO_4$ 수성 전해질 계면에서 과전위 수소흡착에 관한 해석)

  • Chun Jagn Ho;Mun Kyeong Hyeon
    • Journal of the Korean Electrochemical Society
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    • v.3 no.2
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    • pp.109-114
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    • 2000
  • The relation between the phase-shift profile fur the intermediate frequencies and the Langmuir adsorption isotherm at the poly-Ir/0.1 M $H_2SO_4$ aqueous electrolyte interface has been studied using ac impedance measurements, i.e., the phase-shift methods. The simplified interfacial equivalent circuit consists of the serial connection of the electrolyte resistance $(R_s)$, the faradaic resistance $(R_F)$, and the equivalent circuit element $(C_P)$ of the adsorption pseudoca-pacitance $(C_\phi)$. The comparison of the change rates of the $\Delta(-\phi)/{\Delta}E\;and\;\Delta{\theta}/{\Delta}E$ are represented. The delayed phase shift $(\phi)$ depends on both the cathode potential (E) and frequency (f), and is given by $\phi=tan^{-1}[1/2{\pi}f(R_s+R_F)C_P]$. The phase-shift profile $(-\phi\;vs.\;E)$ for the intermediate frequency (ca. 1 Hz) can be used as an experimental method to determine the Langmuir adsorption isotherm $(\theta\;vs.\;E)$. The equilibrium constant (K) for H adsorption and the standard free energy $({\Delta}G_{ads})$ of H adsorption at the poly-Ir/0.1 M $H_2SO_4$ electrolyte interface are $2.0\times10^{-4}$ and 21.1kJ/mol, respectively. The H adsorption is attributed to the over-potentially deposited hydrogen (OPD H).

Demands and distribution of hysteretic energy in moment resistant self-centering steel frames

  • Lopez-Barraza, Arturo;Ruiz, Sonia E.;Reyes-Salazar, Alfredo;Bojorquez, Eden
    • Steel and Composite Structures
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    • v.20 no.5
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    • pp.1155-1171
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    • 2016
  • Post-tensioned (PT) steel moment resisting frames (MRFs) with semi-rigid connections (SRC) can be used to control the hysteretic energy demands and to reduce the maximum inter-story drift (${\gamma}$). In this study the seismic behavior of steel MRFs with PT connections is estimated by incremental nonlinear dynamic analysis in terms of dissipated hysteretic energy ($E_H$) demands. For this aim, five PT steel MRFs are subjected to 30 long duration earthquake ground motions recorded on soft soil sites. To assess the energy dissipated in the frames with PT connections, a new expression is proposed for the hysteretic behavior of semi-rigid connections validated by experimental tests. The performance was estimated not only for the global $E_H$ demands in the steel frames; but also for, the distribution and demands of hysteretic energy in beams, columns and connections considering several levels of deformation. The results show that $E_H$ varies with ${\gamma}$, and that most of $E_H$ is dissipated by the connections. It is observed in all the cases a log-normal distribution of $E_H$ through the building height. The largest demand of $E_H$ occurs between 0.25 and 0.5 of the height. Finally, an equation is proposed to calculate the distribution of $E_H$ in terms of the normalized height of the stories (h/H) and the inter-story drift.

The improvement of the stability of hydrogenated amorphous silicon (수소화된 비정질 실리콘박막의 안정성향상에 관한 연구)

  • 이재희
    • Journal of the Korean Vacuum Society
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    • v.8 no.1
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    • pp.51-54
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    • 1999
  • Hydrogenated amorphous silicon (a-Si:H) films are fabricated by Argon radical annealing (ArRA). The deposition rate of continuously deposited a-Si:H film is 1.9 $\AA$/s. As ArRA time are increased to 0.5 and 1 minute, the deposition rate are increased to 2.8 $\AA$/s and 3.3 $\\AA$/s. The deposition rate of a-si:H films with 2 and 3 minutes ArRA time are 3.3 $\AA$/s. As the ArRA time is increased, the optical band gap and the hydrogen contents in the a-Si:H films are increased and slightly decreased. The light-induced degradation of ArRA treated a-Si:H films are less than that of continuously deposited a-Si:H film. The dark conductivity and the conductivity activation energy ($E_a$) of continuously deposited a-Si:H film are decreased to 1/25 in room temperature and increased to 0.09eV By 1 hour light soaking, respectively. The dark conductivity and $E_a$ of ArRA treated a-Si:H film decreased to 1/3 in room temperature and increased to 0.03eV by 1 hour light soaking, respectively. We could improve the stability of a-Si:H films under the light soaking by ArRA technique and discussed the microscopic process of ArRA technique.

