• Korean Journal of Mathematics
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• v.6 no.2
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• pp.183-194
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• 1998

Making use of a certain operator of fractional derivative, a new subclass $L_p({\alpha},{\beta},{\gamma},{\lambda})$) of analytic and p-valent functions is introduced in the present paper. Apart from various coefficient bounds, many interesting and useful properties of this class of functions are given, some of these properties involve, for example, linear combinations and modified Hadamard product of several functions belonging to the class introduced here.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.513-522
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• 2021

In this current study, we aim to give some applications on fourth-order differential subordination for p-valent meromorphic functions in the region U^* = {z ∈ ℂ : 0 < |z| < 1} = U∖{0}, where U = {z ∈ ℂ : |z| < 1} , involving the linear operator 𝓛^*_pf. By making use of basic concepts in theory of the fourth-order, we find new outcomes.

• Journal of Environmental Science International
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• v.26 no.7
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• pp.859-868
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• 2017

In this study, the reductive dechlorination of triclosan using zero-valent iron (ZVI, $Fe^0$) and modified zero-valent iron (i.e., acid-washed iron (Aw/Fe) and palladium-coated iron (Pd/Fe)) was experimentally investigated, and the reduction characteristics were evaluated by analyzing the reaction kinetics. Triclosan could be reductively decomposed using zero-valent iron. The degradation rates of triclosan were about 50% and 67% when $Fe^0$ and Aw/Fe were used as reductants, respectively, after 8 h of reaction. For the Pd/Fe system, the degradation rate was about 57% after 1 h of reaction. Thus, Pd/Fe exhibited remarkable performance in the reductive degradation of triclosan. Several dechlorinated intermediates were predicted by GC-MS spectrum, and 2-phenoxyphenol was detected as the by-product of the decomposition reaction of triclosan, indicating that reductive dechlorination occurred continuously. As the reaction proceeded, the pH of the solution increased steadily; the pH increase for the Pd/Fe system was smaller than that for the $Fe^0$ and Aw/Fe system. Further, zero-order, first-order, and second-order kinetic models were used to analyze the reaction kinetics. The first-order kinetic model was found to be the best with good correlation for the $Fe^0$ and Aw/Fe system. However, for the Pd/Fe system, the experimental data were evaluated to be well fitted to the second-order kinetic model. The reaction rate constants (k) were in the order of Pd/Fe > Aw/Fe > $Fe^0$, with the rate constant of Pd/Fe being much higher than that of the other two reductants.

• Journal of the Korean GEO-environmental Society
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• v.5 no.2
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• pp.23-31
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• 2004

Trichloroethylene(TCE), Cr(VI), and nitrate removal efficiency of a novel reactive barrier were experimented, and the types of corrosion species that form on the surface of the iron and bentonite as a result of reaction were investigated with Raman spectrophotometer. The reactive barrier is composed of bentonite and zero valent iron(ZVI), and this can substitute conventional geosynthetic clay liners for landfill leachate. Tests were performed in batch reactors for various ZVI content (0, 3, 6, 10, 13, 16, 20, 30, 100 w/w %) and pH. The reduction rates and removal efficiencies of TCE, Cr(VI) and nitrate increase at pH 7 buffered solution. As ZVI content increases, TCE, Cr(VI) and nitrate removal efficiencies increase. From the result of analysis with Raman spectrophotometer, Fe-oxides were observed, which are strong adsorbers of cantaminants. Magnetite can be also beneficial to the long term performance of the iron metal.

• Nuclear Engineering and Technology
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• v.48 no.3
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• pp.744-750
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• 2016

Uranium removal from uranium plant wastewater using zero-valent iron in an ultrasonic field was investigated. Batch experiments designed by the response surface methodology (RSM) were conducted to study the effects of pH, ultrasonic reaction time, and dosage of zero-valent iron on uranium removal efficiency. From the experimental data obtained in this work, it was found that the ultrasonic method employing zero-valent iron powder effectively removes uranium from uranium plant wastewater with a uranium concentration of $2,772.23{\mu}g/L$. The pH ranges widely from 3 to 7 in the ultrasonic field, and the prediction model obtained by the RSM has good agreement with the experimental results.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.627-636
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• 2011

In this paper, we obtain some applications of first order differential subordination and superordination results for higher-order derivatives of p-valent functions involving certain linear operator. Some of our results improve and generalize previously known results.

• East Asian mathematical journal
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• v.5 no.1
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• pp.1-23
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• 1989

Let $S_p*({\alpha},{\beta},{\mu})$ denote the class of functions $f(z)=z^p-{\sum}{\limit}^{\infty}_{n=1}a_{p+n}\;z^{p+n}(a_{p+n}{\geq}o,\;p{\in}N)$ analytic and p-valent in the unit disc $U=\{z:{\mid}z{\mid}<1\}$ and satisfy the condition $${\mid}\frac{\frac{zf'(z)}{f(z)}-p}{\mu\frac{zf'(z)}{f(z)}+p-(1+\mu)\alpha}\mid<\beta,\;z{\in}U$$, where $o{\leq}{\alpha} and $o\leq\mu\leq1$. Further f(z) is said to belong to the class $C_p*({\alpha},{\beta},{\mu})\;if\;zf'(z)/p{\in}S_p*(\alpha,\beta,\mu)$. In this paper we obtain for these classes sharp results concerning coefficient estimates, disortion theorems, closure theorems, Hadamard products and some distortion theorems for the fractional calculus.

• Journal of Korean Society on Water Environment
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• v.25 no.5
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• pp.758-763
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• 2009

This study presents the optimal conditions of zero-valent iron (ZVI) pretreatment for color removal from real dye wastewater. Removal of color by ZVI was strongly subject to the acidity of the wastewater buffering the pH increased after ZVI reduction. The real dye wastewater did not contain a sufficient amount of acidity and thus it was necessary to supplement acid to the dye wastewater before treatment. In continuous operation of iron column, the empty bed contact time (EBCT) and initial pH were varied to find the optimal conditions. A non-linear regression model fitted well the experimental result predicting that the optimal EBCT and pH for 80% removal efficiency was present in the range of 57~90 and 5~5.9, respectively. Color of column effluents could be further removed in the following biological oxidation step and the biodegradability of wastewater was also enhanced after iron pretreatment.

• Kyungpook Mathematical Journal
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• v.23 no.1
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• pp.19-25
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• 1983

• 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.