• Korean Journal of Mathematics
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• 제6권2호
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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.

• 호남수학학술지
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• 제43권3호
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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.

• 한국환경과학회지
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• 제26권7호
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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.

• 한국지반환경공학회 논문집
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• 제5권2호
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• pp.23-31
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• 2004

본 연구에서는 침출수 차수재에 Zero Valent Iron (ZVI)를 포함 시켰을 경우, ZVI 함량과 pH에 따른 TCE, 6가 크롬, 질산성질소의 제거능의 변화를 살피고, 반응이 끝난 후 철과 벤토나이트 표면의 철 산화물을 라만 분광기를 통해서 알아보고자 하였다. ZVI의 함량을 중량비로 벤토나이트의 0, 3, 6, 10, 13, 16, 20, 30, 100 w/w% 로 맞춘 9가지의 샘플을 pH7의 완충 용액을 사용했을 경우와 완충 용액을 사용하지 않을 경우 두 가지로 나누어서 실험하였다. Kinetic test 결과, pH7의 완충 용액을 사용하였을 때가 사용하였지 않았을 때보다 TCE의 경우 330시간에서 300시간으로, 6가 크롬의 경우 20시간에서 4시간으로, 질산성질소는 140시간에서 5시간으로 제거 속도가 빨라졌다. 모든 오염물질의 경우 ZVI 함량이 증가할수록 제거 효율이 높아졌으며, pH 7의 완충 용액을 사용하였을 경우 제거 효율도 더 높아지는 것을 볼 수 있었다. 반응 후 철과 벤토나이트의 표면을 라만 분광기를 이용하여 분석한 결과 여러 가지 철산화물이 확인되었다. 이러한 철산화물은 좋은 흡착제의 역할을 할 수 있으며, 이 중 magnetite는 장기간 동안 오염물질의 제거 성능을 유지시켜 줄 수 있다.

• Nuclear Engineering and Technology
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• 제48권3호
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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.

• 대한수학회보
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• 제48권3호
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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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• 제5권1호
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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.

• 한국물환경학회지
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• 제25권5호
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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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• 제23권1호
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• pp.19-25
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• 1983

• Kyungpook Mathematical Journal
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• 제56권3호
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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.