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Base-Promoted, Ketene-Forming Elimination Reactions. Mechanistic Borderline between E2 and E1cb Mechanisms

  • Pyun, Sang-Yong;Cho, Bong-Rae
    • Bulletin of the Korean Chemical Society
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    • v.26 no.7
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    • pp.1017-1024
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    • 2005
  • Elimination reactions of $XC_6H_4CH_2CO_2C_6H_3-2-Y-4-NO_2$ have been studied under various conditions. When X was moderately electron-withdrawing, Y = H, and base-solvent was $R_2$NH-MeCN, the reaction proceeded by the E2 mechanism via an E1cb-like transition state. Concave downward curve was noted in the Hammett plots. When X = 4-$NO_2$, Y = Cl, $CF_3,\;NO_2$, and the base-solvent was ${R_2NH/R_2NH_2}^+$ in 70 mol % MeCN(aq), the reaction proceeded by the E2 mechanism. The mechanism changed to a competing E2 and E1cb when X = 4-$NO_2$ and Y = H, MeO, and to the E1cb when X = 2,4-($NO_2)_2$, and Y = $NO_2$. From these results, a plausible pathway of the change of the mechanism from E2 to the E1cb extreme is proposed.

Unusual Non-magnetic Metallic State in Narrow Silicon Carbon Nanoribbons by Electron or Hole Doping

  • Lou, Ping;Lee, Jin-Yong
    • Bulletin of the Korean Chemical Society
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    • v.33 no.3
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    • pp.763-769
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    • 2012
  • We investigated the width (N) dependence on the magnetization of N-ZSiC NR with electron and hole doping on the basis of systematic DFT calculations. The critical values of the upper and down critical concentration to give the maximum and zero magnetic moment at edge Si/C atoms by electron/hole doping ($x_{up,e}$, $x_{down,e}$, $x_{up,h}$, and $x_{down,h}$) depend on the width of N-ZSiC NR. Moreover, due to $x_{up,e}\;{\neq}\;x_{up,h}$ and $x_{down,e}\;{\neq}\;x_{down,h}$, the electron and hole doping effect are asymmetry, i.e, the critical electron doping value ($x_{down,e}$) is smaller than the critical hole doping value ($x_{down,h}$) and is almost independent of the width of NZSiC NR though the other critical values of the electron and hole doping that influence the magnetization of N-ZSiC NR depend on the width. It was also found that at $x_{down,e}$ or $x_{down,h}$ doping, the N-ZSiC NR turns into unusual non-magnetic metallic state. The magnetic behavior was discussed based on the band structures and projected density of states (PDOS) under the effect of electron/hole doping.

POSITIVE INTERPOLATION PROBLEMS IN ALG𝓛

  • KANG, JOO HO;KIM, KI SOOK
    • Honam Mathematical Journal
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    • v.26 no.4
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    • pp.379-389
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    • 2004
  • Given operators X and Y acting on a Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for $i=1,2,{\cdots},n$. In this article, we obtained the following : Let ${\mathcal{H}}$ be a Hilbert space and let ${\mathcal{L}}$ be a commutative subspace lattice on ${\mathcal{H}}$. Let X and Y be operators acting on ${\mathcal{H}}$. Then the following statements are equivalent. (1) There exists an operator A in $Alg{\mathcal{L}}$ such that AX = Y, A is positive and every E in ${\mathcal{L}}$ reduces A. (2) sup ${\frac{{\parallel}{\sum}^n_{i=1}\;E_iY\;f_i{\parallel}}{{\parallel}{\sum}^n_{i=1}\;E_iX\;f_i{\parallel}}}:n{\in}{\mathbb{N}},\;E_i{\in}{\mathcal{L}}$ and $f_i{\in}{\mathcal{H}}<{\infty}$ and <${\sum}^n_{i=1}\;E_iY\;f_i$, ${\sum}^n_{i=1}\;E_iX\;f_i>\;{\geq}0$, $n{\in}{\mathbb{N}}$, $E_i{\in}{\mathcal{L}}$ and $f_i{\in}H$.

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