• Title/Summary/Keyword: p-valent

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Kinetics of 2, 4, 6-Trinitrotoluene reduction by zero valent iron (금속 철을 이용한 TNT 환원시의 동역학 산정)

  • 배범한
    • Journal of Korea Soil Environment Society
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    • v.4 no.1
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    • pp.97-108
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    • 1999
  • Reduction 2, 4, 6-trinitrotoluene by zero valent iron was studied in a batch reactor under anoxic conditions. Results showed that the removal of trinitrotoluene (TNT)followed a pseudo-first order reaction and the rate was linearly dependent on the available reactive surfau area of the zero valent iron surface area, resulting a rate constant of 0.0981min$^{1}m$$^{-2}m$. High concentrations of the final product, presumably triaminotoluene which needs to be treated by other means, accumulated in the solution. However , little amount of TAT was extracted from the metal surface by using acetonitrile or phosphate buffered water (pH 7.0). Other common major intermediate in biological TNT degradation, a group of aminodinitrotoluenes, was not detected in the solution. Therefore, it is postulated that the reduction of nitro group by $Fe^0$ occurs simultaneously in all three positions and a TNT reduction model by zero valent iron was suggested.

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On Certain Subclasses of Starlike p-valent Functions

  • Darwish, Hanan Elsayed;Lashin, Abd-el Monem Yousof;Soileh, Soliman Mohammed
    • Kyungpook Mathematical Journal
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    • v.56 no.3
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    • pp.867-876
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    • 2016
  • The object of the present paper is to investigate the starlikeness of the class of functions $f(z)=z^p+{\sum\limits_{k=n}^{\infty}}a_p+k^{z^{p^{+k}}} (p,n{\in}{\mathbb{N}}=\{1,2,{\ldots}\})$ which are analytic and p-valent in the unit disc U and satisfy the condition $\|(1-{\lambda}({\frac{f(z)}{z^p}})^{\alpha}+{\lambda}{\frac{zf^{\prime}(z)}{pf(z)}}({\frac{f(z)}{z^p}})^{\alpha}-1\|$ < ${\mu}$ (0 < ${\mu}{\leq}1$, ${\lambda}{\geq}0$, ${\alpha}$ > 0, $z{\in}U$). The starlikeness of certain integral operator are also discussed. The results obtained generalize the related works of some authors and some other new results are also obtained.

Dechlorination of Atrazine using Zero Valent Iron($Fe^0$) under Neutral pH Condition (중성 pH조건에서 철($Fe^0$)을 이용한 Atrazine의 탈염소화)

  • Kim, Geon-Ha;Jeong, Woo-Hyeok;Choe, Seung-Hee
    • Journal of Korean Society of Environmental Engineers
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    • v.28 no.2
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    • pp.173-177
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    • 2006
  • Pesticides from diffuse pollution sources adsorbed in suspended particles flow into surface water and threats to the public health. In this research, dechlorination constants of Atrazine by zero valent iron were measured with addition of buffer solution for simulating buffer capacity of sediment. When initial concentration of Atrazine was 10, 30, and 50 mg/L, their dechlorination was explained using the pseudo-first order reaction. Dechlorination constants $K_{obs}$ were $3.21{\times}10^{-2}/d$ in average.

SOME EXTENSION RESULTS CONCERNING ANALYTIC AND MEROMORPHIC MULTIVALENT FUNCTIONS

  • Ebadian, Ali;Masih, Vali Soltani;Najafzadeh, Shahram
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.911-927
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    • 2019
  • Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.